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% -*- TeX:EN -*- %%% ==================================================================== %%% $RCSfile: Module2Latex.java,v $ %%% $Revision: 1.28 $ %%% ==================================================================== %%% %%% Generated by class com.meyling.principia.latex.Module2Latex %%% at 2004-09-26T23:33:09+0200. %%% %%% Project Hilbert II - http://www.qedeq.org %%% Copyright 2001, 2002, 2003, 2004 Michael Meyling (mime@qedeq.org) %%% %%% This file is part of *Principia Mathematica II*, the prototype of %%% Hilbert II. %%% %%% Permission is granted to copy, distribute and/or modify this document %%% under the terms of the GNU Free Documentation License, Version 1.2 %%% or any later version published by the Free Software Foundation; %%% with no Invariant Sections, no Front-Cover Texts, and no %%% Back-Cover Texts. %%% \documentclass[a4paper]{article} \usepackage{amsmath,amsthm,amsfonts} \usepackage[]{color} \usepackage{xr} \usepackage{epsfig,longtable} \usepackage{varioref} \usepackage[bookmarksnumbered,colorlinks,breaklinks,plainpages,backref,bookmarksopen=true,pdfpagemode=None]{hyperref} \oddsidemargin 8mm \evensidemargin 9mm \topmargin 0mm \headsep 10mm \marginparsep 2.5mm \marginparwidth 25mm \textwidth 160mm \textheight 220mm \newtheorem{axm}{Axiom}[section] \newtheorem{abr}{Abbreviation}[section] \newtheorem{thm}{Theorem}[section] \newtheorem{dec}{Rule Declaration}[section] \newtheorem{cor}[thm]{Corollary} \newtheorem{prop}{Proposition} \newtheorem{lem}[thm]{Lemma} \theoremstyle{remark} \newtheorem*{rmk}{Remark} \makeindex \makeatletter \externaldocument{prophilbert1_1.00.00_1.00.00.qedeq} \hyperbaseurl{prophilbert1_1.00.00_1.00.00.qedeq} \makeatother \setlength{\LTleft}{0pt} \setlength{\LTright}{0pt} \setlength{\parindent}{0pt} \frenchspacing \sloppy \pagestyle{headings} \title{First theorems of Propositional Calculus} \author{Michael Meyling} \date{\tt <module@qedeq.org>} \begin{document} \maketitle \setlongtables {\small This document is part of the project ``Hilbert II''. To get more information about this project look at:\\ \mbox{\url{http://www.qedeq.org}}. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. See also under \url{http://www.gnu.org/copyleft/} } \section*{Abstract} This module includes first proofs of propositional calculus theorems. The following theorems and proofs are adapted from D. Hilbert and W. Ackermann's `Grundzuege der theoretischen Logik' (Berlin 1928, Springer) \section*{Specification} This document has the following specification: \begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}} Name: & prophilbert1 \\ Version: & 1.00.00 \\ Rule version: & 1.00.00 \\ Orgin: & \url{http://www.qedeq.org/0_00_53/prophilbert1_1.00.00_1.00.00.qedeq} \\ \end{longtable} \medskip Author of this module: \begin{longtable}[h!]{l@{\extracolsep{\fill}}l} Michael Meyling & mime@qedeq.org \\ \end{longtable} \section*{References} This document uses the results of the following documents: \begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}} Name: & propaxiom \\ Version: & 1.00.00 \\ Rule version: & 1.00.00 \\ Orgin: & \url{propaxiom_1.00.00_1.00.00.qedeq} \\ pdf: & \url{propaxiom_1.00.00_1.00.00.pdf} \\ \end{longtable} \section*{Content} First we prove a simple implication, that follows directly from the fourth axiom: \begin{thm}[hilb1] \hypertarget{hilb1}{} \begin{displaymath} (P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb1:1} $1$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb1:2} $2$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((\neg A\ \vee \ P)\ \rightarrow \ (\neg A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $\neg A$ in \hyperref[hilb1:1]{$1$} } \\ \label{hilb1:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (\neg A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb1:2]{$2$} at occurence $1$ } \\ \label{hilb1:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb1:3]{$3$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} This proposition is the form for the Hypothetical Syllogism. \bigskip The self implication could be derived: \begin{thm}[hilb2] \hypertarget{hilb2}{} \begin{displaymath} P\ \rightarrow \ P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb2:1} $1$ & $P\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom2}{axiom2} } \\ \label{hilb2:2} $2$ & $P\ \rightarrow \ (P\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $P$ in \hyperref[hilb2:1]{$1$} } \\ \label{hilb2:3} $3$ & $(P\ \vee \ P)\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom1}{axiom1} } \\ \label{hilb2:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb2:5} $5$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb2:4]{$4$} } \\ \label{hilb2:6} $6$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb2:5]{$5$} } \\ \label{hilb2:7} $7$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb2:6]{$6$} } \\ \label{hilb2:8} $8$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb2:7]{$7$} } \\ \label{hilb2:9} $9$ & $(D\ \rightarrow \ P)\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P$ in \hyperref[hilb2:8]{$8$} } \\ \label{hilb2:10} $10$ & $((P\ \vee \ P)\ \rightarrow \ P)\ \rightarrow \ ((P\ \rightarrow \ (P\ \vee \ P))\ \rightarrow \ (P\ \rightarrow \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ P$ in \hyperref[hilb2:9]{$9$} } \\ \label{hilb2:11} $11$ & $(P\ \rightarrow \ (P\ \vee \ P))\ \rightarrow \ (P\ \rightarrow \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb2:3]{$3$}, \hyperref[hilb2:10]{$10$}} \\ \label{hilb2:12} $12$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb2:2]{$2$}, \hyperref[hilb2:11]{$11$}} \\ & & \qedhere \end{longtable} \end{proof} One form of the classical `tertium non datur' \begin{thm}[hilb3] \hypertarget{hilb3}{} \begin{displaymath} \neg P\ \vee \ P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb3:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{hilb3:2} $2$ & $\neg P\ \vee \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb3:1]{$1$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} The standard form of the excluded middle: \begin{thm}[hilb4] \hypertarget{hilb4}{} \begin{displaymath} P\ \vee \ \neg P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb4:1} $1$ & $\neg P\ \vee \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb3}{hilb3} } \\ \label{hilb4:2} $2$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb4:3} $3$ & $(P\ \vee \ A)\ \rightarrow \ (A\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $A$ in \hyperref[hilb4:2]{$2$} } \\ \label{hilb4:4} $4$ & $(B\ \vee \ A)\ \rightarrow \ (A\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $B$ in \hyperref[hilb4:3]{$3$} } \\ \label{hilb4:5} $5$ & $(B\ \vee \ P)\ \rightarrow \ (P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P$ in \hyperref[hilb4:4]{$4$} } \\ \label{hilb4:6} $6$ & $(\neg P\ \vee \ P)\ \rightarrow \ (P\ \vee \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg P$ in \hyperref[hilb4:5]{$5$} } \\ \label{hilb4:7} $7$ & $P\ \vee \ \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb4:1]{$1$}, \hyperref[hilb4:6]{$6$}} \\ & & \qedhere \end{longtable} \end{proof} Double negation is implicated: \begin{thm}[hilb5] \hypertarget{hilb5}{} \begin{displaymath} P\ \rightarrow \ \neg \neg P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb5:1} $1$ & $P\ \vee \ \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb4}{hilb4} } \\ \label{hilb5:2} $2$ & $\neg P\ \vee \ \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $\neg P$ in \hyperref[hilb5:1]{$1$} } \\ \label{hilb5:3} $3$ & $P\ \rightarrow \ \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb5:2]{$2$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} The reverse is also true: \begin{thm}[hilb6] \hypertarget{hilb6}{} \begin{displaymath} \neg \neg P\ \rightarrow \ P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb6:1} $1$ & $P\ \rightarrow \ \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb5}{hilb5} } \\ \label{hilb6:2} $2$ & $\neg P\ \rightarrow \ \neg \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $\neg P$ in \hyperref[hilb6:1]{$1$} } \\ \label{hilb6:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb6:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb6:3]{$3$} } \\ \label{hilb6:5} $5$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb6:4]{$4$} } \\ \label{hilb6:6} $6$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ D)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb6:5]{$5$} } \\ \label{hilb6:7} $7$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb6:6]{$6$} } \\ \label{hilb6:8} $8$ & $(D\ \rightarrow \ \neg \neg \neg P)\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ \neg \neg \neg P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg \neg \neg P$ in \hyperref[hilb6:7]{$7$} } \\ \label{hilb6:9} $9$ & $(\neg P\ \rightarrow \ \neg \neg \neg P)\ \rightarrow \ ((P\ \vee \ \neg P)\ \rightarrow \ (P\ \vee \ \neg \neg \neg P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg P$ in \hyperref[hilb6:8]{$8$} } \\ \label{hilb6:10} $10$ & $(P\ \vee \ \neg P)\ \rightarrow \ (P\ \vee \ \neg \neg \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb6:2]{$2$}, \hyperref[hilb6:9]{$9$}} \\ \label{hilb6:11} $11$ & $P\ \vee \ \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb4}{hilb4} } \\ \label{hilb6:12} $12$ & $P\ \vee \ \neg \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb6:11]{$11$}, \hyperref[hilb6:10]{$10$}} \\ \label{hilb6:13} $13$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb6:14} $14$ & $(P\ \vee \ A)\ \rightarrow \ (A\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $A$ in \hyperref[hilb6:13]{$13$} } \\ \label{hilb6:15} $15$ & $(B\ \vee \ A)\ \rightarrow \ (A\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $B$ in \hyperref[hilb6:14]{$14$} } \\ \label{hilb6:16} $16$ & $(B\ \vee \ \neg \neg \neg P)\ \rightarrow \ (\neg \neg \neg P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $\neg \neg \neg P$ in \hyperref[hilb6:15]{$15$} } \\ \label{hilb6:17} $17$ & $(P\ \vee \ \neg \neg \neg P)\ \rightarrow \ (\neg \neg \neg P\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb6:16]{$16$} } \\ \label{hilb6:18} $18$ & $\neg \neg \neg P\ \vee \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb6:12]{$12$}, \hyperref[hilb6:17]{$17$}} \\ \label{hilb6:19} $19$ & $\neg \neg P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb6:18]{$18$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} The correct reverse of an implication: \begin{thm}[hilb7] \hypertarget{hilb7}{} \begin{displaymath} (P\ \rightarrow \ Q)\ \rightarrow \ (\neg Q\ \rightarrow \ \neg P)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb7:1} $1$ & $P\ \rightarrow \ \neg \neg P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb5}{hilb5} } \\ \label{hilb7:2} $2$ & $Q\ \rightarrow \ \neg \neg Q$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $Q$ in \hyperref[hilb7:1]{$1$} } \\ \label{hilb7:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb7:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb7:3]{$3$} } \\ \label{hilb7:5} $5$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb7:4]{$4$} } \\ \label{hilb7:6} $6$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ D)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb7:5]{$5$} } \\ \label{hilb7:7} $7$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((\neg P\ \vee \ D)\ \rightarrow \ (\neg P\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg P$ in \hyperref[hilb7:6]{$6$} } \\ \label{hilb7:8} $8$ & $(D\ \rightarrow \ \neg \neg Q)\ \rightarrow \ ((\neg P\ \vee \ D)\ \rightarrow \ (\neg P\ \vee \ \neg \neg Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg \neg Q$ in \hyperref[hilb7:7]{$7$} } \\ \label{hilb7:9} $9$ & $(Q\ \rightarrow \ \neg \neg Q)\ \rightarrow \ ((\neg P\ \vee \ Q)\ \rightarrow \ (\neg P\ \vee \ \neg \neg Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $Q$ in \hyperref[hilb7:8]{$8$} } \\ \label{hilb7:10} $10$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (\neg P\ \vee \ \neg \neg Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb7:2]{$2$}, \hyperref[hilb7:9]{$9$}} \\ \label{hilb7:11} $11$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb7:12} $12$ & $(P\ \vee \ A)\ \rightarrow \ (A\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $A$ in \hyperref[hilb7:11]{$11$} } \\ \label{hilb7:13} $13$ & $(B\ \vee \ A)\ \rightarrow \ (A\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $B$ in \hyperref[hilb7:12]{$12$} } \\ \label{hilb7:14} $14$ & $(B\ \vee \ \neg \neg Q)\ \rightarrow \ (\neg \neg Q\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $\neg \neg Q$ in \hyperref[hilb7:13]{$13$} } \\ \label{hilb7:15} $15$ & $(\neg P\ \vee \ \neg \neg Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg P$ in \hyperref[hilb7:14]{$14$} } \\ \label{hilb7:16} $16$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb7:17} $17$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb7:16]{$16$} } \\ \label{hilb7:18} $18$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb7:17]{$17$} } \\ \label{hilb7:19} $19$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb7:18]{$18$} } \\ \label{hilb7:20} $20$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((\neg P\ \vee \ Q)\ \rightarrow \ D)\ \rightarrow \ ((\neg P\ \vee \ Q)\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg P\ \vee \ Q$ in \hyperref[hilb7:19]{$19$} } \\ \label{hilb7:21} $21$ & $(D\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P))\ \rightarrow \ (((\neg P\ \vee \ Q)\ \rightarrow \ D)\ \rightarrow \ ((\neg P\ \vee \ Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg \neg Q\ \vee \ \neg P$ in \hyperref[hilb7:20]{$20$} } \\ \label{hilb7:22} $22$ & $((\neg P\ \vee \ \neg \neg Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P))\ \rightarrow \ (((\neg P\ \vee \ Q)\ \rightarrow \ (\neg P\ \vee \ \neg \neg Q))\ \rightarrow \ ((\neg P\ \vee \ Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg P\ \vee \ \neg \neg Q$ in \hyperref[hilb7:21]{$21$} } \\ \label{hilb7:23} $23$ & $((\neg P\ \vee \ Q)\ \rightarrow \ (\neg P\ \vee \ \neg \neg Q))\ \rightarrow \ ((\neg P\ \vee \ Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb7:15]{$15$}, \hyperref[hilb7:22]{$22$}} \\ \label{hilb7:24} $24$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb7:10]{$10$}, \hyperref[hilb7:23]{$23$}} \\ \label{hilb7:25} $25$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg \neg Q\ \vee \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb7:24]{$24$} at occurence $1$ } \\ \label{hilb7:26} $26$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg Q\ \rightarrow \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb7:25]{$25$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of an Implication 1. part: \begin{thm}[defimpl1] \hypertarget{defimpl1}{} \begin{displaymath} (P\ \rightarrow \ Q)\ \rightarrow \ (\neg P\ \vee \ Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defimpl1:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defimpl1:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defimpl1:1]{$1$} } \\ \label{defimpl1:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \rightarrow \ Q$ in \hyperref[defimpl1:2]{$2$} } \\ \label{defimpl1:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[defimpl1:3]{$3$} at occurence $3$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of an Implication 2. part: \begin{thm}[defimpl2] \hypertarget{defimpl2}{} \begin{displaymath} (\neg P\ \vee \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defimpl2:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defimpl2:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defimpl2:1]{$1$} } \\ \label{defimpl2:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \rightarrow \ Q$ in \hyperref[defimpl2:2]{$2$} } \\ \label{defimpl2:4} $4$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[defimpl2:3]{$3$} at occurence $2$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of a Conjunction 1. part: \begin{thm}[defand1] \hypertarget{defand1}{} \begin{displaymath} (P\ \wedge \ Q)\ \rightarrow \ \neg (\neg P\ \vee \ \neg Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defand1:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defand1:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defand1:1]{$1$} } \\ \label{defand1:3} $3$ & $(P\ \wedge \ Q)\ \rightarrow \ (P\ \wedge \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \wedge \ Q$ in \hyperref[defand1:2]{$2$} } \\ \label{defand1:4} $4$ & $(P\ \wedge \ Q)\ \rightarrow \ \neg (\neg P\ \vee \ \neg Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{and}{and} in \hyperref[defand1:3]{$3$} at occurence $2$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of a Conjunction 2. part: \begin{thm}[defand2] \hypertarget{defand2}{} \begin{displaymath} \neg (\neg P\ \vee \ \neg Q)\ \rightarrow \ (P\ \wedge \ Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defand2:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defand2:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defand2:1]{$1$} } \\ \label{defand2:3} $3$ & $(P\ \wedge \ Q)\ \rightarrow \ (P\ \wedge \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \wedge \ Q$ in \hyperref[defand2:2]{$2$} } \\ \label{defand2:4} $4$ & $\neg (\neg P\ \vee \ \neg Q)\ \rightarrow \ (P\ \wedge \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{and}{and} in \hyperref[defand2:3]{$3$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of an Equivalence 1. part: \begin{thm}[defequi1] \hypertarget{defequi1}{} \begin{displaymath} (P\ \leftrightarrow \ Q)\ \rightarrow \ ((P\ \rightarrow \ Q)\ \wedge \ (Q\ \rightarrow \ P))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defequi1:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defequi1:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defequi1:1]{$1$} } \\ \label{defequi1:3} $3$ & $(P\ \leftrightarrow \ Q)\ \rightarrow \ (P\ \leftrightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \leftrightarrow \ Q$ in \hyperref[defequi1:2]{$2$} } \\ \label{defequi1:4} $4$ & $(P\ \leftrightarrow \ Q)\ \rightarrow \ ((P\ \rightarrow \ Q)\ \wedge \ (Q\ \rightarrow \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{equi}{equi} in \hyperref[defequi1:3]{$3$} at occurence $2$ } \\ & & \qedhere \end{longtable} \end{proof} Definition of an Equivalence 2. part: \begin{thm}[defequi2] \hypertarget{defequi2}{} \begin{displaymath} ((P\ \rightarrow \ Q)\ \wedge \ (Q\ \rightarrow \ P))\ \rightarrow \ (P\ \leftrightarrow \ Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{defequi2:1} $1$ & $P\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb2}{hilb2} } \\ \label{defequi2:2} $2$ & $A\ \rightarrow \ A$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $A$ in \hyperref[defequi2:1]{$1$} } \\ \label{defequi2:3} $3$ & $(P\ \leftrightarrow \ Q)\ \rightarrow \ (P\ \leftrightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P\ \leftrightarrow \ Q$ in \hyperref[defequi2:2]{$2$} } \\ \label{defequi2:4} $4$ & $((P\ \rightarrow \ Q)\ \wedge \ (Q\ \rightarrow \ P))\ \rightarrow \ (P\ \leftrightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule5}{use abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{equi}{equi} in \hyperref[defequi2:3]{$3$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} A simular formulation for the second axiom: \begin{thm}[hilb8] \hypertarget{hilb8}{} \begin{displaymath} P\ \rightarrow \ (Q\ \vee \ P)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb8:1} $1$ & $P\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom2}{axiom2} } \\ \label{hilb8:2} $2$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb8:3} $3$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb8:4} $4$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb8:3]{$3$} } \\ \label{hilb8:5} $5$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb8:4]{$4$} } \\ \label{hilb8:6} $6$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb8:5]{$5$} } \\ \label{hilb8:7} $7$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb8:6]{$6$} } \\ \label{hilb8:8} $8$ & $(D\ \rightarrow \ (Q\ \vee \ P))\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ P$ in \hyperref[hilb8:7]{$7$} } \\ \label{hilb8:9} $9$ & $((P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P))\ \rightarrow \ ((P\ \rightarrow \ (P\ \vee \ Q))\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ Q$ in \hyperref[hilb8:8]{$8$} } \\ \label{hilb8:10} $10$ & $(P\ \rightarrow \ (P\ \vee \ Q))\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb8:2]{$2$}, \hyperref[hilb8:9]{$9$}} \\ \label{hilb8:11} $11$ & $P\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb8:1]{$1$}, \hyperref[hilb8:10]{$10$}} \\ & & \qedhere \end{longtable} \end{proof} A technical lemma (equal to the third axiom): \begin{thm}[hilb9] \hypertarget{hilb9}{} \begin{displaymath} (P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb9:1} $1$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ & & \qedhere \end{longtable} \end{proof} And another technical lemma (simular to the third axiom): \begin{thm}[hilb10] \hypertarget{hilb10}{} \begin{displaymath} (Q\ \vee \ P)\ \rightarrow \ (P\ \vee \ Q)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb10:1} $1$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb10:2} $2$ & $(P\ \vee \ A)\ \rightarrow \ (A\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $A$ in \hyperref[hilb10:1]{$1$} } \\ \label{hilb10:3} $3$ & $(B\ \vee \ A)\ \rightarrow \ (A\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $B$ in \hyperref[hilb10:2]{$2$} } \\ \label{hilb10:4} $4$ & $(B\ \vee \ P)\ \rightarrow \ (P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $P$ in \hyperref[hilb10:3]{$3$} } \\ \label{hilb10:5} $5$ & $(Q\ \vee \ P)\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q$ in \hyperref[hilb10:4]{$4$} } \\ & & \qedhere \end{longtable} \end{proof} A technical lemma (equal to the first axiom): \begin{thm}[hilb11] \hypertarget{hilb11}{} \begin{displaymath} (P\ \vee \ P)\ \rightarrow \ P\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb11:1} $1$ & $(P\ \vee \ P)\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom1}{axiom1} } \\ & & \qedhere \end{longtable} \end{proof} A simple propositon that follows directly from the second axiom: \begin{thm}[hilb12] \hypertarget{hilb12}{} \begin{displaymath} P\ \rightarrow \ (P\ \vee \ P)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb12:1} $1$ & $P\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom2}{axiom2} } \\ \label{hilb12:2} $2$ & $P\ \rightarrow \ (P\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $P$ in \hyperref[hilb12:1]{$1$} } \\ & & \qedhere \end{longtable} \end{proof} This is a pre form for the associative law: \begin{thm}[hilb13] \hypertarget{hilb13}{} \begin{displaymath} (P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb13:1} $1$ & $P\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb8}{hilb8} } \\ \label{hilb13:2} $2$ & $P\ \rightarrow \ (B\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb13:1]{$1$} } \\ \label{hilb13:3} $3$ & $C\ \rightarrow \ (B\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb13:2]{$2$} } \\ \label{hilb13:4} $4$ & $C\ \rightarrow \ (P\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb13:3]{$3$} } \\ \label{hilb13:5} $5$ & $A\ \rightarrow \ (P\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb13:4]{$4$} } \\ \label{hilb13:6} $6$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb13:7} $7$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb13:6]{$6$} } \\ \label{hilb13:8} $8$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb13:7]{$7$} } \\ \label{hilb13:9} $9$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ D)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb13:8]{$8$} } \\ \label{hilb13:10} $10$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((Q\ \vee \ D)\ \rightarrow \ (Q\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q$ in \hyperref[hilb13:9]{$9$} } \\ \label{hilb13:11} $11$ & $(D\ \rightarrow \ (P\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ D)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ A$ in \hyperref[hilb13:10]{$10$} } \\ \label{hilb13:12} $12$ & $(A\ \rightarrow \ (P\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ A)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A$ in \hyperref[hilb13:11]{$11$} } \\ \label{hilb13:13} $13$ & $(Q\ \vee \ A)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:5]{$5$}, \hyperref[hilb13:12]{$12$}} \\ \label{hilb13:14} $14$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb13:9]{$9$} } \\ \label{hilb13:15} $15$ & $(D\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:14]{$14$} } \\ \label{hilb13:16} $16$ & $((Q\ \vee \ A)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $Q\ \vee \ A$ in \hyperref[hilb13:15]{$15$} } \\ \label{hilb13:17} $17$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:13]{$13$}, \hyperref[hilb13:16]{$16$}} \\ \label{hilb13:18} $18$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb9}{hilb9} } \\ \label{hilb13:19} $19$ & $(P\ \vee \ B)\ \rightarrow \ (B\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb13:18]{$18$} } \\ \label{hilb13:20} $20$ & $(C\ \vee \ B)\ \rightarrow \ (B\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb13:19]{$19$} } \\ \label{hilb13:21} $21$ & $(C\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:20]{$20$} } \\ \label{hilb13:22} $22$ & $(P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P$ in \hyperref[hilb13:21]{$21$} } \\ \label{hilb13:23} $23$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl1}{defimpl1} } \\ \label{hilb13:24} $24$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl2}{defimpl2} } \\ \label{hilb13:25} $25$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ D)\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg (P\ \vee \ (Q\ \vee \ A))$ in \hyperref[hilb13:9]{$9$} } \\ \label{hilb13:26} $26$ & $(D\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ D)\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ P$ in \hyperref[hilb13:25]{$25$} } \\ \label{hilb13:27} $27$ & $((P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:26]{$26$} } \\ \label{hilb13:28} $28$ & $(\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:22]{$22$}, \hyperref[hilb13:27]{$27$}} \\ \label{hilb13:29} $29$ & $(P\ \rightarrow \ B)\ \rightarrow \ (\neg P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb13:23]{$23$} } \\ \label{hilb13:30} $30$ & $(C\ \rightarrow \ B)\ \rightarrow \ (\neg C\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb13:29]{$29$} } \\ \label{hilb13:31} $31$ & $(C\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg C\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:30]{$30$} } \\ \label{hilb13:32} $32$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb13:31]{$31$} } \\ \label{hilb13:33} $33$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb13:34} $34$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb13:33]{$33$} } \\ \label{hilb13:35} $35$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb13:34]{$34$} } \\ \label{hilb13:36} $36$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb13:35]{$35$} } \\ \label{hilb13:37} $37$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ in \hyperref[hilb13:36]{$36$} } \\ \label{hilb13:38} $38$ & $(D\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ in \hyperref[hilb13:37]{$37$} } \\ \label{hilb13:39} $39$ & $((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ in \hyperref[hilb13:38]{$38$} } \\ \label{hilb13:40} $40$ & $(((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:28]{$28$}, \hyperref[hilb13:39]{$39$}} \\ \label{hilb13:41} $41$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:32]{$32$}, \hyperref[hilb13:40]{$40$}} \\ \label{hilb13:42} $42$ & $(\neg P\ \vee \ B)\ \rightarrow \ (P\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb13:24]{$24$} } \\ \label{hilb13:43} $43$ & $(\neg C\ \vee \ B)\ \rightarrow \ (C\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb13:42]{$42$} } \\ \label{hilb13:44} $44$ & $(\neg C\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ (C\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ P$ in \hyperref[hilb13:43]{$43$} } \\ \label{hilb13:45} $45$ & $(\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb13:44]{$44$} } \\ \label{hilb13:46} $46$ & $(D\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ in \hyperref[hilb13:37]{$37$} } \\ \label{hilb13:47} $47$ & $((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ in \hyperref[hilb13:46]{$46$} } \\ \label{hilb13:48} $48$ & $(((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:45]{$45$}, \hyperref[hilb13:47]{$47$}} \\ \label{hilb13:49} $49$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:41]{$41$}, \hyperref[hilb13:48]{$48$}} \\ \label{hilb13:50} $50$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:17]{$17$}, \hyperref[hilb13:49]{$49$}} \\ \label{hilb13:51} $51$ & $(P\ \vee \ A)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $P\ \vee \ A$ in \hyperref[hilb13:1]{$1$} } \\ \label{hilb13:52} $52$ & $P\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom2}{axiom2} } \\ \label{hilb13:53} $53$ & $P\ \rightarrow \ (P\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $A$ in \hyperref[hilb13:52]{$52$} } \\ \label{hilb13:54} $54$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb13:36]{$36$} } \\ \label{hilb13:55} $55$ & $(D\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((P\ \rightarrow \ D)\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:54]{$54$} } \\ \label{hilb13:56} $56$ & $((P\ \vee \ A)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((P\ \rightarrow \ (P\ \vee \ A))\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ A$ in \hyperref[hilb13:55]{$55$} } \\ \label{hilb13:57} $57$ & $(P\ \rightarrow \ (P\ \vee \ A))\ \rightarrow \ (P\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:51]{$51$}, \hyperref[hilb13:56]{$56$}} \\ \label{hilb13:58} $58$ & $P\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:53]{$53$}, \hyperref[hilb13:57]{$57$}} \\ \label{hilb13:59} $59$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ D)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:9]{$9$} } \\ \label{hilb13:60} $60$ & $(D\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ D)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:59]{$59$} } \\ \label{hilb13:61} $61$ & $(P\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P$ in \hyperref[hilb13:60]{$60$} } \\ \label{hilb13:62} $62$ & $((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:58]{$58$}, \hyperref[hilb13:61]{$61$}} \\ \label{hilb13:63} $63$ & $(P\ \vee \ P)\ \rightarrow \ P$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb11}{hilb11} } \\ \label{hilb13:64} $64$ & $(B\ \vee \ B)\ \rightarrow \ B$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $B$ in \hyperref[hilb13:63]{$63$} } \\ \label{hilb13:65} $65$ & $((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:64]{$64$} } \\ \label{hilb13:66} $66$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ D)\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)$ in \hyperref[hilb13:9]{$9$} } \\ \label{hilb13:67} $67$ & $(D\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ D)\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:66]{$66$} } \\ \label{hilb13:68} $68$ & $(((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ ((\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:67]{$67$} } \\ \label{hilb13:69} $69$ & $(\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:65]{$65$}, \hyperref[hilb13:68]{$68$}} \\ \label{hilb13:70} $70$ & $(C\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg C\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:30]{$30$} } \\ \label{hilb13:71} $71$ & $(((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ P$ in \hyperref[hilb13:70]{$70$} } \\ \label{hilb13:72} $72$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ in \hyperref[hilb13:36]{$36$} } \\ \label{hilb13:73} $73$ & $(D\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:72]{$72$} } \\ \label{hilb13:74} $74$ & $((\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ in \hyperref[hilb13:73]{$73$} } \\ \label{hilb13:75} $75$ & $((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A)))))\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:69]{$69$}, \hyperref[hilb13:74]{$74$}} \\ \label{hilb13:76} $76$ & $(((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:71]{$71$}, \hyperref[hilb13:75]{$75$}} \\ \label{hilb13:77} $77$ & $(\neg C\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (C\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:43]{$43$} } \\ \label{hilb13:78} $78$ & $(\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ P$ in \hyperref[hilb13:77]{$77$} } \\ \label{hilb13:79} $79$ & $(D\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:72]{$72$} } \\ \label{hilb13:80} $80$ & $((\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))$ in \hyperref[hilb13:79]{$79$} } \\ \label{hilb13:81} $81$ & $((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (\neg ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ ((((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:78]{$78$}, \hyperref[hilb13:80]{$80$}} \\ \label{hilb13:82} $82$ & $(((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ (Q\ \vee \ (P\ \vee \ A))))\ \rightarrow \ (((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:76]{$76$}, \hyperref[hilb13:81]{$81$}} \\ \label{hilb13:83} $83$ & $((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:62]{$62$}, \hyperref[hilb13:82]{$82$}} \\ \label{hilb13:84} $84$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb13:36]{$36$} } \\ \label{hilb13:85} $85$ & $(D\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ (P\ \vee \ A)$ in \hyperref[hilb13:84]{$84$} } \\ \label{hilb13:86} $86$ & $(((Q\ \vee \ (P\ \vee \ A))\ \vee \ P)\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $(Q\ \vee \ (P\ \vee \ A))\ \vee \ P$ in \hyperref[hilb13:85]{$85$} } \\ \label{hilb13:87} $87$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((Q\ \vee \ (P\ \vee \ A))\ \vee \ P))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:83]{$83$}, \hyperref[hilb13:86]{$86$}} \\ \label{hilb13:88} $88$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb13:50]{$50$}, \hyperref[hilb13:87]{$87$}} \\ & & \qedhere \end{longtable} \end{proof} The associative law for the disjunction (first direction): \begin{thm}[hilb14] \hypertarget{hilb14}{} \begin{displaymath} (P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb14:1} $1$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb9}{hilb9} } \\ \label{hilb14:2} $2$ & $(P\ \vee \ B)\ \rightarrow \ (B\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb14:1]{$1$} } \\ \label{hilb14:3} $3$ & $(C\ \vee \ B)\ \rightarrow \ (B\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb14:2]{$2$} } \\ \label{hilb14:4} $4$ & $(C\ \vee \ A)\ \rightarrow \ (A\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A$ in \hyperref[hilb14:3]{$3$} } \\ \label{hilb14:5} $5$ & $(Q\ \vee \ A)\ \rightarrow \ (A\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q$ in \hyperref[hilb14:4]{$4$} } \\ \label{hilb14:6} $6$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb14:7} $7$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb14:6]{$6$} } \\ \label{hilb14:8} $8$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb14:7]{$7$} } \\ \label{hilb14:9} $9$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ D)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb14:8]{$8$} } \\ \label{hilb14:10} $10$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb14:9]{$9$} } \\ \label{hilb14:11} $11$ & $(D\ \rightarrow \ (A\ \vee \ Q))\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A\ \vee \ Q$ in \hyperref[hilb14:10]{$10$} } \\ \label{hilb14:12} $12$ & $((Q\ \vee \ A)\ \rightarrow \ (A\ \vee \ Q))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $Q\ \vee \ A$ in \hyperref[hilb14:11]{$11$} } \\ \label{hilb14:13} $13$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:5]{$5$}, \hyperref[hilb14:12]{$12$}} \\ \label{hilb14:14} $14$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl1}{defimpl1} } \\ \label{hilb14:15} $15$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl2}{defimpl2} } \\ \label{hilb14:16} $16$ & $(P\ \rightarrow \ B)\ \rightarrow \ (\neg P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb14:14]{$14$} } \\ \label{hilb14:17} $17$ & $(C\ \rightarrow \ B)\ \rightarrow \ (\neg C\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb14:16]{$16$} } \\ \label{hilb14:18} $18$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb14:19} $19$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb14:18]{$18$} } \\ \label{hilb14:20} $20$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb14:19]{$19$} } \\ \label{hilb14:21} $21$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb14:20]{$20$} } \\ \label{hilb14:22} $22$ & $(\neg P\ \vee \ B)\ \rightarrow \ (P\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb14:15]{$15$} } \\ \label{hilb14:23} $23$ & $(\neg C\ \vee \ B)\ \rightarrow \ (C\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb14:22]{$22$} } \\ \label{hilb14:24} $24$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb13}{hilb13} } \\ \label{hilb14:25} $25$ & $(P\ \vee \ (Q\ \vee \ B))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb14:24]{$24$} } \\ \label{hilb14:26} $26$ & $(P\ \vee \ (C\ \vee \ B))\ \rightarrow \ (C\ \vee \ (P\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb14:25]{$25$} } \\ \label{hilb14:27} $27$ & $(D\ \vee \ (C\ \vee \ B))\ \rightarrow \ (C\ \vee \ (D\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb14:26]{$26$} } \\ \label{hilb14:28} $28$ & $(D\ \vee \ (C\ \vee \ Q))\ \rightarrow \ (C\ \vee \ (D\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q$ in \hyperref[hilb14:27]{$27$} } \\ \label{hilb14:29} $29$ & $(D\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (D\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb14:28]{$28$} } \\ \label{hilb14:30} $30$ & $(P\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P$ in \hyperref[hilb14:29]{$29$} } \\ \label{hilb14:31} $31$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb14:21]{$21$} } \\ \label{hilb14:32} $32$ & $(D\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A\ \vee \ (P\ \vee \ Q)$ in \hyperref[hilb14:31]{$31$} } \\ \label{hilb14:33} $33$ & $((P\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ (A\ \vee \ Q)$ in \hyperref[hilb14:32]{$32$} } \\ \label{hilb14:34} $34$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:30]{$30$}, \hyperref[hilb14:33]{$33$}} \\ \label{hilb14:35} $35$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:13]{$13$}, \hyperref[hilb14:34]{$34$}} \\ \label{hilb14:36} $36$ & $(C\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ Q$ in \hyperref[hilb14:3]{$3$} } \\ \label{hilb14:37} $37$ & $(A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb14:36]{$36$} } \\ \label{hilb14:38} $38$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ D)\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg (P\ \vee \ (Q\ \vee \ A))$ in \hyperref[hilb14:9]{$9$} } \\ \label{hilb14:39} $39$ & $(D\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ D)\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb14:38]{$38$} } \\ \label{hilb14:40} $40$ & $((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A\ \vee \ (P\ \vee \ Q)$ in \hyperref[hilb14:39]{$39$} } \\ \label{hilb14:41} $41$ & $(\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:37]{$37$}, \hyperref[hilb14:40]{$40$}} \\ \label{hilb14:42} $42$ & $(C\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg C\ \vee \ (A\ \vee \ (P\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A\ \vee \ (P\ \vee \ Q)$ in \hyperref[hilb14:17]{$17$} } \\ \label{hilb14:43} $43$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb14:42]{$42$} } \\ \label{hilb14:44} $44$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))$ in \hyperref[hilb14:21]{$21$} } \\ \label{hilb14:45} $45$ & $(D\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb14:44]{$44$} } \\ \label{hilb14:46} $46$ & $((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q))))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q))$ in \hyperref[hilb14:45]{$45$} } \\ \label{hilb14:47} $47$ & $(((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ (A\ \vee \ (P\ \vee \ Q))))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:41]{$41$}, \hyperref[hilb14:46]{$46$}} \\ \label{hilb14:48} $48$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:43]{$43$}, \hyperref[hilb14:47]{$47$}} \\ \label{hilb14:49} $49$ & $(\neg C\ \vee \ ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ (C\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb14:23]{$23$} } \\ \label{hilb14:50} $50$ & $(\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb14:49]{$49$} } \\ \label{hilb14:51} $51$ & $(D\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb14:44]{$44$} } \\ \label{hilb14:52} $52$ & $((\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb14:51]{$51$} } \\ \label{hilb14:53} $53$ & $(((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (\neg (P\ \vee \ (Q\ \vee \ A))\ \vee \ ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:50]{$50$}, \hyperref[hilb14:52]{$52$}} \\ \label{hilb14:54} $54$ & $((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ ((P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:48]{$48$}, \hyperref[hilb14:53]{$53$}} \\ \label{hilb14:55} $55$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb14:35]{$35$}, \hyperref[hilb14:54]{$54$}} \\ & & \qedhere \end{longtable} \end{proof} The associative law for the disjunction (second direction): \begin{thm}[hilb15] \hypertarget{hilb15}{} \begin{displaymath} ((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb15:1} $1$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb14}{hilb14} } \\ \label{hilb15:2} $2$ & $(P\ \vee \ (Q\ \vee \ B))\ \rightarrow \ ((P\ \vee \ Q)\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb15:1]{$1$} } \\ \label{hilb15:3} $3$ & $(P\ \vee \ (C\ \vee \ B))\ \rightarrow \ ((P\ \vee \ C)\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb15:2]{$2$} } \\ \label{hilb15:4} $4$ & $(D\ \vee \ (C\ \vee \ B))\ \rightarrow \ ((D\ \vee \ C)\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb15:3]{$3$} } \\ \label{hilb15:5} $5$ & $(D\ \vee \ (C\ \vee \ P))\ \rightarrow \ ((D\ \vee \ C)\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb15:4]{$4$} } \\ \label{hilb15:6} $6$ & $(D\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((D\ \vee \ Q)\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q$ in \hyperref[hilb15:5]{$5$} } \\ \label{hilb15:7} $7$ & $(A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A$ in \hyperref[hilb15:6]{$6$} } \\ \label{hilb15:8} $8$ & $(Q\ \vee \ P)\ \rightarrow \ (P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb10}{hilb10} } \\ \label{hilb15:9} $9$ & $(B\ \vee \ P)\ \rightarrow \ (P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb15:8]{$8$} } \\ \label{hilb15:10} $10$ & $(B\ \vee \ C)\ \rightarrow \ (C\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb15:9]{$9$} } \\ \label{hilb15:11} $11$ & $((Q\ \vee \ P)\ \vee \ C)\ \rightarrow \ (C\ \vee \ (Q\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ P$ in \hyperref[hilb15:10]{$10$} } \\ \label{hilb15:12} $12$ & $((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb15:11]{$11$} } \\ \label{hilb15:13} $13$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg P\ \vee \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl1}{defimpl1} } \\ \label{hilb15:14} $14$ & $(\neg P\ \vee \ Q)\ \rightarrow \ (P\ \rightarrow \ Q)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{defimpl2}{defimpl2} } \\ \label{hilb15:15} $15$ & $(P\ \rightarrow \ Q)\ \rightarrow \ (\neg Q\ \rightarrow \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb7}{hilb7} } \\ \label{hilb15:16} $16$ & $(P\ \rightarrow \ B)\ \rightarrow \ (\neg B\ \rightarrow \ \neg P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb15:15]{$15$} } \\ \label{hilb15:17} $17$ & $(C\ \rightarrow \ B)\ \rightarrow \ (\neg B\ \rightarrow \ \neg C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb15:16]{$16$} } \\ \label{hilb15:18} $18$ & $(C\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg (A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ \neg C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A\ \vee \ (Q\ \vee \ P)$ in \hyperref[hilb15:17]{$17$} } \\ \label{hilb15:19} $19$ & $(((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg (A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ \neg ((Q\ \vee \ P)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:18]{$18$} } \\ \label{hilb15:20} $20$ & $\neg (A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ \neg ((Q\ \vee \ P)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:12]{$12$}, \hyperref[hilb15:19]{$19$}} \\ \label{hilb15:21} $21$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \vee \ P)\ \rightarrow \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom4}{axiom4} } \\ \label{hilb15:22} $22$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb15:21]{$21$} } \\ \label{hilb15:23} $23$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ P)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb15:22]{$22$} } \\ \label{hilb15:24} $24$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \vee \ D)\ \rightarrow \ (B\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb15:23]{$23$} } \\ \label{hilb15:25} $25$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ D)\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:24]{$24$} } \\ \label{hilb15:26} $26$ & $(D\ \rightarrow \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ D)\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:25]{$25$} } \\ \label{hilb15:27} $27$ & $(\neg (A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (A\ \vee \ (Q\ \vee \ P))$ in \hyperref[hilb15:26]{$26$} } \\ \label{hilb15:28} $28$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:20]{$20$}, \hyperref[hilb15:27]{$27$}} \\ \label{hilb15:29} $29$ & $(P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule2}{add axiom} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{axiom3}{axiom3} } \\ \label{hilb15:30} $30$ & $(P\ \vee \ B)\ \rightarrow \ (B\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb15:29]{$29$} } \\ \label{hilb15:31} $31$ & $(C\ \vee \ B)\ \rightarrow \ (B\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb15:30]{$30$} } \\ \label{hilb15:32} $32$ & $(C\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:33} $33$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:32]{$32$} } \\ \label{hilb15:34} $34$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((A\ \rightarrow \ P)\ \rightarrow \ (A\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb1}{hilb1} } \\ \label{hilb15:35} $35$ & $(P\ \rightarrow \ Q)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb15:34]{$34$} } \\ \label{hilb15:36} $36$ & $(P\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ P)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb15:35]{$35$} } \\ \label{hilb15:37} $37$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((B\ \rightarrow \ D)\ \rightarrow \ (B\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb15:36]{$36$} } \\ \label{hilb15:38} $38$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ D)\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P))$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:39} $39$ & $(D\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ D)\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:38]{$38$} } \\ \label{hilb15:40} $40$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:39]{$39$} } \\ \label{hilb15:41} $41$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:33]{$33$}, \hyperref[hilb15:40]{$40$}} \\ \label{hilb15:42} $42$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:28]{$28$}, \hyperref[hilb15:41]{$41$}} \\ \label{hilb15:43} $43$ & $(C\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:44} $44$ & $(\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg (A\ \vee \ (Q\ \vee \ P))$ in \hyperref[hilb15:43]{$43$} } \\ \label{hilb15:45} $45$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:46} $46$ & $(D\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:45]{$45$} } \\ \label{hilb15:47} $47$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P))))\ \rightarrow \ ((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P))$ in \hyperref[hilb15:46]{$46$} } \\ \label{hilb15:48} $48$ & $((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg (A\ \vee \ (Q\ \vee \ P))))\ \rightarrow \ ((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:42]{$42$}, \hyperref[hilb15:47]{$47$}} \\ \label{hilb15:49} $49$ & $(\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:44]{$44$}, \hyperref[hilb15:48]{$48$}} \\ \label{hilb15:50} $50$ & $(P\ \rightarrow \ B)\ \rightarrow \ (\neg P\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb15:13]{$13$} } \\ \label{hilb15:51} $51$ & $(C\ \rightarrow \ B)\ \rightarrow \ (\neg C\ \vee \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb15:50]{$50$} } \\ \label{hilb15:52} $52$ & $(C\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg C\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:51]{$51$} } \\ \label{hilb15:53} $53$ & $((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A\ \vee \ (Q\ \vee \ P)$ in \hyperref[hilb15:52]{$52$} } \\ \label{hilb15:54} $54$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:55} $55$ & $(D\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:54]{$54$} } \\ \label{hilb15:56} $56$ & $((\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:55]{$55$} } \\ \label{hilb15:57} $57$ & $(((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg (A\ \vee \ (Q\ \vee \ P))\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:49]{$49$}, \hyperref[hilb15:56]{$56$}} \\ \label{hilb15:58} $58$ & $((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:53]{$53$}, \hyperref[hilb15:57]{$57$}} \\ \label{hilb15:59} $59$ & $(\neg P\ \vee \ B)\ \rightarrow \ (P\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $B$ in \hyperref[hilb15:14]{$14$} } \\ \label{hilb15:60} $60$ & $(\neg C\ \vee \ B)\ \rightarrow \ (C\ \rightarrow \ B)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $C$ in \hyperref[hilb15:59]{$59$} } \\ \label{hilb15:61} $61$ & $(\neg C\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (C\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:60]{$60$} } \\ \label{hilb15:62} $62$ & $(\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:61]{$61$} } \\ \label{hilb15:63} $63$ & $(D\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:54]{$54$} } \\ \label{hilb15:64} $64$ & $((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:63]{$63$} } \\ \label{hilb15:65} $65$ & $(((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:62]{$62$}, \hyperref[hilb15:64]{$64$}} \\ \label{hilb15:66} $66$ & $((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:58]{$58$}, \hyperref[hilb15:65]{$65$}} \\ \label{hilb15:67} $67$ & $((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:7]{$7$}, \hyperref[hilb15:66]{$66$}} \\ \label{hilb15:68} $68$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((A\ \vee \ D)\ \rightarrow \ (A\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A$ in \hyperref[hilb15:24]{$24$} } \\ \label{hilb15:69} $69$ & $(D\ \rightarrow \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ D)\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ P$ in \hyperref[hilb15:68]{$68$} } \\ \label{hilb15:70} $70$ & $((P\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ P))\ \rightarrow \ ((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ Q$ in \hyperref[hilb15:69]{$69$} } \\ \label{hilb15:71} $71$ & $(A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:29]{$29$}, \hyperref[hilb15:70]{$70$}} \\ \label{hilb15:72} $72$ & $(C\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q\ \vee \ P$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:73} $73$ & $(A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb15:72]{$72$} } \\ \label{hilb15:74} $74$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ D)\ \rightarrow \ ((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A\ \vee \ (P\ \vee \ Q)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:75} $75$ & $(D\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ D)\ \rightarrow \ ((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:74]{$74$} } \\ \label{hilb15:76} $76$ & $((A\ \vee \ (Q\ \vee \ P))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ ((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A\ \vee \ (Q\ \vee \ P)$ in \hyperref[hilb15:75]{$75$} } \\ \label{hilb15:77} $77$ & $((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ (A\ \vee \ (Q\ \vee \ P)))\ \rightarrow \ ((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:73]{$73$}, \hyperref[hilb15:76]{$76$}} \\ \label{hilb15:78} $78$ & $(A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:71]{$71$}, \hyperref[hilb15:77]{$77$}} \\ \label{hilb15:79} $79$ & $(C\ \vee \ A)\ \rightarrow \ (A\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:80} $80$ & $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ Q$ in \hyperref[hilb15:79]{$79$} } \\ \label{hilb15:81} $81$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:82} $82$ & $(D\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ D)\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:81]{$81$} } \\ \label{hilb15:83} $83$ & $((A\ \vee \ (P\ \vee \ Q))\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A\ \vee \ (P\ \vee \ Q)$ in \hyperref[hilb15:82]{$82$} } \\ \label{hilb15:84} $84$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (A\ \vee \ (P\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:78]{$78$}, \hyperref[hilb15:83]{$83$}} \\ \label{hilb15:85} $85$ & $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:80]{$80$}, \hyperref[hilb15:84]{$84$}} \\ \label{hilb15:86} $86$ & $(C\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ \neg C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:17]{$17$} } \\ \label{hilb15:87} $87$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ \neg ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:86]{$86$} } \\ \label{hilb15:88} $88$ & $\neg ((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ \neg ((P\ \vee \ Q)\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:85]{$85$}, \hyperref[hilb15:87]{$87$}} \\ \label{hilb15:89} $89$ & $(D\ \rightarrow \ \neg ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ D)\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb15:25]{$25$} } \\ \label{hilb15:90} $90$ & $(\neg ((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ \neg ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:89]{$89$} } \\ \label{hilb15:91} $91$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:88]{$88$}, \hyperref[hilb15:90]{$90$}} \\ \label{hilb15:92} $92$ & $(C\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:93} $93$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:92]{$92$} } \\ \label{hilb15:94} $94$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:95} $95$ & $(D\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ D)\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:94]{$94$} } \\ \label{hilb15:96} $96$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb15:95]{$95$} } \\ \label{hilb15:97} $97$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((P\ \vee \ Q)\ \vee \ A)))\ \rightarrow \ ((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:93]{$93$}, \hyperref[hilb15:96]{$96$}} \\ \label{hilb15:98} $98$ & $(((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:91]{$91$}, \hyperref[hilb15:97]{$97$}} \\ \label{hilb15:99} $99$ & $(\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:43]{$43$} } \\ \label{hilb15:100} $100$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:101} $101$ & $(D\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:100]{$100$} } \\ \label{hilb15:102} $102$ & $((((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))\ \rightarrow \ ((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)$ in \hyperref[hilb15:101]{$101$} } \\ \label{hilb15:103} $103$ & $((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((A\ \vee \ Q)\ \vee \ P)\ \vee \ \neg ((Q\ \vee \ P)\ \vee \ A)))\ \rightarrow \ ((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:98]{$98$}, \hyperref[hilb15:102]{$102$}} \\ \label{hilb15:104} $104$ & $(\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:99]{$99$}, \hyperref[hilb15:103]{$103$}} \\ \label{hilb15:105} $105$ & $(((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(Q\ \vee \ P)\ \vee \ A$ in \hyperref[hilb15:52]{$52$} } \\ \label{hilb15:106} $106$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:107} $107$ & $(D\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:106]{$106$} } \\ \label{hilb15:108} $108$ & $((\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:107]{$107$} } \\ \label{hilb15:109} $109$ & $((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((Q\ \vee \ P)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:104]{$104$}, \hyperref[hilb15:108]{$108$}} \\ \label{hilb15:110} $110$ & $(((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:105]{$105$}, \hyperref[hilb15:109]{$109$}} \\ \label{hilb15:111} $111$ & $(\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:61]{$61$} } \\ \label{hilb15:112} $112$ & $(D\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:106]{$106$} } \\ \label{hilb15:113} $113$ & $((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ (((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:112]{$112$} } \\ \label{hilb15:114} $114$ & $((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:111]{$111$}, \hyperref[hilb15:113]{$113$}} \\ \label{hilb15:115} $115$ & $(((Q\ \vee \ P)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:110]{$110$}, \hyperref[hilb15:114]{$114$}} \\ \label{hilb15:116} $116$ & $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:67]{$67$}, \hyperref[hilb15:115]{$115$}} \\ \label{hilb15:117} $117$ & $(C\ \vee \ P)\ \rightarrow \ (P\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:118} $118$ & $((A\ \vee \ Q)\ \vee \ P)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A\ \vee \ Q$ in \hyperref[hilb15:117]{$117$} } \\ \label{hilb15:119} $119$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ D)\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $\neg ((P\ \vee \ Q)\ \vee \ A)$ in \hyperref[hilb15:24]{$24$} } \\ \label{hilb15:120} $120$ & $(D\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ ((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ D)\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (A\ \vee \ Q)$ in \hyperref[hilb15:119]{$119$} } \\ \label{hilb15:121} $121$ & $(((A\ \vee \ Q)\ \vee \ P)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ ((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $(A\ \vee \ Q)\ \vee \ P$ in \hyperref[hilb15:120]{$120$} } \\ \label{hilb15:122} $122$ & $(\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:118]{$118$}, \hyperref[hilb15:121]{$121$}} \\ \label{hilb15:123} $123$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:52]{$52$} } \\ \label{hilb15:124} $124$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:125} $125$ & $(D\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))$ in \hyperref[hilb15:124]{$124$} } \\ \label{hilb15:126} $126$ & $((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)$ in \hyperref[hilb15:125]{$125$} } \\ \label{hilb15:127} $127$ & $((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ ((A\ \vee \ Q)\ \vee \ P)))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:122]{$122$}, \hyperref[hilb15:126]{$126$}} \\ \label{hilb15:128} $128$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:123]{$123$}, \hyperref[hilb15:127]{$127$}} \\ \label{hilb15:129} $129$ & $(\neg C\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (C\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (A\ \vee \ Q)$ in \hyperref[hilb15:60]{$60$} } \\ \label{hilb15:130} $130$ & $(\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:129]{$129$} } \\ \label{hilb15:131} $131$ & $(D\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))$ in \hyperref[hilb15:124]{$124$} } \\ \label{hilb15:132} $132$ & $((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))$ in \hyperref[hilb15:131]{$131$} } \\ \label{hilb15:133} $133$ & $((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:130]{$130$}, \hyperref[hilb15:132]{$132$}} \\ \label{hilb15:134} $134$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ ((A\ \vee \ Q)\ \vee \ P))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:128]{$128$}, \hyperref[hilb15:133]{$133$}} \\ \label{hilb15:135} $135$ & $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:116]{$116$}, \hyperref[hilb15:134]{$134$}} \\ \label{hilb15:136} $136$ & $(C\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ C)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $Q$ in \hyperref[hilb15:31]{$31$} } \\ \label{hilb15:137} $137$ & $(A\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ A)$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $A$ in \hyperref[hilb15:136]{$136$} } \\ \label{hilb15:138} $138$ & $(D\ \rightarrow \ C)\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P$ in \hyperref[hilb15:24]{$24$} } \\ \label{hilb15:139} $139$ & $(D\ \rightarrow \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ D)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $Q\ \vee \ A$ in \hyperref[hilb15:138]{$138$} } \\ \label{hilb15:140} $140$ & $((A\ \vee \ Q)\ \rightarrow \ (Q\ \vee \ A))\ \rightarrow \ ((P\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $A\ \vee \ Q$ in \hyperref[hilb15:139]{$139$} } \\ \label{hilb15:141} $141$ & $(P\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:137]{$137$}, \hyperref[hilb15:140]{$140$}} \\ \label{hilb15:142} $142$ & $(D\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))\ \rightarrow \ ((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ D)\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb15:119]{$119$} } \\ \label{hilb15:143} $143$ & $((P\ \vee \ (A\ \vee \ Q))\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))\ \rightarrow \ ((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $P\ \vee \ (A\ \vee \ Q)$ in \hyperref[hilb15:142]{$142$} } \\ \label{hilb15:144} $144$ & $(\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:141]{$141$}, \hyperref[hilb15:143]{$143$}} \\ \label{hilb15:145} $145$ & $(C\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg C\ \vee \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (A\ \vee \ Q)$ in \hyperref[hilb15:51]{$51$} } \\ \label{hilb15:146} $146$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:145]{$145$} } \\ \label{hilb15:147} $147$ & $(D\ \rightarrow \ C)\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ C))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q))$ in \hyperref[hilb15:37]{$37$} } \\ \label{hilb15:148} $148$ & $(D\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))$ in \hyperref[hilb15:147]{$147$} } \\ \label{hilb15:149} $149$ & $((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))$ in \hyperref[hilb15:148]{$148$} } \\ \label{hilb15:150} $150$ & $((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (A\ \vee \ Q))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:144]{$144$}, \hyperref[hilb15:149]{$149$}} \\ \label{hilb15:151} $151$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:146]{$146$}, \hyperref[hilb15:150]{$150$}} \\ \label{hilb15:152} $152$ & $(\neg C\ \vee \ (P\ \vee \ (Q\ \vee \ A)))\ \rightarrow \ (C\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $P\ \vee \ (Q\ \vee \ A)$ in \hyperref[hilb15:60]{$60$} } \\ \label{hilb15:153} $153$ & $(\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $(P\ \vee \ Q)\ \vee \ A$ in \hyperref[hilb15:152]{$152$} } \\ \label{hilb15:154} $154$ & $(D\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ D)\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))$ in \hyperref[hilb15:147]{$147$} } \\ \label{hilb15:155} $155$ & $((\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ (((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))$ in \hyperref[hilb15:154]{$154$} } \\ \label{hilb15:156} $156$ & $((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (\neg ((P\ \vee \ Q)\ \vee \ A)\ \vee \ (P\ \vee \ (Q\ \vee \ A))))\ \rightarrow \ ((((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:153]{$153$}, \hyperref[hilb15:155]{$155$}} \\ \label{hilb15:157} $157$ & $(((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (A\ \vee \ Q)))\ \rightarrow \ (((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A)))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:151]{$151$}, \hyperref[hilb15:156]{$156$}} \\ \label{hilb15:158} $158$ & $((P\ \vee \ Q)\ \vee \ A)\ \rightarrow \ (P\ \vee \ (Q\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule1}{MP} with \hyperref[hilb15:135]{$135$}, \hyperref[hilb15:157]{$157$}} \\ & & \qedhere \end{longtable} \end{proof} Another consequence from hilb13 is the exchange of preconditions: \begin{thm}[hilb16] \hypertarget{hilb16}{} \begin{displaymath} (P\ \rightarrow \ (Q\ \rightarrow \ A))\ \rightarrow \ (Q\ \rightarrow \ (P\ \rightarrow \ A))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb16:1} $1$ & $(P\ \vee \ (Q\ \vee \ A))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb13}{hilb13} } \\ \label{hilb16:2} $2$ & $(P\ \vee \ (Q\ \vee \ B))\ \rightarrow \ (Q\ \vee \ (P\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb16:1]{$1$} } \\ \label{hilb16:3} $3$ & $(P\ \vee \ (C\ \vee \ B))\ \rightarrow \ (C\ \vee \ (P\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb16:2]{$2$} } \\ \label{hilb16:4} $4$ & $(D\ \vee \ (C\ \vee \ B))\ \rightarrow \ (C\ \vee \ (D\ \vee \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb16:3]{$3$} } \\ \label{hilb16:5} $5$ & $(D\ \vee \ (C\ \vee \ A))\ \rightarrow \ (C\ \vee \ (D\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A$ in \hyperref[hilb16:4]{$4$} } \\ \label{hilb16:6} $6$ & $(D\ \vee \ (\neg Q\ \vee \ A))\ \rightarrow \ (\neg Q\ \vee \ (D\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $\neg Q$ in \hyperref[hilb16:5]{$5$} } \\ \label{hilb16:7} $7$ & $(\neg P\ \vee \ (\neg Q\ \vee \ A))\ \rightarrow \ (\neg Q\ \vee \ (\neg P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $\neg P$ in \hyperref[hilb16:6]{$6$} } \\ \label{hilb16:8} $8$ & $(P\ \rightarrow \ (\neg Q\ \vee \ A))\ \rightarrow \ (\neg Q\ \vee \ (\neg P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb16:7]{$7$} at occurence $1$ } \\ \label{hilb16:9} $9$ & $(P\ \rightarrow \ (Q\ \rightarrow \ A))\ \rightarrow \ (\neg Q\ \vee \ (\neg P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb16:8]{$8$} at occurence $1$ } \\ \label{hilb16:10} $10$ & $(P\ \rightarrow \ (Q\ \rightarrow \ A))\ \rightarrow \ (Q\ \rightarrow \ (\neg P\ \vee \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb16:9]{$9$} at occurence $1$ } \\ \label{hilb16:11} $11$ & $(P\ \rightarrow \ (Q\ \rightarrow \ A))\ \rightarrow \ (Q\ \rightarrow \ (P\ \rightarrow \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule6}{reverse abbreviation} \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{impl}{impl} in \hyperref[hilb16:10]{$10$} at occurence $1$ } \\ & & \qedhere \end{longtable} \end{proof} An analogus form for \hyperref[hilb16]{hilb16}: \begin{thm}[hilb17] \hypertarget{hilb17}{} \begin{displaymath} (Q\ \rightarrow \ (P\ \rightarrow \ A))\ \rightarrow \ (P\ \rightarrow \ (Q\ \rightarrow \ A))\end{displaymath} \end{thm} \begin{proof} \mbox{}\\ \begin{longtable}[h!]{r@{\extracolsep{\fill}}p{9cm}@{\extracolsep{\fill}}p{4cm}} \label{hilb17:1} $1$ & $(P\ \rightarrow \ (Q\ \rightarrow \ A))\ \rightarrow \ (Q\ \rightarrow \ (P\ \rightarrow \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule3}{add sentence} \hyperref{}{}{hilb16}{hilb16} } \\ \label{hilb17:2} $2$ & $(P\ \rightarrow \ (Q\ \rightarrow \ B))\ \rightarrow \ (Q\ \rightarrow \ (P\ \rightarrow \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $A$ by $B$ in \hyperref[hilb17:1]{$1$} } \\ \label{hilb17:3} $3$ & $(P\ \rightarrow \ (C\ \rightarrow \ B))\ \rightarrow \ (C\ \rightarrow \ (P\ \rightarrow \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $Q$ by $C$ in \hyperref[hilb17:2]{$2$} } \\ \label{hilb17:4} $4$ & $(D\ \rightarrow \ (C\ \rightarrow \ B))\ \rightarrow \ (C\ \rightarrow \ (D\ \rightarrow \ B))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $P$ by $D$ in \hyperref[hilb17:3]{$3$} } \\ \label{hilb17:5} $5$ & $(D\ \rightarrow \ (C\ \rightarrow \ A))\ \rightarrow \ (C\ \rightarrow \ (D\ \rightarrow \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $B$ by $A$ in \hyperref[hilb17:4]{$4$} } \\ \label{hilb17:6} $6$ & $(D\ \rightarrow \ (P\ \rightarrow \ A))\ \rightarrow \ (P\ \rightarrow \ (D\ \rightarrow \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $C$ by $P$ in \hyperref[hilb17:5]{$5$} } \\ \label{hilb17:7} $7$ & $(Q\ \rightarrow \ (P\ \rightarrow \ A))\ \rightarrow \ (P\ \rightarrow \ (Q\ \rightarrow \ A))$ & {\tiny \hyperref{propaxiom_1.00.00_1.00.00.pdf}{}{rule4}{replace} $D$ by $Q$ in \hyperref[hilb17:6]{$6$} } \\ & & \qedhere \end{longtable} \end{proof} \section{Cross Reference} This module is used by the following modules: \begin{longtable}[h!]{l@{\extracolsep{\fill}}p{12cm}} Name: & prophilbert2 \\ Version: & 1.00.00 \\ Rule version: & 1.00.00 \\ Orgin: & \url{prophilbert2_1.00.00_1.00.00.qedeq} \\ pdf: & \url{prophilbert2_1.00.00_1.00.00.pdf} \\ \end{longtable} \end{document}

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% fermi2.tex edited by bob 25-may-2005 complete \documentclass{ws-procs975x65} \setcounter{footnote}{0} \renewcommand\thefootnote{\arabic{footnote}} \def\addressfont{\normalsize\rmfamily{}} \def\fermisection#1{\bigskip \S\,\,#1.\,--\,} \def\ferminote#1{ \begin{center}{\bf\large Note #1.}\\[\bigskipamount] \end{center}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \title{2.\\ \uppercase{On the electrostatics of a homogeneous}\\ \uppercase{gravitational field and on the weight}\\ \uppercase{of electromagnetic masses} } \address{ ``Sull 'elettrostatica di un campo gravitazionale uniforme\\ e sul peso delle masse elettromagnetiche,''\\ \textit{Nuovo Cimento} \textbf{22}, 176--188 (1921). } \maketitle \begin{center} \textbf{\uppercase{Introduction}} \end{center} \bigskip The aim of the present paper is to investigate in the framework of general relativity how a homogeneous gravitational field modifies the electrostatic phenomena occurring in it. Once the differential equation relating the electrostatic potential to the charge density, which corresponds to the Poisson equation in classical electrostatics, is established, one is able to integrate it at least when the gravitational field is weak enough (and certainly the gravitational field of the Earth amply satisfies this condition), obtaining in this way the corrections to the Coulomb law due to the presence of the gravitational field. In a first application the distribution of the electric charges on a conducting sphere is studied, showing that the sphere polarizes by means of the gravitational field. The second application is devoted to studying the weight of an electromagnetic mass, that is the force exerted on a fixed system of electric charges (e.g., sustained by a rigid dielectric), as a consequence of the presence of the gravitational field. One finds that such a weight is given by the acceleration of gravity times $u/c^2$, where $u$ denotes the electrostatic energy of the charges of the system, and $c$ is the velocity of light. So the gravitational mass, namely the ratio between the weight and the acceleration of gravity, does not coincide in general with the inertial mass for the system under consideration, since the latter is given by $(4/3)u/c^2$ (with the same notation) if the system is endowed with spherical symmetry for example. Besides it is known how special relativity leads us to take $\Delta u/c^2$ as the increase of the \textit{inertial} mass of a system getting an energy $\Delta u$, and this fact can be easily related to the aforementioned result. Finally, it is shown how to find a point having the same properties, with respect to the weight of the considered system of charges, as the center of gravity with respect to the weight of an ordinary system of material masses. \bigskip\begin{center} \textbf{\uppercase{Part 1}}\\[\bigskipamount] \textbf{\uppercase{Electrostatics in a gravitational field}} \end{center}\bigskip \fermisection{1} Let us consider a portion of the spacetime where a homogeneous gravitational field is present, and assume the electrostatic phenomena that we think are taking place in it to be weak enough to neglect the effect they produce on the metric describing the region under consideration. Under this assumption, the line element of the spacetime manifold can be written as \footnote{\textsc{T. Levi-Civita}, Note II. ``Sui $ds^2$ einsteiniani''. \textit{Rend.\ Acc.\ Lincei}, \textbf{27}, $1^\circ$ sem. N$^\circ$ 7.} \begin{equation} \label{eqf1} ds^2=a\,dt^2-dx^2-dy^2-dz^2\ , \end{equation} where $a$ is a function only of $z$. The variables $t,x,y,z$ will also be denoted by $x_0,x_1,x_2,x_3$, and the coefficients of the quadratic form (\ref{eqf1}) by $g_{ik}$. Let $\varphi_i$ be the vector potential, and ${\rm F}_{ik}$ the electromagnetic field. Then we have \begin{equation} \label{eqf2} {\rm F}_{ik}=\varphi_{i,k}-\varphi_{k,i} \ , \end{equation} referring ourselves to the fundamental form (\ref{eqf1}). By limiting our considerations to electrostatic fields, we can set $\varphi_1=\varphi_2=\varphi_3=0$, and, for the sake of brevity, $\varphi_0=\varphi$. Thus one has: \begin{eqnarray*} {\rm F}_{ik}=\varphi_{i,k}-\varphi_{k,i}=\frac{\partial \varphi_i}{\partial x_k}-\frac{\partial \varphi_k}{\partial x_i} \ , \end{eqnarray*} that is \begin{equation} \label{eqf3} \left\{ \begin{array}{c} {\rm F}_{01}=\displaystyle\frac{\partial \varphi}{\partial x}\ ,\qquad {\rm F}_{02}=\displaystyle\frac{\partial \varphi}{\partial y}\ ,\qquad {\rm F}_{03}=\displaystyle\frac{\partial \varphi}{\partial z}\ , \\ \\ {\rm F}_{23}={\rm F}_{31}={\rm F}_{12}=0\ ,\qquad {\rm F}_{ik}=-{\rm F}_{ki}\ ,\qquad {\rm F}_{ij}=0\ . \end{array} \right. \end{equation} In addition one has: \begin{eqnarray*} {\rm F}^{(ik)}=\sum_{hk}g^{(ih)}g^{(jk)}{\rm F}_{(hk)}=g^{(ii)}g^{(jj)}{\rm F}_{(ij)}\ , \end{eqnarray*} from which by noting that: \begin{eqnarray*} g^{(00)}=\frac1a\ , \qquad g^{(11)}=g^{(22)}=g^{(33)}=-1\ , \end{eqnarray*} one obtains \begin{equation} \label{eqf4} \left\{ \begin{array}{c} {\rm F}^{(01)}=-\displaystyle\frac1a\displaystyle\frac{\partial \varphi}{\partial x}\ ,\qquad {\rm F}^{(02)}=-\displaystyle\frac1a\displaystyle\frac{\partial \varphi}{\partial y}\ ,\qquad {\rm F}^{(03)}=-\displaystyle\frac1a\displaystyle\frac{\partial \varphi}{\partial z}\ , \\ \\ {\rm F}^{(23)}={\rm F}^{(31)}={\rm F}^{(12)}=0\ ,\qquad {\rm F}^{(ik)}=-{\rm F}^{(ki)}\ ,\qquad {\rm F}^{(ii)}=0\ . \end{array} \right. \end{equation} In the case under consideration here, the action can be written in the form \begin{equation} \label{eqf5} W=\int_{\omega}\,\sum_{ik}{\rm F}_{ik}{\rm F}^{(ik)}\,d\omega + \int de \int\varphi\, dx_0\ , \end{equation} where \begin{eqnarray*} d\omega =\sqrt{-||g_{ik}||}\,dx_0\,dx_1\,dx_2\,dx_3=\sqrt{a}\,dx\,dy\,dz\,dt\ \end{eqnarray*} is the hypervolume element of the manifold, and the integration corresponding to $d\omega$ has to be performed over a specific region of the manifold, while the integrations corresponding to $de$, $dx_0$ have to be extended to all the elements of electric charge whose world lines cross the region under consideration and to the portions of those world lines lying in it, respectively. \fermisection{2} In the variation of $W$, $\varphi$ can be arbitrarily varied, under the single condition that $\delta\varphi=0$ on the boundary of the integration domain. The variations $\delta x$, $\delta y$, $\delta z$ instead, in addition to the condition $\delta x=\delta y=\delta z=0$ on the boundary, could also be subjected to further conditions to be determined in each particular case. For example, inside a conducting body they will be quite arbitrary, while in a rigid dielectric they will have to represent the components of a rigid virtual displacement, and so on. By putting the quantities (\ref{eqf3}), (\ref{eqf4}) into (\ref{eqf5}), one obtains: \begin{equation} \label{eqf6} W=-\frac12\int\!\!\!\int\!\!\!\int\!\!\!\int\,\frac1{\sqrt{a}}\left\{\left(\frac{\partial \varphi}{\partial x}\right)^2+\left(\frac{\partial \varphi}{\partial y}\right)^2+\left(\frac{\partial \varphi}{\partial z}\right)^2\right\}\,dx\,dy\,dz\,dt + \int de \int\varphi\, dt\ , \end{equation} from which \begin{eqnarray} \label{eqf7} \delta W&=&\int\!\!\!\int\!\!\!\int\!\!\!\int\,\delta \varphi \left[\frac1{\sqrt{a}}\,\Delta_2\,\varphi+\frac{\partial \varphi}{\partial z}\frac{d(1/\sqrt{a})}{dz}+\rho\right]\,dx\,dy\,dz\,dt \nonumber\\ &&+\int\!\!\!\int\!\!\!\int\!\!\!\int\,\rho\left(\frac{\partial \varphi}{\partial x}\,\delta x+\frac{\partial \varphi}{\partial y}\,\delta y+\frac{\partial \varphi}{\partial z}\,\delta z\right)\,dx\,dy\,dz\,dt\ \end{eqnarray} as immediately follows by noting that $dx=dy=dz=0$ along a given world line, as a consequence of our assumptions, and $\rho\,dx\,dy\,dz=de$, since $\rho$ is the electric density. Then in order for $\delta W$ to vanish identically, since $\delta\varphi$ is arbitrary inside the integration domain, one finds that \begin{equation} \label{eqf8} \Delta_2\,\varphi-\frac{d\,\log\sqrt{a}}{dz}\frac{\partial \varphi}{\partial z} =-\rho\sqrt{a}\ . \end{equation} Moreover, one must also have \begin{equation} \label{eqf9} \int\!\!\!\int\!\!\!\int\!\!\!\int\,\rho\left(\frac{\partial \varphi}{\partial x}\,\delta x+\frac{\partial \varphi}{\partial y}\,\delta y+\frac{\partial \varphi}{\partial z}\,\delta z\right)\,dx\,dy\,dz\,dt =0\ , \end{equation} for every system of values for $\delta x$, $\delta y$, $\delta z$ satisfying the assumed constraints. In equation (\ref{eqf8}) is contained the generalization of the Poisson's law, to which the (\ref{eqf8}) reduces if $a$ is constant, that is if the gravitational field is absent. \fermisection{3} If we indicate by $\rm G$ the acceleration of gravity of the field under consideration, namely the acceleration with which a free material point begins to move, one has: \begin{equation} \label{eqf10} {\rm G} =-\frac12\frac{da}{dz}\ . \end{equation} WIth this (\ref{eqf8}) becomes: \begin{equation} \label{eqf11} \Delta_2\,\varphi+\frac{\rm G}{a}\frac{\partial \varphi}{\partial z}=-\rho\sqrt{a}\ . \end{equation} In order to find the solution of (\ref{eqf11}), given $\rho$ at each point, we imagine the electric charges to be contained in a small region around the origin of the coordinates. Moreover, we will set $a=c^2$ at the origin (with $c$ the velocity of light near the origin), and we will assume gravity to be so weak that those terms which contain the square of the ratio $l\,{\rm G}/c^2$ can be neglected, where $l$ represents the maximum length entering into the problem under consideration. Under these assumptions, we can set: \begin{eqnarray*} \sqrt{a}=c+\frac1{2c}\frac{da}{dz}z=c\left(1-\frac{\rm G}{c^2}z\right)\ . \end{eqnarray*} Therefore (\ref{eqf11}) can be written as: \begin{equation} \label{eqf12} \Delta_2\,\varphi+\frac{\rm G}{c^2}\frac{\partial \varphi}{\partial z} =-c\left(1-\frac{\rm G}{c^2}z\right)\rho\ . \end{equation} The integral of that equation in this approximation, as can be directly verified, is given by: \begin{eqnarray} \label{eqf13} \varphi_{\rm P} &=&\frac{c}{4\pi}\int\left(1-\frac{\rm G}{c^2}\right)z_{\rm M}\,d\tau_{\rm M} \left(\frac1r-\frac{\rm G}{2c^2}\frac{z_{\rm P}-z_{\rm M}}{r}\right) \nonumber\\ &=&\frac{c}{4\pi}\int\rho_{\rm M}\,d\tau_{\rm M}\left(\frac1r-\frac{\rm G}{2c^2}\frac{z_{\rm P}+z_{\rm M}}{r}\right)\ , \end{eqnarray} where M is the generic point of the region $\tau_{\rm M}$ containing the electric charges, P is the point at which the potential $\varphi$ is evaluated, and $r$ is the distance MP. Given the linearity of equation (\ref{eqf12}), any integral of the equation: \begin{eqnarray*} \hspace{4.4cm}\Delta_2\,\varphi+\frac{\rm G}{c^2}\frac{\partial \varphi}{\partial z}=0\ , \hspace{4cm} (12)\,{}^* \end{eqnarray*} obtained by setting $\rho=0$ in (\ref{eqf12}), can be added to (\ref{eqf13}). This integral will represent the field due to causes external to $\rho_{\rm M}$. For the application we have in mind it is convenient to consider a particular solution to (12)$\,{}^*$ given by \begin{equation} \label{eqf14} \varphi=-c{\rm E}_x^*x-c{\rm E}_y^*y+\frac{c^2}{\rm G}{\rm E}_z^*e^{-\frac{\rm G}{c^2}z}\ , \end{equation} with ${\rm E}_x^*, {\rm E}_y^*, {\rm E}_z^*$ constants. At the origin one has \begin{eqnarray*} {\rm E}_x=-\frac1c\, {\rm F}_{01}\ , \qquad {\rm E}_y=-\frac1c\, {\rm F}_{02}\ , \qquad {\rm E}_z=-\frac1c\, {\rm F}_{03}\ , \end{eqnarray*} since E is the electric force. From this it follows that the electric force of the external field (\ref{eqf14}) has components \begin{eqnarray*} {\rm E}_x^*\ , \quad {\rm E}_y^*\ , \quad {\rm E}_z^*\ . \end{eqnarray*} \fermisection{4} Let us now calculate the electric field due to a charge $e$ concentrated at the origin of the coordinates. From (\ref{eqf13}) one has: \begin{equation} \label{eqf15} \varphi=\frac{ce}{4\pi}\left(\frac1r-\frac{\rm G}{2c^2}\frac{z}{r}\right)\ , \end{equation} and this formula gives the generalization of the Coulomb's law, as immediately follows by setting $\rm G=0$. Recalling (\ref{eqf3}) one gets: \begin{equation} \label{eqf16} \left\{ \begin{array}{cc} {\rm F}_{01}=&\hspace{-1.1cm}\displaystyle\frac{ce}{4\pi}\left(\frac{x}{r^3} -\frac{\rm G}{2c^2}\frac{zx}{r^3}\right)\ , \\ \\ {\rm F}_{02}=&\hspace{-1.1cm}\displaystyle\frac{ce}{4\pi}\left(\frac{y}{r^3} -\frac{\rm G}{2c^2}\frac{zy}{r^3}\right)\ , \\ \\ {\rm F}_{03}=&\displaystyle\frac{ce}{4\pi}\left(\frac{z}{r^3} -\frac{\rm G}{2c^2}\frac{z^2}{r^3}+\frac{\rm G}{2c^2}\frac1r\right)\ . \end{array} \right. \end{equation} We can summarize all three of the preceding formulas in a single vector formula. In fact by indicating by $\rm F_{0}$ the vector with components $\rm F_{01}, \rm F_{02}, \rm F_{03}$, with $\vec a$ a vector of magnitude 1 and orientation MP, and finally with $\vec G$ a vector of magnitude $\rm G$ and orientation $z$, (\ref{eqf16}) can be written as: \begin{equation} \label{eqf17} {\rm F}_{0}=\frac{ce}{4\pi}\left\{\frac{\vec a}{r^2} +\frac{{\vec {\rm G}}\times\vec a}{2c^2r}\,{\vec a} -\frac1{2c^2r}\,{\vec {\rm G}}\right\}\ . \end{equation} It is interesting to compare this formula with the one which gives the electric force exerted by an electric charge $e$ which in the absence of gravitational attraction has acceleration $\vec \Gamma$, quasi-stationary motion and velocity negligible with respect to the speed of light. Such a force is expressed by \begin{equation} \label{eqf18} {\rm E}=\left\{\frac{\vec a}{r^2} +\frac{{\vec \Gamma}\times\vec a}{c^2r}\,{\vec a} -\frac1{2c^2r}\,{\vec \Gamma}\right\}\ , \end{equation} with the same notation. From here one sees that, by setting \begin{equation} \label{eqf19} \vec \Gamma=-\frac{\vec {\rm G}}2 \end{equation} in (\ref{eqf18}), one obtains \begin{eqnarray*} {\rm F}_{0}=c{\rm E}\ . \end{eqnarray*} This result can be put into words as follows, noting that $c\rm E$ is the electric part of the electromagnetic field generated by the charge in accelerated motion: The electric part ($\rm F_{01}, \rm F_{02}, \rm F_{03}$) of the electromagnetic field (${\rm F}_{ik}$) generated by an electric charge at rest in a homogeneous field of strength $\rm G$ is equal to the electric part of the electromagnetic field which the same charge would produce in the absence of gravitational field if it moved under the conditions indicated above with acceleration $\rm G/2$ in the direction opposite to the gravitational field. \fermisection{5} Now, let us study how the distribution of the electricity over a conductor is modified by the gravitational field. To this end, let us note that since $\delta x$, $\delta y$, $\delta z$ are arbitrary inside the conductor, from (\ref{eqf9}) it follows that $\varphi=constant$ inside, and so $\rho=0$ by (\ref{eqf8}). Thus the electricity is completely at the surface. Then let us assume that our conductor is a sphere with center O at the origin of the coordinates and of radius R. Let us try to satisfy the condition $\varphi=constant$ in the interior by assuming the following expression for the surface electric density at a generic point M of the surface: \begin{equation} \label{eqf20} \frac{e}{4\pi R^2}+\frac{e}{r}\,a\cos\theta\ , \end{equation} where $\theta$ represents the angle spanned by the radius vector OM from the $z-$axis, and $a$ is a constant to be determined, which we assume to be of the order of magnitude of ${\rm G}/c^2$. From (\ref{eqf13}), the potential at a point P inside will be given by: \begin{eqnarray*} \varphi_{\rm P} =\frac{c}{4\pi}\int_{\sigma}\left(\frac{e}{4\pi r^2} +\frac{e}{r}\,a\cos\theta\right) \left(\frac1r-\frac{\rm G}{2c^2}\frac{z_{\rm P}+z_{\rm M}}{r}\right)d\sigma \ , \nonumber\\ \end{eqnarray*} where the integration must be extended over the whole surface $\sigma$ of the sphere. By neglecting terms of order greater than ${\rm G}/c^2$ one obtains: \begin{eqnarray} \label{eqf21} \varphi_{\rm P} &=&\frac{ce}{16\pi^2 r^2}\int \frac{d\sigma}{r} +\frac{cea}{4\pi r}\int\frac{\cos\theta d\sigma}{r}\nonumber\\ &&-\frac{ce{\rm G}z_{\rm P}}{32\pi^2 {\rm R}^2c^2}\int \frac{d\sigma}{r} -\frac{ce{\rm G}}{22\pi^2 R^2c^2}\int \frac{z_{\rm M}d\sigma}{r}\ . \end{eqnarray} However, since P is inside, one has: \begin{eqnarray*} \int \frac{d\sigma}{r}=4\,\pi\, {\rm S}\ , \qquad \int\frac{\cos\theta}{r}\,d\sigma=\frac43\,\pi\, z_{\rm P}\ , \qquad \int \frac{z_{\rm M}}{r}\,d\sigma=\frac43\,\pi\, {\rm R}\,z_{\rm P}\ . \end{eqnarray*} Thus one finds: \begin{eqnarray} \label{eqf22} \varphi_{\rm P} =\frac{ce}{4\pi{\rm R}} +\frac{c}{3}\left(\frac{e}{\rm R}\,a -\frac{e}{2\pi{\rm R}c^3}\right)z_{\rm P}\ . \end{eqnarray} So if we require $\varphi_{\rm P}$ to be constant, we will have to set \begin{eqnarray*} a=\frac{1}{2\pi}\frac{\rm G}{c^2}\ . \end{eqnarray*} By substituting this value into (\ref{eqf20}), one finds the following expression for the surface density: \begin{eqnarray} \label{eqf23} \frac{e}{4\pi{\rm R}^2}+\left(1+\frac{2\rm G}{c^2}\,{\rm R}\,\cos\theta\right)\ . \end{eqnarray} Therefore, the fact of being in a gravitational field produces a polarization of the sphere with moment \begin{eqnarray*} \frac{2}{3}\,\frac{\rm G}{c^2}\,e\,{\rm R}^2 \ . \end{eqnarray*} \bigskip\begin{center} \textbf{\uppercase{Part 2}}\\[\bigskipamount] \textbf{\uppercase{Weight of electromagnetic masses}} \end{center}\bigskip \fermisection{6} Suppose we have a system of charges held by a rigid support in such a way that the $\delta x$, $\delta y$, $\delta z$ of $\S\,\,2$ have to be given the form corresponding to the components of a rigid displacement. Leaving the rotational displacements till later, let us consider now the translational ones, that is say assume that $\delta x$, $\delta y$, $\delta z$ are arbitrary functions of time, but do not depend on $x, y, z$. Then we will try to satisfy (\ref{eqf9}) by thinking of the potential $\varphi_{\rm P}$ at a generic point P as the sum of the potential given by (\ref{eqf13}) and one of the form (\ref{eqf14}). We will denote these two terms by $\varphi_{\rm P}{}'$ and $\varphi_{\rm P}{}''$, and suppose that the ratio between the derivatives of $\varphi_{\rm P}{}'$ and $\varphi_{\rm P}{}''$ with respect to any direction whatsoever is of order $l\,{\rm G}/c^2$, having decided to neglect the quadratic terms. Hence (\ref{eqf9}) can be written: \begin{eqnarray*} \int\,dt\bigg\{\int_{\tau_{\rm P}}\delta x\left(\frac{\partial \varphi{}'}{\partial x} +\frac{\partial \varphi{}''}{\partial x}\right)\rho_{\rm P}\,d\tau_{\rm P} +\delta y\left(\frac{\partial \varphi{}'}{\partial y} +\frac{\partial \varphi{}''}{\partial y}\right)\rho_{\rm P}\,d\tau_{\rm P}\\ +\delta z\left(\frac{\partial \varphi{}'}{\partial z} +\frac{\partial \varphi{}''}{\partial z}\right)\rho_{\rm P}\,d\tau_{\rm P}\bigg\}=0\ . \end{eqnarray*} Given that $\delta x$, $\delta y$, $\delta z$ are arbitrary functions of time, independent of each other, this equation gives rise to the three equivalent equations: \begin{eqnarray} \label{eqf24} \int_{\tau_{\rm P}}\left(\frac{\partial \varphi{}'}{\partial x} +\frac{\partial \varphi{}''}{\partial x}\right)\rho_{\rm P}\,d\tau_{\rm P} =\int_{\tau_{\rm P}}\left(\frac{\partial \varphi{}'}{\partial y} +\frac{\partial \varphi{}''}{\partial y}\right)\rho_{\rm P}\,d\tau_{\rm P} \nonumber\\ =\int_{\tau_{\rm P}}\left(\frac{\partial \varphi{}'}{\partial z} +\frac{\partial \varphi{}''}{\partial z}\right)\rho_{\rm P}\,d\tau_{\rm P}=0\ . \end{eqnarray} Now from the expression (\ref{eqf13}) for $\varphi_{\rm P}{}'$, by noting that \begin{eqnarray*} \frac{\partial r}{\partial x_{\rm P}}=\frac{x_{\rm P}-x_r}{r}\ , \end{eqnarray*} one immediately obtains: \begin{eqnarray*} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial x}\rho_{\rm P}\,d\tau_{\rm P} =-\frac{c}{4\pi}\int_{\tau_{\rm P}}\!\!\int_{\tau_{\rm M}}\rho_{\rm P}\rho_{\rm M} \,d\tau_{\rm P}d\tau_{\rm M} \left\{\frac{x_{\rm P}-x_{\rm M}}{r^3}-\frac{\rm G}{2c^2}\frac{(x_{\rm P} -x_{\rm M})(z_{\rm P}+z_{\rm M})}{r^3}\right\}\ , \end{eqnarray*} where both integrals have to be performed over the region occupied by the charges. By interchanging P and M in the right hand side, which changes nothing, one obtains: \begin{eqnarray*} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial x}\rho_{\rm P}\,d\tau_{\rm P} =-\frac{c}{4\pi}\int_{\tau_{\rm M}}\!\!\int_{\tau_{\rm P}}\rho_{\rm M}\rho_{\rm P} \,d\tau_{\rm M}d\tau_{\rm P} \left\{\frac{x_{\rm M}-x_{\rm P}}{r^3} -\frac{\rm G}{2c^2}\frac{(x_{\rm M} -x_{\rm P})(z_{\rm M}+z_{\rm P})}{r^3}\right\}\ , \end{eqnarray*} from which, by taking half the sum: \begin{equation} \label{eqf25} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial x}\rho_{\rm P}\,d\tau_{\rm P}=0\ . \end{equation} In an completely analogous way: \begin{equation} \label{eqf26} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial y}\rho_{\rm P}\,d\tau_{\rm P}=0\ . \end{equation} On the other hand, similarly: \begin{eqnarray*} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial z}\rho_{\rm P}\,d\tau_{\rm P}=-\frac{c}{4\pi}\int_{\tau_{\rm P}}\!\!\int_{\tau_{\rm M}}\rho_{\rm P}\rho_{\rm M}\,d\tau_{\rm P}d\tau_{\rm M}\bigg\{\frac{z_{\rm P}-z_{\rm M}}{r^3}-\\ -\frac{\rm G}{2c^2}\frac{(z_{\rm P}-z_{\rm M})(z_{\rm P}+z_{\rm M})}{r^3}+\frac{\rm G}{2c^2}\frac1r\bigg\}\ , \end{eqnarray*} interchanging M and P: \begin{eqnarray*} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial z}\rho_{\rm P}\,d\tau_{\rm P} =-\frac{c}{4\pi}\int_{\tau_{\rm M}}\!\!\int_{\tau_{\rm P}}\rho_{\rm M}\rho_{\rm P} \,d\tau_{\rm M}d\tau_{\rm P} \bigg\{\frac{z_{\rm M}-z_{\rm P}}{r^3}\\ -\frac{\rm G}{2c^2}\frac{(z_{\rm M} -z_{\rm P})(z_{\rm M} +z_{\rm P})}{r^3} +\frac{\rm G}{2c^2}\frac1r\bigg\}\ , \end{eqnarray*} and by taking half the sum: \begin{equation} \label{eqf27} \int_{\tau_{\rm P}}\frac{\partial \varphi{}'}{\partial z}\rho_{\rm P}\,d\tau_{\rm P}=-\frac{c}{4\pi}\int_{\tau_{\rm P}}\!\!\int_{\tau_{\rm M}}\frac{\rho_{\rm P}\rho_{\rm M}}{r}\,d\tau_{\rm P}d\tau_{\rm M}=-{\rm G}\,\frac{\rm U}{c^2}\,e\ , \end{equation} denoting by U the electrostatic energy of the system (apart from the gravitational correction terms). As a consequence of the assumptions made about the derivatives of $\varphi_{\rm P}{}''$, we can certainly write, with our approximation: \begin{equation} \label{eqf28} \left\{ \begin{array}{c} \displaystyle\int_{\tau}\frac{\partial \varphi{}''}{\partial x}\rho\,d\tau= -c\,{\rm E}_x^*\, e\ , \nonumber\\[4mm] \displaystyle\int_{\tau}\frac{\partial \varphi{}''}{\partial y}\rho\,d\tau= -c\,{\rm E}_y^*\, e\ , \nonumber\\[4mm] \displaystyle\int_{\tau}\frac{\partial \varphi{}''}{\partial z}\rho\,d\tau= -c\,{\rm E}_z^*\, e\ , \end{array} \right. \end{equation} where $e=\displaystyle\int_{\tau}\rho\,d\tau$ indicates the total charge of the system. By substituting the expression just obtained into (\ref{eqf24}) one finds: \begin{equation} \label{eqf29} \left\{ \begin{array}{l} e\,{\rm E}_x^*=0\ , \nonumber\\[2mm] e\,{\rm E}_y^*=0\ , \nonumber\\[2mm] e\,{\rm E}_z^*=-{\rm G}\,\displaystyle\frac{\rm U}{c^2}\ . \end{array} \right. \end{equation} Our result is contained in these formulas. In fact, they tell us that in order to maintain our system in equilibrium an external field (E$^*$) is required exerting on the system a force given (in the first approximation) by $e\,{\rm E}^*$, which must be understood to balance the weight of the system, which is therefore given by $-e\,{\rm E}^*$, and so has components \begin{equation} \label{eqf30} 0,\,0,\,{\rm G}\,\frac{\rm U}{c^2}\ . \end{equation} With this we conclude that {\it the weight of an electromagnetic mass always has the vertical direction and magnitude equal to the weight of a material mass} $u/c^2$. \fermisection{7} In the preceding section we have taken $\delta x$, $\delta y$, $\delta z$ to be the components of a translational displacement. If instead one takes the components of a virtual rotational displacement with the axis passing through the origin of the coordinates, namely setting \begin{equation} \label{eqf31} \delta x=qz-ry\ ; \qquad \delta y=rx-pz\ ; \qquad \delta z=py-qx\ , \end{equation} the integral (\ref{eqf9}), apart from the contribution due to the external field $\varphi{}''$, becomes: \newpage \begin{eqnarray} \label{eqf32} \int\,d\tau\bigg\{p\int_{\tau}\,\rho\left(y\frac{\partial \varphi}{\partial z} -z\frac{\partial \varphi}{\partial y}\right)\, d\tau +q\int_{\tau}\,\rho\left(z\frac{\partial \varphi}{\partial x} -x\frac{\partial \varphi}{\partial z}\right)\, d\tau \nonumber\\ +r\int_{\tau}\,\rho\left(x\frac{\partial \varphi}{\partial y} -y\frac{\partial \varphi}{\partial x}\right)\, d\tau\bigg\}\ . \end{eqnarray} The integrals between curly brackets are easily evaluated using (\ref{eqf13}) through methods similar to that used in the previous section. They have the values: \begin{equation} \label{eqf33} -\frac{\rm G}{8\pi c}\int\!\!\!\!\int\frac{y_{\rm P}}{r}\rho_{\rm P}\rho_{\rm M} \,d\tau_{\rm P}d\tau_{\rm M}\ ; \quad +\frac{\rm G}{8\pi c}\int\!\!\!\!\int\frac{x_{\rm P}}{r}\rho_{\rm P}\rho_{\rm M} \,d\tau_{\rm P}d\tau_{\rm M}\ ; \quad 0\ . \end{equation} By taking as the origin the point O${}'$ defined by the point O and the vector \begin{eqnarray*} {\rm O{}'}\,\,-\,\,{\rm O} =\frac{1}{2\rm U}\int\!\!\!\!\int\frac{\rm P\,\,-\,\,\rm O}{r} \rho_{\rm P}\rho_{\rm M}\,d\tau_{\rm P}d\tau_{\rm M}\ , \end{eqnarray*} one sees immediately that the three integrals vanish for {\it any} orientation of the system about O${}'$. As a consequence, with respect to the new origin the integral (\ref{eqf9}) is identically zero, namely the moment of the weight with respect to O${}'$ is zero for any orientation of the system; thus O${}'$ enjoys the properties of the center of gravity. {\small Pisa, March 1921.} \end{document}

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\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{*3}{*1} \titlespacing{\subsection}{0pt}{*2}{*0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[T2A]{fontenc} \usepackage[ngerman,greek,polish,english]{babel} \usepackage{float} \begin{document} \title{Genetic structure among the endangered Brazilian Euterpe Edulis Mart (Arecaceae) morphotypes} \author[1]{Gislaine Coelho}% \author[1]{Alesandro Santos}% \author[2]{Ivandilson Menezes}% \author[3]{Roberto Tarazi}% \author[4]{Fernanda Maria Souza}% \author[5]{Maria das Graças Silva}% \author[1]{F. A. Gaiotto}% \affil[1]{Universidade Estadual de Santa Cruz}% \affil[2]{Instituto Federal Goiano}% \affil[3]{BASF Discovery Breeder}% \affil[4]{Universidade Estadual de Santa Cruz Departamento de Ciencias Biologicas}% \affil[5]{5Centro de Pesquisa do Cacau (CEPEC), Comissão Executiva do Plano da Lavoura Cacaueira (CEPLAC)}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} Euterpe edulis (Arecaceae) Mart has high ecological and economic importance providing food resources for more than 58 species of birds and 20 species of mammals, including humans. E. edulis is the second most explored non-timber product from Brazilian Atlantic Forest. Due to overexploitation and destruction of habitats, E. edulis is threatened by extinction. E. edulis populations have large morphological variations, with individuals having green, red or yellow leaf sheath. However, no study has related phenotypic distinctions between populations and their levels of genetic structure. Thus, this study aimed to evaluate the diversity and genetic structure of different E. edulis morphotypes. We sampled 250 adult individuals in eight populations with the different morphotypes. Using 14 microsatellite markers, we access genetic diversity through population genetic parameters calculated in the GenAlex program and the diveRsity package in R. We used the Wilcoxon test to verify population bottlenecks and the genetic distance of Nei and Bayesian analysis for genetic clusters. The eight populations showed low allele richness, low heterogeneity observed and high inbreeding values (f). In addition, six of the eight populations experienced genetic bottlenecks, which would partly explain the low genetic diversity in populations. Cluster analysis identified two clusters (K=2), with green morphotype genetically distinguishing from yellow and red morphotypes. Thus, we show, for the first time, a strong genetic structure among E. edulis morphotypes even for geographically close populations.% \end{abstract}% \sloppy \textbf{INTRODUCTION} Arecaceae is a botanical family with pantropical distribution, with about 183 genera and 2,400 species (Dransfield \emph{et al} ., 2008). Arecaceae species are key components of forest structuring, and are also important because they provide fruits and seeds that maintain a high richness of frugivores in these environments (Galetti \emph{et al.} , 2013; Elena \emph{et al.} , 2014; Benchimol \emph{et al.} , 2016). In Brazil, 37 genera and 297 species of Arecaceae are found, being approximately 46\% of these endemic species (Leitman \emph{et al} ., 2015). Studies show that this high percentage of endemism is probably related to environmental characteristics, such as soil fertility and climatic factors (Salm \emph{et al.} , 2007; Eiserhardt \emph{et al.} , 2011). For the Brazilian Atlantic Forest 61 Arecaceae species are found, which are in constant risk of being lost due to the exacerbated loss of their natural habitat (Leitman \emph{et al} ., 2015; Benchimol \emph{et al.} , 2016). \emph{Euterpe edulis} Mart (Arecaceae) has a great ecological and economic relevance (Reis \emph{et al.} , 2000; Galetti \emph{et al.} , 2013; Elena \emph{et al.} , 2014; Carvalho \emph{et al.} , 2016). In Brazil, this species occurs in forests of Galleries in the Cerrado and widely distributed in the Atlantic Forest, its main habitat of occurrence (Leitman \emph{et al} ., 2015). \emph{E. edulis} seeds and fruits are important food resources for about 58 bird species and 20 mammal species playing an important ecological role in maintaining the diversity of frugivores in the Atlantic Forest (Galetti \emph{et al.} , 2013). In economic terms, the species is the second most exploited non-timber product of the Atlantic Forest Brazilian, through the extraction of its apical meristem called heart-of-palm for human consumption (Silva Matos \emph{et al.} , 1999; Reis \emph{et al.} , 2000; Pizo and Vieira, 2004). This illegal harvesting of heart-of-palm causes the death of individuals, which is a serious problem, since the species does not sprout or have tillering. Therefore, this is one of the causes that led the species to the list of endangered Brazilian flora (Leitman\emph{et al} ., 2015). In addition to the negative impacts of predatory harvesting, the reduction and fragmentation of the Atlantic Forest further threatens this species (Fleury and Galetti, 2006; Carvalho\emph{et al.} , 2015; Santos \emph{et al.} , 2016). \emph{E. edulis} is a monoecious species with predominance of cross-pollination, performed mainly by small bees (eg \emph{Trigona spinipes} ) and seeds dispersed mainly by birds (Reis \emph{et al.} , 2000; Gaiotto \emph{et al.} , 2003; Galetti \emph{et al.} , 2013). The populations of \emph{E. edulis} may present large morphological variations, as for example, leaf sheath color and number of rachila, besides distinct demographic characteristics along their area of occurrence. Motivated by these differences, some scientists have proposed separation into two species and one variety: populations with green sheathed individuals, such as \emph{E. edulis} ; and those with individuals having red sheaths such as \emph{E. spiritosantensis} and; Yellow-sheathed individuals, such as \emph{E. edulis var.clausa} (Bovi\emph{et al} ., 1987; Reis \emph{et al} ., 1996; Mantovani and Morellato, 2000; Silva \emph{et al.} , 2009; Leitman \emph{et al} ., 2015). Although there are evident morphological and demographic differences, currently, it is considered as taxonomically accepted name only \emph{E. edulis}and the others are considered synonyms (Leitman \emph{et al} ., 2015). In this context, despite these peculiarities observed and discussed in the literature, there is a shortage of genetic studies that associate the phenotypic distinctions between natural populations and their levels of genetic structure. Currently, it is only known that populations of\emph{E. edulis} in different environmental conditions are genetically different (Brancalion \emph{et al.} , 2018; Alves-Pereira \emph{et al.} , 2019). However, it is not known whether populations with morphological differences are also genetically different. Thus, this study had as its central objective to evaluate the genetic diversity and to verify if there is genetic differentiation between the different \emph{E. edulis}morphotypes. \textbf{MATERIAL~AND METHODS} \textbf{Sampling Areas} The populations studied were chosen based on their distinct morphotypes (Figure 1 and Table 1) and geographic distances (Figure 2). Eight populations were sampled, being two in gallery forests from the\emph{Cerrado} biome (Brazilian savanna in Distrito Federal - DF, central west of Brazil) and six from the Atlantic Forest (Bahia, northeastern of Brazil) (Figure 2). The two populations sampled in DF are located in gallery forests, which are a type of perennial forest vegetation immersed in savanna formations, which accompany small streams and usually have nutrient-rich soils (Haridasan, 1998). These populations were sampled within protected areas, namely the Brasilia National Park (PNB) and the Roncador Ecological Reserve (IBGE), which are located 10 Km and 20 Km from Brasilia-DF, respectively. The sampled populations in Bahia are located in the region with the largest remnants of the Atlantic Forest of northeastern Brazil (Ribeiro\emph{et al.} , 2009), being considered a priority for conservation due to its high biodiversity (Martini \emph{et al.} , 2007). Of these populations, four are located in protected areas and two in unprotected areas. Protected areas include: (1) The population from the Private Reserve of Natural Patrimony Serra do Teimoso (ST) located in the municipality of Jussari, which consists in a transition between the rainforest found on the tops of hills and a semideciduous forest (forest with a dry period in the year) at the base; (2) The populations of the Ecoparque de Una (EU) and the Una Biological Reserve (BR) which are located in the municipality of Una, inserted in rainforest (Thomas\emph{et al.} , 1998); (3) The population from the Private Reserve of Natural Patrimony Esta\selectlanguage{ngerman}ção Veracel (EV), which is located in the municipality of Eunapolis and has rainforest. The other two populations are not located within conservation units, but they are also inserted in rainforest of the Atlantic Forest, located in particular properties which are in the municipality of Itacaré on Alto da Esperança Farm (AE), and in the municipality of Uruçuca on Boa Sorte Farm (BS). \textbf{Microsatellite Marker Analysis} Samples were collected from the root tissue of 250 randomly chosen adults and the DNA was obtained according to Doyle and Doyle (1987). Posteriorly, the genetic material was amplified with a total of 14 nuclear microsatellite fluorescent primer pairs (\emph{EE2/ EE5/ EE23/ EE32/ EE9/EE25/ EE43/ EE45/ EE47/ EE48/ EE52/ EE54/ EE59/ EE63} ) developed by Gaiotto et al (2001). The amplification reactions~were performed~by PCR~in~a~final volume of~13~\selectlanguage{greek}µ\selectlanguage{english}L containing~7.5~ng~of genomic DNA, 1X buffer (10 mmol/L Tris-HCl, 50~mmol/L KCl and 21.5~mmol/L MgCl, pH 8.3), 0.27 \selectlanguage{greek}µ\selectlanguage{english}mol/L of each primer, 2.0~mmol/L MgCl\textsubscript{2}, 0.25~mg/mL BSA, 0.25~mmol/L dNTP and 1U of Taq DNA~polymerase in ultrapure sterile water. The PCRs were performed under the following conditions: 1 cycle~at 96\selectlanguage{ngerman}°C for 2 min, 34~cycles of 94°C~for 1 min, the annealing of the temperature-specific primer~(TºC) for 1 minute and 72°C for 1 min. The final elongation step was performed at 72°C for 7 min. The analysis of amplicons in a denaturing gel (7 mol/L urea) with 4\% polyacrylamide (Long Ranger 50\% - Cambrex) was performed in a multiplex system, in a semi-automatic ABI 377 sequencer (Applied Biosystems) by using virtual filter D. \textbf{Data Analysis} To estimate the frequency of null alleles, assuming the Hardy-Weinberg equilibrium proportions and to identify possible genotyping errors, we use the MICRO-CHECKER 2.2.3 program (Oosterhout \emph{et al.} , 2004). The populations presented low average frequency of null alleles (\selectlanguage{english}[?]0.08), not compromising our results. Then, we used the spreadsheet obtained of the MICRO-CHECKER with corrections of possible genotyping errors for genetic analysis, thus ensuring greater accuracy in the results. The genetic diversity~of~\emph{E.~edulis} morphotypes was estimated using different population genetics parameters calculated by GenAlex 6.5 (Peakall and Smouse, 2012) and diveRsity package in the R software (Keenan \emph{et al} ., 2013). In the GenAlex, we calculated the mean number of alleles (No); the mean number alleles effectives (Ne) and the mean private alleles (PA). Additionally, in diveRsity package, we used the divBasic function to calculate the allelic richness (AR), expected heterozygosity (H\textsubscript{E}), observed heterozygosity (H\textsubscript{O}) and inbreeding coefficient (\emph{f} ). To consider the 95\% confidence interval of \emph{f} , the standard deviation for H\textsubscript{E} and H\textsubscript{O}, and standard error for AR, we calculated 10,000 bootstraps which the divBasic function. To verify signs of population bottlenecks, we use the Wilcoxon test in software BOTTLENECK version 1.2.02 02 (Cornuet and Luikart, 1996), testing if populations have excess heterozygosity (Piry \emph{et al} ., 1999). The Wilcoxon test is recommended because of its power to detect population bottleneck when few molecular markers (\textless{}20 loci) are used, as is the case in our study. As microsatellites can present different mutational models, we performed the Wilcoxon test considering the Infinite Allele Model (IAM), Stepwise Mutation Model (SMM) and Two Phase Model (TPM) (Piry \emph{et al} ., 1999). For the TPM model, the proportion of SMM in TPM = 0.000, and variance of the geometric distribution for TPM = 0.36, which generally represent the most sensitive values for microsatellite markers (Piry \emph{et al.} , 1999). To estimate the level of genetic structure among the populations, we calculate the observed F\textsubscript{ST} values and the 95\% confidence interval with 10,000 bootstraps, using the diffCalc function of the diveRsity package in software R (Keenan \emph{et al} ., 2013) (http://www.r-project.org/). Subsequently, to assess whether geographic distance (km) influenced in F\textsubscript{ST} values obtained between populations, we performed a Mantel test (Mantel, 1967) using the ecodist package (Goslee and Urban, 2007) in the software R (http://www.r-project.org/). To evaluate the population clustering, we calculated the genetic distance from Nei in GenAlex 6.5 (Peakall and Smouse, 2012) and the Bayesian clustering in Structure program (Evanno \emph{et al} ., 2005). Using Nei's genetic distance, we performed a heatmap analysis with the eight populations of \emph{E. edulis} in heatmaply package (Galili\emph{et al} ., 2017) in software R. To determine the number of groups in the heatmap, we used hierarchical clustering algorithm with the Euclidean distance and the average method, implemented in heatmaply package (Galili \emph{et al} ., 2017) in software R. In Bayesian model, we infer automatically the number of distinct genetic groups according to mixed model that was often correlated. An analysis of the number of populations (K) was performed for values ranging from 1 to 10 with ten independent chains, and each chain had a length of 50000 iterations followed by 100000 repetitions of the MCMC (Markov and Monte Carlo chain). The \selectlanguage{greek}Δ\selectlanguage{english}K (actual number of~groups) was determined~on the basis of the average~values of L (K) as produced for ten repetitions for each K, according to the method proposed by Evanno et al (2005), by using the Structure Harvester program (Earl and VonHoldt, 2011). \textbf{RESULTS} \textbf{Genetic Diversity and population bottlenecks} The eight populations of \emph{Euterpe edulis} showed low to moderate number of alleles and allelic richness (Mean = 7.58 and 5.48 respectively), low number of effective alleles (Mean =4.08), and all of them had private alleles (Table 1). The observed heterozygosity (H\textsubscript{O}) was low to moderate, except for BN and RE with high values (Figure 3A). The expected heterozygosity (H\textsubscript{E}) was moderate to high, with emphasis for AE, BN and RE (Figure 3A). The values of inbreeding coefficient (\emph{f} ) were high, except for BN and RE showing the lowest values, although none values are nonzero (Figure 3B). The different mutational models (IAM, TPM and SMM) used in the Wilcoxon test for population bottlenecks showed divergent results. The IAM model detected significant excess of heterozygosity for the BS, AE, EU, ST, BN and RE populations, while the SMM and TPM models did not detect genetic bottlenecks in any of the eight \emph{E. edulis} populations evaluated (Table 2). \textbf{Genetic Structure} The analysis of the genetic structure with F\textsubscript{ST} revealed that the populations have moderate to high genetic differentiation, with the less value found for BN-RE populations (Figure 4). Although all F\textsubscript{ST} values are moderate or high, they are within the confidence interval and do not differ from zero (Figure 4). The Mantel test showed that the geographical distance does not correlate significantly with the pattern of genetic differentiation found between populations (r = 0.13, p = 0.33, Figure S1). \textbf{Population~clustering} The heatmap with clustering using the Nei's genetic distance, showed that the eight sampled populations form two clusters (Figure 5 and Figure S2). The populations with green morphotypes, which were sampled in the Distrito Federal (BN and RE) and southern Bahia (ST) clustered separately from the red (EU, AE and BR) and yellow (BS and EV) morphotypes sampled in southern Bahia (Figure 5). In Bayesian clustering approaches, the eight sampled populations had the estimated number of population groups of K = 2, as the number of most likely groups (Figure 6 and Figure S3), which demonstrated that they are strongly structured (Figure 6). On average, the shared ancestry among the \emph{E. edulis} palm was 98.8\% and 99.4\% in the groups marked in red and green, respectively. The red group was composed of all individuals sampled in the EU, AE, BR, BS and EV populations in southern Bahia, that have red or yellow morphotypes (Figure 1). The green group contains all the individuals sampled in the RE and BN populations in Distrito Federal and ST in southern Bahia, that have green morphotype (Figure 1). \textbf{DISCUSSION} In the present study, we recorded low genetic variability and genetic bottleneck effect in \emph{E. edulis} populations, which also have unusual genetic structure rate for populations of this species (Gaiotto\emph{et al.} , 2003; Santos \emph{et al.} , 2015). In addition, the evaluated populations formed two genetic clusters, separating typical populations (green morphotype) from populations with yellow or red morphotypes that have restricted occurrence within the Brazilian Atlantic Forest. Thus, we showed, for the first time, that morphologically distinct populations of \emph{E. edulis} have a strong genetic structure, as a possible response to local environmental factors. \textbf{Genetic diversity and population bottlenecks} In general, there is a low genetic diversity in the eight populations of\emph{E. edulis} when considering the number and richness of alleles and the number of effective alleles compared to other populations of the species (Conte \emph{et al.} , 2008; Carvalho \emph{et al.} , 2015, 2017). In theory, several ecological or anthropogenic factors can negatively impact genetic diversity, such as the reduction or inefficiency of dispersers and pollinators, reduction in effective population size, causes related to habitat loss and fragmentation, or even illegal extraction of species (Young \emph{et al.} , 1996; Chung \emph{et al.} , 2014; Browne \emph{et al.} , 2015; Carvalho \emph{et al.} , 2016, 2017; Ellegren and Galtier, 2016). Even in this context, all populations had a considerable proportion of private alleles, demonstrating the importance of these areas for the conservation of this endangered species. Considering the observed heterogeneity (H\textsubscript{O}), six populations have low or moderate values compared to other populations of the species (Carvalho \emph{et al.} , 2017). In addition, expected heterozygosity (H\textsubscript{E}) values are moderate to high and always upper than H\textsubscript{O} values in all populations, indicating an increase in the number of homozygous individuals compared to expected in the drift-mutation equilibrium in an idealized, panmictic population (so-called Wright--Fisher equilibrium). As a consequence of H\textsubscript{O}\textless{}H\textsubscript{E}, all populations have positive and high values of inbreeding (\emph{f} ), indicating non-random mating occurring, which may cause reduction of genetic diversity (Xue\emph{et al.} , 2015). In this scenario, the genetic erosion may arise and even increase over generations, as individuals would become more related to each other as result of non-random mating within populations (Xue \emph{et al.} , 2015). On the other hand, it is important to draw attention to the areas RE and BN, that have the highest values of H\textsubscript{O}, H\textsubscript{E} and the lowest of \emph{f} , indicating the best genetic conservation status among the studied populations. These values are probably influenced by the occurrence of gene flow between RE and BN, which may favor the maintenance of genetic variability over time (Gaiotto \emph{et al.} , 2003; Santos \emph{et al.} , 2016). The Wilcoxon test, with the Infinite Allele Mutational model (IAM), revealed that six of the eight populations studied have recently experienced genetic bottlenecks. However, the Two Phase Model (TPM) and Stepwise Mutation Model (SMM) had divergent results, not detecting genetic bottleneck in any of the evaluated populations. This result was expected to some extent because, although microsatellite markers may adhere to different mutational models (AIM, TPM, or SMM), genetic bottlenecks have been reported mainly for the AIM model (Piry \emph{et al.} , 1999; Santos \emph{et al.} , 2019). The genetic bottleneck or excess of H\textsubscript{E} occurs when the population has experienced a recent reduction in effective population size, causing a reduction in the number of alleles faster than in H\textsubscript{E} (Cornuet and Luikart, 1996; Piry \emph{et al.} , 1999). Thus, populations that have experienced genetic bottlenecks have a H\textsubscript{E} greater than the expected heterozygosity in drift - mutation equilibrium (H\textsubscript{EQ}) (Cornuet and Luikart, 1996; Piry \emph{et al.} , 1999). Thus, as we identified genetic bottleneck effect in most populations evaluated, at least in parts, would explain the reduction in the number and allelic richness and in the number of effective alleles reported. Moreover, even if the population did not go through a genetic bottleneck, such as BR and EV, there is evidence of genetic structure (Figure 4), which could potentially lead to non-random crossing within these areas due to isolation (Mosca \emph{et al.} , 2014; Sexton \emph{et al.} , 2014). Thus, we believe that both the genetic bottleneck and the degree of isolation may explain the reduction of genetic diversity in terms of number and richness of alleles, H\textsubscript{O}\textless{}H\textsubscript{E}, high values of\emph{f,} and presence of private alleles in the populations. \textbf{Genetic~Structure} Considering all populations, F\textsubscript{ST} values were generally moderate to high, indicating a limited gene flow between populations. These F\textsubscript{ST} values indicate unusual genetic divergence among \emph{E. edulis} populations compared to other populations of the species, even when under influence of fragmentation and geographically distant (Conte \emph{et al.} , 2008; Santos \emph{et al.} , 2015). Thus, we believe that the differences found between the populations of this palm tree should not be related to habitat fragmentation, but to naturally occurring evolutionary events, such as local adaptation (Brancalion \emph{et al.} , 2018). In addition, it is important to draw attention to RE and BN that have the same morphotype and are geographically close, with low to moderate F\textsubscript{ST}, indicating occurrence of gene flow, as reported by Gaiotto et al (2003) for these same populations. The occurrence of gene flow between RE and BN, probably favors the highest H\textsubscript{O} and H\textsubscript{E} values and the lowest of \emph{f} reported in present study. However, it is important to note that, although F\textsubscript{ST} values were high in most cases, all values are within the confidence interval and are not statistically different from zero. The pattern of genetic differentiation (F\textsubscript{ST}) is not explained by geographical distance as theoretically expected, in which geographically closer populations are genetically more similar (Wright, 1943; Diniz-filho \emph{et al.} , 2013; Ram\selectlanguage{ngerman}írez\selectlanguage{english}-Barrera \emph{et}al.,2019). Thus, we emphasize that the pattern of genetic differentiation found between populations, is probably influenced mainly by morphological differences, as demonstrated in the cluster analysis. \textbf{Population~clustering} Although F\textsubscript{ST} values were moderate or high between sampled populations, clustering using Nei genetic distance and bayesian analysis identified K = 2 as the most likely number of genetic clusters. It is important to note that no F\textsubscript{ST} value was statistically significant and that values greater than 0.20 allow for more accurate cluster identification and can correctly attribute about 97\% of individuals to a true cluster, when using the bayesian approach (Latch \emph{et al.} , 2006). Thus, the reported F\textsubscript{ST}values probably contributed to a greater inference power of the genetic clusters. The grouping into two clusters (Figure 5 and 6), indicates a greater genetic ancestry between populations with green morphotype that is genetically distinguished from yellow and red morphotypes. Thus, we show for the first time that it is not just a phenotypic plasticity of\emph{E. edulis} , but there is genetic divergence between morphotypes, possibly in response to environmental or ecological divergence (Funk and Murphy, 2010). On the other hand, the grouping of the yellow morphotype with the red indicates that this morphological differentiation is probably more recent compared wich green morphotype. This would potentially explain the sharing of the gene pool between the morphotype grouped. Although we have used microsatellite markers that are considered neutral, we believe that the genetic clusters that distinguish \emph{E. edulis} morphotypes are a consequence of populations being shaping in different environmental or ecological conditions. This hypothesis is based on recent studies using SNPs (Single Nucleotide Polymorphism) markers, demonstrating that \emph{E. edulis} populations inserted in different environmental and ecological conditions are genetically different (Brancalion \emph{et al.} , 2018; Alves-Pereira \emph{et al.} , 2019). Thus, it is believed that there is adaptation of species to different conditions and that this adaptation remains mainly locally, favoring the genetic divergence directed by the environment (Rellstab\emph{et al.} , 2017; Sork, 2017). However, it is important to emphasize that we measured no local environmental variables and used microsatellite markers, which lead us to indicate future studies using potential markers under selection (eg: SNPs) to test our hypothesis of local adaptation with morphological and genetic differentiation. \textbf{CONCLUSION} The genetic grouping of yellow and red morphotypes indicates that these morphological variations found only in the state of Bahia and Espirito Santo in Brazil, are genetically different from the typical populations (green morphotype) of \emph{E. edulis} found in all occurrence areas, including the Brazillian states aforementioned. Thus, we believe that unravel the relationship between phenotypic and genetic variation is an important advance in scientific knowledge for future conservation measures for this endangered species. In this sense, considering the low genetic variability reported in this study, the importance of developing conservation plans is highly recommended, particularly for populations with yellow or red morphotypes that have limited geographical occurrence. \textbf{ACKNOWLEDGEMENTS} This study was financed in part by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Brasil (CAPES) - Finance Code 001. Funding was provided by Universidade Estadual de Santa Cruz (UESC) grant \# 00220.1100.427 and Fundacao de Amparo a Pesquisa do Estado da Bahia (FAPESB) grant \# 857/2004. Conselho de Desenvolvimento Cientifico e Tecnologico (CNPq) and Coordenacao de Aperfeicoamento de Pessoal de nivel Superior (CAPES) provided fellowships to the authors: productivity (FAG) (CNPq \#306160/2017-0), postdoctoral~researcher (ASS) and graduate (GMC). We thank Josiane Amorim, Mariana Barreto, Elaini Oliveira, Marcelo Bramucci, Rodolpho Mafei, and Dario Ahnert for their field support. \textbf{COMPETING INTERESTS STATEMENT} The authors declare no conflict of interest \textbf{DATA ACCESSIBILITY} Relationship between pairwise F\textsubscript{ST} and geographic distances \textbf{(} Figure S1), Estimated number of groups using the average method (Figure S2), Variation of~the second~order of the~average values \selectlanguage{english}\selectlanguage{english}of~maximum likelihood (Figure S3) uploaded as online Supplementary material. 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Diniz-filho JAF, Soares TN, Lima JS, Dobrovolski R, Landeiro VL, Pires M, \emph{et al.} (2013). Mantel test in population genetics. \emph{Genet Mol Biol} \textbf{36} : 475--485. Doyle JJ, Doyle JL (1987). Isolation of plant DNA from fresh tissue. Focus \textbf{12} : 13--15. Dransfield J, Uhl NW, Asmussen CB, Baker WJ, Harley MM, Lewis CE. (2008). Genera Palmarum - the evolution and classification of palms. Royal Botanic Gardens, Kew. pp 732. Eiserhardt WL, Svenning JC, Kissling WD, Balslev H (2011). Geographical ecology of the palms (Arecaceae): Determinants of diversity and distributions across spatial scales. \emph{Ann Bot} \textbf{108} : 1391--1416. Elena A, Rother DC, Brancalion PS, Naves RP, Rodrigues RR, Pizo MA (2014). Can overharvesting of a non-timber-forest-product change the regeneration dynamics of a tropical rainforest? The case study of Euterpe edulis. \emph{For Ecol Manage} \textbf{324} : 117--125. Ellegren H, Galtier N (2016). Determinants of genetic diversity.\emph{Nat Rev Genet} \textbf{17} : 422--433. Evanno G, Regnaut S, Goudet J (2005). Detecting the number f cluster of individuals using the software structure: a simulation study. Mol Ecol\textbf{14} : 2611-2620. doi: 10.1111/j.1365-294X.2005.02553.x. Fleury M, Galetti M (2006). Forest fragment size and microhabitat effects on palm seed predation. \emph{Biol Conserv} \textbf{131} : 1--13. Funk WC, Murphy MA (2010). Testing evolutionary hypotheses for phenotypic divergence using landscape genetics. \emph{Mol Ecol}\textbf{19} : 427--430. Gaiotto FA, Grattapaglia D, Vencovsky R (2003). Genetic Structure, Mating System, and Long-Distance Gene Flow in Heart of Palm (Euterpe edulis Mart.). \emph{J Hered} \textbf{94} : 399--406. Gaiotto FA, Brondani RPV, Grattapaglia D. (2001). Microsatellite markers for Heart of Palm - \emph{Euterpe edulis} and \emph{E. oleracea} Mart. (Palmae). Mol Ecol Notes \textbf{1} : 86-88. doi: https://doi.org/10.1046/j.1471-8278.2001.00036.x. Galetti M, Guevara R, Cortes MC, Fadini R, Matter S Von, Leite AB,\emph{et al.} (2013). Functional Extinction of Birds Drives Rapid Evolutionary Changes in Seed Size. \emph{Science,} \textbf{340} : 1086--1091. Galili T, O'Callaghan A, Sidi J, Sievert C (2017). heatmaply: an R package for creating interactive cluster heatmaps for online publishing.~\emph{Bioinformatics} ,~\textbf{34} : 1600-1602. Goslee SC, Urban DL (2007). The ecodist package for dissimilarity-based analysis of ecological data. Journal of Statistical Software\textbf{22} :1-19. Haridasan M (1998). Solos de Matas de Galeria e Nutricao Mineral de Especies Arboreas em Condicoes Naturais; 19-20pp In Ribeiro JF. (org.).~\emph{Cerrado: matas de galeria} . Planaltina: Embrapa. Keenan K, McGinnity P, Cross TF, Crozier WW, Prodohl PA (2013). diveRsity: An R package for the estimation and ex- ploration ofpopulation genetics parameters and their associ- ated errors. Methods Ecol Evol \textbf{4} :782-788. Latch EK, Dharmarajan G, Glaubitz JC, Jr OER (2006). Relative performance of Bayesian clustering software for inferring population substructure and individual assignment at low levels of population differentiation. \emph{Conserv Genet} \textbf{7} : 295--302. Leitman P, Soares K, Henderson A, Noblick L, Martins RC (2015). Arecaceae in Lista de Especies da Flora do Brasil. Jardim Botanico do Rio de Janeiro. Disponivel~em:~\textless{}http://floradobrasil.jbrj.gov.br/jabot/floradobrasil/FB53\textgreater{}. Acesso em: 16 Dez. 2019 Mantel N (1967). The detection of disease clustering and a generalized regression approach. Cancer Res 27: 209--220. Mantovani A, Morellato LPC (2000). Fenologia da floracao, frutificacao, mudanca foliar e aspectos da biologia floral do palmiteiro. Sellowia\textbf{49-52} :23-3. Martini AMZ, Fiaschi P, Amorim AM, Paixao JL (2007). A hot-point within a hot-spot\selectlanguage{english} : a high diversity site in Brazil's Atlantic Forest.\emph{Biodivers Conserv} \textbf{16} : 3111--3128. Mosca E, Gonzalez-Marti\selectlanguage{polish}ı\selectlanguage{english}nez SC, Neale DB (2014). Environmental versus geographical determinants of genetic structure in two subalpine conifers. \emph{New Phytol} \textbf{201} : 180--192. Oosterhout C Van, Utchinson WF, Wills DPM, Shipley P (2004). MICRO-CHECKER: Software for identifying and correcting genotyping errors in microsatellite data. \emph{Mol Ecol Notes} \textbf{4} : 535--538. Peakall R, Smouse PF (2012). GenAlEx 6.5: genetic analysis in Excel. Population genetic software for teaching and research---An update. Bioinformatics \textbf{28} :2537--2539. doi:10.1111/j.1471-8286. 2005.01155.x Piry S, Luikart G, Cornuet J-M (1999). Computer note. BOTTLENECK: a computer program for detecting recent reductions in the effective size using allele frequency data. \emph{J Hered} \textbf{90} : 502--503. Pizo M, Vieira EM (2004). Palm harvesting affects seed predation of Euterpe edulis, a threatened palm of the Brazilian Atlantic Forest.\emph{Brazilian J Biol} \textbf{64} : 669--676. Ram\selectlanguage{ngerman}írez\selectlanguage{english}-Barrera SM, Velasco JA, Orozco\selectlanguage{english}-Tellez TM, Vazquez\selectlanguage{english}-Lopez AM, Hernandez\selectlanguage{english}-Banos BE (2019). What drives genetic and phenotypic divergence in the Red\selectlanguage{english}-crowned Ant tanager (Habia rubica, Aves: Cardinalidae), a polytypic species? \emph{Ecology and Evolution} ,~9: 12339-12352. Reis A, Kageyama PY, Reis MS, Fantini AC (1996). Demografia de\emph{Euterpe edulis} Martius (Arecaceae) em Floresta Ombrofila Densa, em Blumenau (SC). Sellowia \textbf{45-58} :13-45. Reis MS, Fantini AC, Nodari RO, Reis A, Guerra MP, Mantovani A (2000). Management and Conservation of Natural Populations in Atlantic Rain Forest: The Case Study of Palm Heart (Euterpe edulis Martius).\emph{Biotropica} \textbf{32} : 894--902. Rellstab C, Fischer MC, Zoller S, Graf R, Tedder A, Shimizu KK, \emph{et al.} (2017). Local adaptation (mostly) remains local\selectlanguage{english} : reassessing environmental associations of climate-related candidate SNPs in Arabidopsis halleri. \emph{Heredity} \textbf{118} : 193. Ribeiro MC, Metzger JP, Martensen AC, Ponzoni FJ, Hirota MM (2009). The Brazilian Atlantic Forest: How much is left, and how is the remaining forest distributed? Implications for conservation. \emph{Biol Conserv}\textbf{142} : 1141--1153. Salm R, De Salles NV, Alonso WJ, Schuck-Paim C (2007). Cross-scale determinants of palm species distribution. \emph{Acta Amaz} \textbf{37} : 17--25. Santos AS, Borges DB, Vivas C V., Berg C Van Den, Rodrigues PS, Tarazi R, \emph{et al.} (2019). Gene pool sharing and genetic bottleneck effects in subpopulations of eschweilera ovata (Cambess.) mart. ex miers (lecythidaceae) in the atlantic forest of southern bahia, brazil.\emph{Genet Mol Biol} \textbf{42} : 655--665. Santos AS, Cazetta E, Dodonov P, Faria D, Gaiotto FA (2016). Landscape-scale deforestation decreases gene flow distance of a keystone tropical palm, Euterpe edulis Mart (Arecaceae). \emph{Ecol Evol}\textbf{6} : 6586--6598. Santos AS, Cazetta E, Morante Filho JC, Baumgarten J, Faria D, Gaiotto FA (2015). Lessons from a palm: genetic diversity and structure in anthropogenic landscapes from Atlantic Forest, Brazil. \emph{Conserv Genet} \textbf{16} : 1295--1302. Sexton JP, Hangartner SB, Hoffmann AA (2014). Genetic isolation by environment or distance: Which pattern of gene flow is most common?\emph{Evolution} \textbf{68} : 1--15. Silva MDGCPC, Martini AMZ, Araujo QR De (2009). Estrutura populacional de Euterpe edulis Mart. no Sul da Bahia, Brasil. \emph{Rev Bras Botanica} \textbf{32} : 393--403. Silva Matos DM, Freckleton RP, Watkinson AR (1999). The role of density dependence in the population dynamics of a tropical palm. \emph{Ecology}\textbf{80} : 2635--2650. Sork VL (2017). Genomic Studies of Local Adaptation in Natural Plant Populations. \emph{J Hered} \textbf{109} : 3--15. Thomas WMW, Carvalho AMV, Amorim AA, Garrison J, L. AA (1998). Plant endemism in two forests in southern Bahia , Brazil. \emph{Biodivers Conserv} \textbf{322} : 311--322. Wright S (1943). Isolation by Distance. \emph{Genetics} \textbf{28} : 114--138. Xue Y, Prado-martinez J, Sudmant PH, Narasimhan V, Ayub Q, Szpak M,\emph{et al.} (2015). Mountain gorilla genomes reveal the impact of long-term population decline and inbreeding. \emph{Science}\textbf{348} : 242--245. Young A, Boyle T, Brown T (1996). The population genetic consequences of habitat fragmentation for plants. \emph{Trends Ecol Evol} \textbf{11} : 413--418. \textbf{Table 1} \emph{E. edulis} populations sampled with their respective morphotypes, sample size, and estimation of genetic parameters.\selectlanguage{english} \begin{longtable}[]{@{}lllllll@{}} \toprule Population & Morphotype & N & Na & Ne & PA & AR\tabularnewline \midrule \endhead EV & Yellow & 16 & 5.28 (0.6) & 3.04 (0.3) & 1.07 (0.4) & 4.41 (0.4)\tabularnewline BS & Yellow & 40 & 8.36 (1.0) & 4.68 (0.7) & 0.57 (0.2) & 5.65 (0.6)\tabularnewline BR & Red & 40 & 8.28 (1.0) & 3.88 (0.5) & 0.64 (0.2) & 5.32 (0.6)\tabularnewline AE & Red & 40 & 8.93 (1.0) & 4.94 (0.6) & 1.35 (0.3) & 5.98 (0.5)\tabularnewline EU & Red & 33 & 6.64 (0.6) & 3.95 (0.5) & 0.86 (0.3) & 4.94 (0.4)\tabularnewline ST & Green & 20 & 5.50 (0.6) & 3.29 (0.4) & 0.78 (0.3) & 4.42 (0.5)\tabularnewline BN & Green & 28 & 8.36 (0.7) & 4.38 (0.3) & 0.71 (0.2) & 6.52 (0.4)\tabularnewline RE & Green & 33 & 9.28 (0.7) & 4.53 (0.4) & 1.00 (0.3) & 6.63 (0.5)\tabularnewline Mean total & - & 31,25 & 7.58 & 4.08 & 0.87 & 5.48\tabularnewline \bottomrule \end{longtable} Abbreviations: N = Size samples; Na = Mean number of alleles; Ne = Mean number alleles effectives; Pa = Mean private alleles; AR = Allelic richness; ( ) estimative standard error. *EV = Private Reserve of Natural Patrimony Esta\selectlanguage{ngerman}ção Veracel; BS = Boa~Sorte Farm; BR = Una Biological Reserve; AE = Farm Alto da Esperança; EU = Ecoparque de Una; ST = Private Reserve of Natural Patrimony Serra do Teimoso; BN = Brasilia National Park; RE = Roncador Ecological Reserve. \textbf{Table 2} Results of the Wilcoxon sign-rank test.\selectlanguage{english} \begin{longtable}[]{@{}llll@{}} \toprule Population & IAM & TPM & SMM\tabularnewline \midrule \endhead EV & 0.076 & 0.891 & 0.979\tabularnewline BS & \textbf{0.020} & 0.749 & 0.982\tabularnewline BR & 0.291 & 0.979 & 0.991\tabularnewline AE & \textbf{0.000} & 0.786 & 0.948\tabularnewline EU & \textbf{0.010} & 0.786 & 0.987\tabularnewline ST & \textbf{0.039} & 0.891 & 0.991\tabularnewline BN & \textbf{0.002} & 0.913 & 0.985\tabularnewline RE & \textbf{0.052} & 0.985 & 0.998\tabularnewline \bottomrule \end{longtable} Abbreviations: IAM = Infinite Alleles Model; TPM = Two-Phase Model; SMM = Stepwise Mutation Model. Significant values are shown in bold. EV = Private Reserve of Natural Patrimony Esta\selectlanguage{ngerman}ção Veracel; BS = Farm Boa~Sorte; BR = Una Biological Reserve; AE = Farm Alto da Esperança; EU = Ecoparque de Una; ST = Private Reserve of Natural Patrimony Serra do Teimoso; BN = Brasilia National Park; RE = Roncador Ecological Reserve. \textbf{APPENDIX} \textbf{Figure S1} Relationship between pairwise F\textsubscript{ST} and geographic distances for the eight populations sampled of \emph{E. edulis} , with Mantel test (r=0.134, p=0.33).\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/image1/image1} \end{center} \end{figure} \textbf{Figure S2} Estimated number of groups using the average method for the number of~populations~K~in 250~individuals~of \emph{E.~edulis}of the eight populations sampled.\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/image2/image2} \end{center} \end{figure} \textbf{Figure S3} Variation of~the second~order of the~average values of~maximum likelihood~for the number of~populations~K~in 250~individuals~of \emph{E. edulis} of the eight populations sampled.\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/image3/image3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure1/Figure1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure2/Figure2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure3/Figure3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure4/Figure4} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure5/Figure5} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Figure6/Figure6} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}

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\documentclass[12pt]{article} \usepackage{amsmath,amssymb,amsfonts} \begin{document} A search for a Higgs boson in the four-lepton decay channel H to ZZ, with each Z boson decaying to an electron or muon pair, is reported. The search covers Higgs boson mass hypotheses in the range 110 < mH < 600 GeV. The analysis uses data corresponding to an integrated luminosity of 4.7 inverse femtobarns recorded by the CMS detector in pp collisions at sqrt(s) = 7 TeV from the LHC. Seventy-two events are observed with four-lepton invariant mass m[4 leptons] > 100 GeV (with thirteen below 160 GeV), while 67.1 +/- 6.0 (9.5 +/-1.3) events are expected from background. The four-lepton mass distribution is consistent with the expectation of standard model background production of ZZ pairs. Upper limits at 95% confidence level exclude the standard model Higgs boson in the ranges 134-158 GeV, 180-305 GeV, and 340 -465 GeV. Small excesses of events are observed around masses of 119, 126, and 320 GeV, making the observed limits weaker than expected in the absence of a signal \end{document}

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To create different variants of the same feature, but avoid code duplications within plugins, you have multiple options\+: \begin{DoxyItemize} \item Define a needs clause in a \href{/home/markus/Projekte/Elektra/current/doc/CONTRACT.ini}{\tt contract} and reuse another plugin as it is. This should be preferred for filter and validation tasks. \item Have common code together in a helper library (or core library), see the C\+Make function {\ttfamily add\+\_\+lib} for creating such a library (in the folder libs). This should be used for rather common functionality that might be useful for many plugins or even applications. \item Have configuration for plugins (See \href{https://doc.libelektra.org/api/latest/html/group__plugin.html}{\tt elektra\+Plugin\+Get\+Config()} and dynamically switch with {\ttfamily if} according to the configuration. This should be preferred when you want to (de)activate some features of a plugin at run-\/time. \item Or use compilation variants to compile the plugin code multiple times with different {\ttfamily C\+O\+M\+P\+I\+L\+E\+\_\+\+D\+E\+F\+I\+N\+I\+T\+I\+O\+NS} (that are Macro definitions). This should be preferred when different macro definitions lead to different plugins. It should especially be used when the resulting plugins have different dependencies\+: it is possible to have different {\ttfamily L\+I\+N\+K\+\_\+\+L\+I\+B\+R\+A\+R\+I\+ES}. \end{DoxyItemize} The advantage of compilation variants are\+: \begin{DoxyItemize} \item No run-\/time overhead \item Can be used during bootstrapping (when no configuration is available) \item Different compilation variants can be built at once (no recompilation with different C\+Make flags required) \item Different compilation variants can have different dependencies \item Different compilation variants can be mounted without {\ttfamily \#refnames} \end{DoxyItemize} \subsection*{How to use It} To use compilation variants, add your plugin in the C\+Make Cache Variable {\ttfamily P\+L\+U\+G\+I\+NS} multiple times. Then there can be an arbitrary number of variants. As naming convention you should have a base name with an additional variant appended with underscore, e.\+g.\+: \begin{DoxyCode} myplugin\_varianta;myplugin\_variantb \end{DoxyCode} In the C\+Make\+Lists.\+txt of your plugin, you have two options. Option (A)\+: When you can easily enlist every variant you simply list all plugins one after the other ({\itshape outside of} {\ttfamily if (D\+E\+P\+E\+N\+D\+E\+N\+C\+Y\+\_\+\+P\+H\+A\+SE)})\+: \begin{DoxyCode} add\_plugin(myplugin\_varianta SOURCES <your sources for varianta here..> COMPILE\_DEFINITIONS VARIANTA ELEKTRA\_VARIANT=varianta LINK\_LIBRARIES <libraries for varianta> ) add\_plugin(myplugin\_variantb SOURCES <your sources for variantb here..> COMPILE\_DEFINITIONS VARIANTB ELEKTRA\_VARIANT=variantb LINK\_LIBRARIES <libraries for variantb> ) \end{DoxyCode} Option (B)\+: If you cannot enlist every possible compilation variant, you can iterate over all P\+L\+U\+G\+I\+NS and check which names are requested. Then you create a plugin for every name that matches\+: \begin{DoxyCode} foreach (plugin $\{PLUGINS\}) if ($\{plugin\} MATCHES "myplugin\_.*") # somehow process the variant names and include # or change sources and compile definitions # based on that. add\_plugin($\{plugin\} SOURCES <your sources here..> COMPILE\_DEFINITIONS <definitions here..> ELEKTRA\_VARIANT=$\{plugin without prefix\} LINK\_LIBRARIES <libraries for variantb> if ($\{plugin\} MATCHES "ALL") # handle categories of plugins add\_plugin(myplugin\_all1, ...) add\_plugin(myplugin\_all2, ...) \end{DoxyCode} For the categories such as {\ttfamily A\+LL}, however, you need to automatically append (using {\ttfamily add\+\_\+plugin}) a useful set of plugins. Note that every plugin needs to have {\ttfamily E\+L\+E\+K\+T\+R\+A\+\_\+\+V\+A\+R\+I\+A\+NT} differently set in {\ttfamily C\+O\+M\+P\+I\+L\+E\+\_\+\+D\+E\+F\+I\+N\+I\+T\+I\+O\+NS}, otherwise you will get a linker error that {\ttfamily libelektra\+\_\+$<$pluginname$>$\+\_\+\+L\+T\+X\+\_\+elektra\+Plugin\+Symbol} has multiple definitions. Now every public function of the plugin conflicts with itself. To avoid that, you can use\+: \begin{DoxyItemize} \item static functions, but they are only visible within one file. This should be preferred, when possible. \item use helper libraries using {\ttfamily add\+\_\+lib} to share code between compilation variants (only if code is also potentially useful for other plugins/applications) \item Get a unique name for every variant using the macro {\ttfamily \hyperlink{group__plugin_ga34d1a66f0a6e89cfd20f4014a9975a2a}{E\+L\+E\+K\+T\+R\+A\+\_\+\+P\+L\+U\+G\+I\+N\+\_\+\+F\+U\+N\+C\+T\+I\+O\+N(myplugin, open)}} where myplugin is the name of the plugin and the second argument is how the function should be called. \item Including a readme for every variant (with {\ttfamily \#ifdef} for different text) using the macro {\ttfamily \#include \hyperlink{group__plugin_ga78d616f68bf9fb0942f66478597467c6}{E\+L\+E\+K\+T\+R\+A\+\_\+\+R\+E\+A\+D\+M\+E(myplugin)}} \end{DoxyItemize} As a summary, you can have many plugins build out of the same source. Using {\ttfamily pluginname\+\_\+variantnames} many plugins will be compiled, each with other {\ttfamily S\+O\+U\+R\+C\+ES} or {\ttfamily C\+O\+M\+P\+I\+L\+E\+\_\+\+D\+E\+F\+I\+N\+I\+T\+I\+O\+NS} and even {\ttfamily L\+I\+N\+K\+\_\+\+L\+I\+B\+R\+A\+R\+I\+ES}\+: If you, e.\+g. just set the variants name as macro you can use \begin{DoxyCode} \textcolor{preprocessor}{#ifdef varianta} \textcolor{preprocessor}{#endif} \end{DoxyCode} within the code and can have two plugins\+: one (called {\ttfamily myplugin\+\_\+varianta}) compiled included the {\ttfamily \#ifdef} the other (base variant called {\ttfamily myplugin}) without. Currently compilation variants are used in \href{https://libelektra.org/tree/master/src/plugins/resolver/resolver.c}{\tt the resolver plugin}.

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\documentclass[]{article} \usepackage{amssymb,amsmath} \usepackage{ifxetex,ifluatex} \ifxetex \usepackage{fontspec,xltxtra,xunicode} \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} \else \ifluatex \usepackage{fontspec} \defaultfontfeatures{Mapping=tex-text,Scale=MatchLowercase} \else \usepackage[utf8]{inputenc} \fi \fi \usepackage{listings} \lstnewenvironment{code}{\lstset{language=Haskell,basicstyle=\small\ttfamily}}{} \ifxetex \usepackage[setpagesize=false, % page size defined by xetex unicode=false, % unicode breaks when used with xetex xetex, colorlinks=true, linkcolor=blue]{hyperref} \else \usepackage[unicode=true, colorlinks=true, linkcolor=blue]{hyperref} \fi \hypersetup{breaklinks=true, pdfborder={0 0 0}} \setlength{\parindent}{0pt} \setlength{\parskip}{6pt plus 2pt minus 1pt} \setlength{\emergencystretch}{3em} % prevent overfull lines \setcounter{secnumdepth}{0} \begin{document} \section{lhs test} \texttt{unsplit} is an arrow that takes a pair of values and combines them to return a single value: \begin{code} unsplit :: (Arrow a) => (b -> c -> d) -> a (b, c) d unsplit = arr . uncurry -- arr (\op (x,y) -> x `op` y) \end{code} \texttt{(***)} combines two arrows into a new arrow by running the two arrows on a pair of values (one arrow on the first item of the pair and one arrow on the second item of the pair). \begin{verbatim} f *** g = first f >>> second g \end{verbatim} Block quote: \begin{quote} foo bar \end{quote} \end{document}

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\part{Dokumenttypen} \label{sec:typen} Dokumenttypen dienen dazu, Vorgaben für spezielle Arten von Dokumenten zu machen und entsprechende Makros bereitzustellen. Üblicherweise wird eine bestimmte Dokumentklasse für die Verwendung empfohlen, grundsätzlich sind die Dokumenttypen aber unabhängig von der verwendeten Klasse. Die Typen werden über die Paketoption \option{typ} geladen. Ist der Typ unbekannt, wird ein Arbeitsblatt gesetzt und der die Bezeichnung des Dokuments wird auf den angegebenen Typ eingestellt. Wird kein Typ angegeben, ist der Kompatibilitätsmodus zum alten Schule-Paket aktiv. Es wird folglich kein Dokumenttyp geladen. Ebensowenig wird ein Dokumenttyp geladen, wenn der Typ auf \keyis{typ}{ohne} gesetzt wird, da sich das Paket dann im eingebetteten Modus befindet, also kein eigenständiges Dokument gesetzt werden soll. Somit lässt sich \pkg{schule} auch in Präsentationen mit \cls{beamer} setzen, siehe \prettyref{example:bsp-beamer}. \input{typAb} % \input{typBrief} \input{typKl} % \input{typKursbuch} \input{typLeitprogramm} % \input{typLogbuch} \input{typLzk} \input{typUeb} \input{typUb} \input{typFolie} \input{typBeurteilung}

https://www.zentralblatt-math.org/matheduc/en/?id=119897&type=tex

zentralblatt-math.org

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\input zb-basic \input zb-matheduc \iteman{ZMATH 1990f.00496} \itemau{Renaud, P.P.} \itemti{Finally a new program for math education for adults. Pt. 3. Enfin un nouveau programme de mathematiques a l'education des adultes. Part 3. Endlich ein neuer Mathematiklehrplan fuer die Erwachsenenbildung. T. 3.} \itemso{Envol (Laval). (Mar 1989) (no.67) p. 21-22, 27-35.} \itemab \itemrv{~} \itemcc{B78} \itemut{Syllabus; Further Education; Canada; ; Lehrplan; Weiterbildung; Kanada} \itemli{} \end

https://www.mimuw.edu.pl/~jsbien/BW/SSSP/SSSP.tex

mimuw.edu.pl

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%\documentclass[a5paper, twoside, titlepage]{article} \documentclass[twoside, titlepage, a4paper]{mwrep} \usepackage[latin2]{inputenc} \usepackage{polski} \usepackage{fancyhdr} \usepackage{multicol} \usepackage{url} \fancyfoot[C]{\thepage} \newcommand{\lx}[1]{\hangafter1 \hangindent10pt \textbf{#1}\markboth{#1}{#1}} % można zrobić osobnš definicję dla nie-czasowników % proszę popatrzeć na ramraru i -randa % lxx sprawia, ze hasla bez myslnikow sa wciete \newcommand{\lxx}[1]{\textbf{\phantom{-}#1}\markboth{#1}{#1}} \newcommand{\ps}[1]{\emph{#1}} \newcommand{\clsg}[1]{#1} %\newcommand{\clpl}[1]{#1} % tak wygodniej: %\newcommand{\clsgpl}[2]{#1/#1} % trzeba stosować \clsgpl lub dopisywać %, jak w pierwszym % lub kasować spację między klamrami, jak w radi %\newcommand{\pfpl}[1]{#1} \newcommand{\glp}[1]{#1} %\newcommand{\exsw}[1]{\emph{#1}} %\newcommand{\expl}[1]{#1} %\newcommand{\uwag} %\newcommand{\kosz} %\newcommand{\uwag}{} %\newcommand{\kosz}[1]{} %\newcommand{\dt}[1]{}\\ % z dokumentacji fancyhdr: % Now you do a \markboth{#1}{#1} for each dictionary or concordance % entry #1 and use \rightmark for the first entry defined on the page % and \leftmark for the last one. \fancyhead[LE]{\rightmark} \fancyhead[RE]{\leftmark} \fancyhead[LO]{\rightmark} \fancyhead[RO]{\leftmark} \def\dictfile{test} \title{Studencki słownik suahilijsko-polski} \author{Ania Pytluk} \begin{document} %\maketitle \begin{titlepage} %\vspace{\stretch{1}} \vbox{} \vfill \begin{center} \LARGE{\textbf{STUDENCKI SŁOWNIK\\ SUAHILIJSKO-POLSKI}} \bigskip \large{\textit{Wersja wstępna (1320 haseł)}} % \medskip % \normalsize{Zawiera 1320 haseł.} \bigskip \bigskip \bigskip %\vspace{\stretch{1}} \textbf{Przygotowanie haseł}:\\[1ex] \textsc{\large Anna Pytluk} \bigskip \textbf{Redakcja merytoryczna},\\[.5ex] % {\small skład i łamanie za pomocą systemu \LaTeXe:}\\[1ex] {skład i łamanie:}\\[1ex] \textsc{\large Beata Wójtowicz}\\ \normalsize{Zakład Zastosowań Informatycznych\\ Instytut Orientalistyczny\\ Uniwersytet Warszawski} \vfill \Large{Warszawa, 20.05.2003.\\} \medskip \small{\url{http://www.orient.uw.edu.pl/~jsbien/BW/SSSP/SSSP.pdf}} \end{center} \end{titlepage} \noindent Niniejszy \textit{Studencki słownik suahilijsko-polski} powstał na podstawie haseł opracowanych i wprowadzonych do komputera (za pomocą programu MS~Access) przez \textsc{Annę Pytluk}, studentkę Zakładu Języków i Kultur Afryki Instytutu Orientalistycznego Uniwersytetu Warszawskiego; do składu i łamania wykorzystano system \LaTeXe. Obecnie słownik zawiera 1320 haseł obejmujących zakres materiału z pierwszego roku nauki języka suahili. Słownik jest dostępny na zasadach licencji GNU FDL\footnote{Tekst licencji jest podany w załączniku.} m.in.\ w formacie PDF pod adresem \url{http://www.orient.uw.edu.pl/~jsbien/BW/SSSP/} i jest replikowany pod adresem \url{http://www.mimuw.edu.pl/~jsbien/BW/SSSP/}. \vfill \begin{center} Objaśnienie skrótów stosowanych przez autorkę haseł \bigskip \small %\begin{tabular}{|l|l|l|}\hline \begin{tabular}{|l|p{6cm}|l|}\hline Skrót & Opis & Przykład\\ \hline V0&czasowniki jednosylabowe i nieregularne&ja \\ \hline V1&czasowniki regularne zakończone samogłoską a; formy podstawowe&soma\\ \hline V2&czasowniki zakończone w formie podstawowej 2 samogłoskami&chukua\\ \hline V3&czasowniki zakończone na i&fikiri\\ \hline V4&czasowniki zakończone na u&husu\\ \hline W&czasowniki w formie wzajemnej&onana\\ \hline D&czasowniki w formie kierunkowej&pikia\\ \hline K&czasowniki w formie kauzatywnej&somesha\\ \hline S&czasowniki w formie statywnej&vunjika\\ \hline Z&czasowniki w stronie zwrotnej&jifunza\\ \hline B&czasowniki w stronie biernej&andikwa\\ \hline N1&rzeczowniki w klasie 1 mające liczbę mnogą w klasie 2&mjomba / wajomba\\ \hline N3&rzeczowniki w klasie 3 mające liczbę mnogą w klasie 4&mti / miti\\ \hline N5&rzeczowniki w klasie 5 mające liczbę mnogą w klasie 6&debe / madebe\\ \hline N6&rzeczowniki będące zazwyczaj tylko w klasie 6&maji\\ \hline N7&rzeczowniki w klasie 7 mające liczbę mnogą w klasie 8&kijiko / vijiko\\ \hline N9&rzeczowniki w klasie 9 mające liczbę mnogą w klasie 10&ajili / ajili\\ \hline N11/14&rzeczowniki w klasie 11/14; lp jak kl.3, lm jak kl.10&ukuta / kuta; unywele / nywele\\ \hline %N3/1&rzeczowniki będące w klasie 3, ale odmieniające się jak klasa 1& \\ \hline N5/1&rzeczowniki w klasie 5, ale odmieniające się jak klasa 1&bwana / mabwana\\ \hline N7/1&rzeczowniki w klasie 7, ale odmieniające się jak klasa 1&kijana / vijana\\ \hline N9/1&rzeczowniki w klasie 9, ale odmieniające się jak klasa 1&ndege / ndege\\ \hline A1&przymiotniki uzgadniajace się z rzeczownikiem (rodzime)&embamba\\ \hline A2&przymiotniki nieuzgadniające się z rzeczownikiem ( zapożyczenia )&maalumu\\ \hline A3&przymiotniki składające się z wyrażenia (wielowyrazowe)&aina kwa aina\\ \hline P1&przysłówki jednowyrazowe&karibu\\ \hline P2&przysłówki składające się z wyrażenia (wielowyrazowe)&hivi karibuni\\ \hline \end{tabular} \end{center} \vfill %\end{document} \newpage \pagestyle{fancy} \parindent0pt \begin{center} \LARGE{A} \end{center} \columnseprule0.1pt \begin{multicols}{2} %\lx{a } %\ps{prep} %\clsg{} %\glp{``ang.of'' } \lx{-a kigeni } \ps{adj } \clsg{A3 } \glp{obcy } \lx{-a kimataifa } \ps{adj } \clsg{A3 } \glp{zagraniczny } \lx{-a kireno } \ps{adj } \clsg{A3 } \glp{portugalski } \lx{-a kitaaluma } \ps{adj } \clsg{A3 } \glp{akademicki } \lx{-a kutosha } \ps{adv } \clsg{P2 } \glp{wystarczająco } \lx{-a pekee } \ps{adj } \clsg{A3 } \glp{jedyny, niepowtarzalny} \lx{abudu } \ps{v } \clsg{V4 } \glp{czcić } \lx{acha } \ps{v } \clsg{V1 } \glp{zostawiać; pozwalać} \lx{adhibu } \ps{v } \clsg{V4 } \glp{ukarać } \lx{adhimisha } \ps{v } \clsg{V1 } \glp{świętować } \lx{adhuhuri } \ps{n } \clsg{N9 } \glp{pora dnia między godziną 12.00 a 13.00 } \lx{adui } \ps{n } \clsg{N5/1 } \glp{wróg } \lx{afadhali } \ps{adv } \clsg{P1 } \glp{lepiej... } \lx{afya } \ps{n } \clsg{N9 } \glp{zdrowie } \lx{aga } \ps{v } \clsg{V1 } \glp{żegnać } \lx{agana } \ps{v } \clsg{V1W } \glp{pożegnać się (ze sobą) } \lx{Agano Jipya } \ps{n } \clsg{N5 } \glp{Nowy Testament } \lx{Agano la Kale } \ps{n } \clsg{N5 } \glp{Stary Testament } \lx{agiza } \ps{v } \clsg{V1 } \glp{zamówić } \lx{aina } \ps{n } \clsg{N9 } \glp{rodzaj } \lx{aisikrimi } \ps{n } \clsg{N9 } \glp{lody } \lx{ajabu } \ps{n } \clsg{N9 } \glp{zadziwiająca rzecz; cud} \lx{ajali } \ps{n } \clsg{N9 } \glp{wypadek } \lx{ake } \ps{adj } \clsg{A1P } \glp{jego } \lx{akili } \ps{n } \clsg{N9 } \glp{umysł; rozum} \lx{akina } \ps{n } \clsg{N9 } \glp{państwo } \lx{akiwa } \ps{conj } \clsg{ } \glp{gdy; podczas} \lx{ako } \ps{adj } \clsg{A1P } \glp{twój } \lx{alasiri } \ps{n } \clsg{N9 } \glp{pora dnia między godziną 13.00 a 17.00 } \lx{alfajiri } \ps{n } \clsg{N9 } \glp{pora dnia między godziną 3.00 a 6.00 } \lx{alhamis } \ps{n } \clsg{N9 } \glp{czwartek } \lx{alika } \ps{v } \clsg{V1 } \glp{zaprosić } \lx{amani } \ps{n } \clsg{N9 } \glp{pokój } \lx{amba- } \ps{pron } \clsg{WZ } \glp{który } \lx{ambia } \ps{v } \clsg{V2 } \glp{mówić } \lx{ambukiza } \ps{v } \clsg{V1 } \glp{zarażać } \lx{amini } \ps{v } \clsg{V3 } \glp{wierzyć } \lx{amka } \ps{v } \clsg{V1 } \glp{budzić się; wstawać } \lx{amua } \ps{v } \clsg{V2 } \glp{decydować } \lx{andaa } \ps{v } \clsg{V2 } \glp{przygotować } \lx{andamana } \ps{v } \clsg{V1W } \glp{towarzyszyć sobie } \lx{andika } \ps{v } \clsg{V1 } \glp{pisać } \lx{angalia } \ps{v } \clsg{V2 } \glp{uważać; dbać; obserwować} \lx{angu } \ps{adj } \clsg{A1P } \glp{mój } \lx{angua } \ps{v } \clsg{V2 } \glp{wybuchnąć (o śmiechu/łzach) } \lx{anguka } \ps{v } \clsg{V1 } \glp{spaść } \lx{anwani } \ps{n } \clsg{N9 } \glp{adres } \lx{anza } \ps{v } \clsg{V1 } \glp{zaczynać } \lx{ardhi } \ps{n } \clsg{N9 } \glp{ziemia } \lx{arobaini } \ps{num } \clsg{ } \glp{czterdzieści } \lx{asali } \ps{n } \clsg{N9 } \glp{miód } \lx{asante } \ps{interj } \clsg{ } \glp{dziękuję } \lx{asimilia } \ps{n } \clsg{N9 } \glp{procent } \lx{askari } \ps{n } \clsg{N9/1 } \glp{mundurowy; żołnierz} \lx{asubuhi } \ps{n } \clsg{N9 } \glp{rano } \lx{aya } \ps{n } \clsg{N9 } \glp{paragraf } \lx{azima } \ps{v } \clsg{V1 } \glp{pożyczyć } \end{multicols} \begin{center} \LARGE{B} \end{center} \begin{multicols}{2} \lx{baa } \ps{n } \clsg{N9 } \glp{bar } \lx{baada ya } \ps{adv } \clsg{P3 } \glp{po } \lx{baadaye } \ps{adv } \clsg{P1 } \glp{później } \lx{baadhi } \ps{adj } \clsg{A2 } \glp{niektórzy } \lx{baba } \ps{n } \clsg{N5/1 } \glp{ojciec, tata} \lx{badala ya } \ps{adv } \clsg{P1 } \glp{zamiast } \lx{badili } \ps{v } \clsg{V3 } \glp{zmieniać } \lx{bado } \ps{adv } \clsg{ } \glp{wciąż; jeszcze} \lx{bafu } \ps{n } \clsg{N9 } \glp{łazienka; wanna} \lx{bahasha } \ps{n } \clsg{N9 } \glp{koperta } \lx{bahati } \ps{n } \clsg{N9 } \glp{szczęście } \lx{bahati mbaya } \ps{n } \clsg{N9 } \glp{pech } \lx{bahati nzuri } \ps{n } \clsg{N9 } \glp{szczęście } \lx{bahiri } \ps{adj } \clsg{A2 } \glp{skąpy } \lx{baina ya ... na } \ps{adv } \clsg{P1 } \glp{pomiędzy ... i ... } \lx{baisikeli } \ps{n } \clsg{N9 } \glp{rower } \lx{baki } \ps{v } \clsg{V3 } \glp{zostać } \lx{bakshishi } \ps{n } \clsg{N9 } \glp{napiwek } \lx{bali } \ps{conj } \clsg{ } \glp{ale; lecz} \lx{balozi } \ps{n } \clsg{N9/1 } \glp{ambasador } \lx{banda } \ps{n } \clsg{N6 } \glp{chata } \lx{bangili } \ps{n } \clsg{N9 } \glp{bransoletka } \lx{bao } \ps{n } \clsg{N9 } \glp{deska } \lx{bara } \ps{n } \clsg{N9 } \glp{kontynent; ląd} \lx{barabara } \ps{n } \clsg{N9 } \glp{droga } \lx{baraka } \ps{n } \clsg{N9 } \glp{błogosławieństwo } \lx{baridi } \ps{n } \clsg{N9 } \glp{zimno } \lx{barua } \ps{n } \clsg{N9 } \glp{list } \lx{barua umeme } \ps{n } \clsg{N9 } \glp{e-mail } \lx{basi } \ps{n } \clsg{N9 } \glp{autobus } \lx{basi } \ps{interj } \clsg{ } \glp{więc; basta , koniec} \lx{baya } \ps{adj } \clsg{A1 } \glp{zły } \lx{beba } \ps{v } \clsg{V1 } \glp{nieść } \lx{bee } \ps{interj } \clsg{ } \glp{odpowiedź kobiety na wezwanie } \lx{bega } \ps{n } \clsg{N5 } \glp{ramię } \lx{bei } \ps{n } \clsg{N9 } \glp{cena } \lx{benki } \ps{n } \clsg{N9 } \glp{bank } \lx{bia } \ps{n } \clsg{N9 } \glp{piwo } \lx{biashara } \ps{n } \clsg{N9 } \glp{handel } \lx{bibi } \ps{n } \clsg{N5/1 } \glp{kobieta; żona} \lx{bichi } \ps{adj } \clsg{A1 } \glp{niedojrzały, nieugotowany} \lx{bidi } \ps{v } \clsg{V3 } \glp{musieć, trzeba} \lx{bila } \ps{conj } \clsg{ } \glp{bez; wyłączając} \lx{bilauri } \ps{n } \clsg{N9 } \glp{szklanka } \lx{binadamu } \ps{n } \clsg{N9/1 } \glp{człowiek; istota ludzka} \lx{binti } \ps{n } \clsg{N9/1 } \glp{córka } \lx{bisha hodi } \ps{v } \clsg{V1 } \glp{pukać do drzwi okrzykiem } \lx{bivu } \ps{adj } \clsg{A1 } \glp{dojrzały; świeży} \lx{blauzi } \ps{n } \clsg{N9 } \glp{bluzka } \lx{buluu } \ps{adj } \clsg{A2 } \glp{niebieski } \lx{bomba } \ps{n } \clsg{N5 } \glp{rura } \lx{bombo } \ps{n } \clsg{N9 } \glp{przeziębienie } \lx{bora } \ps{adj } \clsg{A2 } \glp{wspaniały } \lx{breki } \ps{n } \clsg{N9 } \glp{hamulec } \lx{buibui } \ps{n } \clsg{N5 } \glp{pająk; czarna płachta do obwiązywania się} \lx{bunduki } \ps{n } \clsg{N9 } \glp{broń } \lx{bunge } \ps{n } \clsg{N9 } \glp{parlament } \lx{bure } \ps{adv } \clsg{P1 } \glp{na próżno / darmo } \lx{busara } \ps{n } \clsg{N9 } \glp{mądrość } \lx{bustani } \ps{n } \clsg{N9 } \glp{ogród } \lx{bwana } \ps{n } \clsg{N5/1 } \glp{pan,mężczyzna; mąż} \end{multicols} \begin{center} \LARGE{C} \end{center} \begin{multicols}{2} \lx{chache } \ps{adv } \clsg{P1 } \glp{mało, niewiele} \lx{chafu } \ps{adj } \clsg{A1 } \glp{brudny } \lx{chagua } \ps{v } \clsg{V2 } \glp{wybrać } \lx{chai } \ps{n } \clsg{N9 } \glp{herbata } \lx{chaki } \ps{n } \clsg{N9 } \glp{kreda } \lx{chakula } \ps{n } \clsg{N7 } \glp{jedzenie } \lx{chakula cha jioni } \ps{n } \clsg{N7 } \glp{kolacja } \lx{chama } \ps{n } \clsg{N7 } \glp{partia } \lx{changamfu } \ps{adj } \clsg{A2 } \glp{pogodny; szczęśliwy} \lx{chapa } \ps{v } \clsg{V1 } \glp{bić; uderzać } \lx{chawa } \ps{n } \clsg{N5 } \glp{wesz } \lx{cheka } \ps{v } \clsg{V1 } \glp{śmiać się } \lx{chelewa } \ps{v } \clsg{V0B } \glp{spóźnić się } \lx{chemka } \ps{v } \clsg{V1 } \glp{wrzeć } \lx{chemsha } \ps{v } \clsg{V1K } \glp{gotować } \lx{cheza } \ps{v } \clsg{V1 } \glp{grać ; bawić się } \lx{cheza karata } \ps{v } \clsg{V1 } \glp{grać w karty } \lx{chini } \ps{n } \clsg{N9 } \glp{spód } \lx{chini ya } \ps{adv } \clsg{P3 } \glp{pod } \lx{choka } \ps{v } \clsg{V1 } \glp{zmęczyć się } \lx{chokaa } \ps{n } \clsg{N9 } \glp{gips } \lx{chokoleti } \ps{n } \clsg{N9 } \glp{czekolada } \lx{choma } \ps{v } \clsg{V1 } \glp{wkłuwać } \lx{chombo } \ps{n } \clsg{N7 } \glp{naczynie; narzędzie; środek (do)} \lx{chomoa } \ps{v } \clsg{V1R } \glp{wykłuwać } \lx{chomoka } \ps{v } \clsg{V1RK } \glp{wyjść poza} \lx{choo } \ps{n } \clsg{N7 } \glp{toaleta} \lx{chosha } \ps{v } \clsg{V1K } \glp{męczyć} \lx{chotara } \ps{n } \clsg{N9/1 } \glp{mieszaniec} \lx{chozi } \ps{n } \clsg{N5 } \glp{łza} \lx{chui } \ps{n } \clsg{N9/1 } \glp{leopard} \lx{chukia } \ps{v } \clsg{V2 } \glp{nienawidzić} \lx{chukua } \ps{v } \clsg{V2 } \glp{brać} \lx{chuma } \ps{n } \clsg{N7 } \glp{żelazo} \lx{chumba } \ps{n } \clsg{N7 } \glp{pokój} \lx{chumbia } \ps{v } \clsg{V1D } \glp{zaręczyć się} \lx{chungu } \ps{n } \clsg{N9 } \glp{mnóstwo} \lx{chungu nzima } \ps{n } \clsg{N9 } \glp{całe mnóstwo} \lx{chungwa } \ps{n } \clsg{N5 } \glp{pomarańcza} \lx{chuo } \ps{n } \clsg{N7 } \glp{college (ang.)} \lx{chuo kikuu } \ps{n } \clsg{N7 } \glp{uniwersytet} \lx{chupa } \ps{n } \clsg{N7 } \glp{butelka } \lx{chupi } \ps{n } \clsg{N9 } \glp{majtki } \end{multicols} \begin{center} \LARGE{D} \end{center} \begin{multicols}{2} \lx{dada } \ps{n } \clsg{N9/1 } \glp{siostra } \lx{daftari } \ps{n } \clsg{N5 } \glp{książka rachunków; zeszyt} \lx{dakika } \ps{n } \clsg{N9 } \glp{minuta } \lx{daktari wa meno } \ps{n } \clsg{N5 } \glp{dentysta } \lx{daladala } \ps{n } \clsg{N9 } \glp{autobus } \lx{damu } \ps{n } \clsg{N9 } \glp{krew } \lx{danganya } \ps{v } \clsg{V1 } \glp{kłamać } \lx{dansa } \ps{n } \clsg{N9 } \glp{taniec } \lx{daraja } \ps{n } \clsg{N9 } \glp{most } \lx{darasa } \ps{n } \clsg{N5 } \glp{lekcja } \lx{dawa } \ps{n } \clsg{N5 } \glp{lekarstwo } \lx{dawati } \ps{n } \clsg{N5 } \glp{biurko } \lx{dereva } \ps{n } \clsg{N9/1 } \glp{kierowca } \lx{dhahabu } \ps{n } \clsg{N9 } \glp{złoto } \lx{dharau } \ps{v } \clsg{V4 } \glp{obrażać; gardzić } \lx{dhidi ya } \ps{conj } \clsg{ } \glp{przeciwko, przeciw } \lx{dhulumu } \ps{v } \clsg{V4 } \glp{traktować niesprawiedliwie } \lx{dirisha } \ps{n } \clsg{N5 } \glp{okno } \lx{doa } \ps{n } \clsg{N5 } \glp{plama } \lx{dobi } \ps{n } \clsg{N5/1 } \glp{pracz } \lx{dogo } \ps{adj } \clsg{A1 } \glp{mały; młody/szy } \lx{dondoka } \ps{v } \clsg{V2K } \glp{spaść } \lx{doti } \ps{n } \clsg{N5 } \glp{para (o ubraniu), komplet } \lx{dua } \ps{n } \clsg{N9 } \glp{modlitwa; prośba } \lx{duka } \ps{n } \clsg{N5 } \glp{sklep } \lx{duka la dawa } \ps{n } \clsg{N5 } \glp{apteka } \lx{dumisha } \ps{v } \clsg{V4K } \glp{podtrzymywać } \lx{dunda } \ps{v } \clsg{V1 } \glp{bić; uderzać; tętnić} \lx{dunia } \ps{n } \clsg{N9 } \glp{świat } \end{multicols} \begin{center} \LARGE{E} \end{center} \begin{multicols}{2} \lx{ekundu } \ps{adj } \clsg{A1 } \glp{czerwony } \lx{elekea } \ps{v } \clsg{V1D } \glp{udać się (dokądś), kierować się } \lx{elewa } \ps{v } \clsg{V2B } \glp{rozumieć } \lx{elfu } \ps{num } \clsg{ } \glp{1000 } \lx{elimu } \ps{n } \clsg{N9 } \glp{nauka; wykształcenie } \lx{elimu ya afya } \ps{n } \clsg{N9 } \glp{higiena; medycyna } \lx{ema } \ps{adj } \clsg{A1 } \glp{dobry } \lx{embe } \ps{n } \clsg{N9 } \glp{mango } \lx{enda } \ps{v } \clsg{V0 } \glp{iść; jechać; posuwać się do przodu, rozwijać się} \lx{enda z-(zaim.dzierż.) } \ps{v } \clsg{V0 } \glp{iść sobie } \lx{endea } \ps{v } \clsg{V1D } \glp{udać się } \lx{endelea } \ps{v } \clsg{V1D } \glp{kontynuować } \lx{endesha } \ps{v } \clsg{V0K } \glp{kierować } \lx{eneza } \ps{v } \clsg{V2K } \glp{rozprzestrzenić } \lx{enyewe } \ps{adj } \clsg{A1 } \glp{sam } \lx{epesi } \ps{adj } \clsg{A1 } \glp{lekki; szybki } \lx{epuka } \ps{v } \clsg{V1 } \glp{unikać } \lx{epukana na } \ps{v } \clsg{V1W } \glp{unikać } \lx{eti } \ps{interj } \clsg{ } \glp{określenie na wątpliwość; określenie na zdziwienie} \lx{eupe } \ps{adj } \clsg{A1 } \glp{biały } \lx{eusi } \ps{adj } \clsg{A1 } \glp{czarny } \end{multicols} \begin{center} \LARGE{F} \end{center} \begin{multicols}{2} \lx{fa } \ps{v } \clsg{V0 } \glp{umrzeć } \lx{fagia } \ps{v } \clsg{V1 } \glp{zamiatać } \lx{fahali } \ps{n } \clsg{N9/1 } \glp{byk } \lx{fahamisha } \ps{v } \clsg{V4K } \glp{wyjaśnić } \lx{fahamu } \ps{v } \clsg{V4 } \glp{rozumieć; znać} \lx{familia } \ps{n } \clsg{N9 } \glp{rodzina } \lx{fanya } \ps{v } \clsg{V1 } \glp{robić } \lx{farasi } \ps{n } \clsg{N9/1 } \glp{koń } \lx{fasihi } \ps{n } \clsg{N9 } \glp{literatura } \lx{fataki } \ps{n } \clsg{N9 } \glp{fajerwerki } \lx{fedha } \ps{n } \clsg{N9 } \glp{srebro; pieniądze} \lx{ficha } \ps{v } \clsg{V1 } \glp{chować; ukrywać} \lx{fika } \ps{v } \clsg{V1 } \glp{przybywać } \lx{fikiri } \ps{v } \clsg{V3 } \glp{myśleć } \lx{fisi } \ps{n } \clsg{N9/1 } \glp{hiena } \lx{fomu } \ps{n } \clsg{N9 } \glp{formularz } \lx{fua } \ps{v } \clsg{V2 } \glp{prać } \lx{fuata } \ps{v } \clsg{V1 } \glp{podążać, iść za kimś} \lx{fuatana } \ps{v } \clsg{V1W } \glp{przebywać w towarzystwie } \lx{fufua } \ps{v } \clsg{V2 } \glp{wskrzesić, wrócić do życia po śmierci} \lx{fujo } \ps{n } \clsg{N5 } \glp{chaos } \lx{fulani } \ps{adj } \clsg{ } \glp{pewien, jakiś} \lx{fumba } \ps{v } \clsg{V1 } \glp{zamykać oczy } \lx{fumbua } \ps{v } \clsg{V1K } \glp{otwierać oczy } \lx{fundi } \ps{n } \clsg{N9/1 } \glp{mistrz; rzemieślnik} \lx{fundi ya saa } \ps{n } \clsg{N5/1 } \glp{zegarmistrz } \lx{fundisha } \ps{v } \clsg{V1 } \glp{uczyć kogoś } \lx{funga } \ps{v } \clsg{V1 } \glp{zamykać; zawiązywać} \lx{funga mizigo } \ps{v } \clsg{ } \glp{pakować się } \lx{funga safari } \ps{v } \clsg{V1 } \glp{rozpocząć podróż } \lx{fungua } \ps{v } \clsg{V1R } \glp{otwierać } \lx{fupi } \ps{adj } \clsg{A1 } \glp{niski } \lx{furahi } \ps{v } \clsg{V3 } \glp{cieszyć się } \lx{futa } \ps{v } \clsg{V1 } \glp{wycierać } \end{multicols} \begin{center} \LARGE{G} \end{center} \begin{multicols}{2} \lx{gani } \ps{adj } \clsg{A1 } \glp{jaki, który } \lx{gari } \ps{n } \clsg{N5 } \glp{samochód } \lx{gauni } \ps{n } \clsg{N9 } \glp{sukienka } \lx{gawanya } \ps{v } \clsg{V1 } \glp{dzielić } \lx{gazeti } \ps{n } \clsg{N5 } \glp{gazeta } \lx{gereza } \ps{n } \clsg{N9 } \glp{więzienie } \lx{geuka } \ps{v } \clsg{V1 } \glp{skręcić } \lx{ghali } \ps{adj } \clsg{A2 } \glp{drogi } \lx{ghere } \ps{n } \clsg{N9 } \glp{zazdrość; zawiść} \lx{ghorofa } \ps{n } \clsg{N9 } \glp{piętro } \lx{giza } \ps{n } \clsg{N9 } \glp{ciemność } \lx{glasi } \ps{n } \clsg{N9 } \glp{szklanka } \lx{gombana } \ps{v } \clsg{V1W } \glp{kłócić się } \lx{gonga } \ps{v } \clsg{V1 } \glp{upaść } \lx{gonjwa } \ps{n } \clsg{N5 } \glp{choroba } \lx{goti } \ps{n } \clsg{N9 } \glp{kolano } \lx{gumu } \ps{adj } \clsg{A1 } \glp{twardy; trudny} \end{multicols} \newpage \begin{center} \LARGE{H} \end{center} \nobreak \begin{multicols}{2} \lx{habari } \ps{n } \clsg{N9 } \glp{wiadomości } \lx{hadhiti } \ps{n } \clsg{N9 } \glp{opowiadanie } \lx{hai } \ps{v } \clsg{V3 } \glp{być żywym; przeżyć} \lx{haja } \ps{n } \clsg{N9 } \glp{potrzeba } \lx{halafu } \ps{adv } \clsg{P1 } \glp{później, potem} \lx{halisi } \ps{adj } \clsg{A2 } \glp{naturalny } \lx{hamaki } \ps{n } \clsg{N9 } \glp{złość } \lx{hamsini } \ps{num } \clsg{ } \glp{50 } \lx{hamu } \ps{n } \clsg{N9 } \glp{chęć; potrzeba} \lx{hapa } \ps{adv } \clsg{P1 } \glp{tutaj } \lx{hapana } \ps{interj } \clsg{ } \glp{nie } \lx{hapo } \ps{adv } \clsg{P1 } \glp{właśnie wtedy } \lx{haraka } \ps{n } \clsg{N9 } \glp{pośpiech } \lx{haribu } \ps{v } \clsg{V4 } \glp{niszczyć } \lx{hasa } \ps{adv } \clsg{P1 } \glp{dokładnie; specjalne; właśnie} \lx{hata } \ps{conj } \clsg{ } \glp{aż } \lx{hata hivyo } \ps{conj } \clsg{ } \glp{pomimo to } \lx{hata kidogo } \ps{adv } \clsg{P2 } \glp{wcale, ani trochę } \lx{hatari } \ps{adj } \clsg{A2 } \glp{niebezpieczny } \lx{hatua } \ps{n } \clsg{N9 } \glp{krok } \lx{haya } \ps{adv } \clsg{P1 } \glp{dobrze, w porządku } \lx{hekalu } \ps{n } \clsg{N9 } \glp{świątynia } \lx{hereni } \ps{n } \clsg{N9 } \glp{kolczyk } \lx{hesabu } \ps{n } \clsg{N9 } \glp{liczenie; matematyka; rachunki} \lx{heti } \ps{n } \clsg{N9 } \glp{czapka } \lx{himiza } \ps{v } \clsg{V1 } \glp{popędzać, poganiać} \lx{historia ya kisasa } \ps{n } \clsg{N9 } \glp{historia współczesna } \lx{hitaji } \ps{v } \clsg{V3 } \glp{potrzebować } \lx{hitajika } \ps{v } \clsg{V3S } \glp{być potrzebnym } \lx{hivi } \ps{adv } \clsg{P1 } \glp{około } \lx{hivi hivi } \ps{adv } \clsg{P2 } \glp{tak sobie; trochę} \lx{hivi karibuni } \ps{adv } \clsg{P2 } \glp{zaraz; niedawno} \lx{hivyo } \ps{adv } \clsg{P1 } \glp{tak; w ten sposób} \lx{hodari } \ps{adj } \clsg{A2 } \glp{zdolny } \lx{hodi! } \ps{interj } \clsg{ } \glp{(pukanie) czy mogę...? } \lx{hofu } \ps{n } \clsg{N9 } \glp{strach } \lx{hoji } \ps{v } \clsg{V3 } \glp{wypytywać, przepytywać} \lx{homa } \ps{n } \clsg{N9 } \glp{gorączka } \lx{homa ya manjano } \ps{n } \clsg{N9 } \glp{żółta febra } \lx{hospitali } \ps{n } \clsg{N9 } \glp{szpital } \lx{hoteli } \ps{n } \clsg{N9 } \glp{hotel } \lx{hudhuria } \ps{v } \clsg{V3D } \glp{uczestniczyć; być obecnym } \lx{huduma } \ps{n } \clsg{N9 } \glp{usługi } \lx{hudumia } \ps{v } \clsg{V4D } \glp{obsługiwać } \lx{hujumu } \ps{v } \clsg{V4 } \glp{sabotować } \lx{huko } \ps{adv } \clsg{P1 } \glp{tam } \lx{humu } \ps{adv } \clsg{P1 } \glp{tutaj } \lx{hundi } \ps{n } \clsg{N9 } \glp{czek } \lx{huzuni } \ps{n } \clsg{N9 } \glp{smutek } \lx{huzunika } \ps{v } \clsg{V1 } \glp{zasmucić się } \end{multicols} \begin{center} \LARGE{I} \end{center} \begin{multicols}{2} \lx{iba } \ps{v } \clsg{V1 } \glp{kraść } \lx{idara } \ps{n } \clsg{N9 } \glp{biuro; oddział; katedra (na uczelni)} \lx{ijumaa } \ps{n } \clsg{N9 } \glp{piątek } \lx{ikiwa } \ps{conj } \clsg{ } \glp{czy (w zdaniach podrzędnych); jeśli } \lx{imba } \ps{v } \clsg{V1 } \glp{śpiewać } \lx{inama } \ps{v } \clsg{V1 } \glp{schylić się } \lx{ingawa } \ps{conj } \clsg{ } \glp{chociaż } \lx{ingi } \ps{adj } \clsg{A1 } \glp{wiele, dużo } \lx{ingia } \ps{v } \clsg{V2 } \glp{wchodzić } \lx{ingine } \ps{adj } \clsg{A1 } \glp{niektóry/rzy; inny } \lx{insha } \ps{n } \clsg{N9 } \glp{wypracowanie } \lx{inuka } \ps{v } \clsg{V1K } \glp{wstawać } \lx{inzi } \ps{n } \clsg{N9/1 } \glp{mucha } \lx{isha } \ps{v } \clsg{V1 } \glp{kończyć } \lx{ishara } \ps{n } \clsg{N9 } \glp{symbol } \lx{ishi } \ps{v } \clsg{V3 } \glp{żyć; mieszkać } \lx{ishirini } \ps{num } \clsg{ } \glp{20 } \lx{isimu } \ps{n } \clsg{N9 } \glp{charakter; istota } \lx{isimu ya lugha } \ps{n } \clsg{N9 } \glp{lingwistyka } \lx{ita } \ps{v } \clsg{V1 } \glp{wołać; nazywać; dzwonić (telefonem)} \end{multicols} \begin{center} \LARGE{J} \end{center} \begin{multicols}{2} \lx{ja } \ps{v } \clsg{V0 } \glp{przychodzić } \lx{jaa } \ps{v } \clsg{V2 } \glp{być pełnym } \lx{jahanamu } \ps{n } \clsg{N9 } \glp{piekło } \lx{jamaa } \ps{n } \clsg{N9/1 } \glp{kolega; rodzina duża } \lx{jambo } \ps{n } \clsg{N5 } \glp{sprawa; rzecz } \lx{jamhuri } \ps{n } \clsg{N9 } \glp{republika } \lx{jana } \ps{n } \clsg{N9 } \glp{wczoraj } \lx{janga } \ps{n } \clsg{N5 } \glp{nieszczęście } \lx{jani } \ps{n } \clsg{N5 } \glp{liść; trawka } \lx{jaribu } \ps{v } \clsg{V4 } \glp{próbować } \lx{jawabu } \ps{n } \clsg{N5 } \glp{sprawa; odpowiedź; produkt} \lx{jaza } \ps{v } \clsg{V2K } \glp{wypełniać } \lx{je } \ps{conj } \clsg{ } \glp{czy } \lx{jela } \ps{n } \clsg{N9 } \glp{więzienie } \lx{jembe } \ps{n } \clsg{N5 } \glp{motyka } \lx{jengo } \ps{n } \clsg{N5 } \glp{budynek } \lx{jiandaa } \ps{v } \clsg{V2 } \glp{przygotowywać się } \lx{jibu } \ps{v } \clsg{V4 } \glp{odpowiadać } \lx{jicho } \ps{n } \clsg{N5 } \glp{oko } \lx{jifanya } \ps{v } \clsg{V1Z } \glp{udawać } \lx{jifungua } \ps{v } \clsg{V1ZR } \glp{urodzić; mieć rozwiązanie} \lx{jifunza } \ps{v } \clsg{V1Z } \glp{uczyć się } \lx{jiko } \ps{n } \clsg{N5 } \glp{kuchnia } \lx{jikwaa } \ps{v } \clsg{V2Z } \glp{potknąć się } \lx{jina } \ps{n } \clsg{N5 } \glp{imię, nazwisko; nazwa} \lx{jino } \ps{n } \clsg{N5 } \glp{ząb } \lx{jinsi } \ps{n } \clsg{N9 } \glp{sposób } \lx{jiografia } \ps{n } \clsg{N9 } \glp{geografia } \lx{jioni } \ps{n } \clsg{N9 } \glp{wieczór } \lx{jipokeza } \ps{v } \clsg{V1ZK } \glp{zgubić się } \lx{jirani } \ps{n } \clsg{N5 } \glp{sąsiad } \lx{jitahidi } \ps{v } \clsg{V3Z } \glp{starać się } \lx{jiunga } \ps{v } \clsg{V1Z } \glp{dołączyć } \lx{jiuzulu } \ps{v } \clsg{V1Z } \glp{podać się do dymisji } \lx{jivuna } \ps{v } \clsg{V1Z } \glp{popisywać się } \lx{jiwe } \ps{n } \clsg{N5 } \glp{kamień } \lx{joho } \ps{n } \clsg{N5 } \glp{płaszcz muzułmański } \lx{joto } \ps{n } \clsg{N9 } \glp{ciepło; gorączka } \lx{jua } \ps{v } \clsg{V2 } \glp{wiedzieć; umieć; potrafić} \lx{jua } \ps{n } \clsg{N5 } \glp{słońce } \lx{juishana } \ps{v } \clsg{V1KW } \glp{informować się nawzajem; powiadamiać się } \lx{juisi } \ps{n } \clsg{N9 } \glp{sok } \lx{juma } \ps{n } \clsg{N9 } \glp{tydzień } \lx{jumamosi } \ps{n } \clsg{N9 } \glp{sobota } \lx{jumanne } \ps{n } \clsg{N9 } \glp{wtorek } \lx{jumapili } \ps{n } \clsg{N9 } \glp{niedziela } \lx{jumatano } \ps{n } \clsg{N9 } \glp{środa } \lx{jumatatu } \ps{n } \clsg{N9 } \glp{poniedziałek } \lx{jumba } \ps{n } \clsg{N5 } \glp{duży dom; duży pokój; budynek} \lx{jumba la umeme } \ps{n } \clsg{N5 } \glp{elektrownia } \lx{jumlisha } \ps{v } \clsg{V1 } \glp{dodawać } \lx{juu ya } \ps{adv } \clsg{P1 } \glp{na; nad; o} \lx{juzi } \ps{n } \clsg{N9 } \glp{przedwczoraj } \end{multicols} \begin{center} \LARGE{K} \end{center} \begin{multicols}{2} \lx{kaa } \ps{v } \clsg{V2 } \glp{mieszkać; siedzieć; $\sim$pasować} \lx{kabati } \ps{n } \clsg{N5 } \glp{szafa; kredens } \lx{kabisa } \ps{adv } \clsg{P1 } \glp{dobrze; odpowiednio; wystarczająco} \lx{kabla } \ps{adv } \clsg{P1 } \glp{po } \lx{kabla ya } \ps{adv } \clsg{P1 } \glp{przed (czasowe) } \lx{kaburi } \ps{n } \clsg{N5 } \glp{grób } \lx{kadhaa } \ps{adj } \clsg{A2 } \glp{kilka; niewiele } \lx{kadi } \ps{n } \clsg{N9 } \glp{kartka (pocztowa; z życzeniami) } \lx{kahawa } \ps{n } \clsg{N9 } \glp{kawa } \lx{kaka } \ps{n } \clsg{N9/1 } \glp{brat } \lx{kali } \ps{adj } \clsg{A1 } \glp{surowy, okrutny; ostry, gorzki; mocny} \lx{kama } \ps{conj } \clsg{ } \glp{jak; jeśli; czy} \lx{kamera } \ps{n } \clsg{N9 } \glp{aparat fotograficzny } \lx{kamili } \ps{adv } \clsg{P1 } \glp{dokładnie } \lx{kamusi } \ps{n } \clsg{N9 } \glp{słownik } \lx{kana } \ps{v } \clsg{V1 } \glp{wyrzec się } \lx{kanda } \ps{v } \clsg{V1 } \glp{masować, robić masaż } \lx{kando ya } \ps{adv } \clsg{P1 } \glp{obok; na brzegu; na skraju} \lx{kanisa } \ps{n } \clsg{N9 } \glp{kościół } \lx{kantini } \ps{n } \clsg{N9 } \glp{stołówka } \lx{kanzu } \ps{n } \clsg{N9 } \glp{sukienka męska } \lx{kaptura } \ps{n } \clsg{N9 } \glp{krótkie spodnie } \lx{karamu } \ps{n } \clsg{N9 } \glp{impreza } \lx{karani } \ps{n } \clsg{N9/1 } \glp{urzędnik } \lx{karata } \ps{n } \clsg{N9 } \glp{karty } \lx{karatasi } \ps{n } \clsg{N9 } \glp{kartka; papier } \lx{karibia } \ps{v } \clsg{V2 } \glp{przybliżyć się } \lx{karibisha } \ps{v } \clsg{V1 } \glp{zaprosić } \lx{karibu } \ps{interj } \clsg{ } \glp{proszę; blisko, prawie; przybliżać (się)} \lx{karibu na } \ps{adv } \clsg{P3 } \glp{blisko } \lx{karimu } \ps{adj } \clsg{A1 } \glp{chojny } \lx{kasi } \ps{adv } \clsg{P1 } \glp{szybko } \lx{kasirika } \ps{v } \clsg{V1 } \glp{rozłościć się } \lx{kaskazini } \ps{n } \clsg{N9 } \glp{północ } \lx{kata } \ps{v } \clsg{V1 } \glp{ciąć; przerywać} \lx{kata shauri } \ps{v } \clsg{V1 } \glp{powziąć decyzję } \lx{kata tamaa } \ps{v } \clsg{V1 } \glp{stracić chęć } \lx{kataa } \ps{v } \clsg{V2 } \glp{odmówić } \lx{katibu } \ps{n } \clsg{N9/1 } \glp{sekretarz } \lx{katikati ya } \ps{adv } \clsg{P1 } \glp{po środku } \lx{katlesi } \ps{n } \clsg{N9 } \glp{kotlet } \lx{katoni } \ps{n } \clsg{N5 } \glp{karton } \lx{kaunta } \ps{n } \clsg{N9 } \glp{okienko; lada} \lx{kazi } \ps{n } \clsg{N9 } \glp{praca; zajęcie} \lx{kebeji } \ps{n } \clsg{N9 } \glp{kapusta } \lx{kebichi } \ps{n } \clsg{N9 } \glp{kapusta } \lx{keki } \ps{n } \clsg{N9 } \glp{ciasto } \lx{kemea } \ps{v } \clsg{V2 } \glp{krzyczeć; ganić} \lx{kesho } \ps{n } \clsg{N9 } \glp{jutro } \lx{kesho kutwa } \ps{n } \clsg{N9 } \glp{pojutrze } \lx{keti } \ps{v } \clsg{V3 } \glp{siadać } \lx{kheri } \ps{n } \clsg{N9 } \glp{powodzenie; szczęście} \lx{kiatu } \ps{n } \clsg{N7 } \glp{but } \lx{kiazi } \ps{n } \clsg{N7 } \glp{ziemniak } \lx{kibanda } \ps{n } \clsg{N7 } \glp{chata; szopa} \lx{kibidhi } \ps{v } \clsg{V3 } \glp{wręczyć; dać} \lx{kibiriti } \ps{n } \clsg{N7 } \glp{zapałka; paczka zapałek} \lx{kiboko } \ps{n } \clsg{N7/1 } \glp{hipopotam; bat ze skóry} \lx{kichaa } \ps{n } \clsg{N7/1 } \glp{szaleniec } \lx{kicheko } \ps{n } \clsg{N7 } \glp{śmiech } \lx{kichorochoro } \ps{n } \clsg{N7 } \glp{zaułek } \lx{kichwa } \ps{n } \clsg{N7 } \glp{głowa } \lx{kidani } \ps{n } \clsg{N7 } \glp{naszyjnik } \lx{kidole } \ps{n } \clsg{N7 } \glp{palec } \lx{kidonge } \ps{n } \clsg{N7 } \glp{tabletka; pastylka} \lx{kifaranga } \ps{n } \clsg{N7 } \glp{kurczaczek } \lx{kifaru } \ps{n } \clsg{N7/1 } \glp{nosorożec; czołg} \lx{kifo } \ps{n } \clsg{N7 } \glp{śmierć } \lx{kifua } \ps{n } \clsg{N7 } \glp{klatka piersiowa } \lx{kifurushi } \ps{n } \clsg{N7 } \glp{paczka } \lx{kijana } \ps{n } \clsg{N7/1 } \glp{młodzieniec } \lx{kijiji } \ps{n } \clsg{N7 } \glp{miasteczko } \lx{kijiko } \ps{n } \clsg{N7 } \glp{łyżka } \lx{kikapu } \ps{n } \clsg{N7 } \glp{kosz } \lx{kiko } \ps{n } \clsg{N7 } \glp{fajka } \lx{kikombe } \ps{n } \clsg{N7 } \glp{filiżanka; kubek} \lx{kila } \ps{adj } \clsg{A2 } \glp{każdy / a } \lx{kilabu } \ps{n } \clsg{N7 } \glp{klub; bar} \lx{kilabu cha mazoezi } \ps{n } \clsg{N7 } \glp{fitness klub } \lx{kilemba } \ps{n } \clsg{N7 } \glp{turban } \lx{kilio } \ps{n } \clsg{N7 } \glp{płacz } \lx{kima } \ps{n } \clsg{N9 } \glp{pulpet; mięso mielone} \lx{kima } \ps{n } \clsg{N9/1 } \glp{małpa } \lx{kimya } \ps{n } \clsg{N7 } \glp{cisza } \lx{kinga } \ps{v } \clsg{V1 } \glp{bronić; chronić} \lx{kinga } \ps{n } \clsg{N9 } \glp{obrona; ochrona} \lx{kingajua } \ps{n } \clsg{N9 } \glp{daszek u czapki } \lx{kiniozi } \ps{n } \clsg{N7/1 } \glp{fryzjer; golibroda} \lx{kinywaji } \ps{n } \clsg{N7 } \glp{napój } \lx{kiongozi } \ps{n } \clsg{N7/1 } \glp{przewodniczący } \lx{kioo } \ps{n } \clsg{N7 } \glp{lustro } \lx{kipande } \ps{n } \clsg{N7 } \glp{kawałek } \lx{kipindi } \ps{n } \clsg{N7 } \glp{lekcja } \lx{kipindupindu } \ps{n } \clsg{N7 } \glp{cholera } \lx{kishujaa } \ps{adv } \clsg{P1 } \glp{odważnie; bohatersko} \lx{kisima } \ps{n } \clsg{N7 } \glp{studnia } \lx{kisingino } \ps{n } \clsg{N7 } \glp{łokieć; kolano} \lx{kisu } \ps{n } \clsg{N7 } \glp{nóż } \lx{kitabu } \ps{n } \clsg{N7 } \glp{książka } \lx{kitako } \ps{n } \clsg{N7 } \glp{pośladek } \lx{kitambaa } \ps{n } \clsg{N7 } \glp{chustka; obrus} \lx{kitambo } \ps{n } \clsg{N7 } \glp{krótki odcinek czasu; krótki odcinek drogi} \lx{kitambulisho } \ps{n } \clsg{N7 } \glp{legitymacja } \lx{kitana } \ps{n } \clsg{N7 } \glp{grzebień } \lx{kitanda } \ps{n } \clsg{N7 } \glp{łóżko } \lx{kitenge } \ps{n } \clsg{N7 } \glp{materiał, którym okrywają się kobiety } \lx{kitivo } \ps{n } \clsg{N7 } \glp{wydział } \lx{kito } \ps{n } \clsg{N7 } \glp{biżuteria } \lx{kitu } \ps{n } \clsg{N7 } \glp{rzecz; coś} \lx{kitunguu } \ps{n } \clsg{N7 } \glp{cebula } \lx{kituo cha basi } \ps{n } \clsg{N7 } \glp{przystanek autobusowy} \lx{kiu } \ps{n } \clsg{N9 } \glp{pragnienie} \lx{kiulizi } \ps{n } \clsg{N7 } \glp{pytajnik} \lx{kivuko } \ps{n } \clsg{N7 } \glp{przejście} \lx{kivuli } \ps{n } \clsg{N7 } \glp{cień} \lx{kiwanda } \ps{n } \clsg{N7 } \glp{fabryka} \lx{kiwanja cha mpira } \ps{n } \clsg{N7 } \glp{boisko} \lx{kiwanja cha ndege } \ps{n } \clsg{N7 } \glp{lotnisko} \lx{kizibau } \ps{n } \clsg{N7 } \glp{kamizelka} \lx{kodi } \ps{n } \clsg{N9 } \glp{podatek} \lx{kofi } \ps{n } \clsg{N5 } \glp{dłoń} \lx{kofia } \ps{n } \clsg{N9 } \glp{czapka w stylu muzułmańskim} \lx{kohoa } \ps{v } \clsg{V2 } \glp{kaszleć} \lx{koma } \ps{v } \clsg{V1 } \glp{przestać} \lx{kompyuta } \ps{n } \clsg{N9 } \glp{komputer} \lx{kona } \ps{n } \clsg{N9 } \glp{róg} \lx{koo } \ps{n } \clsg{N5 } \glp{gardło } \lx{kopa } \ps{v } \clsg{V1 } \glp{pożyczyć; dać kredyt } \lx{kope } \ps{n } \clsg{N5 } \glp{rzęsa } \lx{kosa } \ps{v } \clsg{V1 } \glp{błądzić; brakować } \lx{koti } \ps{n } \clsg{N9 } \glp{palto; płaszcz } \lx{koti la mvua } \ps{n } \clsg{N9 } \glp{płaszcz przeciwdeszczowy } \lx{kubali } \ps{v } \clsg{V3 } \glp{zgadzać się } \lx{kubwa } \ps{adj } \clsg{A1 } \glp{duży, wielki; ciężki, ważny, mocny; stary} \lx{kugawa } \ps{n } \clsg{N15 } \glp{dzielenie } \lx{kuhara } \ps{n } \clsg{N15 } \glp{biegunka } \lx{kuhusu } \ps{n } \clsg{N15 } \glp{dotyczący } \lx{kujumlisha } \ps{n } \clsg{N15 } \glp{dodawanie } \lx{kuku } \ps{n } \clsg{N9/1 } \glp{kurczak } \lx{kulia } \ps{n } \clsg{N9 } \glp{prawa strona } \lx{lima } \ps{v } \clsg{V1 } \glp{uprawiać rolę } \lx{kumbuka } \ps{v } \clsg{V1 } \glp{pamiętać; przypominać sobie } \lx{kumi na tisa } \ps{num } \clsg{ } \glp{19} \lx{kunde } \ps{n } \clsg{N5 } \glp{bób} \lx{kundi } \ps{n } \clsg{N9 } \glp{stado} \lx{kunguni } \ps{n } \clsg{N9 } \glp{pluskwy} \lx{kuni } \ps{n } \clsg{N9 } \glp{drewno} \lx{kupe } \ps{n } \clsg{N9 } \glp{kleszcz bydlęcy lub psi} \lx{kushoto } \ps{n } \clsg{N9 } \glp{lewa strona} \lx{kusini } \ps{n } \clsg{N9 } \glp{południe} \lx{kuta } \ps{v } \clsg{V1 } \glp{spotkać} \lx{kutahamaki } \ps{adv } \clsg{P1 } \glp{nagle} \lx{kutana } \ps{v } \clsg{V1W } \glp{spotykać się (z...)} \lx{kutoa } \ps{n } \clsg{N15 } \glp{odejmowanie} \lx{kutoka } \ps{conj } \clsg{ } \glp{z} \lx{kutua } \ps{adv } \clsg{P1 } \glp{jak} \lx{kuu } \ps{adj } \clsg{A1 } \glp{główny} \lx{kuza } \ps{v } \clsg{V2K } \glp{uprawiać} \lx{kuzidisha } \ps{n } \clsg{N15 } \glp{mnożenie } \lx{kwa ajili } \ps{adv } \clsg{P2 } \glp{z powodu; dla (dobra) ... (+) } \lx{kwa bahati mbaya } \ps{conj } \clsg{ } \glp{niestety } \lx{kwa bidii } \ps{adv } \clsg{P2 } \glp{pilnie } \lx{kwa heri } \ps{adv } \clsg{P2 } \glp{do widzenia } \lx{kwa jumla } \ps{adv } \clsg{P2 } \glp{w sumie } \lx{kwa kila hali } \ps{conj } \clsg{ } \glp{w każdym razie } \lx{kwa moyo } \ps{adv } \clsg{P2 } \glp{na pamięć } \lx{kwa vile } \ps{conj } \clsg{ } \glp{ponieważ } \lx{kwako } \ps{adj } \clsg{A2P } \glp{dla ciebie; twój; u ciebie} \lx{kwamba } \ps{conj } \clsg{ } \glp{że } \lx{kwanza } \ps{adv } \clsg{P1 } \glp{najpierw } \lx{kweli } \ps{adv } \clsg{P1 } \glp{naprawdę; rzeczywiście; prawda} \lx{kwenye } \ps{conj } \clsg{ } \glp{w } \end{multicols} \begin{center} \LARGE{L} \end{center} \begin{multicols}{2} \lx{la } \ps{v } \clsg{V0 } \glp{jeść } \lx{la } \ps{interj } \clsg{ } \glp{nie (stanowczo) } \lx{laanifu } \ps{adj } \clsg{A1 } \glp{przeklęty } \lx{labda } \ps{conj } \clsg{ } \glp{być może } \lx{labeka } \ps{interj } \clsg{ } \glp{odpowiedź kobiety na wezwanie } \lx{lahaja } \ps{n } \clsg{N9 } \glp{dialekt } \lx{laini } \ps{adj } \clsg{A2 } \glp{gładki; delikatny} \lx{lakini } \ps{conj } \clsg{ } \glp{ale, lecz } \lx{lala } \ps{v } \clsg{V1 } \glp{spać } \lx{lango } \ps{n } \clsg{N5 } \glp{brama } \lx{laza } \ps{v } \clsg{V1K } \glp{uśpić } \lx{lazima } \ps{adv } \clsg{P1 } \glp{trzeba } \lx{lea } \ps{v } \clsg{V2 } \glp{wychowywać } \lx{lenga } \ps{v } \clsg{V1 } \glp{lać się; zalewać się} \lx{lenga } \ps{v } \clsg{V1 } \glp{celować } \lx{lengo } \ps{n } \clsg{N5 } \glp{cel } \lx{leo } \ps{n } \clsg{N9 } \glp{dziś, dzisiaj } \lx{leta } \ps{v } \clsg{V1 } \glp{przynosić } \lx{lewa } \ps{v } \clsg{V1 } \glp{upić się } \lx{lia } \ps{v } \clsg{V2 } \glp{płakać; krzyczeć } \lx{likizo } \ps{n } \clsg{N9 } \glp{ferie } \lx{lini } \ps{adv } \clsg{P1 } \glp{kiedy } \lx{lipa } \ps{v } \clsg{V1 } \glp{płacić } \lx{lori } \ps{n } \clsg{N5 } \glp{ciężarówka } \lx{lugha } \ps{n } \clsg{N9 } \glp{język (środ. komunikacji) } \end{multicols} \begin{center} \LARGE{M} \end{center} \begin{multicols}{2} \lx{maafa } \ps{n } \clsg{N6 } \glp{przerażenie; groza; terror} \lx{maana } \ps{n } \clsg{N9 } \glp{znaczenie } \lx{maana yake } \ps{conj } \clsg{ } \glp{co to znaczy } \lx{maelfu } \ps{n } \clsg{N6 } \glp{tysiące } \lx{maendeleo } \ps{n } \clsg{N6 } \glp{rozwój } \lx{mafua } \ps{n } \clsg{N6 } \glp{przeziębienie } \lx{mafuta } \ps{n } \clsg{N6 } \glp{olej } \lx{magharibi } \ps{n } \clsg{N9 } \glp{zachód } \lx{mahali } \ps{n } \clsg{N16 } \glp{miejsce } \lx{maharagwe } \ps{n } \clsg{N6 } \glp{fasola } \lx{maili } \ps{n } \clsg{N9 } \glp{mila } \lx{maisha } \ps{n } \clsg{N6 } \glp{życie } \lx{maiti } \ps{n } \clsg{N5 } \glp{martwe ciało } \lx{maji } \ps{n } \clsg{N6 } \glp{woda } \lx{maji ya machungwa } \ps{n } \clsg{N6 } \glp{sok pomarańczowy } \lx{majivu } \ps{n } \clsg{N6 } \glp{popiół } \lx{majuto } \ps{n } \clsg{N6 } \glp{żal } \lx{makala } \ps{n } \clsg{N6 } \glp{artykuły } \lx{makini } \ps{n } \clsg{N6 } \glp{uwaga; spokój; godność} \lx{maktaba } \ps{n } \clsg{N6 } \glp{biblioteka } \lx{makumi } \ps{n } \clsg{N6 } \glp{dziesiątki } \lx{malaria } \ps{n } \clsg{N9 } \glp{malaria } \lx{mali } \ps{n } \clsg{N9 } \glp{majątek; bogactwo } \lx{maliza } \ps{v } \clsg{V1 } \glp{kończyć } \lx{mama } \ps{n } \clsg{N5/1 } \glp{matka, mama } \lx{mamba } \ps{n } \clsg{N9/1 } \glp{krokodyl } \lx{mamia } \ps{n } \clsg{N6 } \glp{setki } \lx{mamilioni } \ps{n } \clsg{N6 } \glp{miliony } \lx{mamoja } \ps{n } \clsg{N6 } \glp{jedności } \lx{manjano } \ps{n } \clsg{N9 } \glp{kurkuma } \lx{maoni } \ps{n } \clsg{N6 } \glp{opinie } \lx{mapema } \ps{adv } \clsg{P1 } \glp{wcześnie } \lx{mapinduzi } \ps{n } \clsg{N6 } \glp{rewolucja } \lx{mapokezi } \ps{n } \clsg{N6 } \glp{recepcja } \lx{mara } \ps{n } \clsg{N9 } \glp{raz; nagle} \lx{mara moja } \ps{adv } \clsg{P1 } \glp{nagle } \lx{maradhi } \ps{n } \clsg{N6 } \glp{choroba } \lx{maradhi } \ps{n } \clsg{N6 } \glp{choroby } \lx{marehemu } \ps{n } \clsg{N9 } \glp{nieboszczyk } \lx{marikiti } \ps{n } \clsg{N9 } \glp{supermarket; duży sklep} \lx{marudio } \ps{n } \clsg{N6 } \glp{powtórzenie } \lx{marukufu } \ps{adj } \clsg{A2 } \glp{zabroniony } \lx{masafa } \ps{n } \clsg{N6 } \glp{odległość } \lx{mashairi } \ps{n } \clsg{N6 } \glp{poezja } \lx{mashariki } \ps{n } \clsg{N9 } \glp{wschód } \lx{maskini } \ps{adj } \clsg{A2 } \glp{biedny; biedak} \lx{masomo } \ps{n } \clsg{N6 } \glp{studia } \lx{matata } \ps{n } \clsg{N6 } \glp{kłopot, problem} \lx{mate } \ps{n } \clsg{N6 } \glp{ślina } \lx{matembezi } \ps{n } \clsg{N6 } \glp{spacer } \lx{matokeo } \ps{n } \clsg{N6 } \glp{wyniki } \lx{matope } \ps{n } \clsg{N6 } \glp{błoto } \lx{matumizi } \ps{n } \clsg{N6 } \glp{użycie; wydatki} \lx{maumivu } \ps{n } \clsg{N6 } \glp{ból } \lx{mauti } \ps{n } \clsg{N6 } \glp{śmierć } \lx{mawasiliano } \ps{n } \clsg{N6 } \glp{komunikacja } \lx{mazingira } \ps{n } \clsg{N6 } \glp{środowisko } \lx{mazishi } \ps{n } \clsg{N6 } \glp{pogrzeb } \lx{maziwa } \ps{n } \clsg{N6 } \glp{mleko } \lx{mbaazi } \ps{n } \clsg{N3 } \glp{groch } \lx{mbali na } \ps{adv } \clsg{P1 } \glp{daleko } \lx{mbao } \ps{n } \clsg{N3 } \glp{deska; tablica} \lx{mbati } \ps{n } \clsg{N1 } \glp{pijak } \lx{mbati } \ps{n } \clsg{N9 } \glp{dachówka } \lx{mbele ya } \ps{adv } \clsg{P1 } \glp{przed (miejscowe) } \lx{mbili tatu } \ps{adv } \clsg{P2 } \glp{parę; kilka} \lx{mbio } \ps{adv } \clsg{P1 } \glp{szybko } \lx{mboga } \ps{n } \clsg{N9 } \glp{warzywa } \lx{mboga } \ps{n } \clsg{N3 } \glp{tykwa } \lx{mbona } \ps{interj } \clsg{ } \glp{dlaczego; określenie na zdziwienie} \lx{mbu } \ps{n } \clsg{N9 } \glp{komar } \lx{mbuga } \ps{n } \clsg{N3 } \glp{park; sawanna} \lx{mbuga } \ps{n } \clsg{N3 } \glp{park } \lx{mbuni } \ps{n } \clsg{N1 } \glp{twórca } \lx{mbuni } \ps{n } \clsg{N3 } \glp{drzewko kawowe } \lx{mbuni } \ps{n } \clsg{N9/1 } \glp{struś } \lx{mbuyu } \ps{n } \clsg{N3 } \glp{baobab } \lx{mbuzi } \ps{n } \clsg{N9/1 } \glp{koza } \lx{mbwa } \ps{n } \clsg{N1 } \glp{pies } \lx{mbwawa } \ps{n } \clsg{N3 } \glp{basen; jeziorko} \lx{mchana } \ps{n } \clsg{N9 } \glp{popołudnie } \lx{mchawi } \ps{n } \clsg{N1 } \glp{czarownica } \lx{mchele } \ps{n } \clsg{N3 } \glp{ryż niegotowany łuskany } \lx{mchezo } \ps{n } \clsg{N3 } \glp{gra; zabawa} \lx{mchumba } \ps{n } \clsg{N1 } \glp{nanony } \lx{mchungwa } \ps{n } \clsg{N3 } \glp{drzewko pomarańczowe } \lx{mchuzi } \ps{n } \clsg{N3 } \glp{sos } \lx{mdali } \ps{n } \clsg{N9 } \glp{medalik } \lx{mdogo wa kike } \ps{n } \clsg{N1 } \glp{młodsza siostra } \lx{mdogo wa kiume } \ps{n } \clsg{N1 } \glp{młodszy brat } \lx{mdomo } \ps{n } \clsg{N3 } \glp{usta } \lx{mdudu } \ps{n } \clsg{N1 } \glp{owad } \lx{meli } \ps{n } \clsg{N9 } \glp{statek } \lx{mende } \ps{n } \clsg{N9 } \glp{karaluch } \lx{meneja } \ps{n } \clsg{N9 } \glp{dyrektor; kierownik } \lx{meza } \ps{n } \clsg{N9 } \glp{stół } \lx{meza } \ps{v } \clsg{V1 } \glp{połykać } \lx{mfalme } \ps{n } \clsg{N1 } \glp{król } \lx{mfanyakazi } \ps{n } \clsg{N1 } \glp{robotnik; pracownik } \lx{mfereji } \ps{n } \clsg{N3 } \glp{kanał; wodociąg } \lx{mfuko } \ps{n } \clsg{N3 } \glp{torba; kieszeń; torebka} \lx{mfupa } \ps{n } \clsg{N3 } \glp{kość } \lx{mgahawa } \ps{n } \clsg{N3 } \glp{kawiarnia } \lx{mganga } \ps{n } \clsg{N1 } \glp{zielarz; znachor } \lx{mgeni } \ps{n } \clsg{N1 } \glp{gość; obcy } \lx{mgongo } \ps{n } \clsg{N3 } \glp{grzbiet; plecy} \lx{mgonjwa } \ps{n } \clsg{N1 } \glp{chory } \lx{mguu } \ps{n } \clsg{N3 } \glp{noga } \lx{mhadhara } \ps{n } \clsg{N9 } \glp{lektura; lektorat} \lx{mhuni } \ps{n } \clsg{N1 } \glp{łobuz } \lx{mhusika } \ps{n } \clsg{N1 } \glp{bohater (książki) } \lx{mia } \ps{num } \clsg{ } \glp{100 } \lx{miadi } \ps{n } \clsg{N9 } \glp{randka } \lx{miaka } \ps{n } \clsg{N4 } \glp{wiek (liczba lat) } \lx{milele } \ps{n } \clsg{N9 } \glp{wieczność; [wiecznie]} \lx{mimi } \ps{pron } \clsg{PN } \glp{ja } \lx{miongoni kwa } \ps{adv } \clsg{P1 } \glp{pomiędzy } \lx{miwani } \ps{n } \clsg{N4 } \glp{okulary } \lx{mjamzito } \ps{n } \clsg{N1 } \glp{kobieta w ciąży } \lx{mjanja } \ps{v } \clsg{V1 } \glp{mędrzec } \lx{mji } \ps{n } \clsg{N3 } \glp{miasto } \lx{mjinga } \ps{n } \clsg{N1 } \glp{ignorant } \lx{mjumbe } \ps{n } \clsg{N1 } \glp{posłaniec } \lx{mkahawa } \ps{n } \clsg{N3 } \glp{kawiarnia } \lx{mkate } \ps{n } \clsg{N3 } \glp{chleb } \lx{mkazi } \ps{n } \clsg{N1 } \glp{mieszkaniec } \lx{mke } \ps{n } \clsg{N1 } \glp{żona } \lx{mkeka } \ps{n } \clsg{N3 } \glp{mata } \lx{mkesha } \ps{n } \clsg{N3 } \glp{wigilia; czuwanie;} \lx{mkoa } \ps{n } \clsg{N3 } \glp{okręg } \lx{mkoba } \ps{n } \clsg{N3 } \glp{torebka } \lx{mkono } \ps{n } \clsg{N3 } \glp{ręka } \lx{mkopo } \ps{n } \clsg{N3 } \glp{pożyczka } \lx{mkuki } \ps{n } \clsg{N3 } \glp{dzida } \lx{mkulima } \ps{n } \clsg{N1 } \glp{rolnik } \lx{mkutano } \ps{n } \clsg{N3 } \glp{zebranie } \lx{mla watu } \ps{n } \clsg{N1 } \glp{ludożerca } \lx{mlango } \ps{n } \clsg{N3 } \glp{drzwi } \lx{mlevi } \ps{n } \clsg{N1 } \glp{pijak } \lx{mlima } \ps{n } \clsg{N3 } \glp{góra } \lx{mlio } \ps{n } \clsg{N3 } \glp{krzyk } \lx{mnazi } \ps{n } \clsg{N3 } \glp{palma kokosowa } \lx{mnunuzi } \ps{n } \clsg{N1 } \glp{klient; kupujący } \lx{mnyama } \ps{n } \clsg{N1 } \glp{zwierzę } \lx{moja } \ps{num } \clsg{ } \glp{jeden } \lx{moja kwa moja } \ps{adv } \clsg{P2 } \glp{prosto; bezpośrednio; od razu} \lx{moshi } \ps{n } \clsg{N3 } \glp{dym } \lx{moto } \ps{n } \clsg{N3 } \glp{ogień } \lx{motokaa } \ps{n } \clsg{N9 } \glp{samochód; motocykl } \lx{moyo } \ps{n } \clsg{N3 } \glp{serce } \lx{mpaka } \ps{n } \clsg{N3/4 } \glp{granica } \lx{mpaka } \ps{conj } \clsg{ } \glp{do } \lx{mpando } \ps{n } \clsg{N3 } \glp{górka } \lx{mpiga picha } \ps{n } \clsg{N1 } \glp{fotograf } \lx{mpira } \ps{n } \clsg{N3 } \glp{piłka; guma} \lx{mpishi } \ps{n } \clsg{N1 } \glp{kucharz } \lx{mpokeaji } \ps{n } \clsg{N1 } \glp{recepcjonista } \lx{mrembo } \ps{n } \clsg{N1 } \glp{piękna kobieta; ślicznotka} \lx{msaada } \ps{n } \clsg{N3 } \glp{pomoc } \lx{msalaba } \ps{n } \clsg{N3 } \glp{krzyż } \lx{mshangao } \ps{n } \clsg{N3 } \glp{zdziwienie } \lx{mshikaki } \ps{n } \clsg{N3 } \glp{szaszłyk } \lx{mshonaji } \ps{n } \clsg{N1 } \glp{krawiec } \lx{mshumaa } \ps{n } \clsg{N3 } \glp{świeca } \lx{msiba } \ps{n } \clsg{N3 } \glp{nieszczęście } \lx{msichana } \ps{n } \clsg{N1 } \glp{dziewczyna } \lx{msikiti } \ps{n } \clsg{N3 } \glp{meczet } \lx{mtalii } \ps{n } \clsg{N1 } \glp{turysta } \lx{mtego } \ps{n } \clsg{N3 } \glp{pułapka } \lx{mtengenezaji nywele } \ps{n } \clsg{N1 } \glp{fryzjer } \lx{mteremko } \ps{n } \clsg{N3 } \glp{dołek } \lx{mtihani } \ps{n } \clsg{N3 } \glp{egzamin } \lx{mto } \ps{n } \clsg{N3 } \glp{rzeka } \lx{mtoto } \ps{n } \clsg{N1 } \glp{dziecko } \lx{mtu } \ps{n } \clsg{N1 } \glp{człowiek } \lx{mtumishi } \ps{n } \clsg{N1 } \glp{kelner; służący } \lx{muda } \ps{n } \clsg{N3 } \glp{okres } \lx{muhtasari } \ps{n } \clsg{N9 } \glp{podsumowanie } \lx{mume } \ps{n } \clsg{N1 } \glp{mąż } \lx{mvi } \ps{n } \clsg{N9 } \glp{siwizna } \lx{mvinyo } \ps{n } \clsg{N3 } \glp{wino; alkohol } \lx{mviringo } \ps{n } \clsg{N3 } \glp{koło; okrąg } \lx{mvua } \ps{n } \clsg{N9 } \glp{deszcz } \lx{mvulana } \ps{n } \clsg{N1 } \glp{chłopak } \lx{mvungu } \ps{n } \clsg{N3 } \glp{spód; podłoga; na podłodze} \lx{mvuvi } \ps{n } \clsg{N1 } \glp{rybak } \lx{mwaga } \ps{v } \clsg{V1 } \glp{wlewać; nalewać} \lx{mwaka } \ps{n } \clsg{N3 } \glp{rok } \lx{mwaliko } \ps{n } \clsg{N3 } \glp{zaproszenie } \lx{mwalimu } \ps{n } \clsg{N1 } \glp{nauczyciel } \lx{mwamvuli } \ps{n } \clsg{N3 } \glp{parasol } \lx{mwana } \ps{n } \clsg{N1 } \glp{dziecko; syn} \lx{mwana elimu nafsi } \ps{n } \clsg{N1 } \glp{psycholog } \lx{mwanafunzi } \ps{n } \clsg{N1 } \glp{uczeń; student} \lx{mwanaharamu } \ps{n } \clsg{N1 } \glp{łajdak; bękart} \lx{mwanamke } \ps{n } \clsg{N1 } \glp{kobieta } \lx{mwanamume } \ps{n } \clsg{N1 } \glp{mężczyzna } \lx{mwananchi } \ps{n } \clsg{N1 } \glp{rodak; obywatel} \lx{mwanga } \ps{n } \clsg{N3 } \glp{jasność; światło} \lx{mwangaza } \ps{n } \clsg{N3 } \glp{światło } \lx{mwanzo } \ps{n } \clsg{N3 } \glp{początek } \lx{mwenda wazimu } \ps{n } \clsg{N1 } \glp{wariat } \lx{mwendo } \ps{n } \clsg{N3 } \glp{prędkość; ruch} \lx{mwenyeji } \ps{n } \clsg{N1 } \glp{człowiek stąd; miejscowy} \lx{mwenyekiti } \ps{n } \clsg{N1 } \glp{kierownik } \lx{mwenzi } \ps{n } \clsg{N1 } \glp{kompan } \lx{mwezi } \ps{n } \clsg{N3 } \glp{miesiąc; księżyc} \lx{mwili } \ps{n } \clsg{N3 } \glp{ciało } \lx{mwisho } \ps{n } \clsg{N3 } \glp{koniec } \lx{mwitu } \ps{n } \clsg{N3 } \glp{las } \lx{mwizi } \ps{n } \clsg{N1 } \glp{złodziej } \lx{mwoga } \ps{n } \clsg{N1 } \glp{tchórz } \lx{mwongo } \ps{n } \clsg{N3 } \glp{kłamstwo } \lx{mwuguzi } \ps{n } \clsg{N1 } \glp{pielęgniarka } \lx{mwungano } \ps{n } \clsg{N3 } \glp{federacja } \lx{mzazi } \ps{n } \clsg{N1 } \glp{rodzic } \lx{mzee } \ps{n } \clsg{N1 } \glp{starsza osoba; rodzic} \lx{mzigo } \ps{n } \clsg{N3 } \glp{bagaż } \lx{Mzungu } \ps{n } \clsg{N1 } \glp{Europejczyk } \end{multicols} \begin{center} \LARGE{N} \end{center} \begin{multicols}{2} \lx{na } \ps{conj } \clsg{ } \glp{i; a } \lx{naam } \ps{interj } \clsg{ } \glp{odpowiedź mężczyzny na wezwanie } \lx{nafuu } \ps{adj } \clsg{A2 } \glp{korzystny } \lx{namba } \ps{n } \clsg{N9 } \glp{liczba } \lx{nambari } \ps{n } \clsg{N9 } \glp{liczba } \lx{nanasi } \ps{n } \clsg{N5 } \glp{ananas } \lx{nani } \ps{adv } \clsg{P1 } \glp{kto; jaki (o człowieku); który (o człowieku)} \lx{nauli } \ps{n } \clsg{N9 } \glp{opłata za przejazd } \lx{nawa } \ps{v } \clsg{V1 } \glp{myć ręce lub twarz lub stopy } \lx{nawisha } \ps{v } \clsg{V1K } \glp{moknąć; nasiąkać } \lx{nazi } \ps{n } \clsg{N9 } \glp{orzech kokosowy } \lx{nchi } \ps{n } \clsg{N9 } \glp{kraj } \lx{ndani ya } \ps{adv } \clsg{P1 } \glp{wewnątrz } \lx{ndege } \ps{n } \clsg{N9/1 } \glp{ptak; samolot } \lx{ndini } \ps{n } \clsg{N9 } \glp{religia } \lx{ndiyo } \ps{interj } \clsg{ } \glp{tak } \lx{ndizi } \ps{n } \clsg{N9 } \glp{banan } \lx{ndugu } \ps{n } \clsg{N9 } \glp{krewny; rodzeństwo } \lx{nenepa } \ps{v } \clsg{V1 } \glp{utyć } \lx{neno } \ps{n } \clsg{N5 } \glp{słowo } \lx{nesi } \ps{n } \clsg{N5/1 } \glp{pielęgniarka } \lx{ngamia } \ps{n } \clsg{N9/1 } \glp{wielbłąd } \lx{ngano } \ps{n } \clsg{N9 } \glp{ziarno; żyto; pszenica} \lx{ngapi } \ps{adv } \clsg{P1 } \glp{ile } \lx{nge } \ps{n } \clsg{N9/1 } \glp{skorpion } \lx{ng'oa } \ps{v } \clsg{V2 } \glp{wyrywać } \lx{ngoja } \ps{v } \clsg{V1 } \glp{czekać } \lx{ngoma } \ps{n } \clsg{N9 } \glp{bęben } \lx{ng'ombe } \ps{n } \clsg{N9 } \glp{krowa; bydło } \lx{ngozi } \ps{n } \clsg{N9 } \glp{skóra } \lx{ngumi } \ps{n } \clsg{N9 } \glp{pięść } \lx{nguo } \ps{n } \clsg{N9 } \glp{ubranie } \lx{nguruwe } \ps{n } \clsg{N9/1 } \glp{świnia } \lx{nguvu } \ps{n } \clsg{N9 } \glp{siła } \lx{nia } \ps{n } \clsg{N9 } \glp{chęć; zamierzenie } \lx{nini } \ps{adv } \clsg{P1 } \glp{co; jaki; który (o ny)} \lx{njaa } \ps{n } \clsg{N9 } \glp{głód } \lx{nje ya } \ps{adv } \clsg{P1 } \glp{na zewnątrz } \lx{njia } \ps{n } \clsg{N9 } \glp{droga } \lx{njia panda } \ps{n } \clsg{N9 } \glp{skrzyżowanie } \lx{noti } \ps{n } \clsg{N9 } \glp{banknot } \lx{nukta } \ps{n } \clsg{N9 } \glp{kropka; chwila } \lx{nusu } \ps{n } \clsg{N9 } \glp{pół } \lx{nyama } \ps{n } \clsg{N9 } \glp{mięso } \lx{nyamaza } \ps{v } \clsg{V1 } \glp{być cicho; milczeć } \lx{nyati } \ps{n } \clsg{N9/1 } \glp{bawół } \lx{nyesha } \ps{v } \clsg{V1 } \glp{deszczyć } \lx{nyima } \ps{v } \clsg{V1 } \glp{odmawiać } \lx{nyinyi } \ps{pron } \clsg{PN } \glp{wy } \lx{nyoa } \ps{v } \clsg{V2 } \glp{ogolić } \lx{nyoka } \ps{n } \clsg{N9/1 } \glp{wąż } \lx{nyonge } \ps{adj } \clsg{A1 } \glp{samotny } \lx{nyota } \ps{n } \clsg{N9 } \glp{gwiazda } \lx{nyuki } \ps{n } \clsg{N9/1 } \glp{pszczoła } \lx{nyuma } \ps{n } \clsg{N9 } \glp{tył } \lx{nyumba } \ps{n } \clsg{N9 } \glp{dom; rodzina; budynek} \lx{nyusi } \ps{n } \clsg{N11/14 } \glp{brew } \lx{nywa } \ps{v } \clsg{V0 } \glp{pić } \lx{nywele } \ps{n } \clsg{N9 } \glp{włosy } \lx{nzi } \ps{n } \clsg{N9/1 } \glp{mucha } \end{multicols} \begin{center} \LARGE{O} \end{center} \begin{multicols}{2} \lx{o -ote } \ps{adj } \clsg{A1 } \glp{jakakolwiek/jakikolwiek } \lx{oa } \ps{v } \clsg{V2 } \glp{ożenić się } \lx{oda } \ps{n } \clsg{N9 } \glp{zamówienie } \lx{ofisi } \ps{n } \clsg{N9 } \glp{biuro } \lx{oga } \ps{v } \clsg{V1 } \glp{myć się; brać prysznic } \lx{ogelea } \ps{v } \clsg{V1D } \glp{pływać } \lx{ogopa } \ps{v } \clsg{V1 } \glp{bać się } \lx{omba } \ps{v } \clsg{V1 } \glp{prosić; modlić się o... } \lx{ona } \ps{v } \clsg{V1 } \glp{patrzeć; widzieć; postrzegać, uważać} \lx{onana } \ps{v } \clsg{V1W } \glp{widzieć się nawzajem; postrzegać się nawzajem } \lx{ondoa } \ps{v } \clsg{V2 } \glp{usunąć; zabrać } \lx{ondoka } \ps{v } \clsg{V2K } \glp{wyjechać; odejść; umrzeć} \lx{onekana } \ps{v } \clsg{V1SW } \glp{być widzianym } \lx{ongeza } \ps{v } \clsg{V2K } \glp{dołożyć } \lx{onya } \ps{v } \clsg{V1K } \glp{ostrzegać } \lx{onyesha } \ps{v } \clsg{V1K } \glp{pokazywać } \lx{onyesho } \ps{n } \clsg{N5 } \glp{scena (w sztuce); wystawa; scena (w teatrze)} \lx{orodha } \ps{n } \clsg{N9 } \glp{lista } \lx{orodha ya vyakula } \ps{n } \clsg{N9 } \glp{menu } \lx{osha } \ps{v } \clsg{V1 } \glp{myć; zmywać} \lx{ote } \ps{adj } \clsg{A1 } \glp{wszyscy } \end{multicols} \begin{center} \LARGE{P} \end{center} \begin{multicols}{2} \lx{pa } \ps{v } \clsg{V0 } \glp{dawać } \lx{pa lifti } \ps{v } \clsg{V0 } \glp{podwieść } \lx{paa } \ps{n } \clsg{N9/1 } \glp{gazela; antylopa} \lx{pafu } \ps{n } \clsg{N5 } \glp{płuco } \lx{pahala } \ps{n } \clsg{N16 } \glp{miejsce } \lx{paka } \ps{n } \clsg{N9 } \glp{kot } \lx{paka } \ps{v } \clsg{V1 } \glp{malować } \lx{pakacha } \ps{n } \clsg{N9 } \glp{koszyczek } \lx{pakua } \ps{v } \clsg{V2R } \glp{rozładować; rozpakować} \lx{pamoja na } \ps{adv } \clsg{P1 } \glp{razem z } \lx{pana } \ps{adj } \clsg{A1 } \glp{szeroki } \lx{panda } \ps{v } \clsg{V1 } \glp{wchodzic pod górę; wchodzić na / do} \lx{pande } \ps{n } \clsg{N9 } \glp{kierunek } \lx{panga } \ps{n } \clsg{N9 } \glp{miecz } \lx{pangusa } \ps{v } \clsg{V1 } \glp{wycierać } \lx{panza } \ps{v } \clsg{V1K } \glp{wnosić do góry/pod górę } \lx{papai } \ps{n } \clsg{N5 } \glp{papaja } \lx{papasa } \ps{v } \clsg{V1 } \glp{dotykać } \lx{papasi } \ps{n } \clsg{N9 } \glp{kleszcz } \lx{pasua } \ps{v } \clsg{V2 } \glp{rozerwać } \lx{pasuka } \ps{v } \clsg{V1K } \glp{rwać } \lx{paswa } \ps{v } \clsg{V1B } \glp{musieć; być wymaganym } \lx{pata } \ps{v } \clsg{V1 } \glp{otrzymać; znaleźć } \lx{patana } \ps{v } \clsg{V1W } \glp{dogadać się; pogodzić się } \lx{patikana } \ps{v } \clsg{V1SW } \glp{być dostępnym; być złapanym; być znalezionym} \lx{pazia } \ps{n } \clsg{N5 } \glp{zasłona } \lx{peke y-(adj.dzierż.) } \ps{adj } \clsg{A2 } \glp{sam } \lx{pekua } \ps{v } \clsg{V2 } \glp{przeszukiwać } \lx{peleka } \ps{v } \clsg{V1 } \glp{zawieść; przewieść; wysłać} \lx{penda } \ps{v } \clsg{V1 } \glp{lubić; kochać} \lx{pendekeza } \ps{v } \clsg{V1K } \glp{zaproponować } \lx{pendelea } \ps{v } \clsg{V1D } \glp{woleć } \lx{penseli } \ps{n } \clsg{N9 } \glp{ołówek } \lx{pesa } \ps{n } \clsg{N9 } \glp{pieniądz/e } \lx{pete } \ps{n } \clsg{N9 } \glp{pierścionek } \lx{pia } \ps{adv } \clsg{P1 } \glp{także } \lx{picha } \ps{n } \clsg{N9 } \glp{zdjęcie; obrazek} \lx{piga deki } \ps{v } \clsg{V1 } \glp{myć podłogę } \lx{piga hodi } \ps{v } \clsg{V1 } \glp{pukać (do drzwi) } \lx{piga pasi } \ps{v } \clsg{V1 } \glp{prasować } \lx{piga picha } \ps{v } \clsg{V1 } \glp{robić zdjęcia } \lx{piga simu } \ps{v } \clsg{V1 } \glp{dzwonić (telefonem) } \lx{piga sindano } \ps{v } \clsg{V1 } \glp{zrobić zastrzyk } \lx{pika } \ps{v } \clsg{V1 } \glp{gotować } \lx{pima } \ps{v } \clsg{V1 } \glp{mierzyć; ważyć} \lx{pima joto } \ps{v } \clsg{V1 } \glp{mierzyć temperaturę } \lx{pinda } \ps{v } \clsg{V1 } \glp{skręcić } \lx{pinki } \ps{adj } \clsg{A2 } \glp{różowy } \lx{pita } \ps{v } \clsg{V1 } \glp{przejść; wpaść (gdzieś lub do kogoś)} \lx{pole } \ps{v } \clsg{V5 } \glp{ochłonąć } \lx{pombe } \ps{n } \clsg{N9 } \glp{drink; piwo} \lx{pona } \ps{v } \clsg{V1 } \glp{wyzdrowieć } \lx{ponda } \ps{v } \clsg{V1 } \glp{miażdżyć; gnieść} \lx{ponga } \ps{v } \clsg{V1 } \glp{potrącić } \lx{pori } \ps{n } \clsg{N5 } \glp{step } \lx{posta } \ps{n } \clsg{N9 } \glp{poczta } \lx{potea } \ps{v } \clsg{V2 } \glp{zgubić się } \lx{poteza } \ps{v } \clsg{V2K } \glp{tracić; gubić} \lx{pua } \ps{n } \clsg{N9 } \glp{nos } \lx{pumbavu } \ps{adj } \clsg{A2 } \glp{głupi } \lx{pumua } \ps{v } \clsg{V2 } \glp{oddychać } \lx{pumzika } \ps{v } \clsg{V1 } \glp{odpoczywać; iść na emeryturę } \lx{punda } \ps{n } \clsg{N9/1 } \glp{osioł } \lx{punda milia } \ps{n } \clsg{N9/1 } \glp{zebra } \lx{punde } \ps{n } \clsg{N9 } \glp{moment; chwila } \lx{punga } \ps{v } \clsg{V1 } \glp{machać } \lx{punguza } \ps{v } \clsg{V1K } \glp{obniżyć } \lx{pwani } \ps{n } \clsg{N9 } \glp{wybrzeże } \lx{pya } \ps{adj } \clsg{A1 } \glp{nowy } \end{multicols} \begin{center} \LARGE{R} \end{center} \begin{multicols}{2} \lx{radhi } \ps{n } \clsg{N9 } \glp{wybaczenie } \lx{rafiki } \ps{n } \clsg{N9/1 } \glp{przyjaciel } \lx{rahisi } \ps{adj } \clsg{A2 } \glp{tani; łatwy; prosty} \lx{rais } \ps{n } \clsg{N5/1 } \glp{prezydent; przewodniczący, prezes } \lx{ramani } \ps{n } \clsg{N9 } \glp{mapa } \lx{rangi } \ps{n } \clsg{N9 } \glp{kolor } \lx{rasmi } \ps{adj } \clsg{A2 } \glp{oficjalny } \lx{redio } \ps{n } \clsg{N9 } \glp{radio } \lx{rejesta } \ps{n } \clsg{N9 } \glp{polecony (list) } \lx{rekebisha } \ps{v } \clsg{V1 } \glp{wyregulować; naprawić; uzupełnić} \lx{resheni } \ps{n } \clsg{N9 } \glp{przydział } \lx{risasi } \ps{n } \clsg{N9 } \glp{grafit } \lx{robo } \ps{n } \clsg{N9 } \glp{kwadrans } \lx{roho } \ps{n } \clsg{N9 } \glp{dusza; duch } \lx{rudi } \ps{v } \clsg{V3 } \glp{wracać } \lx{rudia } \ps{n } \clsg{V1D } \glp{powtarzać; zawracać } \lx{ruhusa } \ps{v } \clsg{V1 } \glp{pozwolić } \lx{ruhusu } \ps{v } \clsg{V4 } \glp{pozwolić } \lx{ruka } \ps{v } \clsg{V1 } \glp{latać; skakać } \end{multicols} \begin{center} \LARGE{S} \end{center} \begin{multicols}{2} \lx{saa } \ps{n } \clsg{N9 } \glp{godzina; zegarek } \lx{sababisha } \ps{v } \clsg{V1 } \glp{powodować } \lx{sabini } \ps{num } \clsg{ } \glp{70 } \lx{sabuni } \ps{n } \clsg{N9 } \glp{mydło } \lx{safari } \ps{n } \clsg{N9 } \glp{podróż } \lx{safi } \ps{adj } \clsg{A2 } \glp{czysty } \lx{safiri } \ps{v } \clsg{V3 } \glp{podróżować } \lx{safisha } \ps{v } \clsg{V1 } \glp{czyścić; sprzątać } \lx{sahani } \ps{n } \clsg{N9 } \glp{talerz } \lx{sahau } \ps{v } \clsg{V4 } \glp{zapomnieć } \lx{sahihi } \ps{adj } \clsg{A2 } \glp{właściwy; poprawny; prawdziwy} \lx{salaam } \ps{n } \clsg{N9 } \glp{pozdrowienie } \lx{salale } \ps{interj } \clsg{ } \glp{o Boże! } \lx{salama } \ps{adj } \clsg{A2 } \glp{spokojny } \lx{salamu } \ps{n } \clsg{N9 } \glp{pozdrowienie } \lx{sali } \ps{v } \clsg{V1 } \glp{modlić się } \lx{salimia } \ps{v } \clsg{V4D } \glp{pozdrowić } \lx{salimu } \ps{v } \clsg{V4 } \glp{powitać, pozdrowić; ocalić; poddać się} \lx{samahani } \ps{interj } \clsg{ } \glp{przepraszam } \lx{samaki } \ps{n } \clsg{N9 } \glp{ryba } \lx{samawati } \ps{n } \clsg{N9 } \glp{niebo } \lx{sambusa } \ps{n } \clsg{N9 } \glp{pieróg } \lx{sana } \ps{adv } \clsg{P1 } \glp{bardzo } \lx{sanaa } \ps{n } \clsg{N9 } \glp{sztuka } \lx{sanamu } \ps{n } \clsg{N9 } \glp{rzeźba; posąg} \lx{sare } \ps{n } \clsg{N9 } \glp{mundurek } \lx{sarufi } \ps{n } \clsg{N9 } \glp{gramatyka } \lx{sasa } \ps{adv } \clsg{P1 } \glp{teraz } \lx{sasa hivi } \ps{adv } \clsg{P1 } \glp{natychmiast; od zaraz} \lx{sauti } \ps{n } \clsg{N9 } \glp{głos } \lx{sawa } \ps{adj } \clsg{A2 } \glp{równy; w porządku} \lx{sawa sawa } \ps{interj } \clsg{ } \glp{równa się } \lx{sayansi } \ps{n } \clsg{N9 } \glp{nauka ścisła } \lx{sehemu } \ps{n } \clsg{N9 } \glp{część } \lx{sekunde } \ps{n } \clsg{N9 } \glp{sekunda } \lx{sema } \ps{v } \clsg{V1 } \glp{mówić } \lx{serikali } \ps{n } \clsg{N9 } \glp{rząd } \lx{seyfu } \ps{n } \clsg{N9 } \glp{miecz } \lx{shairi } \ps{n } \clsg{N5 } \glp{wiersz } \lx{shaka } \ps{n } \clsg{N5 } \glp{wątpliwość } \lx{shamba } \ps{n } \clsg{N6 } \glp{wieś; pole} \lx{shanga } \ps{n } \clsg{N5 } \glp{paciorki } \lx{sharti } \ps{adv } \clsg{P1 } \glp{jest konieczne; trzeba} \lx{shati } \ps{n } \clsg{N5 } \glp{koszula; bluzka} \lx{shehena } \ps{n } \clsg{N9 } \glp{ładunek } \lx{shemeji } \ps{n } \clsg{N9/1 } \glp{szwagier, szwagierka} \lx{sherehe } \ps{n } \clsg{N9 } \glp{święto } \lx{sherehekea } \ps{v } \clsg{V2 } \glp{świętować } \lx{shiba } \ps{v } \clsg{V1 } \glp{najeść się, być sytym} \lx{shibe } \ps{n } \clsg{N5 } \glp{sytość } \lx{shida } \ps{n } \clsg{N5 } \glp{kłopot, problem} \lx{shika } \ps{v } \clsg{V1 } \glp{trzymać } \lx{shimo } \ps{n } \clsg{N5 } \glp{dziura } \lx{shinda } \ps{v } \clsg{V1 } \glp{pokonać, wygrywać } \lx{shingo } \ps{n } \clsg{N9 } \glp{szyja } \lx{shirika } \ps{n } \clsg{N9 } \glp{spółka; przedsiębiorstwo } \lx{shona } \ps{v } \clsg{V1 } \glp{szyć } \lx{shtuka } \ps{v } \clsg{V1 } \glp{zaskoczyć się; przerazić się; wzdrygnąć się} \lx{shujaa } \ps{n } \clsg{N5/1 } \glp{bohater } \lx{shuka } \ps{n } \clsg{N5 } \glp{prześcieradło } \lx{shuka } \ps{v } \clsg{V1 } \glp{schodzić } \lx{shukuru } \ps{v } \clsg{V4 } \glp{dziękować; być wdzięcznym } \lx{shule } \ps{n } \clsg{N9 } \glp{szkoła } \lx{shule ya chini } \ps{n } \clsg{N9 } \glp{szkoła podstawowa } \lx{shule ya msingi } \ps{n } \clsg{N9 } \glp{szkoła podstawowa } \lx{shule ya sekondari } \ps{n } \clsg{N9 } \glp{liceum } \lx{shusha } \ps{v } \clsg{V1K } \glp{wysadzić; sprawić by ktoś wyszedł } \lx{siafu } \ps{n } \clsg{N9/1 } \glp{mrówka } \lx{siagi } \ps{n } \clsg{N9 } \glp{masło } \lx{siasa } \ps{n } \clsg{N9 } \glp{polityka } \lx{sidiria } \ps{n } \clsg{N9 } \glp{stanik } \lx{sifuri } \ps{n } \clsg{N9 } \glp{zero } \lx{sigara } \ps{n } \clsg{N9 } \glp{papieros } \lx{sikia } \ps{v } \clsg{V1D } \glp{słyszeć } \lx{sikiliza } \ps{v } \clsg{V2K } \glp{słyszeć } \lx{sikio } \ps{n } \clsg{N5 } \glp{ucho } \lx{sikitika } \ps{v } \clsg{V1 } \glp{żałować } \lx{siku } \ps{n } \clsg{N9 } \glp{dzień } \lx{siku zote } \ps{adv } \clsg{P2 } \glp{zawsze } \lx{simama } \ps{v } \clsg{V1 } \glp{stać } \lx{simba } \ps{n } \clsg{N9/1 } \glp{lew } \lx{simba wa bara hindi } \ps{n } \clsg{N9/1 } \glp{tygrys } \lx{simu } \ps{n } \clsg{N9 } \glp{telegram; telefon} \lx{simu ya mkononi } \ps{n } \clsg{N9 } \glp{telefon komórkowy } \lx{sindano } \ps{n } \clsg{N9 } \glp{zastrzyk } \lx{sindikiza } \ps{v } \clsg{V1 } \glp{towarzyszyć; odprowadzać} \lx{sinema } \ps{n } \clsg{N9 } \glp{kino } \lx{siri } \ps{n } \clsg{N9 } \glp{sekret } \lx{sisi } \ps{pron } \clsg{PN } \glp{my } \lx{sita } \ps{v } \clsg{V1 } \glp{wahać się } \lx{sitini } \ps{num } \clsg{ } \glp{60 } \lx{siyo } \ps{adv } \clsg{P1 } \glp{nie } \lx{skafu } \ps{n } \clsg{N9 } \glp{szalik } \lx{sketi } \ps{n } \clsg{N9 } \glp{spódnica } \lx{soko } \ps{n } \clsg{N5 } \glp{targ } \lx{soksi } \ps{n } \clsg{N9 } \glp{skarpetki } \lx{soma } \ps{v } \clsg{V1 } \glp{uczyć się; czytać} \lx{somesha } \ps{v } \clsg{V1K } \glp{uczyć kogoś } \lx{somo } \ps{n } \clsg{N5 } \glp{lekcja } \lx{songa mbele } \ps{v } \clsg{V1 } \glp{iść naprzód } \lx{staajabu } \ps{v } \clsg{V4 } \glp{zadziwiać } \lx{stakabadhi } \ps{n } \clsg{N9 } \glp{rachunek; pokwitowanie} \lx{starehe } \ps{n } \clsg{N9 } \glp{rozrywka } \lx{stempu } \ps{n } \clsg{N9 } \glp{znaczek } \lx{stesheni } \ps{n } \clsg{N9 } \glp{stacja } \lx{stimu } \ps{n } \clsg{N9 } \glp{elektryczność } \lx{stovu } \ps{n } \clsg{N9 } \glp{kuchenka } \lx{subiri } \ps{v } \clsg{V3 } \glp{oczekiwać; czekać cierpliwie} \lx{sufuri } \ps{n } \clsg{N9 } \glp{zero } \lx{sufuria } \ps{n } \clsg{N9 } \glp{garnek (metalowy) } \lx{sukari } \ps{n } \clsg{N9 } \glp{cukier } \lx{sukuma } \ps{v } \clsg{V1 } \glp{prowadzić } \lx{sulubu } \ps{v } \clsg{V4 } \glp{prześladować } \lx{sumbua } \ps{v } \clsg{V2 } \glp{męczyć } \lx{sumu } \ps{n } \clsg{N9 } \glp{trucizna } \lx{sungura } \ps{n } \clsg{N9/1 } \glp{zając; królik} \lx{sura } \ps{n } \clsg{N9 } \glp{wygląd } \lx{suruali } \ps{n } \clsg{N9 } \glp{spodnie } \lx{suti } \ps{n } \clsg{N9 } \glp{garnitur } \lx{swahiba } \ps{n } \clsg{N5 } \glp{przyjaciel } \lx{swali } \ps{n } \clsg{N5 } \glp{pytanie } \lx{sweta } \ps{n } \clsg{N9 } \glp{sweter } \end{multicols} \begin{center} \LARGE{T} \end{center} \begin{multicols}{2} \lx{taa } \ps{n } \clsg{N9 } \glp{lampa } \lx{taa za stimu } \ps{n } \clsg{N9 } \glp{światło elektryczne } \lx{taabani } \ps{adj } \clsg{A2 } \glp{wyczerpany } \lx{taaluma } \ps{n } \clsg{N9 } \glp{nauka; kształcenie} \lx{taarifa } \ps{n } \clsg{N9 } \glp{informacja } \lx{tabasamu } \ps{v } \clsg{V4 } \glp{uśmiechać się } \lx{tabibu } \ps{n } \clsg{N5/1 } \glp{lekarz } \lx{tabu } \ps{n } \clsg{N9 } \glp{kłopot, problem} \lx{tafauti } \ps{n } \clsg{N9 } \glp{różnica } \lx{tafrija } \ps{n } \clsg{N9 } \glp{impreza; przyjęcie} \lx{tafuta } \ps{v } \clsg{V1 } \glp{szukać } \lx{tahadhari } \ps{v } \clsg{V3 } \glp{być ostrożnym } \lx{taifa } \ps{n } \clsg{N9 } \glp{naród } \lx{tajiri } \ps{adj } \clsg{A2 } \glp{bogaty } \lx{tajiri } \ps{n } \clsg{N9/1 } \glp{bogacz } \lx{taka } \ps{v } \clsg{V1 } \glp{chcieć } \lx{talizo } \ps{n } \clsg{N5 } \glp{kłopot, problem} \lx{tamaa } \ps{n } \clsg{N9 } \glp{chęć } \lx{tambua } \ps{v } \clsg{V2 } \glp{zorientować się } \lx{tamu } \ps{adj } \clsg{A1 } \glp{słodki; smaczny} \lx{tanga } \ps{v } \clsg{V1 } \glp{chodzić bez celu } \lx{tangaza } \ps{v } \clsg{V1 } \glp{ogłosić } \lx{tangu } \ps{conj } \clsg{ } \glp{od } \lx{tangulia } \ps{v } \clsg{V2 } \glp{iść przodem } \lx{tarakimu } \ps{n } \clsg{N9 } \glp{cyfra } \lx{tarehe } \ps{n } \clsg{N9 } \glp{data } \lx{tatua } \ps{v } \clsg{V1R } \glp{rozwiązać problem } \lx{tawa } \ps{adj } \clsg{A1 } \glp{pobożny; święty } \lx{tazama } \ps{v } \clsg{V1 } \glp{oglądać } \lx{tega } \ps{v } \clsg{V1 } \glp{zastawiać pułapki } \lx{tegua } \ps{v } \clsg{V1R } \glp{uwalniać z pułapki } \lx{tele } \ps{adv } \clsg{P1 } \glp{wiele; dużo } \lx{teleza } \ps{v } \clsg{V1 } \glp{ślizgać się; pośliznąć się } \lx{tembea } \ps{v } \clsg{V2 } \glp{spacerować } \lx{tembelea } \ps{v } \clsg{V2D } \glp{odwiedzić } \lx{tembo } \ps{n } \clsg{N9/1 } \glp{słoń } \lx{tena } \ps{conj } \clsg{ } \glp{poza tym; jeszcze; znowu} \lx{tende } \ps{n } \clsg{N5 } \glp{daktyl } \lx{tengeneza } \ps{v } \clsg{V1 } \glp{przygotować } \lx{teremka } \ps{v } \clsg{V1 } \glp{schodzić } \lx{teso } \ps{n } \clsg{N5 } \glp{grzech } \lx{tetemeka } \ps{v } \clsg{V1 } \glp{trząść się } \lx{thelathini } \ps{num } \clsg{ } \glp{30 } \lx{theluji } \ps{n } \clsg{N9 } \glp{śnieg } \lx{themanini } \ps{num } \clsg{ } \glp{80 } \lx{thiata } \ps{n } \clsg{N9 } \glp{teatr } \lx{tia } \ps{v } \clsg{V2 } \glp{nalać; położyć; wkładać} \lx{timiza } \ps{v } \clsg{V1 } \glp{wypełniać } \lx{tisha } \ps{v } \clsg{V1 } \glp{przerażać; przestraszać } \lx{tisini } \ps{num } \clsg{ } \glp{90 } \lx{toa } \ps{v } \clsg{V2 } \glp{układać; wykładać, wyjmować; odejmować} \lx{toa damu } \ps{v } \clsg{V2 } \glp{pobrać krew } \lx{toa oda } \ps{v } \clsg{V2 } \glp{składać zamówienie } \lx{tofali } \ps{n } \clsg{N5 } \glp{cegła } \lx{tofauti } \ps{n } \clsg{N9 } \glp{różnica } \lx{toka } \ps{v } \clsg{V1 } \glp{iść skądś; wychodzić; pochodzić} \lx{tokea } \ps{v } \clsg{V1D } \glp{zdarzyć się; pojawić się } \lx{toroka } \ps{v } \clsg{V1 } \glp{uciec } \lx{tosha } \ps{v } \clsg{V1 } \glp{wystarczać } \lx{toweka } \ps{v } \clsg{V1 } \glp{zniknąć; zaginąć} \lx{tua } \ps{v } \clsg{V2 } \glp{wylądować } \lx{tuama } \ps{v } \clsg{V1 } \glp{stać } \lx{tufaa } \ps{n } \clsg{N5 } \glp{jabłko } \lx{tukana } \ps{v } \clsg{V1W } \glp{obrażać się } \lx{tuliza } \ps{v } \clsg{V2K } \glp{uspokoić się; zatrzymać (np.. wzrok)} \lx{tuma } \ps{v } \clsg{V1 } \glp{wysyłać } \lx{tumaini } \ps{v } \clsg{V3 } \glp{mieć nadzieję; spodziewać się} \lx{tumbo } \ps{n } \clsg{N5 } \glp{brzuch } \lx{tumia } \ps{v } \clsg{V2 } \glp{używać; stosować} \lx{tumika } \ps{v } \clsg{V1S } \glp{być używanym } \lx{tumikia } \ps{v } \clsg{V2SD } \glp{służyć komuś } \lx{tunda } \ps{n } \clsg{N5 } \glp{owoc } \lx{tundu } \ps{adj } \clsg{A1 } \glp{niegnny } \lx{tundu } \ps{n } \clsg{N5 } \glp{dziura; gniazdo} \lx{tunza } \ps{v } \clsg{V1 } \glp{opiekować się; troszczyć się} \lx{tupa } \ps{v } \clsg{V1 } \glp{rzucać } \lx{tuta } \ps{n } \clsg{N5 } \glp{grządka } \lx{twiga } \ps{n } \clsg{N9/1 } \glp{żyrafa } \end{multicols} \begin{center} \LARGE{U} \end{center} \begin{multicols}{2} \lx{ua } \ps{n } \clsg{N5 } \glp{kwiat } \lx{ua } \ps{v } \clsg{V2 } \glp{zabijać } \lx{ubalozi } \ps{n } \clsg{N11/14 } \glp{ambasada } \lx{ubao } \ps{n } \clsg{N11/14 } \glp{deska; tablica} \lx{ubishi } \ps{n } \clsg{N11/14 } \glp{spór; kłótnia} \lx{uchumi } \ps{n } \clsg{N11/14 } \glp{ekonomia } \lx{uchumi } \ps{n } \clsg{N11/14 } \glp{handel; ekonomia} \lx{udevu } \ps{n } \clsg{N11/14 } \glp{włos z brody } \lx{udhi } \ps{v } \clsg{V3 } \glp{urazić; zranić} \lx{udongo } \ps{n } \clsg{N11/14 } \glp{glina } \lx{ufa } \ps{n } \clsg{N11/14 } \glp{dziura } \lx{ufagio } \ps{n } \clsg{N11/14 } \glp{szczotka } \lx{ufunguo } \ps{n } \clsg{N11/14 } \glp{klucz } \lx{ufupi } \ps{n } \clsg{N11/14 } \glp{skrót; krótkość } \lx{ufupisho } \ps{n } \clsg{N11/14 } \glp{streszczenie } \lx{ugali } \ps{n } \clsg{N11/14 } \glp{gęsta kaszka } \lx{ugawaji } \ps{n } \clsg{N11/14 } \glp{dystrybucja } \lx{ugonjwa } \ps{n } \clsg{N11/14 } \glp{choroba } \lx{uhuru } \ps{n } \clsg{N11/14 } \glp{wolność } \lx{uhusiano } \ps{n } \clsg{N11/14 } \glp{stosunek; relacja; związek} \lx{ujamaa } \ps{n } \clsg{N11/14 } \glp{wspólnota; socjalizm } \lx{ujasiri } \ps{n } \clsg{N11/14 } \glp{odwaga } \lx{uji } \ps{n } \clsg{N11/14 } \glp{rzadka kaszka } \lx{ukarimu } \ps{n } \clsg{N11/14 } \glp{grzeczność; szacunek } \lx{ukubwa } \ps{n } \clsg{N11/14 } \glp{wielkość } \lx{ukucha } \ps{n } \clsg{N11/14 } \glp{paznokieć } \lx{ukulima } \ps{n } \clsg{N11/14 } \glp{rolnictwo } \lx{ukurasa } \ps{n } \clsg{N11/14 } \glp{strona; numer strony } \lx{ukuta } \ps{n } \clsg{N11/14 } \glp{ściana } \lx{Ulaya } \ps{n } \clsg{N11/14 } \glp{Europa } \lx{ulimwengu } \ps{n } \clsg{N11/14 } \glp{świat } \lx{uliza } \ps{v } \clsg{V1 } \glp{pytać } \lx{ulizana hali } \ps{v } \clsg{V1W } \glp{pytać się nawzajem o zdrowie } \lx{uma } \ps{v } \clsg{V1 } \glp{ugryźć; boleć} \lx{uma } \ps{n } \clsg{N11/14 } \glp{widelec } \lx{umande } \ps{n } \clsg{N11/14 } \glp{mgła } \lx{umaskini } \ps{n } \clsg{N11/14 } \glp{bieda } \lx{umbali } \ps{n } \clsg{N11/14 } \glp{odległość } \lx{umbo } \ps{n } \clsg{N11/14 } \glp{kształt; postać} \lx{umbu } \ps{n } \clsg{N9/1 } \glp{brat kobiety; siostra mężczyzny} \lx{umeme } \ps{n } \clsg{N11/14 } \glp{elektryczność } \lx{umoja } \ps{n } \clsg{N11/14 } \glp{jedność } \lx{umri } \ps{n } \clsg{N11/14 } \glp{wiek } \lx{unga } \ps{n } \clsg{N11/14 } \glp{mąka; kokaina, heroina} \lx{ungamana } \ps{v } \clsg{V1SW } \glp{połączyć się } \lx{unganisha } \ps{v } \clsg{V1K } \glp{połączyć } \lx{Unguja } \ps{n } \clsg{N11/14 } \glp{Zanzibar } \lx{unyenyekevu } \ps{n } \clsg{N11/14 } \glp{skromność } \lx{unyevunyevu } \ps{n } \clsg{N11/14 } \glp{wilgotność } \lx{unywele } \ps{n } \clsg{N11/14 } \glp{włos } \lx{upande } \ps{n } \clsg{N11/14 } \glp{strona; część} \lx{upepo } \ps{n } \clsg{N11/14 } \glp{wiatr } \lx{upesi } \ps{adv } \clsg{P1 } \glp{szybko } \lx{urefu } \ps{n } \clsg{N11/14 } \glp{długość } \lx{usaha } \ps{n } \clsg{N11/14 } \glp{ropa } \lx{ushindi } \ps{n } \clsg{N11/14 } \glp{zwycięstwo } \lx{usiku } \ps{n } \clsg{N9 } \glp{noc } \lx{usiku wa manane } \ps{n } \clsg{N9 } \glp{pora dnia między godziną 24.00 a 3.00; środek nocy} \lx{usingizi } \ps{n } \clsg{N9 } \glp{senność } \lx{uso } \ps{n } \clsg{N11/14 } \glp{twarz } \lx{ustawi } \ps{n } \clsg{N11/14 } \glp{dobro } \lx{utajiri } \ps{n } \clsg{N11/14 } \glp{bogactwo; skarb } \lx{uthibitisho } \ps{n } \clsg{N11/14 } \glp{pewność; przekonanie; dowód} \lx{utu } \ps{n } \clsg{N11/14 } \glp{człowieczeństwo } \lx{utungaji } \ps{n } \clsg{N11/14 } \glp{wypracowanie } \lx{uuzaji } \ps{n } \clsg{N11/14 } \glp{sklep } \lx{uvumilivu } \ps{n } \clsg{N11/14 } \glp{tolerancja; cierpliwość } \lx{uza } \ps{v } \clsg{V1 } \glp{sprzedawać } \lx{uzima } \ps{n } \clsg{N11/14 } \glp{zdrowie } \lx{uzuri } \ps{n } \clsg{N11/14 } \glp{piękno } \end{multicols} \begin{center} \LARGE{V} \end{center} \begin{multicols}{2} \lx{vaa } \ps{v } \clsg{V2 } \glp{ubrać się } \lx{vagi } \ps{n } \clsg{N9 } \glp{brzuch } \lx{vazi } \ps{n } \clsg{N9 } \glp{ubrania } \lx{vibaya } \ps{adv } \clsg{P1 } \glp{źle } \lx{vilevile } \ps{conj } \clsg{ } \glp{też; tak samo } \lx{vimba } \ps{v } \clsg{V1 } \glp{puchnąć } \lx{vinywaji vikali } \ps{n } \clsg{N8 } \glp{mocne alkohole } \lx{vita } \ps{n } \clsg{N9 } \glp{wojna } \lx{vivu } \ps{adj } \clsg{A1 } \glp{leniwy } \lx{vua } \ps{v } \clsg{V2 } \glp{łowić; rozbierać} \lx{vuka } \ps{v } \clsg{V1 } \glp{przekroczyć } \lx{vuka } \ps{v } \clsg{V1 } \glp{minąć } \lx{vumbi } \ps{n } \clsg{N9 } \glp{kurz } \lx{vunja } \ps{v } \clsg{V1 } \glp{złamać } \lx{vunjika } \ps{v } \clsg{V1S } \glp{rozbić się } \lx{vurugika } \ps{v } \clsg{V1 } \glp{być pomieszanym } \lx{vuta } \ps{v } \clsg{V1 } \glp{palić (papierosy); ciągnąć} \lx{vyombo } \ps{n } \clsg{N8 } \glp{środki } \end{multicols} \begin{center} \LARGE{W} \end{center} \begin{multicols}{2} \lx{wa } \ps{v } \clsg{V0 } \glp{być } \lx{wa na } \ps{v } \clsg{V0 } \glp{mieć } \lx{wahi } \ps{v } \clsg{V3 } \glp{zdążyć; mieć okazję} \lx{waka } \ps{v } \clsg{V1 } \glp{palić się } \lx{wakati } \ps{n } \clsg{N11/14 } \glp{czas } \lx{wala } \ps{conj } \clsg{ } \glp{ani } \lx{wali } \ps{n } \clsg{N11/14 } \glp{gotowany ryż } \lx{wao } \ps{pron } \clsg{PN } \glp{oni } \lx{wapi } \ps{adv } \clsg{P1 } \glp{gdzie } \lx{waridi } \ps{n } \clsg{N9 } \glp{róża } \lx{washa } \ps{v } \clsg{V1K } \glp{zapalać } \lx{wasiwasi } \ps{n } \clsg{N9 } \glp{niepokój } \lx{wastani } \ps{adj } \clsg{A2 } \glp{przeciętny } \lx{waza } \ps{v } \clsg{V1 } \glp{myśleć } \lx{wazi } \ps{adj } \clsg{A2 } \glp{otwarty; wolny, pusty; oczywisty} \lx{wazimu } \ps{n } \clsg{N11/14 } \glp{szaleństwo } \lx{waziri } \ps{n } \clsg{N5/1 } \glp{minister } \lx{wazo } \ps{n } \clsg{N5 } \glp{myśl; pogląd } \lx{weka } \ps{v } \clsg{V1 } \glp{położyć; postawić } \lx{wewe } \ps{pron } \clsg{PN } \glp{ty } \lx{weza } \ps{v } \clsg{V1 } \glp{móc } \lx{wezekana } \ps{v } \clsg{V1SW } \glp{być możliwym } \lx{wia radhi } \ps{v } \clsg{V0D } \glp{wybaczyć } \lx{wifi } \ps{n } \clsg{N9/1 } \glp{szwagierka } \lx{wiki } \ps{n } \clsg{N9 } \glp{tydzień } \lx{wimbo } \ps{n } \clsg{N11/14 } \glp{piosenka } \lx{winda } \ps{v } \clsg{V1 } \glp{polować } \lx{wino } \ps{n } \clsg{N11/14 } \glp{atrament } \lx{wizara } \ps{n } \clsg{N11/14 } \glp{ministerstwo } \end{multicols} \begin{center} \LARGE{Y} \end{center} \begin{multicols}{2} \lx{yaani } \ps{conj } \clsg{ } \glp{to znaczy } \lx{yai } \ps{n } \clsg{N5 } \glp{jajko } \lx{yakhe } \ps{n } \clsg{N9/1 } \glp{brat (zwrot do dobrego znajomego) } \lx{yeye } \ps{pron } \clsg{PN } \glp{on, ona, ono } \lx{yeyuka } \ps{v } \clsg{V1 } \glp{rozpuścić się; roztopić się} \lx{yumba } \ps{v } \clsg{V1 } \glp{chwiać się } \end{multicols} \newpage \begin{center} \LARGE{Z} \end{center} \nobreak \begin{multicols}{2} \lx{zabibu } \ps{n } \clsg{N9 } \glp{winogrona } \lx{zaburi } \ps{n } \clsg{N9 } \glp{psalm } \lx{zamani } \ps{adv } \clsg{P1 } \glp{kiedyś; dawno } \lx{zambarau } \ps{n } \clsg{N9 } \glp{śliwka } \lx{zamu } \ps{n } \clsg{N9 } \glp{zmiana } \lx{zawadi } \ps{n } \clsg{N9 } \glp{prezent } \lx{zero } \ps{n } \clsg{N9 } \glp{zero } \lx{ziara } \ps{n } \clsg{N5 } \glp{wizyta } \lx{ziba } \ps{v } \clsg{V1 } \glp{zatkać; zamknąć } \lx{zidi } \ps{v } \clsg{V3 } \glp{powiększać, zwiększać; kontynuować} \lx{zidisha } \ps{v } \clsg{V3K } \glp{zwiększać; mnożyć } \lx{zika } \ps{v } \clsg{V1 } \glp{grzebać } \lx{zima } \ps{adj } \clsg{A1 } \glp{cały } \lx{zima taa } \ps{v } \clsg{V1 } \glp{zgasić światło } \lx{zindua } \ps{v } \clsg{V2 } \glp{ocknąć się; zbudzić się } \lx{zito } \ps{adj } \clsg{A1 } \glp{ciężki } \lx{ziwa } \ps{n } \clsg{N5 } \glp{jezioro } \lx{zizi } \ps{n } \clsg{N5 } \glp{obora } \lx{zoea } \ps{v } \clsg{V2 } \glp{przyzwyczaić się } \lx{zoezi } \ps{n } \clsg{N5 } \glp{ćwiczenie } \lx{zua } \ps{v } \clsg{V2 } \glp{dziurawić } \lx{zuia } \ps{v } \clsg{V2 } \glp{przeszkadzać } \lx{zulia} \ps{n} \clsg{N5} \glp{dywan} \lx{zungumza } \ps{v } \clsg{V1 } \glp{rozmawiać } \lx{zuri } \ps{adj } \clsg{A1 } \glp{ładny; 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|\AC| & $\AC$ & basic \\ |\A| & $\A$ & full \\ |\ACC| & $\ACC$ & basic \\ |\AH| & $\AH$ & basic \\ |\AL| & $\AL$ & basic \\ |\AlgP| & $\AlgP$ & full \\ |\AM| & $\AM$ & basic \\ |\AMEXP| & $\AMEXP$ & basic \\ |\Amp| & $\Amp$ & full \\ |\AmpMP| & $\AmpMP$ & full \\ |\AmpPBQP| & $\AmpPBQP$ & full \\ |\AP| & $\AP$ & basic \\ |\APP| & $\APP$ & full \\ |\APX| & $\APX$ & full \\ |\AUCSPACE| & $\AUCSPACE$ & full \\ |\AuxPDA| & $\AuxPDA$ & full \\ |\AVBPP| & $\AVBPP$ & full \\ |\AvE| & $\AvE$ & full \\ |\AvP| & $\AvP$ & full \\ |\AW| & $\AW$ & full \\ |\AWPP| & $\AWPP$ & full \\ |\betaP| & $\betaP$ & full \\ |\BH| & $\BH$ & basic \\ |\BP| & $\BP$ & full \\ |\BPE| & $\BPE$ & basic \\ |\BPEE| & $\BPEE$ & basic \\ |\BPHSPACE| & $\BPHSPACE$ & full \\ |\BPL| & $\BPL$ & full \\ |\BPP| & $\BPP$ & basic \\ |\BPPOBDD| & $\BPPOBDD$ & full \\ |\BPPpath| & $\BPPpath$ & full \\ |\BPQP| & $\BPQP$ & full \\ |\BPSPACE| & $\BPSPACE$ & basic \\ |\BPTIME| & $\BPTIME$ & basic \\ |\BQNC| & $\BQNC$ & full \\ |\BQNP| & $\BQNP$ & full \\ |\BQP| & $\BQP$ & basic \\ |\BQPOBDD| & $\BQPOBDD$ & full \\ |\BQTIME| & $\BQTIME$ & basic \\ |\C| & $\C$ & basic \\ |\cc| & $\cc$ & basic \\ |\CeL| & $\CeL$ & basic \\ |\CeP| & $\CeP$ & basic \\ |\CFL| & $\CFL$ & basic \\ |\CH| & $\CH$ & basic \\ %|\Check| & $\Check$ & full \\ |\CkP| & $\CkP$ & basic \\ |\CLOG| & $\CLOG$ & full \\ |\CNP| & $\CNP$ & full \\ |\coAM| & $\coAM$ & basic \\ |\coBPP| & $\coBPP$ & basic \\ |\coCeP| & $\coCeP$ & basic \\ |\cofrIP| & $\cofrIP$ & full \\ |\Coh| & $\Coh$ & full \\ |\coMA| & $\coMA$ & basic \\ |\compIP| & $\compIP$ & full \\ |\compNP| & $\compNP$ & full \\ |\coNE| & $\coNE$ & basic \\ |\coNEXP| & $\coNEXP$ & basic \\ |\coNL| & $\coNL$ & basic \\ |\coNP| & $\coNP$ & basic \\ |\coNQP| & $\coNQP$ & basic \\ |\coRE| & $\coRE$ & basic \\ |\coRNC| & $\coRNC$ & basic \\ |\coRP| & $\coRP$ & basic \\ |\coSL| & $\coSL$ & basic \\ |\coUCC| & $\coUCC$ & full \\ |\coUP| & $\coUP$ & basic \\ |\CP| & $\CP$ & full \\ |\CSIZE| & $\CSIZE$ & basic \\ |\CSL| & $\CSL$ & full \\ |\CZK| & $\CZK$ & full \\ |\D| & $\D$ & full \\ |\DCFL| & $\DCFL$ & full \\ |\DET| & $\DET$ & basic \\ |\DiffAC| & $\DiffAC$ & full \\ |\DisNP| & $\DisNP$ & full \\ |\DistNP| & $\DistNP$ & full \\ |\DP| & $\DP$ & full \\ |\DQP| & $\DQP$ & full \\ |\DSPACE| & $\DSPACE$ & basic \\ |\DTIME| & $\DTIME$ & basic \\ |\DTISP| & $\DTISP$ & basic \\ |\Dyn| & $\Dyn$ & full \\ |\DynFO| & $\DynFO$ & full \\ |\E| & $\E$ & basic \\ |\EE| & $\EE$ & basic \\ |\EEE| & $\EEE$ & basic \\ |\EESPACE| & $\EESPACE$ & basic \\ |\EEXP| & $\EEXP$ & basic \\ |\EH| & $\EH$ & basic \\ |\EL| & $\EL$ & full \\ |\ELEMENTARY| & $\ELEMENTARY$ & full \\ |\ELkP| & $\ELkP$ & full \\ |\EPTAS| & $\EPTAS$ & basic \\ |\EQBP| & $\EQBP$ & full \\ |\EQP| & $\EQP$ & full \\ |\EQTIME| & $\EQTIME$ & full \\ |\ESPACE| & $\ESPACE$ & basic \\ |\ExistsBPP| & $\ExistsBPP$ & full \\ |\ExistsNISZK| & $\ExistsNISZK$ & full \\ |\EXP| & $\EXP$ & basic \\ |\EXPSPACE| & $\EXPSPACE$ & basic \\ |\FBQP| & $\FBQP$ & full \\ |\Few| & $\Few$ & full \\ |\FewP| & $\FewP$ & full \\ |\FH| & $\FH$ & full \\ |\FNL| & $\FNL$ & basic \\ |\FNP| & $\FNP$ & basic \\ |\FO| & $\FO$ & full \\ |\FOLL| & $\FOLL$ & full \\ |\FP| & $\FP$ & basic \\ |\FPR| & $\FPR$ & full \\ |\FPRAS| & $\FPRAS$ & basic \\ |\FPT| & $\FPT$ & full \\ |\FPTAS| & $\FPTAS$ & full \\ |\FPTnu| & $\FPTnu$ & full \\ |\FPTsu| & $\FPTsu$ & full \\ |\FQMA| & $\FQMA$ & basic \\ |\frIP| & $\frIP$ & full \\ |\FTAPE| & $\FTAPE$ & full \\ |\FTIME| & $\FTIME$ & full \\ |\G| & $\G$ & full \\ |\GA| & $\GA$ & basic \\ |\GANSPACE| & $\GANSPACE$ & full \\ |\Gap| & $\Gap$ & basic \\ |\GapAC| & $\GapAC$ & basic \\ |\GapL| & $\GapL$ & basic \\ |\GapP| & $\GapP$ & basic \\ |\GC| & $\GC$ & full \\ |\GCSL| & $\GCSL$ & full \\ |\GI| & $\GI$ & basic \\ |\GPCD| & $\GPCD$ & full \\ |\Heur| & $\Heur$ & basic \\ |\HeurBPP| & $\HeurBPP$ & basic \\ |\HeurBPTIME| & $\HeurBPTIME$ & basic \\ |\HkP| & $\HkP$ & full \\ |\HSPACE| & $\HSPACE$ & basic \\ |\HVSZK| & $\HVSZK$ & full \\ |\IC| & $\IC$ & full \\ |\IP| & $\IP$ & basic \\ |\IPP| & $\IPP$ & full \\ |\K| & $\K$ & basic \\ |\kBQBP| & $\kBQBP$ & full \\ |\kBWBP| & $\kBWBP$ & full \\ |\kEQBP| & $\kEQBP$ & full \\ |\kPBP| & $\kPBP$ & full \\ |\KT| & $\KT$ & basic \\ |\L| & $\L$ & basic \\ |\LIN| & $\LIN$ & basic \\ |\LkP| & $\LkP$ & full \\ |\LOGCFL| & $\LOGCFL$ & full \\ |\LogFew| & $\LogFew$ & basic \\ |\LogFewNL| & $\LogFewNL$ & basic \\ |\LOGNP| & $\LOGNP$ & full \\ |\LOGSNP| & $\LOGSNP$ & full \\ |\LWPP| & $\LWPP$ & full \\ |\M| & $\M$ & full \\ |\MA| & $\MA$ & basic \\ |\MAC| & $\MAC$ & basic \\ |\MAE| & $\MAE$ & basic \\ |\MAEXP| & $\MAEXP$ & basic \\ |\mAL| & $\mAL$ & basic \\ |\MaxNP| & $\MaxNP$ & basic \\ |\MaxPB| & $\MaxPB$ & basic \\ |\MaxSNP| & $\MaxSNP$ & basic \\ |\mcoNL| & $\mcoNL$ & basic \\ |\MinPB| & $\MinPB$ & basic \\ |\MIP| & $\MIP$ & basic \\ |\MkP| & $\MkP$ & full \\ |\mL| & $\mL$ & basic \\ |\mNC| & $\mNC$ & basic \\ |\mNL| & $\mNL$ & basic \\ |\mNP| & $\mNP$ & basic \\ |\ModkL| & $\ModkL$ & basic \\ |\ModkP| & $\ModkP$ & basic \\ |\ModP| & $\ModP$ & basic \\ |\ModZkL| & $\ModZkL$ & full \\ |\mP| & $\mP$ & basic \\ |\MP| & $\MP$ & basic \\ |\MPC| & $\MPC$ & basic \\ |\mTC| & $\mTC$ & basic \\ |\NAuxPDA| & $\NAuxPDA$ & full \\ |\NC| & $\NC$ & basic \\ |\NE| & $\NE$ & basic \\ |\NEE| & $\NEE$ & basic \\ |\NEEE| & $\NEEE$ & basic \\ |\NEEXP| & $\NEEXP$ & basic \\ |\NEXP| & $\NEXP$ & basic \\ |\NIPZK| & $\NIPZK$ & full \\ |\NIQPZK| & $\NIQPZK$ & full \\ |\NIQSZK| & $\NIQSZK$ & full \\ |\NISZK| & $\NISZK$ & full \\ |\NL| & $\NL$ & basic \\ |\NLIN| & $\NLIN$ & basic \\ |\NLOG| & $\NLOG$ & full \\ |\NP| & $\NP$ & basic \\ |\NPC| & $\NPC$ & basic \\ |\NPI| & $\NPI$ & basic \\ |\NPMV| & $\NPMV$ & full \\ |\NPMVsel| & $\NPMVsel$ & full \\ |\NPO| & $\NPO$ & full \\ |\NPOPB| & $\NPOPB$ & full \\ |\NPSPACE| & $\NPSPACE$ & basic \\ |\NPSV| & $\NPSV$ & full \\ |\NPSVsel| & $\NPSVsel$ & full \\ |\NQP| & $\NQP$ & basic \\ |\NSPACE| & $\NSPACE$ & basic \\ |\NT| & $\NT$ & full \\ |\NTIME| & $\NTIME$ & basic \\ |\OBDD| & $\OBDD$ & full \\ |\OCQ| & $\OCQ$ & full \\ |\Opt| & $\Opt$ & basic \\ |\OptP| & $\OptP$ & basic \\ |\p| & $\p$ & basic \\ |\P| & $\P$ & basic \\ |\PAC| & $\PAC$ & basic \\ |\PBP| & $\PBP$ & full \\ |\PCD| & $\PCD$ & basic \\ |\Pclose| & $\Pclose$ & full \\ |\PCP| & $\PCP$ & basic \\ |\PermUP| & $\PermUP$ & full \\ |\PEXP| & $\PEXP$ & basic \\ |\PF| & $\PF$ & full \\ |\PFCHK| & $\PFCHK$ & full \\ |\PH| & $\PH$ & basic \\ |\PhP| & $\PhP$ & full \\ |\PINC| & $\PINC$ & full \\ |\PIO| & $\PIO$ & full \\ |\PKC| & $\PKC$ & full \\ |\PL| & $\PL$ & basic \\ |\PLF| & $\PLF$ & full \\ |\PLL| & $\PLL$ & full \\ |\PLS| & $\PLS$ & full \\ |\POBDD| & $\POBDD$ & full \\ |\PODN| & $\PODN$ & full \\ |\polyL| & $\polyL$ & full \\ |\PostBQP| & $\PostBQP$ & full \\ |\PP| & $\PP$ & basic \\ |\PPA| & $\PPA$ & full \\ |\PPAD| & $\PPAD$ & full \\ |\PPADS| & $\PPADS$ & full \\ |\Ppoly| & $\Ppoly$ & basic \\ |\PPP| & $\PPP$ & full \\ |\PPSPACE| & $\PPSPACE$ & basic \\ |\PQUERY| & $\PQUERY$ & full \\ |\PR| & $\PR$ & full \\ |\PrHSPACE| & $\PrHSPACE$ & full \\ |\Promise| & $\Promise$ & basic \\ |\PromiseBPP| & $\PromiseBPP$ & basic \\ |\PromiseBQP| & $\PromiseBQP$ & basic \\ |\PromiseP| & $\PromiseP$ & basic \\ |\PromiseRP| & $\PromiseRP$ & basic \\ |\PrSPACE| & $\PrSPACE$ & basic \\ |\PSel| & $\PSel$ & full \\ |\PSK| & $\PSK$ & full \\ |\PSPACE| & $\PSPACE$ & basic \\ |\PT| & $\PT$ & basic \\ |\PTAPE| & $\PTAPE$ & full \\ |\PTAS| & $\PTAS$ & basic \\ |\PTWK| & $\PTWK$ & basic \\ |\PZK| & $\PZK$ & full \\ |\QAC| & $\QAC$ & basic \\ |\QACC| & $\QACC$ & basic \\ |\QAM| & $\QAM$ & basic \\ |\QCFL| & $\QCFL$ & basic \\ |\QCMA| & $\QCMA$ & basic \\ |\QH| & $\QH$ & basic \\ |\QIP| & $\QIP$ & basic \\ |\QMA| & $\QMA$ & basic \\ |\QMAM| & $\QMAM$ & basic \\ |\QMIP| & $\QMIP$ & basic \\ |\QMIPle| & $\QMIPle$ & full \\ |\QMIPne| & $\QMIPne$ & full \\ |\QNC| & $\QNC$ & basic \\ |\QP| & $\QP$ & basic \\ |\QPLIN| & $\QPLIN$ & full \\ |\Qpoly| & $\Qpoly$ & full \\ |\QPSPACE| & $\QPSPACE$ & basic \\ |\QSZK| & $\QSZK$ & full \\ |\R| & $\R$ & basic \\ |\RE| & $\RE$ & basic \\ |\REG| & $\REG$ & basic \\ |\RevSPACE| & $\RevSPACE$ & full \\ |\RHL| & $\RHL$ & full \\ |\RHSPACE| & $\RHSPACE$ & full \\ |\RL| & $\RL$ & basic \\ |\RNC| & $\RNC$ & basic \\ |\RNP| & $\RNP$ & full \\ |\RP| & $\RP$ & basic \\ |\RPP| & $\RPP$ & full \\ |\RSPACE| & $\RSPACE$ & basic \\ |\S| & $\S$ & basic \\ |\SAC| & $\SAC$ & basic \\ |\SAPTIME| & $\SAPTIME$ & full \\ |\SBP| & $\SBP$ & full \\ |\SC| & $\SC$ & basic \\ |\SE| & $\SE$ & basic \\ |\SEH| & $\SEH$ & basic \\ |\Sel| & $\Sel$ & full \\ |\SelfNP| & $\SelfNP$ & full \\ |\SF| & $\SF$ & full \\ |\SIZE| & $\SIZE$ & basic \\ |\SKC| & $\SKC$ & basic \\ |\SL| & $\SL$ & basic \\ |\SLICEWISEPSPACE| & $\SLICEWISEPSPACE$ & full \\ |\SNP| & $\SNP$ & full \\ |\SOE| & $\SOE$ & full \\ |\SP| & $\SP$ & full \\ |\SPACE| & $\SPACE$ & basic \\ |\spanP| & $\spanP$ & full \\ |\SPARSE| & $\SPARSE$ & basic \\ |\SPL| & $\SPL$ & basic \\ |\SPP| & $\SPP$ & basic \\ |\SUBEXP| & $\SUBEXP$ & basic \\ |\symP| & $\symP$ & full \\ |\SZK| & $\SZK$ & basic \\ |\TALLY| & $\TALLY$ & full \\ |\TC| & $\TC$ & basic \\ |\TFNP| & $\TFNP$ & full \\ |\ThC| & $\ThC$ & full \\ |\TreeBQP| & $\TreeBQP$ & full \\ |\TREEREGULAR| & $\TREEREGULAR$ & full \\ |\UAP| & $\UAP$ & full \\ |\UCC| & $\UCC$ & full \\ |\UE| & $\UE$ & full \\ |\UL| & $\UL$ & full \\ |\UP| & $\UP$ & basic \\ |\US| & $\US$ & full \\ |\VNC| & $\VNC$ & full \\ |\VNP| & $\VNP$ & full \\ |\VP| & $\VP$ & full \\ |\VQP| & $\VQP$ & full \\ |\W| & $\W$ & basic \\ |\WAPP| & $\WAPP$ & full \\ |\WPP| & $\WPP$ & full \\ |\XORMIP| & $\XORMIP$ & full \\ |\XP| & $\XP$ & full \\ |\XPuniform| & $\XPuniform$ & full \\ |\YACC| & $\YACC$ & full \\ |\ZPE| & $\ZPE$ & basic \\ |\ZPP| & $\ZPP$ & basic \\ |\ZPTIME| & $\ZPTIME$ & basic \\

http://arxmliv.kwarc.info/sty/sig-alt-release2.cls

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% SIG-ALT-RELEASE2.CLS - VERSION 1.6 % "COMPATIBLE" WITH THE "ACM_PROC_ARTICLE-SP.CLS" V3.2SP % PRODUCES A 'TIGHTER' PAPER AND DOES INCLUDE A RELEASE STATEMENT % Gerald Murray - April 22nd. 2009 % % ---- Start of 'updates' ---- % % April 22nd. 2009 - Fixed 'Natbib' incompatibility problem - Gerry % April 22nd. 2009 - Fixed 'Babel' incompatibility problem - Gerry % April 22nd. 2009 - Inserted various bug-fixes and improvements - Gerry % % To produce Type 1 fonts in the document plus allow for 'normal LaTeX accenting' in the critical areas; % title, author block, section-heads, confname, etc. etc. % i.e. the whole purpose of this version update is to NOT resort to 'inelegant accent patches'. % After much research, three extra .sty packages were added to the the tail (ae, aecompl, aeguill) to solve, % in particular, the accenting problem(s). We _could_ ask authors (via instructions/sample file) to 'include' these in % the source .tex file - in the preamble - but if everything is already provided ('behind the scenes' - embedded IN the .cls) % then this is less work for authors and also makes everything appear 'vanilla'. % NOTE: all 'patchwork accenting" has been commented out (here) and is no longer 'used' in the sample .tex file (either). % Gerry June 2007 % % Patch for accenting in conference name/location. Gerry May 3rd. 2007 % Rule widths changed to .5, author count (>6) fixed, roll-back for Type 3 problem. Gerry March 20th. 2007 % Changes made to 'modernize' the fontnames but esp. for MikTeX users V2.4/2.5 - Nov. 30th. 2006 % Updated the \email definition to allow for its use inside of 'shared affiliations' - Nov. 30th. 2006 % Fixed the 'section number depth value' - Nov. 30th. 2006 % % Footnotes inside table cells using \minipage (Oct. 2002) % Georgia fixed bug in sub-sub-section numbering in paragraphs (July 29th. 2002) % JS/GM fix to vertical spacing before Proofs (July 30th. 2002) % % Made the Permission Statement / Conference Info / Copyright Info % 'user definable' in the source .tex file OR automatic if % not specified. % % Allowance made to switch default fonts between those systems using % normal/modern font names and those using 'Type 1' or 'Truetype' fonts. % See LINE NUMBER 255 for details. % Also provided for enumerated/annotated Corollaries 'surrounded' by % enumerated Theorems (line 848). % Gerry November 11th. 1999 % % ---- End of 'updates' ---- % \def\fileversion{v1.6} % for ACM's tracking purposes \def\filedate{April 22, 2009} % Gerry Murray's tracking data \def\docdate {Wednesday 22nd. April 2009} % Gerry Murray (with deltas to doc} \usepackage{epsfig} \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % Need this for accents in Arial/Helvetica %\usepackage[T1]{fontenc} % Gerry March 12, 2007 - causes Type 3 problems (body text) %\usepackage{textcomp} % % SIG-ALT-RELEASE2 DOCUMENT STYLE % G.K.M. Tobin August-October 1999 % adapted from ARTICLE document style by Ken Traub, Olin Shivers % also using elements of esub2acm.cls % HEAVILY MODIFIED, SUBSEQUENTLY, BY GERRY MURRAY 2000 % ARTICLE DOCUMENT STYLE -- Released 16 March 1988 % for LaTeX version 2.09 % Copyright (C) 1988 by Leslie Lamport % % %%% sig-alt-release2.cls is an 'ALTERNATE-RELEASE' document style for producing %%% two-column camera-ready pages for ACM conferences. %%% THIS FILE DOES NOT STRICTLY ADHERE TO THE SIGS (BOARD-ENDORSED) %%% PROCEEDINGS STYLE. It has been designed to produce a 'tighter' %%% paper in response to concerns over page budgets. %%% The main features of this style are: %%% %%% 1) Two columns. %%% 2) Side and top margins of 4.5pc, bottom margin of 6pc, column gutter of %%% 2pc, hence columns are 20pc wide and 55.5pc tall. (6pc =3D 1in, approx) %%% 3) First page has title information, and an extra 6pc of space at the %%% bottom of the first column for the ACM copyright notice. %%% 4) Text is 9pt on 10pt baselines; titles (except main) are 9pt bold. %%% %%% %%% There are a few restrictions you must observe: %%% %%% 1) You cannot change the font size; ACM wants you to use 9pt. %%% 3) You must start your paper with the \maketitle command. Prior to the %%% \maketitle you must have \title and \author commands. If you have a %%% \date command it will be ignored; no date appears on the paper, since %%% the proceedings will have a date on the front cover. %%% 4) Marginal paragraphs, tables of contents, lists of figures and tables, %%% and page headings are all forbidden. %%% 5) The `figure' environment will produce a figure one column wide; if you %%% want one that is two columns wide, use `figure*'. %%% % %%% Copyright Space: %%% This style automatically reserves 1" blank space at the bottom of page 1/ %%% column 1. This space can optionally be filled with some text using the %%% \toappear{...} command. If used, this command must be BEFORE the \maketitle %%% command. If this command is defined AND [preprint] is on, then the %%% space is filled with the {...} text (at the bottom); otherwise, it is %%% blank. If you use \toappearbox{...} instead of \toappear{...} then a %%% box will be drawn around the text (if [preprint] is on). %%% %%% A typical usage looks like this: %%% \toappear{To appear in the Ninth AES Conference on Medievil Lithuanian %%% Embalming Technique, June 1991, Alfaretta, Georgia.} %%% This will be included in the preprint, and left out of the conference %%% version. %%% %%% WARNING: %%% Some dvi-ps converters heuristically allow chars to drift from their %%% true positions a few pixels. This may be noticeable with the 9pt sans-serif %%% bold font used for section headers. %%% You may turn this hackery off via the -e option: %%% dvips -e 0 foo.dvi >foo.ps %%% \typeout{Document Class 'sig-alt-release2' <22nd. April '09>. Modified by G.K.M. Tobin/Gerry Murray} \typeout{Based in part upon document Style `acmconf' <22 May 89>. Hacked 4/91 by} \typeout{shivers@cs.cmu.edu, 4/93 by theobald@cs.mcgill.ca} \typeout{Excerpts were taken from (Journal Style) 'esub2acm.cls'.} \typeout{****** Bugs/comments/suggestions/technicalities to Gerry Murray -- murray@hq.acm.org ******} \typeout{Questions on the style, SIGS policies, etc. to Gerry Murray at ACM murray@acm.org} \oddsidemargin 4.5pc \evensidemargin 4.5pc \advance\oddsidemargin by -1in % Correct for LaTeX gratuitousness \advance\evensidemargin by -1in % Correct for LaTeX gratuitousness \marginparwidth 0pt % Margin pars are not allowed. \marginparsep 11pt % Horizontal space between outer margin and % marginal note % Top of page: \topmargin 4.5pc % Nominal distance from top of page to top of % box containing running head. \advance\topmargin by -1in % Correct for LaTeX gratuitousness \headheight 0pt % Height of box containing running head. \headsep 0pt % Space between running head and text. % Bottom of page: \footskip 30pt % Distance from baseline of box containing foot % to baseline of last line of text. \@ifundefined{footheight}{\newdimen\footheight}{}% this is for LaTeX2e \footheight 12pt % Height of box containing running foot. %% Must redefine the top margin so there's room for headers and %% page numbers if you are using the preprint option. Footers %% are OK as is. Olin. \advance\topmargin by -37pt % Leave 37pt above text for headers \headheight 12pt % Height of box containing running head. \headsep 25pt % Space between running head and text. \textheight 666pt % 9 1/4 column height \textwidth 42pc % Width of text line. % For two-column mode: \columnsep 2pc % Space between columns \columnseprule 0pt % Width of rule between columns. \hfuzz 1pt % Allow some variation in column width, otherwise it's % too hard to typeset in narrow columns. \footnotesep 5.6pt % Height of strut placed at the beginning of every % footnote =3D height of normal \footnotesize strut, % so no extra space between footnotes. \skip\footins 8.1pt plus 4pt minus 2pt % Space between last line of text and % top of first footnote. \floatsep 11pt plus 2pt minus 2pt % Space between adjacent floats moved % to top or bottom of text page. \textfloatsep 18pt plus 2pt minus 4pt % Space between main text and floats % at top or bottom of page. \intextsep 11pt plus 2pt minus 2pt % Space between in-text figures and % text. \@ifundefined{@maxsep}{\newdimen\@maxsep}{}% this is for LaTeX2e \@maxsep 18pt % The maximum of \floatsep, % \textfloatsep and \intextsep (minus % the stretch and shrink). \dblfloatsep 11pt plus 2pt minus 2pt % Same as \floatsep for double-column % figures in two-column mode. \dbltextfloatsep 18pt plus 2pt minus 4pt% \textfloatsep for double-column % floats. \@ifundefined{@dblmaxsep}{\newdimen\@dblmaxsep}{}% this is for LaTeX2e \@dblmaxsep 18pt % The maximum of \dblfloatsep and % \dbltexfloatsep. \@fptop 0pt plus 1fil % Stretch at top of float page/column. (Must be % 0pt plus ...) \@fpsep 8pt plus 2fil % Space between floats on float page/column. \@fpbot 0pt plus 1fil % Stretch at bottom of float page/column. (Must be % 0pt plus ... ) \@dblfptop 0pt plus 1fil % Stretch at top of float page. (Must be 0pt plus ...) \@dblfpsep 8pt plus 2fil % Space between floats on float page. \@dblfpbot 0pt plus 1fil % Stretch at bottom of float page. (Must be % 0pt plus ... ) \marginparpush 5pt % Minimum vertical separation between two marginal % notes. \parskip 0pt plus 1pt % Extra vertical space between paragraphs. \parindent 9pt % GM July 2000 / was 0pt - width of paragraph indentation. \partopsep 2pt plus 1pt minus 1pt% Extra vertical space, in addition to % \parskip and \topsep, added when user % leaves blank line before environment. \@lowpenalty 51 % Produced by \nopagebreak[1] or \nolinebreak[1] \@medpenalty 151 % Produced by \nopagebreak[2] or \nolinebreak[2] \@highpenalty 301 % Produced by \nopagebreak[3] or \nolinebreak[3] \@beginparpenalty -\@lowpenalty % Before a list or paragraph environment. \@endparpenalty -\@lowpenalty % After a list or paragraph environment. \@itempenalty -\@lowpenalty % Between list items. %\@namedef{ds@10pt}{\@latexerr{The `10pt' option is not allowed in the `acmconf' \@namedef{ds@10pt}{\ClassError{The `10pt' option is not allowed in the `acmconf' % January 2008 document style.}\@eha} %\@namedef{ds@11pt}{\@latexerr{The `11pt' option is not allowed in the `acmconf' \@namedef{ds@11pt}{\ClassError{The `11pt' option is not allowed in the `acmconf' % January 2008 document style.}\@eha} %\@namedef{ds@12pt}{\@latexerr{The `12pt' option is not allowed in the `acmconf' \@namedef{ds@12pt}{\ClassError{The `12pt' option is not allowed in the `acmconf' % January 2008 document style.}\@eha} \@options \lineskip 2pt % \lineskip is 1pt for all font sizes. \normallineskip 2pt \def\baselinestretch{1} \abovedisplayskip 9pt plus2pt minus4.5pt% \belowdisplayskip \abovedisplayskip \abovedisplayshortskip \z@ plus3pt% \belowdisplayshortskip 5.4pt plus3pt minus3pt% \let\@listi\@listI % Setting of \@listi added 9 Jun 87 \def\small{\@setsize\small{9pt}\viiipt\@viiipt \abovedisplayskip 7.6pt plus 3pt minus 4pt% \belowdisplayskip \abovedisplayskip \abovedisplayshortskip \z@ plus2pt% \belowdisplayshortskip 3.6pt plus2pt minus 2pt \def\@listi{\leftmargin\leftmargini %% Added 22 Dec 87 \topsep 4pt plus 2pt minus 2pt\parsep 2pt plus 1pt minus 1pt \itemsep \parsep}} \def\footnotesize{\@setsize\footnotesize{9pt}\ixpt\@ixpt \abovedisplayskip 6.4pt plus 2pt minus 4pt% \belowdisplayskip \abovedisplayskip \abovedisplayshortskip \z@ plus 1pt% \belowdisplayshortskip 2.7pt plus 1pt minus 2pt \def\@listi{\leftmargin\leftmargini %% Added 22 Dec 87 \topsep 3pt plus 1pt minus 1pt\parsep 2pt plus 1pt minus 1pt \itemsep \parsep}} \newcount\aucount \newcount\originalaucount \newdimen\auwidth \auwidth=\textwidth \newdimen\auskip \newcount\auskipcount \newdimen\auskip \global\auskip=1pc \newdimen\allauboxes \allauboxes=\auwidth \newtoks\addauthors \newcount\addauflag \global\addauflag=0 %Haven't shown additional authors yet \newtoks\subtitletext \gdef\subtitle#1{\subtitletext={#1}} \gdef\additionalauthors#1{\addauthors={#1}} \gdef\numberofauthors#1{\global\aucount=#1 \ifnum\aucount>3\global\originalaucount=\aucount \global\aucount=3\fi %g} \global\auskipcount=\aucount\global\advance\auskipcount by 1 \global\multiply\auskipcount by 2 \global\multiply\auskip by \auskipcount \global\advance\auwidth by -\auskip \global\divide\auwidth by \aucount} % \and was modified to count the number of authors. GKMT 12 Aug 1999 \def\alignauthor{% % \begin{tabular} \end{tabular}% \begin{tabular}[t]{p{\auwidth}}\centering}% % *** NOTE *** NOTE *** NOTE *** NOTE *** % If you have 'font problems' then you may need % to change these, e.g. 'arialb' instead of "arialbd". % Gerry Murray 11/11/1999 % *** OR ** comment out block A and activate block B or vice versa. % ********************************************** % % -- Start of block A -- (Type 1 or Truetype fonts) %\newfont{\secfnt}{timesbd at 12pt} % was timenrb originally - now is timesbd %\newfont{\secit}{timesbi at 12pt} %13 Jan 00 gkmt %\newfont{\subsecfnt}{timesi at 11pt} % was timenrri originally - now is timesi %\newfont{\subsecit}{timesbi at 11pt} % 13 Jan 00 gkmt -- was times changed to timesbi gm 2/4/2000 % % because "normal" is italic, "italic" is Roman %\newfont{\ttlfnt}{arialbd at 18pt} % was arialb originally - now is arialbd %\newfont{\ttlit}{arialbi at 18pt} % 13 Jan 00 gkmt %\newfont{\subttlfnt}{arial at 14pt} % was arialr originally - now is arial %\newfont{\subttlit}{ariali at 14pt} % 13 Jan 00 gkmt %\newfont{\subttlbf}{arialbd at 14pt} % 13 Jan 00 gkmt %\newfont{\aufnt}{arial at 12pt} % was arialr originally - now is arial %\newfont{\auit}{ariali at 12pt} % 13 Jan 00 gkmt %\newfont{\affaddr}{arial at 10pt} % was arialr originally - now is arial %\newfont{\affaddrit}{ariali at 10pt} %13 Jan 00 gkmt %\newfont{\eaddfnt}{arial at 12pt} % was arialr originally - now is arial %\newfont{\ixpt}{times at 9pt} % was timenrr originally - now is times %\newfont{\confname}{timesi at 8pt} % was timenrri - now is timesi %\newfont{\crnotice}{times at 8pt} % was timenrr originally - now is times %\newfont{\ninept}{times at 9pt} % was timenrr originally - now is times % ********************************************* % -- End of block A -- % % % -- Start of block B -- UPDATED FONT NAMES % ********************************************* % Gerry Murray 11/30/2006 % ********************************************* \newfont{\secfnt}{ptmb8t at 12pt} \newfont{\secit}{ptmbi8t at 12pt} %13 Jan 00 gkmt \newfont{\subsecfnt}{ptmri8t at 11pt} \newfont{\subsecit}{ptmbi8t at 11pt} % \newfont{\ttlfnt}{phvb8t at 18pt} \newfont{\ttlit}{phvbo8t at 18pt} % GM 2/4/2000 \newfont{\subttlfnt}{phvr8t at 14pt} \newfont{\subttlit}{phvro8t at 14pt} % GM 2/4/2000 \newfont{\subttlbf}{phvb8t at 14pt} % 13 Jan 00 gkmt \newfont{\aufnt}{phvr8t at 12pt} \newfont{\auit}{phvro8t at 12pt} % GM 2/4/2000 \newfont{\affaddr}{phvr8t at 10pt} \newfont{\affaddrit}{phvro8t at 10pt} % GM 2/4/2000 \newfont{\eaddfnt}{phvr8t at 12pt} \newfont{\ixpt}{ptmr8t at 9pt} \newfont{\confname}{ptmri8t at 8pt} \newfont{\crnotice}{ptmr8t at 8pt} \newfont{\ninept}{ptmr8t at 9pt} % +++++++++++++++++++++++++++++++++++++++++++++ % -- End of block B -- %\def\email#1{{{\eaddfnt{\vskip 4pt#1}}}} % If we have an email, inside a "shared affiliation" then we need the following instead \def\email#1{{{\eaddfnt{\par #1}}}} % revised - GM - 11/30/2006 \def\addauthorsection{\ifnum\originalaucount>6 % was 3 - Gerry March 2007 \section{Additional Authors}\the\addauthors \fi} \newcount\savesection \newcount\sectioncntr \global\sectioncntr=1 \setcounter{secnumdepth}{3} \def\appendix{\par \section*{APPENDIX} \setcounter{section}{0} \setcounter{subsection}{0} \def\thesection{\Alph{section}} } \leftmargini 22.5pt \leftmarginii 19.8pt % > \labelsep + width of '(m)' \leftmarginiii 16.8pt % > \labelsep + width of 'vii.' \leftmarginiv 15.3pt % > \labelsep + width of 'M.' \leftmarginv 9pt \leftmarginvi 9pt \leftmargin\leftmargini \labelsep 4.5pt \labelwidth\leftmargini\advance\labelwidth-\labelsep \def\@listI{\leftmargin\leftmargini \parsep 3.6pt plus 2pt minus 1pt% \topsep 7.2pt plus 2pt minus 4pt% \itemsep 3.6pt plus 2pt minus 1pt} \let\@listi\@listI \@listi \def\@listii{\leftmargin\leftmarginii \labelwidth\leftmarginii\advance\labelwidth-\labelsep \topsep 3.6pt plus 2pt minus 1pt \parsep 1.8pt plus 0.9pt minus 0.9pt \itemsep \parsep} \def\@listiii{\leftmargin\leftmarginiii \labelwidth\leftmarginiii\advance\labelwidth-\labelsep \topsep 1.8pt plus 0.9pt minus 0.9pt \parsep \z@ \partopsep 1pt plus 0pt minus 1pt \itemsep \topsep} \def\@listiv{\leftmargin\leftmarginiv \labelwidth\leftmarginiv\advance\labelwidth-\labelsep} \def\@listv{\leftmargin\leftmarginv \labelwidth\leftmarginv\advance\labelwidth-\labelsep} \def\@listvi{\leftmargin\leftmarginvi \labelwidth\leftmarginvi\advance\labelwidth-\labelsep} \def\labelenumi{\theenumi.} \def\theenumi{\arabic{enumi}} \def\labelenumii{(\theenumii)} \def\theenumii{\alph{enumii}} \def\p@enumii{\theenumi} \def\labelenumiii{\theenumiii.} \def\theenumiii{\roman{enumiii}} \def\p@enumiii{\theenumi(\theenumii)} \def\labelenumiv{\theenumiv.} \def\theenumiv{\Alph{enumiv}} \def\p@enumiv{\p@enumiii\theenumiii} \def\labelitemi{$\bullet$} \def\labelitemii{\bf --} \def\labelitemiii{$\ast$} \def\labelitemiv{$\cdot$} \def\verse{\let\\=\@centercr \list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]} \let\endverse\endlist \def\quotation{\list{}{\listparindent 1.5em \itemindent\listparindent \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]} \let\endquotation=\endlist \def\quote{\list{}{\rightmargin\leftmargin}\item[]} \let\endquote=\endlist \def\descriptionlabel#1{\hspace\labelsep \bf #1} \def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin \let\makelabel\descriptionlabel}} \let\enddescription\endlist \def\theequation{\arabic{equation}} \arraycolsep 4.5pt % Half the space between columns in an array environment. \tabcolsep 5.4pt % Half the space between columns in a tabular environment. \arrayrulewidth .5pt % Width of rules in array and tabular environment. % (was .4) updated Gerry March 20 2007 \doublerulesep 1.8pt % Space between adjacent rules in array or tabular env. \tabbingsep \labelsep % Space used by the \' command. (See LaTeX manual.) \skip\@mpfootins =\skip\footins \fboxsep =2.7pt % Space left between box and text by \fbox and \framebox. \fboxrule =.5pt % Width of rules in box made by \fbox and \framebox. % (was .4) updated Gerry March 20 2007 \def\thepart{\Roman{part}} % Roman numeral part numbers. \def\thesection {\arabic{section}} \def\thesubsection {\thesection.\arabic{subsection}} %\def\thesubsubsection {\thesubsection.\arabic{subsubsection}} % GM 7/30/2002 %\def\theparagraph {\thesubsubsection.\arabic{paragraph}} % GM 7/30/2002 \def\thesubparagraph {\theparagraph.\arabic{subparagraph}} \def\@pnumwidth{1.55em} \def\@tocrmarg {2.55em} \def\@dotsep{4.5} \setcounter{tocdepth}{3} %\def\tableofcontents{\@latexerr{\tableofcontents: Tables of contents are not % allowed in the `acmconf' document style.}\@eha} \def\tableofcontents{\ClassError{% \string\tableofcontents\space is not allowed in the `acmconf' document % January 2008 style}\@eha} \def\l@part#1#2{\addpenalty{\@secpenalty} \addvspace{2.25em plus 1pt} % space above part line \begingroup \@tempdima 3em % width of box holding part number, used by \parindent \z@ \rightskip \@pnumwidth %% \numberline \parfillskip -\@pnumwidth {\large \bf % set line in \large boldface \leavevmode % TeX command to enter horizontal mode. #1\hfil \hbox to\@pnumwidth{\hss #2}}\par \nobreak % Never break after part entry \endgroup} \def\l@section#1#2{\addpenalty{\@secpenalty} % good place for page break \addvspace{1.0em plus 1pt} % space above toc entry \@tempdima 1.5em % width of box holding section number \begingroup \parindent \z@ \rightskip \@pnumwidth \parfillskip -\@pnumwidth \bf % Boldface. \leavevmode % TeX command to enter horizontal mode. \advance\leftskip\@tempdima %% added 5 Feb 88 to conform to \hskip -\leftskip %% 25 Jan 88 change to \numberline #1\nobreak\hfil \nobreak\hbox to\@pnumwidth{\hss #2}\par \endgroup} \def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}} \def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}} \def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}} \def\l@subparagraph{\@dottedtocline{5}{10em}{5em}} %\def\listoffigures{\@latexerr{\listoffigures: Lists of figures are not % allowed in the `acmconf' document style.}\@eha} \def\listoffigures{\ClassError{% \string\listoffigures\space is not allowed in the `acmconf' document % January 2008 style}\@eha} \def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}} %\def\listoftables{\@latexerr{\listoftables: Lists of tables are not % allowed in the `acmconf' document style.}\@eha} %\let\l@table\l@figure \def\listoftables{\ClassError{% \string\listoftables\space is not allowed in the `acmconf' document % January 2008 style}\@eha} \let\l@table\l@figure \def\footnoterule{\kern-3\p@ \hrule width .5\columnwidth % (was .4) updated Gerry March 20 2007 \kern 2.6\p@} % The \hrule has default height of .4pt % (was .4) updated Gerry March 20 2007 % ------ \long\def\@makefntext#1{\noindent %\hbox to .5em{\hss$^{\@thefnmark}$}#1} % original \hbox to .5em{\hss\textsuperscript{\@thefnmark}}#1} % C. Clifton / GM Oct. 2nd. 2002 % ------- \long\def\@maketntext#1{\noindent #1} \long\def\@maketitlenotetext#1#2{\noindent \hbox to 1.8em{\hss$^{#1}$}#2} \setcounter{topnumber}{2} \def\topfraction{.7} \setcounter{bottomnumber}{1} \def\bottomfraction{.3} \setcounter{totalnumber}{3} \def\textfraction{.2} \def\floatpagefraction{.5} \setcounter{dbltopnumber}{2} \def\dbltopfraction{.7} \def\dblfloatpagefraction{.5} % \long\def\@makecaption#1#2{ \vskip \baselineskip \setbox\@tempboxa\hbox{\textbf{#1: #2}} \ifdim \wd\@tempboxa >\hsize % IF longer than one line: \textbf{#1: #2}\par % THEN set as ordinary paragraph. \else % ELSE center. \hbox to\hsize{\hfil\box\@tempboxa\hfil}\par \fi} % \long\def\@makecaption#1#2{ \vskip 10pt \setbox\@tempboxa\hbox{\textbf{#1: #2}} \ifdim \wd\@tempboxa >\hsize % IF longer than one line: \textbf{#1: #2}\par % THEN set as ordinary paragraph. \else % ELSE center. \hbox to\hsize{\hfil\box\@tempboxa\hfil} \fi} \@ifundefined{figure}{\newcounter {figure}} % this is for LaTeX2e \def\fps@figure{tbp} \def\ftype@figure{1} \def\ext@figure{lof} \def\fnum@figure{Figure \thefigure} \def\figure{\@float{figure}} %\let\endfigure\end@float \def\endfigure{\end@float} % Gerry January 2008 \@namedef{figure*}{\@dblfloat{figure}} \@namedef{endfigure*}{\end@dblfloat} \@ifundefined{table}{\newcounter {table}} % this is for LaTeX2e \def\fps@table{tbp} \def\ftype@table{2} \def\ext@table{lot} \def\fnum@table{Table \thetable} \def\table{\@float{table}} %\let\endtable\end@float \def\endtable{\end@float} % Gerry January 2008 \@namedef{table*}{\@dblfloat{table}} \@namedef{endtable*}{\end@dblfloat} \newtoks\titleboxnotes \newcount\titleboxnoteflag \def\maketitle{\par \begingroup \def\thefootnote{\fnsymbol{footnote}} \def\@makefnmark{\hbox to 0pt{$^{\@thefnmark}$\hss}} \twocolumn[\@maketitle] \@thanks \endgroup \setcounter{footnote}{0} \let\maketitle\relax \let\@maketitle\relax \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\gdef\@subtitle{}\let\thanks\relax \@copyrightspace} %% CHANGES ON NEXT LINES \newif\if@ll % to record which version of LaTeX is in use \expandafter\ifx\csname LaTeXe\endcsname\relax % LaTeX2.09 is used \else% LaTeX2e is used, so set ll to true \global\@lltrue \fi \if@ll \NeedsTeXFormat{LaTeX2e} \ProvidesClass{sig-alt-release2} [2009/04/22 - V1.6 - based on acmproc.cls V1.3 <Nov. 30 '99>] \RequirePackage{latexsym}% QUERY: are these two really needed? \let\dooptions\ProcessOptions \else \let\dooptions\@options \fi %% END CHANGES \def\@height{height} \def\@width{width} \def\@minus{minus} \def\@plus{plus} \def\hb@xt@{\hbox to} \newif\if@faircopy \@faircopyfalse \def\ds@faircopy{\@faircopytrue} \def\ds@preprint{\@faircopyfalse} \@twosidetrue \@mparswitchtrue \def\ds@draft{\overfullrule 5\p@} %% CHANGE ON NEXT LINE \dooptions \lineskip \p@ \normallineskip \p@ \def\baselinestretch{1} \def\@ptsize{0} %needed for amssymbols.sty %% CHANGES ON NEXT LINES \if@ll% allow use of old-style font change commands in LaTeX2e \@maxdepth\maxdepth % \DeclareOldFontCommand{\rm}{\ninept\rmfamily}{\mathrm} \DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} \DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} \DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} \DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} \DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl} \DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc} \DeclareRobustCommand*{\cal}{\@fontswitch{\relax}{\mathcal}} \DeclareRobustCommand*{\mit}{\@fontswitch{\relax}{\mathnormal}} \fi % \if@ll \renewcommand{\rmdefault}{cmr} % was 'ttm' % Note! I have also found 'mvr' to work ESPECIALLY well. % Gerry - October 1999 % You may need to change your LV1times.fd file so that sc is % mapped to cmcsc - -for smallcaps -- that is if you decide % to change {cmr} to {times} above. (Not recommended) \renewcommand{\@ptsize}{} \renewcommand{\normalsize}{% \@setfontsize\normalsize\@ixpt{10.5\p@}%\ninept% \abovedisplayskip 6\p@ \@plus2\p@ \@minus\p@ \belowdisplayskip \abovedisplayskip \abovedisplayshortskip 6\p@ \@minus 3\p@ \belowdisplayshortskip 6\p@ \@minus 3\p@ \let\@listi\@listI } \else \def\@normalsize{%changed next to 9 from 10 \@setsize\normalsize{9\p@}\ixpt\@ixpt \abovedisplayskip 6\p@ \@plus2\p@ \@minus\p@ \belowdisplayskip \abovedisplayskip \abovedisplayshortskip 6\p@ \@minus 3\p@ \belowdisplayshortskip 6\p@ \@minus 3\p@ \let\@listi\@listI }% \fi \if@ll \newcommand\scriptsize{\@setfontsize\scriptsize\@viipt{8\p@}} \newcommand\tiny{\@setfontsize\tiny\@vpt{6\p@}} \newcommand\large{\@setfontsize\large\@xiipt{14\p@}} \newcommand\Large{\@setfontsize\Large\@xivpt{18\p@}} \newcommand\LARGE{\@setfontsize\LARGE\@xviipt{20\p@}} \newcommand\huge{\@setfontsize\huge\@xxpt{25\p@}} \newcommand\Huge{\@setfontsize\Huge\@xxvpt{30\p@}} \else \def\scriptsize{\@setsize\scriptsize{8\p@}\viipt\@viipt} \def\tiny{\@setsize\tiny{6\p@}\vpt\@vpt} \def\large{\@setsize\large{14\p@}\xiipt\@xiipt} \def\Large{\@setsize\Large{18\p@}\xivpt\@xivpt} \def\LARGE{\@setsize\LARGE{20\p@}\xviipt\@xviipt} \def\huge{\@setsize\huge{25\p@}\xxpt\@xxpt} \def\Huge{\@setsize\Huge{30\p@}\xxvpt\@xxvpt} \fi \normalsize % make aubox hsize/number of authors up to 3, less gutter % then showbox gutter showbox gutter showbox -- GKMT Aug 99 \newbox\@acmtitlebox \def\@maketitle{\newpage \null \setbox\@acmtitlebox\vbox{% \baselineskip 20pt \vskip 2em % Vertical space above title. \begin{center} {\ttlfnt \@title\par} % Title set in 18pt Helvetica (Arial) bold size. \vskip 1.5em % Vertical space after title. %This should be the subtitle. {\subttlfnt \the\subtitletext\par}\vskip 1.25em%\fi {\baselineskip 16pt\aufnt % each author set in \12 pt Arial, in a \lineskip .5em % tabular environment \begin{tabular}[t]{c}\@author \end{tabular}\par} \vskip 1.5em % Vertical space after author. \end{center}} \dimen0=\ht\@acmtitlebox \advance\dimen0 by -12.75pc\relax % Increased space for title box -- KBT \unvbox\@acmtitlebox \ifdim\dimen0<0.0pt\relax\vskip-\dimen0\fi} \newcount\titlenotecount \global\titlenotecount=0 \newtoks\tntoks \newtoks\tntokstwo \newtoks\tntoksthree \newtoks\tntoksfour \newtoks\tntoksfive \def\abstract{ \ifnum\titlenotecount>0 % was =1 \insert\footins{% \reset@font\footnotesize \interlinepenalty\interfootnotelinepenalty \splittopskip\footnotesep \splitmaxdepth \dp\strutbox \floatingpenalty \@MM \hsize\columnwidth \@parboxrestore \protected@edef\@currentlabel{% }% \color@begingroup \ifnum\titlenotecount=1 \@maketntext{% \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\@finalstrut\strutbox}% \fi \ifnum\titlenotecount=2 \@maketntext{% \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\@finalstrut\strutbox}% \fi \ifnum\titlenotecount=3 \@maketntext{% \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\@finalstrut\strutbox}% \fi \ifnum\titlenotecount=4 \@maketntext{% \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\S$}\rule\z@\footnotesep\ignorespaces\the\tntoksfour\@finalstrut\strutbox}% \fi \ifnum\titlenotecount=5 \@maketntext{% \raisebox{4pt}{$\ast$}\rule\z@\footnotesep\ignorespaces\the\tntoks\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\dagger$}\rule\z@\footnotesep\ignorespaces\the\tntokstwo\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\ddagger$}\rule\z@\footnotesep\ignorespaces\the\tntoksthree\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\S$}\rule\z@\footnotesep\ignorespaces\the\tntoksfour\par\@finalstrut\strutbox}% \@maketntext{% \raisebox{4pt}{$\P$}\rule\z@\footnotesep\ignorespaces\the\tntoksfive\@finalstrut\strutbox}% \fi \color@endgroup} %g} \fi \setcounter{footnote}{0} \section*{ABSTRACT}\normalsize%\ninept } \def\endabstract{\if@twocolumn\else\endquotation\fi} \def\keywords{\if@twocolumn \section*{Keywords} \else \small \quotation \fi} \def\terms{\if@twocolumn \section*{General Terms} \else \small \quotation \fi} % -- Classification needs to be a bit smart due to optionals - Gerry/Georgia November 2nd. 1999 \newcount\catcount \global\catcount=1 \def\category#1#2#3{% \ifnum\catcount=1 \section*{Categories and Subject Descriptors} \advance\catcount by 1\else{\unskip; }\fi \@ifnextchar [{\@category{#1}{#2}{#3}}{\@category{#1}{#2}{#3}[]}% } \def\@category#1#2#3[#4]{% \begingroup \let\and\relax #1 [\textbf{#2}]% \if!#4!% \if!#3!\else : #3\fi \else :\space \if!#3!\else #3\kern\z@---\hskip\z@\fi \textit{#4}% \fi \endgroup } % %%% This section (written by KBT) handles the 1" box in the lower left %%% corner of the left column of the first page by creating a picture, %%% and inserting the predefined string at the bottom (with a negative %%% displacement to offset the space allocated for a non-existent %%% caption). %%% \newtoks\copyrightnotice \def\ftype@copyrightbox{8} \def\@copyrightspace{ \@float{copyrightbox}[b] \begin{center} \setlength{\unitlength}{1pc} %\begin{picture}(20,6) %Space for copyright notice \begin{picture}(20,1) %Space for copyright notice \put(0,-0.95){\crnotice{\@toappear}} \end{picture} \end{center} \end@float} \def\@toappear{} % Default setting blank - commands below change this. \long\def\toappear#1{\def\@toappear{\parbox[b]{20pc}{\baselineskip 9pt#1}}} \def\toappearbox#1{\def\@toappear{\raisebox{5pt}{\framebox[20pc]{\parbox[b]{19pc}{#1}}}}} \newtoks\conf \newtoks\confinfo \def\conferenceinfo#1#2{\global\conf={#1}\global\confinfo{#2}} %\def\marginpar{\@latexerr{The \marginpar command is not allowed in the % `acmconf' document style.}\@eha} \def\marginpar{\ClassError{% \string\marginpar\space is not allowed in the `acmconf' document % January 2008 style}\@eha} \mark{{}{}} % Initializes TeX's marks \def\today{\ifcase\month\or January\or February\or March\or April\or May\or June\or July\or August\or September\or October\or November\or December\fi \space\number\day, \number\year} \def\@begintheorem#1#2{% \parskip 0pt % GM July 2000 (for tighter spacing) \trivlist \item[% \hskip 10\p@ \hskip \labelsep {{\sc #1}\hskip 5\p@\relax#2.}% ] \it } \def\@opargbegintheorem#1#2#3{% \parskip 0pt % GM July 2000 (for tighter spacing) \trivlist \item[% \hskip 10\p@ \hskip \labelsep {\sc #1\ #2\ % This mod by Gerry to enumerate corollaries \setbox\@tempboxa\hbox{(#3)} % and bracket the 'corollary title' \ifdim \wd\@tempboxa>\z@ % and retain the correct numbering of e.g. theorems \hskip 5\p@\relax % if they occur 'around' said corollaries. \box\@tempboxa % Gerry - Nov. 1999. \fi.}% ] \it } \newif\if@qeded \global\@qededfalse % -- original %\def\proof{% % \vspace{-\parskip} % GM July 2000 (for tighter spacing) % \global\@qededfalse % \@ifnextchar[{\@xproof}{\@proof}% %} % -- end of original % (JSS) Fix for vertical spacing bug - Gerry Murray July 30th. 2002 \def\proof{% \vspace{-\lastskip}\vspace{-\parsep}\penalty-51% \global\@qededfalse \@ifnextchar[{\@xproof}{\@proof}% } \def\endproof{% \if@qeded\else\qed\fi \endtrivlist } \def\@proof{% \trivlist \item[% \hskip 10\p@ \hskip \labelsep {\sc Proof.}% ] \ignorespaces } \def\@xproof[#1]{% \trivlist \item[\hskip 10\p@\hskip \labelsep{\sc Proof #1.}]% \ignorespaces } \def\qed{% \unskip \kern 10\p@ \begingroup \unitlength\p@ \linethickness{.4\p@}% \framebox(6,6){}% \endgroup \global\@qededtrue } \def\newdef#1#2{% \expandafter\@ifdefinable\csname #1\endcsname {\@definecounter{#1}% \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}% \global\@namedef{#1}{\@defthm{#1}{#2}}% \global\@namedef{end#1}{\@endtheorem}% }% } \def\@defthm#1#2{% \refstepcounter{#1}% \@ifnextchar[{\@ydefthm{#1}{#2}}{\@xdefthm{#1}{#2}}% } \def\@xdefthm#1#2{% \@begindef{#2}{\csname the#1\endcsname}% \ignorespaces } \def\@ydefthm#1#2[#3]{% \trivlist \item[% \hskip 10\p@ \hskip \labelsep {\it #2% % \savebox\@tempboxa{#3}% \saveb@x\@tempboxa{#3}% % January 2008 \ifdim \wd\@tempboxa>\z@ \ \box\@tempboxa \fi.% }]% \ignorespaces } \def\@begindef#1#2{% \trivlist \item[% \hskip 10\p@ \hskip \labelsep {\it #1\ \rm #2.}% ]% } \def\theequation{\arabic{equation}} \newcounter{part} \newcounter{section} \newcounter{subsection}[section] \newcounter{subsubsection}[subsection] \newcounter{paragraph}[subsubsection] \def\thepart{\Roman{part}} \def\thesection{\arabic{section}} \def\thesubsection{\thesection.\arabic{subsection}} \def\thesubsubsection{\thesubsection.\arabic{subsubsection}} %removed \subsecfnt 29 July 2002 gkmt \def\theparagraph{\thesubsubsection.\arabic{paragraph}} %removed \subsecfnt 29 July 2002 gkmt \newif\if@uchead \@ucheadfalse %% CHANGES: NEW NOTE %% NOTE: OK to use old-style font commands below, since they were %% suitably redefined for LaTeX2e %% END CHANGES \setcounter{secnumdepth}{3} \def\part{% \@startsection{part}{9}{\z@}{-10\p@ \@plus -4\p@ \@minus -2\p@} {4\p@}{\normalsize\@ucheadtrue}% } \def\section{% \@startsection{section}{1}{\z@}{-10\p@ \@plus -4\p@ \@minus -2\p@}% GM {4\p@}{\baselineskip 14pt\secfnt\@ucheadtrue}% } \def\subsection{% \@startsection{subsection}{2}{\z@}{-8\p@ \@plus -2\p@ \@minus -\p@} {4\p@}{\secfnt}% } \def\subsubsection{% \@startsection{subsubsection}{3}{\z@}{-8\p@ \@plus -2\p@ \@minus -\p@}% {4\p@}{\subsecfnt}% } %\def\paragraph{% % \vskip 12pt\@startsection{paragraph}{3}{\z@}{6\p@ \@plus \p@}% original % {-5\p@}{\subsecfnt}% %} % If one wants sections, subsections and subsubsections numbered, % but not paragraphs, one usually sets secnumepth to 3. % For that, the "depth" of paragraphs must be given correctly % in the definition (``4'' instead of ``3'' as second argument % of @startsection): \def\paragraph{% \vskip 12pt\@startsection{paragraph}{4}{\z@}{6\p@ \@plus \p@}% % GM and Wolfgang May - 11/30/06 {-5\p@}{\subsecfnt}% } \let\@period=. \def\@startsection#1#2#3#4#5#6{% \if@noskipsec %gkmt, 11 aug 99 \global\let\@period\@empty \leavevmode \global\let\@period.% \fi \par % \@tempskipa #4\relax \@afterindenttrue \ifdim \@tempskipa <\z@ \@tempskipa -\@tempskipa \@afterindentfalse \fi \if@nobreak \everypar{}% \else \addpenalty\@secpenalty \addvspace\@tempskipa \fi \parskip=0pt % GM July 2000 (non numbered) section heads \@ifstar {\@ssect{#3}{#4}{#5}{#6}} {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}% } \def\@sect#1#2#3#4#5#6[#7]#8{% \ifnum #2>\c@secnumdepth \let\@svsec\@empty \else \refstepcounter{#1}% \edef\@svsec{% \begingroup %\ifnum#2>2 \noexpand\rm \fi % changed to next 29 July 2002 gkmt \ifnum#2>2 \noexpand#6 \fi \csname the#1\endcsname \endgroup \ifnum #2=1\relax .\fi \hskip 1em }% \fi \@tempskipa #5\relax \ifdim \@tempskipa>\z@ \begingroup #6\relax \@hangfrom{\hskip #3\relax\@svsec}% \begingroup \interlinepenalty \@M \if@uchead \uppercase{#8}% \else #8% \fi \par \endgroup \endgroup \csname #1mark\endcsname{#7}% \vskip -12pt %gkmt, 11 aug 99 and GM July 2000 (was -14) - numbered section head spacing \addcontentsline{toc}{#1}{% \ifnum #2>\c@secnumdepth \else \protect\numberline{\csname the#1\endcsname}% \fi #7% }% \else \def\@svsechd{% #6% \hskip #3\relax \@svsec \if@uchead \uppercase{#8}% \else #8% \fi \csname #1mark\endcsname{#7}% \addcontentsline{toc}{#1}{% \ifnum #2>\c@secnumdepth \else \protect\numberline{\csname the#1\endcsname}% \fi #7% }% }% \fi \@xsect{#5}\hskip 1pt \par } \def\@xsect#1{% \@tempskipa #1\relax \ifdim \@tempskipa>\z@ \par \nobreak \vskip \@tempskipa \@afterheading \else \global\@nobreakfalse \global\@noskipsectrue \everypar{% \if@noskipsec \global\@noskipsecfalse \clubpenalty\@M \hskip -\parindent \begingroup \@svsechd \@period \endgroup \unskip \@tempskipa #1\relax \hskip -\@tempskipa \else \clubpenalty \@clubpenalty \everypar{}% \fi }% \fi \ignorespaces } \def\@trivlist{% \@topsepadd\topsep \if@noskipsec \global\let\@period\@empty \leavevmode \global\let\@period.% \fi \ifvmode \advance\@topsepadd\partopsep \else \unskip \par \fi \if@inlabel \@noparitemtrue \@noparlisttrue \else \@noparlistfalse \@topsep\@topsepadd \fi \advance\@topsep \parskip \leftskip\z@skip \rightskip\@rightskip \parfillskip\@flushglue \@setpar{\if@newlist\else{\@@par}\fi} \global\@newlisttrue \@outerparskip\parskip } %%% Actually, 'abbrev' works just fine as the default %%% Bibliography style. \typeout{Using 'Abbrev' bibliography style} \newcommand\bibyear[2]{% \unskip\quad\ignorespaces#1\unskip \if#2..\quad \else \quad#2 \fi } \newcommand{\bibemph}[1]{{\em#1}} \newcommand{\bibemphic}[1]{{\em#1\/}} \newcommand{\bibsc}[1]{{\sc#1}} \def\@normalcite{% \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}% } \def\@citeNB{% \def\@cite##1##2{##1\if@tempswa , ##2\fi}% } \def\@citeRB{% \def\@cite##1##2{##1\if@tempswa , ##2\fi]}% } \def\start@cite#1#2{% \edef\citeauthoryear##1##2##3{% ###1% \ifnum#2=\z@ \else\ ###2\fi }% \ifnum#1=\thr@@ \let\@@cite\@citeyear \else \let\@@cite\@citenormal \fi \@ifstar{\@citeNB\@@cite}{\@normalcite\@@cite}% } %\def\cite{\start@cite23} \DeclareRobustCommand\cite{\start@cite23} % January 2008 \def\citeNP{\cite*} % No Parentheses e.g. 5 %\def\citeA{\start@cite10} \DeclareRobustCommand\citeA{\start@cite10} % January 2008 \def\citeANP{\citeA*} %\def\shortcite{\start@cite23} \DeclareRobustCommand\shortcite{\start@cite23} % January 2008 \def\shortciteNP{\shortcite*} %\def\shortciteA{\start@cite20} \DeclareRobustCommand\shortciteA{\start@cite20} % January 2008 \def\shortciteANP{\shortciteA*} %\def\citeyear{\start@cite30} \DeclareRobustCommand\citeyear{\start@cite30} % January 2008 \def\citeyearNP{\citeyear*} %\def\citeN{% \DeclareRobustCommand\citeN{% % January 2008 \@citeRB \def\citeauthoryear##1##2##3{##1\ [##3% \def\reserved@a{##1}% \def\citeauthoryear####1####2####3{% \def\reserved@b{####1}% \ifx\reserved@a\reserved@b ####3% \else \errmessage{Package acmart Error: author mismatch in \string\citeN^^J^^J% See the acmart package documentation for explanation}% \fi }% }% \@ifstar\@citeyear\@citeyear } %\def\shortciteN{% \DeclareRobustCommand\shortciteN{% % January 2008 \@citeRB \def\citeauthoryear##1##2##3{##2\ [##3% \def\reserved@a{##2}% \def\citeauthoryear####1####2####3{% \def\reserved@b{####2}% \ifx\reserved@a\reserved@b ####3% \else \errmessage{Package acmart Error: author mismatch in \string\shortciteN^^J^^J% See the acmart package documentation for explanation}% \fi }% }% \@ifstar\@citeyear\@citeyear % GM July 2000 } \def\@citenormal{% \@ifnextchar [{\@tempswatrue\@citex;}% % original {\@tempswafalse\@citex,[]}% was ; Gerry 2/24/00 {\@tempswafalse\@citex[]}% % GERRY FIX FOR BABEL 3/20/2009 } \def\@citeyear{% \@ifnextchar [{\@tempswatrue\@citex,}% % original {\@tempswafalse\@citex,[]}% {\@tempswafalse\@citex[]}% % GERRY FIX FOR BABEL 3/20/2009 } \def\@citex#1[#2]#3{% \let\@citea\@empty \@cite{% \@for\@citeb:=#3\do{% \@citea % original \def\@citea{#1 }% \def\@citea{#1, }% % GERRY FIX FOR BABEL 3/20/2009 -- SO THAT YOU GET [1, 2] IN THE BODY TEXT \edef\@citeb{\expandafter\@iden\@citeb}% \if@filesw \immediate\write\@auxout{\string\citation{\@citeb}}% \fi \@ifundefined{b@\@citeb}{% {\bf ?}% \@warning{% Citation `\@citeb' on page \thepage\space undefined% }% }% {\csname b@\@citeb\endcsname}% }% }{#2}% } %\let\@biblabel\@gobble % Dec. 2008 - Gerry % ---- \def\@biblabelnum#1{[#1]} % Gerry's solution #1 - for Natbib -- April 2009 \let\@biblabel=\@biblabelnum % Gerry's solution #1 - for Natbib -- April 2009 \def\newblock{\relax} % Gerry Dec. 2008 % --- \newdimen\bibindent \setcounter{enumi}{1} \bibindent=0em \def\thebibliography#1{% \ifnum\addauflag=0\addauthorsection\global\addauflag=1\fi \section[References]{% <=== OPTIONAL ARGUMENT ADDED HERE {References} % was uppercased but this affects pdf bookmarks (SP/GM October 2004) {\vskip -9pt plus 1pt} % GM Nov. 2006 / GM July 2000 (for somewhat tighter spacing) \@mkboth{{\refname}}{{\refname}}% }% \list{[\arabic{enumi}]}{% \settowidth\labelwidth{[#1]}% \leftmargin\labelwidth \advance\leftmargin\labelsep \advance\leftmargin\bibindent \parsep=0pt\itemsep=1pt % GM July 2000 \itemindent -\bibindent \listparindent \itemindent \usecounter{enumi} }% \let\newblock\@empty \raggedright % GM July 2000 \sloppy \sfcode`\.=1000\relax } \gdef\balancecolumns {\vfill\eject \global\@colht=\textheight \global\ht\@cclv=\textheight } \newcount\colcntr \global\colcntr=0 %\newbox\savebox \newbox\saveb@x % January 2008 \gdef \@makecol {% \global\advance\colcntr by 1 \ifnum\colcntr>2 \global\colcntr=1\fi \ifvoid\footins \setbox\@outputbox \box\@cclv \else \setbox\@outputbox \vbox{% \boxmaxdepth \@maxdepth \@tempdima\dp\@cclv \unvbox \@cclv \vskip-\@tempdima \vskip \skip\footins \color@begingroup \normalcolor \footnoterule \unvbox \footins \color@endgroup }% \fi \xdef\@freelist{\@freelist\@midlist}% \global \let \@midlist \@empty \@combinefloats \ifvbox\@kludgeins \@makespecialcolbox \else \setbox\@outputbox \vbox to\@colht {% \@texttop \dimen@ \dp\@outputbox \unvbox \@outputbox \vskip -\dimen@ \@textbottom }% \fi \global \maxdepth \@maxdepth } \def\titlenote{\@ifnextchar[\@xtitlenote{\stepcounter\@mpfn \global\advance\titlenotecount by 1 \ifnum\titlenotecount=1 \raisebox{9pt}{$\ast$} \fi \ifnum\titlenotecount=2 \raisebox{9pt}{$\dagger$} \fi \ifnum\titlenotecount=3 \raisebox{9pt}{$\ddagger$} \fi \ifnum\titlenotecount=4 \raisebox{9pt}{$\S$} \fi \ifnum\titlenotecount=5 \raisebox{9pt}{$\P$} \fi \@titlenotetext }} \long\def\@titlenotetext#1{\insert\footins{% \ifnum\titlenotecount=1\global\tntoks={#1}\fi \ifnum\titlenotecount=2\global\tntokstwo={#1}\fi \ifnum\titlenotecount=3\global\tntoksthree={#1}\fi \ifnum\titlenotecount=4\global\tntoksfour={#1}\fi \ifnum\titlenotecount=5\global\tntoksfive={#1}\fi \reset@font\footnotesize \interlinepenalty\interfootnotelinepenalty \splittopskip\footnotesep \splitmaxdepth \dp\strutbox \floatingpenalty \@MM \hsize\columnwidth \@parboxrestore \protected@edef\@currentlabel{% }% \color@begingroup \color@endgroup}} %%%%%%%%%%%%%%%%%%%%%%%%% \ps@plain \baselineskip=11pt \let\thepage\relax % For NO page numbers - GM Nov. 30th. 1999 and July 2000 \def\setpagenumber#1{\global\setcounter{page}{#1}} %\pagenumbering{arabic} % Arabic page numbers GM July 2000 \twocolumn % Double column. \flushbottom % Even bottom -- alas, does not balance columns at end of document \pagestyle{plain} % Need Copyright Year and Copyright Data to be user definable (in .tex file). % Gerry Nov. 30th. 1999 \newtoks\copyrtyr \newtoks\acmcopyr \newtoks\boilerplate \global\acmcopyr={}%X-XXXXX-XX-X/XX/XX} % Default - 5/11/2001 *** Gerry \global\copyrtyr={200X} % Default - 3/3/2003 *** Gerry \def\CopyrightYear#1{\global\copyrtyr{#1}} \def\crdata#1{\global\acmcopyr{#1}} \def\permission#1{\global\boilerplate{#1}} % \global\boilerplate={}%Copyright is held by the author/owner(s).} \newtoks\copyrightetc \global\copyrightetc{}%ACM \the\acmcopyr} \toappear{\the\boilerplate\par {\confname{\the\conf}} \the\confinfo\par \the\copyrightetc.} %\DeclareFixedFont{\altcrnotice}{OT1}{tmr}{m}{n}{8} % << patch needed for accenting e.g. Montreal - Gerry, May 2007 %\DeclareFixedFont{\altconfname}{OT1}{tmr}{m}{it}{8} % << patch needed for accenting in italicized confname - Gerry, May 2007 % %{\altconfname{{\the\conf}}} {\altcrnotice\the\confinfo\par} \the\copyrightetc.} % << Gerry, May 2007 % %% End of sig-alt-release2.cls -- V1.6 - 4/22/2009 -- %% Gerry Murray -- Wednesday April 22nd. 2009 % % The following section (i.e. 3 .sty inclusions) was added in May 2007 so as to fix the problems that many % authors were having with accents. Sometimes accents would occur, but the letter-character would be of a different % font. Conversely the letter-character font would be correct but, e.g. a 'bar' would appear superimposed on the % character instead of, say, an unlaut/diaresis. Sometimes the letter-character would NOT appear at all. % Using [T1]{fontenc} outright was not an option as this caused 99% of the authors to 'produce' a Type-3 (bitmapped) % PDF file - useless for production. % % For proper (font) accenting we NEED these packages to be part of the .cls file i.e. 'ae', 'aecompl' and 'aeguil' % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ %% This is file `ae.sty' \def\fileversion{1.3} \def\filedate{2001/02/12} \NeedsTeXFormat{LaTeX2e} %\ProvidesPackage{ae}[\filedate\space\fileversion\space % GM % Almost European Computer Modern] % GM - keeping the log file clean(er) \newif\if@ae@slides \@ae@slidesfalse \DeclareOption{slides}{\@ae@slidestrue} \ProcessOptions \fontfamily{aer} \RequirePackage[T1]{fontenc} \if@ae@slides \renewcommand{\sfdefault}{laess} \renewcommand{\rmdefault}{laess} % no roman \renewcommand{\ttdefault}{laett} \else \renewcommand{\sfdefault}{aess} \renewcommand{\rmdefault}{aer} \renewcommand{\ttdefault}{aett} \fi \endinput %% %% End of file `ae.sty'. % % \def\fileversion{0.9} \def\filedate{1998/07/23} \NeedsTeXFormat{LaTeX2e} %\ProvidesPackage{aecompl}[\filedate\space\fileversion\space % GM %T1 Complements for AE fonts (D. Roegel)] % GM -- keeping the log file clean(er) \def\@ae@compl#1{{\fontencoding{T1}\fontfamily{cmr}\selectfont\symbol{#1}}} \def\guillemotleft{\@ae@compl{19}} \def\guillemotright{\@ae@compl{20}} \def\guilsinglleft{\@ae@compl{14}} \def\guilsinglright{\@ae@compl{15}} \def\TH{\@ae@compl{222}} \def\NG{\@ae@compl{141}} \def\ng{\@ae@compl{173}} \def\th{\@ae@compl{254}} \def\DJ{\@ae@compl{208}} \def\dj{\@ae@compl{158}} \def\DH{\@ae@compl{208}} \def\dh{\@ae@compl{240}} \def\@perthousandzero{\@ae@compl{24}} \def\textperthousand{\%\@perthousandzero} \def\textpertenthousand{\%\@perthousandzero\@perthousandzero} \endinput % % %% This is file `aeguill.sty' % This file gives french guillemets (and not guillemots!) % built with the Polish CMR fonts (default), WNCYR fonts, the LASY fonts % or with the EC fonts. % This is useful in conjunction with the ae package % (this package loads the ae package in case it has not been loaded) % and with or without the french(le) package. % % In order to get the guillemets, it is necessary to either type % \guillemotleft and \guillemotright, or to use an 8 bit encoding % (such as ISO-Latin1) which selects these two commands, % or, if you use the french package (but not the frenchle package), % to type << or >>. % % By default, you get the Polish CMR guillemets; if this package is loaded % with the `cm' option, you get the LASY guillemets; with `ec,' you % get the EC guillemets, and with `cyr,' you get the cyrillic guillemets. % % In verbatim mode, you always get the EC/TT guillemets. % % The default option is interesting in conjunction with PDF, % because there is a Type 1 version of the Polish CMR fonts % and these guillemets are very close in shape to the EC guillemets. % There are no free Type 1 versions of the EC fonts. % % Support for Polish CMR guillemets was kindly provided by % Rolf Niepraschk <niepraschk@ptb.de> in version 0.99 (2000/05/22). % Bernd Raichle provided extensive simplifications to the code % for version 1.00. % % This package is released under the LPPL. % % Changes: % Date version % 2001/04/12 1.01 the frenchle and french package are now distinguished. % \def\fileversion{1.01} \def\filedate{2001/04/12} \NeedsTeXFormat{LaTeX2e} %\ProvidesPackage{aeguill}[2001/04/12 1.01 % % GM %AE fonts with french guillemets (D. Roegel)] % GM - keeping the log file clean(er) %\RequirePackage{ae} % GM May 2007 - already embedded here \newcommand{\@ae@switch}[4]{#4} \DeclareOption{ec}{\renewcommand\@ae@switch[4]{#1}} \DeclareOption{cm}{\renewcommand\@ae@switch[4]{#2}} \DeclareOption{cyr}{\renewcommand\@ae@switch[4]{#3}} \DeclareOption{pl}{\renewcommand\@ae@switch[4]{#4}} \ExecuteOptions{pl} \ProcessOptions % % Load necessary packages % \@ae@switch{% ec % do nothing }{% cm \RequirePackage{latexsym}% GM - May 2007 - already 'mentioned as required' up above }{% cyr \RequirePackage[OT2,T1]{fontenc}% }{% pl \RequirePackage[OT4,T1]{fontenc}% } % The following command will be compared to \frenchname, % as defined in french.sty and frenchle.sty. \def\aeguillfrenchdefault{french}% \let\guill@verbatim@font\verbatim@font \def\verbatim@font{\guill@verbatim@font\ecguills{cmtt}% \let\guillemotleft\@oguills\let\guillemotright\@fguills} \begingroup \catcode`\<=13 \catcode`\>=13 \def\x{\endgroup \def\ae@lfguill{<<}% \def\ae@rfguill{>>}% }\x \newcommand{\ecguills}[1]{% \def\selectguillfont{\fontencoding{T1}\fontfamily{#1}\selectfont}% \def\@oguills{{\selectguillfont\symbol{19}}}% \def\@fguills{{\selectguillfont\symbol{20}}}% } \newcommand{\aeguills}{% \ae@guills % We redefine \guillemotleft and \guillemotright % in order to catch them when they are used % with \DeclareInputText (in latin1.def for instance) % We use \auxWARNINGi as a safe indicator that french.sty is used. \gdef\guillemotleft{\ifx\auxWARNINGi\undefined \@oguills % neither french.sty nor frenchle.sty \else \ifx\aeguillfrenchdefault\frenchname \ae@lfguill % french.sty \else \@oguills % frenchle.sty \fi \fi}% \gdef\guillemotright{\ifx\auxWARNINGi\undefined \@fguills % neither french.sty nor frenchle.sty \else \ifx\aeguillfrenchdefault\frenchname \ae@rfguill % french.sty \else \@fguills % frenchle.sty \fi \fi}% } % % Depending on the class option % define the internal command \ae@guills \@ae@switch{% ec \newcommand{\ae@guills}{% \ecguills{cmr}}% }{% cm \newcommand{\ae@guills}{% \def\selectguillfont{\fontencoding{U}\fontfamily{lasy}% \fontseries{m}\fontshape{n}\selectfont}% \def\@oguills{\leavevmode\nobreak \hbox{\selectguillfont (\kern-.20em(\kern.20em}\nobreak}% \def\@fguills{\leavevmode\nobreak \hbox{\selectguillfont \kern.20em)\kern-.2em)}% \ifdim\fontdimen\@ne\font>\z@\/\fi}}% }{% cyr \newcommand{\ae@guills}{% \def\selectguillfont{\fontencoding{OT2}\fontfamily{wncyr}\selectfont}% \def\@oguills{{\selectguillfont\symbol{60}}}% \def\@fguills{{\selectguillfont\symbol{62}}}} }{% pl \newcommand{\ae@guills}{% \def\selectguillfont{\fontencoding{OT4}\fontfamily{cmr}\selectfont}% \def\@oguills{{\selectguillfont\symbol{174}}}% \def\@fguills{{\selectguillfont\symbol{175}}}} } \AtBeginDocument{% \ifx\GOfrench\undefined \aeguills \else \let\aeguill@GOfrench\GOfrench \gdef\GOfrench{\aeguill@GOfrench \aeguills}% \fi } \endinput % %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

http://mirrors.nic.cz/tex-archive/support/latexindent/documentation/sec-indent-config-and-settings.tex

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% arara: pdflatex: {shell: yes, files: [latexindent]} \section{indentconfig.yaml, local settings and the -y switch }\label{sec:indentconfig} The behaviour of \texttt{latexindent.pl} is controlled from the settings specified in any of the YAML files that you tell it to load. By default, \texttt{latexindent.pl} will only load \texttt{defaultSettings.yaml}, but there are a few ways that you can tell it to load your own settings files. \subsection{indentconfig.yaml and .indentconfig.yaml} \texttt{latexindent.pl} will always check your home directory for \texttt{indentconfig.yaml} and \texttt{.indentconfig.yaml} (unless it is called with the \texttt{-d} switch), which is a plain text file you can create that contains the \emph{absolute} paths for any settings files that you wish \texttt{latexindent.pl} to load. There is no difference between \texttt{indentconfig.yaml} and \texttt{.indentconfig.yaml}, other than the fact that \texttt{.indentconfig.yaml} is a `hidden' file; thank you to \cite{jacobo-diaz-hidden-config} for providing this feature. In what follows, we will use \texttt{indentconfig.yaml}, but it is understood that this could equally represent \texttt{.indentconfig.yaml}. If you have both files in existence then \texttt{indentconfig.yaml} takes priority. For Mac and Linux users, their home directory is \texttt{~/username} while Windows (Vista onwards) is \lstinline!C:\Users\username!\footnote{If you're not sure where to put \texttt{indentconfig.yaml}, don't worry \texttt{latexindent.pl} will tell you in the log file exactly where to put it assuming it doesn't exist already.} \Cref{lst:indentconfig} shows a sample \texttt{indentconfig.yaml} file. \begin{yaml}{\texttt{indentconfig.yaml} (sample)}{lst:indentconfig} # Paths to user settings for latexindent.pl # # Note that the settings will be read in the order you # specify here- each successive settings file will overwrite # the variables that you specify paths: - /home/cmhughes/Documents/yamlfiles/mysettings.yaml - /home/cmhughes/folder/othersettings.yaml - /some/other/folder/anynameyouwant.yaml - C:\Users\chughes\Documents\mysettings.yaml - C:\Users\chughes\Desktop\test spaces\more spaces.yaml \end{yaml} Note that the \texttt{.yaml} files you specify in \texttt{indentconfig.yaml} will be loaded in the order in which you write them. Each file doesn't have to have every switch from \texttt{defaultSettings.yaml}; in fact, I recommend that you only keep the switches that you want to \emph{change} in these settings files. To get started with your own settings file, you might like to save a copy of \texttt{defaultSettings.yaml} in another directory and call it, for example, \texttt{mysettings.yaml}. Once you have added the path to \texttt{indentconfig.yaml} you can change the switches and add more code-block names to it as you see fit -- have a look at \cref{lst:mysettings} for an example that uses four tabs for the default indent, adds the \texttt{tabbing} environment/command to the list of environments that contains alignment delimiters; you might also like to refer to the many YAML files detailed throughout the rest of this documentation. \index{indentation!defaultIndent using YAML file} \begin{yaml}{\texttt{mysettings.yaml} (example)}{lst:mysettings} # Default value of indentation defaultIndent: "\t\t\t\t" # environments that have tab delimiters, add more # as needed lookForAlignDelims: tabbing: 1 \end{yaml} You can make sure that your settings are loaded by checking \texttt{indent.log} for details -- if you have specified a path that \texttt{latexindent.pl} doesn't recognise then you'll get a warning, otherwise you'll get confirmation that \texttt{latexindent.pl} has read your settings file \footnote{Windows users may find that they have to end \texttt{.yaml} files with a blank line}. \index{warning!editing YAML files} \begin{warning} When editing \texttt{.yaml} files it is \emph{extremely} important to remember how sensitive they are to spaces. I highly recommend copying and pasting from \texttt{defaultSettings.yaml} when you create your first \texttt{whatevernameyoulike.yaml} file. If \texttt{latexindent.pl} can not read your \texttt{.yaml} file it will tell you so in \texttt{indent.log}. \end{warning} If you find that% \announce{2021-06-19}{encoding option for indentconfig.yaml} \texttt{latexindent.pl} does not read your YAML file, then it might be as a result of the default commandline encoding not being UTF-8; normally this will only occcur for Windows users. In this case, you might like to explore the \texttt{encoding} option for \texttt{indentconfig.yaml} as demonstrated in \cref{lst:indentconfig-encoding}. \cmhlistingsfromfile{demonstrations/encoding.yaml}[yaml-TCB]{The \texttt{encoding} option for \texttt{indentconfig.yaml}}{lst:indentconfig-encoding} Thank you to \cite{qiancy98} for this contribution; please see \vref{app:encoding} and details within \cite{encoding} for further information. \subsection{localSettings.yaml and friends}\label{sec:localsettings} The \texttt{-l} switch tells \texttt{latexindent.pl} to look for \texttt{localSettings.yaml} and/or friends in the \emph{same directory} as \texttt{myfile.tex}. For% \announce{2021-03-14}*{-l switch: localSettings and friends} example, if you use the following command \index{switches!-l demonstration} \begin{commandshell} latexindent.pl -l myfile.tex \end{commandshell} then \texttt{latexindent.pl} will search for and then, assuming they exist, load each of the following files in the following order: \begin{enumerate} \item localSettings.yaml \item latexindent.yaml \item .localSettings.yaml \item .latexindent.yaml \end{enumerate} These files will be assumed to be in the same directory as \texttt{myfile.tex}, or otherwise in the current working directory. You do not need to have all of the above files, usually just one will be sufficient. In what follows, whenever we refer to \texttt{localSettings.yaml} it is assumed that it can mean any of the four named options listed above. If you'd prefer to name your \texttt{localSettings.yaml} file something different, (say, \texttt{mysettings.yaml} as in \cref{lst:mysettings}) then you can call \texttt{latexindent.pl} using, for example, \begin{commandshell} latexindent.pl -l=mysettings.yaml myfile.tex \end{commandshell} Any settings file(s) specified using the \texttt{-l} switch will be read \emph{after} \texttt{defaultSettings.yaml} and, assuming they exist, any user setting files specified in \texttt{indentconfig.yaml}. Your settings file can contain any switches that you'd like to change; a sample is shown in \cref{lst:localSettings}, and you'll find plenty of further examples throughout this manual. \index{verbatim!verbatimEnvironments demonstration (-l switch)} \begin{yaml}{\texttt{localSettings.yaml} (example)}{lst:localSettings} # verbatim environments - environments specified # here will not be changed at all! verbatimEnvironments: cmhenvironment: 0 myenv: 1 \end{yaml} You can make sure that your settings file has been loaded by checking \texttt{indent.log} for details; if it can not be read then you receive a warning, otherwise you'll get confirmation that \texttt{latexindent.pl} has read your settings file. \subsection{The -y|yaml switch}\label{sec:yamlswitch} You% \announce{2017-08-21}{demonstration of the -y switch} may use the \texttt{-y} switch to load your settings; for example, if you wished to specify the settings from \cref{lst:localSettings} using the \texttt{-y} switch, then you could use the following command: \index{verbatim!verbatimEnvironments demonstration (-y switch)} \begin{commandshell} latexindent.pl -y="verbatimEnvironments:cmhenvironment:0;myenv:1" myfile.tex \end{commandshell} Note the use of \texttt{;} to specify another field within \texttt{verbatimEnvironments}. This is shorthand, and equivalent, to using the following command: \index{switches!-y demonstration} \begin{commandshell} latexindent.pl -y="verbatimEnvironments:cmhenvironment:0,verbatimEnvironments:myenv:1" myfile.tex \end{commandshell} You may, of course, specify settings using the \texttt{-y} switch as well as, for example, settings loaded using the \texttt{-l} switch; for example, \index{switches!-l demonstration} \index{switches!-y demonstration} \begin{commandshell} latexindent.pl -l=mysettings.yaml -y="verbatimEnvironments:cmhenvironment:0;myenv:1" myfile.tex \end{commandshell} Any settings specified using the \texttt{-y} switch will be loaded \emph{after} any specified using \texttt{indentconfig.yaml} and the \texttt{-l} switch. If you wish to specify any regex-based settings using the \texttt{-y} switch, \index{regular expressions!using -y switch} it is important not to use quotes surrounding the regex; for example, with reference to the `one sentence per line' feature (\vref{sec:onesentenceperline}) and the listings within \vref{lst:sentencesEndWith}, the following settings give the option to have sentences end with a semicolon \index{switches!-y demonstration} \begin{commandshell} latexindent.pl -m --yaml='modifyLineBreaks:oneSentencePerLine:sentencesEndWith:other:\;' \end{commandshell} \subsection{Settings load order}\label{sec:loadorder} \texttt{latexindent.pl} loads the settings files in the following order: \index{switches!-l in relation to other settings} \begin{enumerate} \item \texttt{defaultSettings.yaml} is always loaded, and can not be renamed; \item \texttt{anyUserSettings.yaml} and any other arbitrarily-named files specified in \texttt{indentconfig.yaml}; \item \texttt{localSettings.yaml} but only if found in the same directory as \texttt{myfile.tex} and called with \texttt{-l} switch; this file can be renamed, provided that the call to \texttt{latexindent.pl} is adjusted accordingly (see \cref{sec:localsettings}). You may specify both relative and absolute% \announce{2017-08-21}*{-l absolute paths} paths to other YAML files using the \texttt{-l} switch, separating multiple files using commas; \item any settings% \announce{2017-08-21}{-y switch load order} specified in the \texttt{-y} switch. \end{enumerate} A visual representation of this is given in \cref{fig:loadorder}. \begin{figure}[!htb] \centering \input{figure-schematic} \caption{Schematic of the load order described in \cref{sec:loadorder}; solid lines represent mandatory files, dotted lines represent optional files. \texttt{indentconfig.yaml} can contain as many files as you like. The files will be loaded in order; if you specify settings for the same field in more than one file, the most recent takes priority. } \label{fig:loadorder} \end{figure}

http://www.rcnp.osaka-u.ac.jp/~panic02/paper/abs/sample.tex

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% % Sample Abstract PANIC02 % \documentstyle[epsfig,12pt]{article} \setlength{\textwidth}{160mm} \setlength{\textheight}{240mm} \setlength{\oddsidemargin}{0mm} \setlength{\evensidemargin}{0mm} \setlength{\topmargin}{0mm} \setlength{\parindent}{0mm} \pagestyle{empty} % no page number \begin{document} % title {\large\bf Instructions for Abstract} \vspace*{6mm} % authors {Author1$^a$ and Author2$^b$ }\\ % institutions {\small \it $^a$ Institution1 \\ $^b$ Institution2} \vspace*{6mm} % abstract \medskip Instructions for the abstract: \begin{itemize} \item Abstract should be in 1 page. (maximum size 16cm x 24cm, no page number) \item Use bold face for the title and italic for the institution and address. \item Only ps or pdf file ready to print is accepted. \item Abstracts should be submitted at http://www.rcnp.osaka-u.ac.jp/\~{}panic02/paper/abs. \item DEADLINE April 26, 2002 \end{itemize} \begin{figure}[htb] \centerline{\epsfig{file=sample.eps,width=8.0cm}} \caption{figure caption. } \end{figure} % references \vspace{6mm} {\bf References }\\ {}[1] Author1 and Author2, Journal {\bf Volume} (year) page. \end{document}

http://ftp.rz.uni-wuerzburg.de/tex/latex2e/contrib/rec-thy/rec-thy.tex

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% % untitled % % Created by Peter M. Gerdes on 2010-10-14. % Copyright (c) 2010 . All rights reserved. % \documentclass[11pt,oneside]{article} \usepackage{amsfonts} \usepackage{rec-thy} \usepackage{multirow} \usepackage{booktabs} \usepackage{xtab} \usepackage{hyperref} \newcommand{\tab}{\hspace{1cm}} % Uncomment some of the following if you use the features % % Running Headers and footers %\usepackage{fancyhdr} %\usepackage[parfill]{parskip} %\usepackage{setspace} % Multipart figures %\usepackage{subfigure} % Surround parts of graphics with box %\usepackage{boxedminipage} % Package for including code in the document %\usepackage{listings} % If you want to generate a toc for each chapter (use with book) %\usepackage{minitoc} %\usepackage[pdftex]{graphicx} %\DeclareGraphicsExtensions{.pdf, .jpg, .tif} \title{The rec-thy Package} \author{Peter M. Gerdes (gerdes@invariant.org)} \date{2011-01-01: Version 1.2} \begin{document} \maketitle \begin{abstract} The rec-thy package is designed to help mathematicians publishing papers in the area of recursion theory (aka Computability Theory) easily use standard notation. This includes easy commands to denote Turing reductions, Turing functionals, \ce sets, stagewise computations, forcing and syntactic classes. \end{abstract} \section{Introduction} This package aims to provide a useful set of \LaTeX { }macros covering basic computability theory notation. Given the variation in usage in several areas this package had to pick particular notational conventions. The package author would like to encourage uniformity in these conventions but has included a multitude of package options to allow individual authors to choose alternative conventions or exclude that part of the package. Some effort has been made to align the semantic content of documents created with this package with the \LaTeX { }source. The author hopes that eventually this package may be incorporated into some larger package for typesetting papers in mathematical logic. While computability theory is now the more popular name for the subject also known as recursion theory the author deliberately choose to title this package rec-thy to avoid confusion with the proliferation of packages for typesetting computer science related disciplines. While the subject matter of computability theory and theoretical computer science overlap significantly the notational conventions often differ. Comments, patches, suggestions etc.. are all welcome. This project is hosted on github at \href{https://github.com/TruePath/Recursion-Theory-Latex-Package}{https://github.com/TruePath/Recursion-Theory-Latex-Package}. \section{Usage} Include the package in your document by placing \verb=\usepackage{rec-thy}= into your preamble after placing rec-thy.sty somewhere \TeX{ } can find it. The commands in this package have been divided into related groups. The commands in a given section can be disabled by passing the appropriate package option. For instance to disable the commands in the general mathematics section and the delimiters section you would include the following in your preamble \verb=\usepackage[nomath,nodelim]{rec-thy}=. The commands in each subsection along with their results are listed below and the options to disable the commands in each grouping or modify their behavior are listed in that subsection. Aliases and variants of a command are listed below the initial version of a command and aliases are indented. Significant use is made in this package of optional arguments delimited either by square brackets or parenthesis. Users of the package should take care to wrap arguments that may themselves include brackets or parenthesis in braces. For example \verb=\REset(\REset(X){e}){i}= should be fixed to \verb=\REset({\REset(X){e}}){i}=. \section{Commands} A few general conventions are usually followed in the commands. Whenever an operator can be used as a binary operator (as in \( X \union Y \)) and as an operation on some collection \( \Union_{i \in \omega} X_i \) the binary operator will begin with a lowercase letter \verb=\union= and the operation on the collection will begin with a capital letter \verb=\Union=. If the first letter is already capitalized then the second letter is used instead. Objects that have a natural stagewise approximation generally admit an optional argument in brackets to specify a stage. For instance \( \verb=\REset[s]{e}= \) yields \( \REset[s]{e} \). An optional argument in parenthesis is used for relativization. For instance \( \verb=\REset(X){e}= \) produces \( \REset(X){e} \). A notable exception to this rule are the formula classes where square brackets are used to indicate an oracle to be placed in the superscript, e.g., \( \verb=\pizn[X]{2}= \) yields \( \pizn[X]{2} \), so as not to generate confusion with the alternative notion \( \pizn{2}(X) \). Also a lowercase first letter in a formula class indicates the lightface version while a capital first letter indicates the boldface version. Unless indicated otherwise all macros are to be used inside math mode. Indented commands indicate an alias for the command on the line above \subsection{Computations} To disable these commands pass the option \verb=nocomputations=. \\ \begin{xtabular}{l | l | l}\toprule \verb=\murec{x}{f(x)>1}= & \( \murec{x}{f(x)>1} \) & Least \( x \) satisfying condition. \\ \midrule \verb=\recfnl{e}{Y}{x}= & \( \recfnl{e}{Y}{x} \) &\multirow{4}{*}{Computable functions/functionals} \\[6pt] \verb=\recfnl[s]{e}{Y}{x}= & \( \recfnl[s]{e}{Y}{x} \) & \\[6pt] \verb=\recfnl{e}{Y}{}= & \( \recfnl{e}{Y}{} \) & \\[6pt] \verb=\recfnl{e}{}{x}= & \( \recfnl{e}{}{x} \) & \\[6pt] \verb=\recfnl{e}{}{}= & \( \recfnl{e}{}{} \) & \\ \midrule \verb=\recfnl{e}{}{} \cequiv \recfnl{i}{}{}= & \( \recfnl{e}{}{} \cequiv \recfnl{i}{}{} \) & Equivalent computations\\ \midrule \verb=\recfnl{e}{}{} \ncequiv \recfnl{i}{}{}= & \( \recfnl{e}{}{} \ncequiv \recfnl{i}{}{} \) & Inequivalent computations\\ \midrule \verb=\recfnl{e}{}{x}\conv= & \( \recfnl{e}{}{x}\conv \) &\multirow{2}{*}{Convergence} \\[6pt] \tab \verb=\recfnl{e}{}{x}\conv[s]= & \( \recfnl{e}{}{x}\conv[s] \) & \\ \midrule \verb=\recfnl{e}{}{x}\nconv= & \( \recfnl{e}{}{x}\nconv \) &\multirow{2}{*}{Divergence} \\[6pt] \tab \verb=\recfnl{e}{}{x}\nconv[s]= & \( \recfnl{e}{}{x}\nconv[s] \) & \\ \midrule \verb=\use{\recfnl{e}{Y}{x}}= & \( \use{\recfnl{e}{Y}{x}} \) & Use of a computation. \\ \midrule \verb=\REset{e}= & \( \REset{e} \) & \multirow{4}{*}{c.e. sets} \\[6pt] \verb=\REset[s]{e}= & \( \REset[s]{e} \) & \\[6pt] \verb=\REset(X){e}= & \( \REset(X){e} \) & \\[6pt] \verb=\REset[s](X){e}= & \( \REset[s](X){e} \) & \\ \midrule \verb=\iREAop{e}(\eset)= & \multirow{2}{*}{\( \iREAop{e}(\eset) \)} &\multirow{2}{*}{1-REA operator} \\ \tab \verb=\reaop*{e}(\eset)= & & \\ \midrule \verb=\alphaREAop{\alpha}(\eset)= & \multirow{2}{*}{\( \alphaREAop{\alpha}(\eset) \)} &\multirow{2}{*}{\( \alpha \)-REA operator} \\[6pt] \tab \verb=\reaop{\alpha}(\eset)= & & \\[6pt] \verb=\alphaREAop[f]{\alpha}(\eset)= & \multirow{2}{*}{\( \alphaREAop[f]{\alpha}(\eset) \)} & \multirow{2}{*}{with particular witness to uniformity}\\[6pt] \tab \verb=\reaop[f]{\alpha}(\eset)= & & \\ \bottomrule \end{xtabular} \\ \subsection{Degrees} To disable these commands pass the option \verb=nodegrees=. \\ \begin{xtabular}{l | l | l}\toprule \verb=\Tdeg{d}= & \( \Tdeg{d} \) & Turing degree \\ \midrule \verb=\Tjump{X}= & \multirow{2}{*}{\( \Tjump{X} \)} & \multirow{2}{*}{Turing jump} \\ \tab \verb=\jump{X}= & & \\ \midrule \verb=\jjump{X}= & \( \jjump{X} \) & \\ \midrule \verb=\jumpn{X}{n}= & \( \jumpn{X}{n} \) & \\ \midrule \verb=\Tzero= & \( \Tzero \) & Computable degree \\ \midrule \verb=\zeroj= & \( \zeroj \) & \\ \midrule \verb=\zerojj= & \( \zerojj \) & \\ \midrule \verb=\zerojjj= & \( \zerojjj \) & \\ \midrule \verb=\zeron{n}= & \( \zeron{n} \) & \\ \midrule \verb=X \Tequiv Y= & \multirow{2}{*}{\( X \Tequiv Y \)} & \multirow{2}{*}{Turing equivalence}\\ \tab \verb=X \Teq Y= & & \\ \midrule \verb=X \nTequiv Y= & \multirow{2}{*}{\( X \nTequiv Y \)} & \multirow{2}{*}{Turing inequivalence} \\ \tab \verb=X \nTeq Y= & & \\ \midrule \verb=X \Tlneq Y= & \( X \Tlneq Y \) & \\ \midrule \verb=X \Tleq Y= & \( X \Tleq Y \) & \\ \midrule \verb=X \Tgneq Y= & \( X \Tgneq Y \) & \\ \midrule \verb=X \Tgeq Y= & \( X \Tgeq Y \) & \\ \midrule \verb=X \Tgtr Y= & \( X \Tgtr Y \) & \\ \midrule \verb=X \Tless Y= & \( X \Tless Y \) & \\ \midrule \verb=X \nTleq Y= & \( X \nTleq Y \) & \\ \midrule \verb=X \nTgeq Y= & \( X \nTgeq Y \) & \\ \midrule \verb=\Tdeg{d} \Tdegjoin \Tdeg{d'}= & \( \Tdeg{d} \Tdegjoin \Tdeg{d'} \) & Join of degrees\\ \midrule \verb=\Tdeg{d} \Tdegmeet \Tdeg{d'}= & \multirow{2}{*}{\( \Tdeg{d} \Tdegmeet \Tdeg{d'} \)} & \multirow{2}{*}{Meet of degrees (when defined)} \\ \tab \verb=\Tdeg{d} \Tmeet \Tdeg{d'}= & & \\ \midrule \verb=X \Tplus Y= & \multirow{2}{*}{\( X \Tplus Y \)} & \multirow{4}{*}{Effective join of sets} \\ \tab \verb=X \Tjoin Y= & & \\ \verb=\TPlus_{i \in \omega} X_i= & \multirow{2}{*}{\( \TPlus_{i \in \omega} X_i \)} & \\ \tab \verb=\TJoin_{i \in \omega} X_i= & & \\ \midrule % \verb=\ttSYM= & \( \ttSYM \) & \\ \midrule \verb=X \ttlneq Y= & \( X \ttlneq Y \) & Truth table reducibilities\\ \midrule \verb=X \ttleq Y= & \( X \ttleq Y \) & \\ \midrule \verb=X \ttgneq Y= & \( X \ttgneq Y \) & \\ \midrule \verb=X \ttgeq Y= & \( X \ttgeq Y \) & \\ \midrule \verb=X \ttgtr Y= & \( X \ttgtr Y \) & \\ \midrule \verb=X \ttless Y= & \( X \ttless Y \) & \\ \midrule \verb=X \ttTleq Y= & \( X \ttTleq Y \) & \\ \midrule \verb=X \ttTgeq Y= & \( X \ttTgeq Y \) & \\ \bottomrule \end{xtabular} \\ \subsection{General Math Commands} To disable these commands pass the option \verb=nomath=. \\ \begin{tabular}{l | l | l}\toprule \verb=\eqdef= & \( \eqdef \) & Definitional equals\\ \midrule \verb=\iffdef= & \( \iffdef \) & Definitional equivalence\\ \midrule \verb=\aut= & \( \aut \) & Automorphisms of some structure\\ \midrule \verb=\Ord= & \( \Ord \) & Set of ordinals\\\midrule \verb=x \meet y= & \( x \meet y \) & \multirow{2}{*}{Meet operation} \\[6pt] \verb=\Meet_{i\in \omega} x_i= & \( \Meet_{i\in \omega} x_i \) & \\ \midrule \verb=x \join y= & \(x \join y \) & \multirow{2}{*}{Join operation} \\[6pt] \verb=\Join_{i\in \omega} x_i= & \( \Join_{i\in \omega} x_i \) & \\ \midrule \verb=\abs{x}= & \( \abs{x} \) & Absolute value\\ \midrule \verb=\dom= & \( \dom \) & Domain \\ \midrule \verb=\rng= & \( \rng \) & Range\\ \midrule \verb=f\restr{X}= & \( f\restr{X} \) & Restriction\\ \midrule \verb=\ordpair{x}{y}= & \( \ordpair{x}{y} \)& Ordered Pair\\ \midrule \verb=f\map{X}{Y}= & \( f\map{X}{Y} \) & \multirow{2}{*}{Function specification} \\ \verb=\functo{f}{X}{Y}= & \( \functo{f}{X}{Y} \) &\\ \midrule \verb=f \compfunc g= & \multirow{3}{*}{\( f \compose g \)} & \multirow{3}{*}{Function composition}\\ \tab \verb=f \funcomp g= & &\\ \tab \verb=f \compose g= & &\\ \midrule \verb=\( \ensuretext{blah} \)= & \multirow{2}{*}{\( \ensuretext{blah} \)}& \multirow{2}{*}{Types argument in text mode} \\ \tab \verb=\ensuretext{blah}= & & \\ \bottomrule \end{tabular} \\ \newpage \subsection{Set Notation} To disable these commands pass the option \verb=nosets=.\\ \begin{tabular}{l | l | l}\toprule \verb=\set{(x,y)}{x > y}= & \( \set{(x,y)}{x > y} \) & \multirow{2}{*}{Set notation} \\[6pt] \verb=\set{(x,y)}}{}= & \( \set{(x,y)}{} \) & \\ \midrule \verb=\card{X}= & \( \card{X} \) & Cardinality \\ \midrule \verb=X \union Y= & \( X \union Y \) & \multirow{2}{*}{Union} \\[6pt] \verb=\Union_{i \in \omega} X_i= & \( \Union_{i \in \omega} X_i \) & \\ \midrule \verb=X \isect Y= & \( X \isect Y \) & \multirow{2}{*}{Intersection} \\[6pt] \verb=\Isect_{i \in \omega} X_i= & \( \Isect_{i \in \omega} X_i \) & \\ \midrule \verb=X \cross Y= & \( X \cross Y \) & \multirow{2}{*}{Cartesian product (Cross Product)} \\[6pt] \verb=\Cross_{i \in \omega} X_i= & \( \Cross_{i \in \omega} X_i \) & \\ \midrule \verb=\powset{\omega}= & \( \powset{\omega} \) & Powerset \\ \midrule \verb=\eset= & \( \eset \) & Emptyset abbreviation\\ \midrule \verb=x \nin A= & \( x \nin A \) & not an element\\ \midrule \verb=\setcmp{X}= & \( \setcmp{X} \) & Set compliment\\[6pt] & \( \setminuscmp{X} \) & With option \verb=minussetcmp= \\ \midrule \verb=X \setminus Y= & \( X \setminus Y \) & Set difference \\ \midrule \verb=X \symdiff Y= & \( X \symdiff Y \) & Symmetric difference \\ \midrule \verb=\interior X= & \( \interior X \) & Interior \\ \midrule \verb=\closure X= & \( \closure X \) & Closure \\ \midrule \bottomrule \end{tabular} \\ \subsection{Delimiters} To disable these commands pass the option \verb=nodelim=. \\ \begin{tabular}{l | l | l}\toprule \verb=\gcode{\phi}= & \multirow{3}{*}{\( \gcode{\phi} \)} & \multirow{3}{*}{Godel Code/Corner Quotes}\\ \tab \verb=\godelnum{\phi}= & &\\ \tab \verb=\cornerquote{\phi}= & &\\ \midrule \verb=\llangle x,y,z \rrangle= & \( \llangle x,y,z \rrangle \) & Properly spaced double angle brackets\\ \bottomrule \end{tabular} \subsection{Recursive vs. Computable} To disable these commands pass the option \verb=nonames=. To use recursive, r.e. and recursively enumerable everywhere pass the option \verb=re=. To use computable, c.e. and computably enumerable everywhere pass the option \verb=ce=. To force REA and CEA use the options \verb=rea= and \verb=cea=. If none of these options are passed the macros will expand as below. All macros in this section work in both text and math modes.\\ \begin{tabular}{l | l }\toprule \verb=\re= & \re \\ \midrule \verb=\ce= & \ce \\ \midrule \verb=\REA= & \REA \\ \midrule \verb=\CEA= & \CEA \\ \midrule \verb=\recursive= & \recursive \\ \midrule \verb=\computable= & \computable \\ \midrule \verb=\recursivelyEnumerable= & \recursivelyEnumerable \\ \midrule \verb=\computablyEnumerable= & \computablyEnumerable \\ \midrule \verb=\Recursive= & \Recursive \\ \midrule \verb=\Computable= & \Computable \\ \midrule \verb=\RecursivelyEnumerable= & \RecursivelyEnumerable \\ \midrule \verb=\ComputablyEnumerable= & \ComputablyEnumerable \\ \midrule \bottomrule \end{tabular} \subsection{Quantifiers \& Connectives} To disable these commands pass the option \verb=noquants=. The commands \verb=\exists= and \verb=\forall= are standard but the package extends them.\\ \begin{tabular}{l | l | l}\toprule \verb=\exists[x < y]= & \( \exists[x < y ] \) & \\[6pt] \verb=\exists(x < y)= & \( \exists(x < y ) \) & \\ \midrule \verb=\exists*= & \multirow{2}{*}{\( \exists* \)} & \\[6pt] \tab \verb=\existsinf= & & \\[6pt] \verb=\exists*[x < y]= & \( \exists*[x < y ] \) & \\[6pt] \verb=\exists*(x < y)= & \( \exists*(x < y ) \) & \\ \midrule \verb=\nexists[x < y]= & \( \nexists[x < y ] \) & \\[6pt] \verb=\nexists(x < y)= & \( \nexists(x < y ) \) & \\ \midrule \verb=\nexists*= & \multirow{2}{*}{\( \nexists* \)} & \\[6pt] \tab \verb=\nexistsinf= & & \\[6pt] \verb=\nexists*[x < y]= & \( \nexists*[x < y ] \) & \\[6pt] \verb=\nexists*(x < y)= & \( \nexists*(x < y ) \) & \\ \midrule \verb=\forall[x < y]= & \( \forall[x < y ] \) & \\[6pt] \tab \verb=\forall(x < y)= & \( \forall(x < y ) \) & \\ \midrule \verb=\forall*= & \multirow{2}{*}{\( \forall* \)} &\multirow{4}{*}{For almost all.} \\ \tab \verb=\forallae= & & \\[6pt] \verb=\forall*[x < y]= & \( \forall*[x < y ] \) & \\[6pt] \verb=\forall*(x < y)= & \( \forall*(x < y ) \) & \\ \midrule \verb=\True= & \( \True \) & \\ \midrule \verb=\False= & \( \False \) & \\ \midrule \verb=\Land \phi_i= & \( \Land \phi_i \) & Operator form of and\\ \midrule \verb=\Lor \phi_i= & \( \Lor \phi_i \) & Operator form of or\\ \midrule \verb=\LLand \phi_i= & \( \LLand \phi_i \) & Infinitary conjunction\\ \midrule \verb=\LLor \phi_i= & \( \LLor \phi_i \) & Infinitary disjunction\\ \bottomrule \end{tabular} \subsection{Spaces} To disable these commands pass the option \verb=nospaces=.\\ \begin{tabular}{l | l | l}\toprule \verb=\bstrs= & \( \bstrs \) & Finite binary strings \\ \midrule \verb=\wstrs= & \( \wstrs \) & Finite sequences of integers \\ \midrule \verb=\cantor= & \( \cantor \) & Cantor space \\ \midrule \verb=\baire= & \( \baire \) & Baire space \\[6pt] \verb=\Baire= & \( \Baire \) & Alternate baire space \\ \bottomrule \end{tabular} \subsection{Strings} To disable these commands pass the option \verb=nostrings=.\\ \begin{tabular}{l | l | l}\toprule \verb=\str{1,0,1}= & \( \str{1,0,1} \) & \multirow{2}{*}{Strings/Codes for strings} \\ \tab \verb=\code{5,8,13}= & \( \code{5,8,13} \) & \\ \midrule \verb=\EmptyStr= & \( \EmptyStr \) & \multirow{2}{*}{Empty string} \\[6pt] \tab \verb=\estr= & \( \estr \) & \\ \midrule \verb=\decode{\sigma}{3}= & \( \decode{\sigma}{3} \) & Alternate notation for \( \sigma(3) \) \\ \midrule \verb=\sigma\concat\tau= & \( \sigma\concat\tau \) & \multirow{2}{*}{Concatenation} \\[6pt] \verb=\sigma\concat[0]= & \( \sigma\concat[0] \) & \\ \midrule \verb=\strpred{\sigma}= & \( \strpred{\sigma} \) & The immediate predecessor of \( \sigma \) \\ \midrule \verb=\lh{\sigma}= & \( \lh{\sigma} \) & Length of \( \sigma \) \\ \midrule \verb=\sigma \incompat \tau= & \( \sigma \incompat \tau \) & \multirow{2}{*}{Incompatible strings} \\ \tab \verb=\sigma \incomp \tau= & \( \sigma \incomp \tau \) & \\ \midrule \verb=\sigma \compat \tau= & \( \sigma \compat \tau \) & Compatible strings \\ \midrule \verb=\pair{x}{y}= & \( \pair{x}{y} \) & Code for the pair \( (x,y) \) \\ \midrule \verb=\setcol{X}{n}= & \( \setcol{X}{n} \) & \( \set{y}{\pair{n}{y} \in X} \) \\ \midrule \verb=\setcol{X}{\leq n}= & \( \setcol{X}{\leq n} \) & \( \set{ \pair{x}{y}}{\pair{x}{y} \in X \land x \leq n} \) \\ \bottomrule \end{tabular} \subsection{Trees} To disable these commands pass the option \verb=notrees=.\\ \begin{tabular}{l | l | l}\toprule \verb=\CBderiv{T}= & \( \CBderiv{T} \) & \multirow{2}{*}{Cantor-Bendixson Derivative} \\[6pt] \verb=\CBderiv[\alpha]{T}= & \( \CBderiv[\alpha]{T} \) & \\ \midrule \verb=\pruneTree{T}= & \( \pruneTree{T} \) & \( \set{\sigma \in T}{\exists(g)(g \in [T] \land \sigma \subset g)} \) \\ \midrule \verb=\hgt{T}= & \( \hgt{T} \) & \\ \bottomrule \end{tabular} \subsection{Set Relations} To disable these commands pass the option \verb=nosetrels=.\\ Note that many of these commands are extensions of existing commands. \begin{tabular}{l | l | l}\toprule \verb=X \subset* Y= & \( X \subset* Y\) & \multirow{2}{*}{All but finitely much of \( X \) is in \( Y \)} \\ \verb=X \subseteq* Y= & \( X \subseteq* Y\) & \\ \midrule \verb=X \supset* Y= & \( X \supset* Y\) & \multirow{2}{*}{All but finitely much of \( Y \) is in \( X \)} \\ \verb=X \supseteq* Y= & \( X \supseteq* Y\) & \\ \midrule \verb=X \eq Y= & \( X \eq Y\) & Macro for \verb~=~ \\ \midrule \verb=X \eq* Y= & \multirow{2}{*}{\( X \eq* Y\)} & \multirow{2}{*}{Equal mod finite} \\ \tab \verb=X \eqae Y= & & \\ \midrule \verb=X \infsubset Y= & \( X \infsubset Y\) & \( X \subset Y \land \card{Y \setminus X}=\omega \) \\ \midrule \verb=X \infsubset* Y= & \( X \infsubset* Y\) & \( X \subset* Y \land \card{Y \setminus X}=\omega \) \\ \midrule \verb=X \infsupset Y= & \( X \infsupset Y\) & \( Y \subset X \land \card{X \setminus Y}=\omega \) \\ \midrule \verb=X \infsupset* Y= & \( X \infsupset* Y\) & \( Y \subset* X \land \card{X \setminus Y}=\omega \) \\ \midrule \verb=X \majsubset Y= & \( X \majsubset Y\) & \( X \) is a major subset of \( Y \) \\ \midrule \verb=X \majsupset Y= & \( X \majsupset Y\) & \( Y \) is a major subset of \( X \) \\ \bottomrule \end{tabular} \subsection{Ordinal Notations} To disable these commands pass the option \verb=noordinalnotations=.\\ \begin{tabular}{l | l | l}\toprule \verb=\wck= & \( \wck \) & First non-computable ordinal \\ \midrule \verb=\ordzero= & \( \ordzero \) & Notation for ordinal \( 0 \)\\ \midrule \verb=\abs{\alpha}= & \( \abs{\alpha} \) & Ordinal \( \alpha \) denotes \\ \midrule \verb=\kleeneO= & \multirow{2}{*}{\( \kleeneO \)} & \multirow{2}{*}{Set of ordinal notations} \\[6pt] \tab \verb=\ordNotations= & & \\[6pt] \verb=\kleeneO*= & \multirow{3}{*}{\( \kleeneO* \)} & \multirow{3}{*}{Unique set of ordinal notations} \\[6pt] \tab \verb=\uniqOrdNotations= & & \\[6pt] \tab \verb=\kleeneOuniq= & & \\[6pt] \verb=\kleeneO(X)= & \( \kleeneO(X) \) & Relativized ordinal notations \\[6pt] \verb=\kleeneO[\alpha]= & \( \kleeneO[\alpha] \) & Ordinal notations for ordinals \( < \abs{\alpha} \) \\[6pt] \verb=\kleeneO*(X)[\alpha]= & \( \kleeneO*(X)[\alpha] \) & \\ \midrule \verb=\alpha \kleeneless \beta= & \( \alpha \kleeneless \beta \) & Ordering on notations \\ \midrule \verb=\alpha \kleenel \beta= & \( \alpha \kleenel \beta \) & \\ \midrule \verb=\alpha \kleeneleq \beta= & \( \alpha \kleeneleq \beta \) & \\ \midrule \verb=\alpha \kleenegtr \beta= & \( \alpha \kleenegtr \beta \) & \\ \midrule \verb=\alpha \kleenegeq \beta= & \( \alpha \kleenegeq \beta \) & \\ \midrule \verb=\alpha \kleenePlus \beta= & \( \alpha \kleenePlus \beta \) & Effective addition of notations \\ \midrule \verb=\alpha \kleeneMul \beta= & \( \alpha \kleeneMul \beta \) & Effective multiplication of notations \\ \midrule \verb=\kleenelim{\lambda}{n}= & \( \kleenelim{\lambda}{n} \) & The \( n \)-th element in effective limit defining notation \( \lambda \)\\ \midrule \verb=\kleenepred{\alpha}= & \( \kleenepred{\alpha} \) & Predecessor of \( \alpha \) if defined \\ \midrule \verb=\kleenehgt{R}= & \multirow{2}{*}{\( \kleenehgt{R} \)} & Heigh of computable relation \( R \) \\ \tab \verb=\hgtO{R}= & & \\ \bottomrule \end{tabular} \subsection{Forcing} To disable these commands pass the option \verb=noforcing=.\\ \begin{tabular}{l | l | l}\toprule \verb=\sigma \forces \phi= & \multirow{2}{*}{\( \sigma \forces \phi \)} & \multirow{2}{*}{\( \sigma \) forces \( \phi \)}\\ \tab \verb=\sigma \frc \phi= & & \\ \verb=\sigma \forces(X) \phi= & \( \sigma \forces(X)[T] \phi \) & \( \phi \) is formula relative to \( X \) \\ \verb=\sigma \forces[T] \phi= & \( \sigma \forces(X)[T] \phi \) & Local forcing on \( T \)\\ \verb=\sigma \forces* \phi= & \( \sigma \forces* \phi \) & Strong forcing \\ \bottomrule \end{tabular} \subsection{Syntax} To disable these commands pass the option \verb=nosyntax=.\\ All syntax classes can be relativized with an optional argument in square brackets even when not listed below. Only the \( \Delta \) formula classes are listed below since the syntax is identical for \( \Sigma \) and \( \Pi \). Capitalizing the first letter gives the boldface version in all cases (except the computable infinitary formulas as this doesn't make sense). Not all formulas/abbreviations are demonstrated below given the huge number but the enough are included to make it clear what command is required to generate the desired formula class, e.g., substituting pi for delta does what you think it does. To change the syntax for the computable infinitary formulas you can pass the options \verb=cdeltasym=, \verb=csigmasym= and \verb=cpisym= set equal to the command to produce your desired symbol. This is UNTESTED and quite likely doesn't work yet. If you desire this feature and it doesn't work send me a bug report. \begin{xtabular}{l | l | l}\toprule \verb=\Cdeltan[X]{\alpha}= & \( \Cdeltan[X]{2} \) & The computable \( \delta^{X}_\alpha \) formulas \\ \midrule \verb=\deltan{2}= & \( \deltan{2} \) & \\ \midrule \verb=\deltan[X]{2}= & \( \deltan[X]{2} \) & \\ \midrule \verb=\deltaZeroN[X]{2}= & \multirow{2}{*}{\( \deltaZeroN[X]{2} \)} & \\ \tab \verb=\deltazn[X]{2}= & & \\ \midrule \verb=\deltaZeroOne[X]= & \multirow{2}{*}{\( \deltaZeroOne[X] \)} & \\ \tab \verb=\deltazi[X]= & & \\ \midrule \verb=\sigmaZeroTwo[X]= & \multirow{2}{*}{\( \deltaZeroTwo[X] \)} & \\ \tab \verb=\sigmazii[X]= & & \\ \midrule \verb=\deltaZeroThree[X]= & \multirow{2}{*}{\( \deltaZeroThree[X]\)} & \\ \tab \verb=\deltaziii[X]= & & \\ \midrule \verb=\deltaOneN[X]{2}= & \multirow{2}{*}{\( \deltaOneN[X]{2} \)} & \\ \tab \verb=\deltaIn[X]{2}= & & \\ \midrule \verb=\deltaOneOne[X]= & \multirow{2}{*}{\( \deltaOneOne[X] \)} & \\ \tab \verb=\deltaIi[X]= & & \\ \midrule \verb=\deltaOneTwo[X]= & \multirow{2}{*}{\( \deltaOneTwo[X] \)} & \\ \tab \verb=\deltaIii[X]= & & \\ \midrule \verb=\deltaOneThree[X]= & \multirow{2}{*}{\( \deltaOneThree[X] \)} & \\ \tab \verb=\deltaIiii[X]= & & \\ \midrule \verb=\pizi= & \( \pizi \) & \\ \midrule \verb=\pizn[X]{n}= & \( \pizn[X]{n} \) & \\ \midrule \verb=\Deltan{2}= & \( \Deltan{2} \) & \\ \midrule \verb=\DeltaOneN[X]{n}= & \( \DeltaOneN[X]{n} \) & \\ \midrule \verb=\logic{\omega_1}{\omega}= & \( \logic{\omega_1}{\omega} \) & Indicates the kind of infinitary logic\\ \bottomrule \end{xtabular} \subsection{MRref} Finally to enable the mrref helper macros pass the option \verb=mrref=.\\ These macros normalize the formating of mathscinet references for supported bibliography styles and ensure the MR numbers link to the mathscinet page of the article. Unless you have a good reason (like journal formatting guidelines) there is no reason not to always pass this option. Note this option requires the hyperref package. \section{Release Notes} \begin{itemize} \item[1.3] 06/20/2012 - Added abbreviations for computable infinitary formulas and made a few minor fixes. \item[1.2] 01/01/2011 - Fixed awful option processing bug preventing most options from being recognized and added mrref option. \item[1.0] 10/15/2010 - Initial public release \end{itemize} \end{document}

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%====================================================================% % MORIOND.TEX 2-Feb-1995 % % This latex file rewritten from various sources for use in the % % preparation of the standard proceedings Volume, latest version % % for the Neutrino'96 Helsinki conference proceedings % % by Susan Hezlet with acknowledgments to Lukas Nellen. % % Some changes are due to David Cassel. % % % % Updated to LaTeX2e and adapted to Moriond 2001 conditions % % by F.Montanet 24/04/2001 % %====================================================================% \documentclass[11pt]{article} \usepackage{moriond,epsfig} %\documentstyle[11pt,moriond,epsfig]{article} \bibliographystyle{unsrt} % for BibTeX - sorted numerical labels by order of % first citation. % A useful Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)} % Some useful journal names \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} A} \def\NPB{{\em Nucl. Phys.} B} \def\PLB{{\em Phys. Lett.} B} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} D} \def\ZPC{{\em Z. Phys.} C} % Some other macros used in the sample text \def\st{\scriptstyle} \def\sst{\scriptscriptstyle} \def\mco{\multicolumn} \def\epp{\epsilon^{\prime}} \def\vep{\varepsilon} \def\ra{\rightarrow} \def\ppg{\pi^+\pi^-\gamma} \def\vp{{\bf p}} \def\ko{K^0} \def\kb{\bar{K^0}} \def\al{\alpha} \def\ab{\bar{\alpha}} \def\be{\begin{equation}} \def\ee{\end{equation}} \def\bea{\begin{eqnarray}} \def\eea{\end{eqnarray}} \def\CPbar{\hbox{{\rm CP}\hskip-1.80em{/}}} %temp replacement due to no font %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % BEGINNING OF TEXT % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} \vspace*{4cm} \title{INSTRUCTIONS FOR PRODUCING A CAMERA-READY MANUSCRIPT} \author{ A.B. AUTHOR } \address{Department of Physics, Theoretical Physics, 1 Keble Road,\\ Oxford OX1 3NP, England} \maketitle\abstracts{ This is where the abstract should be placed. It should consist of one paragraph and give a concise summary of the material in the article below. Replace the title, authors, and addresses within the curly brackets with your own title, authors, and addresses; please use capital letters for the title and the authors. You may have as many authors and addresses as you wish. It's preferable not to use footnotes in the abstract or the title; the acknowledgments for funding bodies etc. are placed in a separate section at the end of the text.} \section{Guidelines} \subsection{Producing the Hard Copy}\label{subsec:prod} The hard copy may be printed using the procedure given below. You should use two files: \footnote{You can get these files from our WWW pages at {\sf http://moriond.in2p3.fr/EW/2006/Proceedings/index.html}.} \noindent {\em moriond.sty} --- the style file that provides the higher level latex commands for the proceedings. Don't change these parameters. \noindent {\em moriond.tex} --- the main text. You can delete our sample text and replace it with your own contribution to the volume, however we recommend keeping an initial version of the file for reference. Strip off any mail headers and then latex the tex file. The command for latexing is {\sf latex moriond}, do this twice to sort out the cross-referencing. These files will work with standard latex 2.09 and latex2e. If there is an abbreviation defined in the new definitions at the top of the file {\em moriond.tex} that conflicts with one of your own macros, then delete the appropriate command and revert to longhand. Failing that, please consult your local texpert to check for other conflicting macros that may be unique to your computer system. {\bf Page numbers should not appear.} \subsection{Headings and Text and Equations} Please preserve the style of the headings, text fonts and line spacing to provide a uniform style for the proceedings volume. Equations should be centered and numbered consecutively, as in Eq.~\ref{eq:murnf}, and the {\em eqnarray} environment may be used to split equations into several lines, for example in Eq.~\ref{eq:sp}, or to align several equations. An alternative method is given in Eq.~\ref{eq:spa} for long sets of equations where only one referencing equation number is wanted. In latex, it is simplest to give the equation a label, as in Eq.~\ref{eq:murnf} where we have used {\em $\backslash$label\{eq:murnf\}} to identify the equation. You can then use the reference {\em $\backslash$ref\{eq:murnf\}} when citing the equation in the text which will avoid the need to manually renumber equations due to later changes. (Look at the source file for some examples of this.) The same method can be used for referring to sections and subsections. \subsection{Tables} The tables are designed to have a uniform style throughout the proceedings volume. It doesn't matter how you choose to place the inner lines of the table, but we would prefer the border lines to be of the style shown in Table~\ref{tab:exp}. The top and bottom horizontal lines should be single (using {\em $\backslash$hline}), and there should be single vertical lines on the perimeter, (using {\em $\backslash$begin\{tabular\}\{$|...|$\}}). For the inner lines of the table, it looks better if they are kept to a minimum. We've chosen a more complicated example purely as an illustration of what is possible. The caption heading for a table should be placed at the top of the table. \begin{table}[t] \caption{Experimental Data bearing on $\Gamma(K \ra \pi \pi \gamma)$ for the $\ko_S, \ko_L$ and $K^-$ mesons.\label{tab:exp}} \vspace{0.4cm} \begin{center} \begin{tabular}{|c|c|c|l|} \hline & & & \\ & $\Gamma(\pi^- \pi^0)\; s^{-1}$ & $\Gamma(\pi^- \pi^0 \gamma)\; s^{-1}$ & \\ \hline \mco{2}{|c|}{Process for Decay} & & \\ \cline{1-2} $K^-$ & $1.711 \times 10^7$ & \begin{minipage}{1in} $2.22 \times 10^4$ \\ (DE $ 1.46 \times 10^3)$ \end{minipage} & \begin{minipage}{1.5in} No (IB)-E1 interference seen but data shows excess events relative to IB over $E^{\ast}_{\gamma} = 80$ to $100MeV$ \end{minipage} \\ & & & \\ \hline \end{tabular} \end{center} \end{table} \subsection{Figures}\label{subsec:fig} If you wish to `embed' a postscript figure in the file, then remove the \% mark from the declaration of the postscript figure within the figure description and change the filename to an appropriate one. Also remove the comment mark from the {\em input epsfig} command at the top of the file. You may need to play around with this as different computer systems appear to use different commands. Next adjust the scaling of the figure until it's correctly positioned, and remove the declarations of the lines and any anomalous spacing. If you prefer to use some other method then it's very important to leave the correct amount of vertical space in the figure declaration to accomodate your figure (remove the lines and change the vspace in the example.) Send the hard copy figures on separate pages with clear instructions to match them to the correct space in the final hard copy text. Please ensure the final hard copy figure is correctly scaled to fit the space available (this ensures the figure is legible.) The caption heading for a figure should be placed below the figure. \subsection{Limitations on the Placement of Tables, Equations and Figures}\label{sec:plac} Very large figures and tables should be placed on a page by themselves. One can use the instruction {\em $\backslash$begin\{figure\}$[$p$]$} or {\em $\backslash$begin\{table\}$[$p$]$} to position these, and they will appear on a separate page devoted to figures and tables. We would recommend making any necessary adjustments to the layout of the figures and tables only in the final draft. It is also simplest to sort out line and page breaks in the last stages. \subsection{Acknowledgments, Appendices, Footnotes and the Bibliography} If you wish to have acknowledgments to funding bodies etc., these may be placed in a separate section at the end of the text, before the Appendices. This should not be numbered so use {\em $\backslash$section$\ast$\{Acknowledgments\}}. It's preferable to have no appendices in a brief article, but if more than one is necessary then simply copy the {\em $\backslash$section$\ast$\{Appendix\}} heading and type in Appendix A, Appendix B etc. between the brackets. Footnotes are denoted by a letter superscript in the text,\footnote{Just like this one.} and references are denoted by a number superscript. We have used {\em $\backslash$bibitem} to produce the bibliography. Citations in the text use the labels defined in the bibitem declaration, for example, the first paper by Jarlskog~\cite{ja} is cited using the command {\em $\backslash$cite\{ja\}}. If you more commonly use the method of square brackets in the line of text for citation than the superscript method, please note that you need to adjust the punctuation so that the citation command appears after the punctuation mark. \subsection{Final Manuscript} The final hard copy that you send must be absolutely clean and unfolded. It will be printed directly without any further editing. Use a printer that has a good resolution (300 dots per inch or higher). There should not be any corrections made on the printed pages, nor should adhesive tape cover any lettering. Photocopies are not acceptable. The manuscript will not be reduced or enlarged when filmed so please ensure that indices and other small pieces of text are legible. A paper version should be sent by the {\bf 15th of May 2006} to:\\ {\bf Patricia Chemali\\ LAL, Bat. 200 \\ Universite Paris-Sud \\ 91898 Orsay Cedex \\ France }\\ The following may be (and has been) described as `dangerously irrelevant' physics. The Lorentz-invariant phase space integral for a general n-body decay from a particle with momentum $P$ and mass $M$ is given by: \begin{equation} I((P - k_i)^2, m^2_i, M) = \frac{1}{(2 \pi)^5}\! \int\!\frac{d^3 k_i}{2 \omega_i} \! \delta^4(P - k_i). \label{eq:murnf} \end{equation} The only experiment on $K^{\pm} \ra \pi^{\pm} \pi^0 \gamma$ since 1976 is that of Bolotov {\it et al}.~\cite{bu} There are two necessary conditions required for any acceptable parametrization of the quark mixing matrix. The first is that the matrix must be unitary, and the second is that it should contain a CP violating phase $\delta$. In Sec.~\ref{subsec:fig} the connection between invariants (of form similar to J) and unitarity relations will be examined further for the more general $ n \times n $ case. The reason is that such a matrix is not a faithful representation of the group, i.e. it does not cover all of the parameter space available. \begin{equation} \begin{array}{rcl} \bf{K} & = & Im[V_{j, \alpha} {V_{j,\alpha + 1}}^* {V_{j + 1,\alpha }}^* V_{j + 1, \alpha + 1} ] \\ & & + Im[V_{k, \alpha + 2} {V_{k,\alpha + 3}}^* {V_{k + 1,\alpha + 2 }}^* V_{k + 1, \alpha + 3} ] \\ & & + Im[V_{j + 2, \beta} {V_{j + 2,\beta + 1}}^* {V_{j + 3,\beta }}^* V_{j + 3, \beta + 1} ] \\ & & + Im[V_{k + 2, \beta + 2} {V_{k + 2,\beta + 3}}^* {V_{k + 3,\beta + 2 }}^* V_{k + 3, \beta + 3}] \\ & & \\ \bf{M} & = & Im[{V_{j, \alpha}}^* V_{j,\alpha + 1} V_{j + 1,\alpha } {V_{j + 1, \alpha + 1}}^* ] \\ & & + Im[V_{k, \alpha + 2} {V_{k,\alpha + 3}}^* {V_{k + 1,\alpha + 2 }}^* V_{k + 1, \alpha + 3} ] \\ & & + Im[{V_{j + 2, \beta}}^* V_{j + 2,\beta + 1} V_{j + 3,\beta } {V_{j + 3, \beta + 1}}^* ] \\ & & + Im[V_{k + 2, \beta + 2} {V_{k + 2,\beta + 3}}^* {V_{k + 3,\beta + 2 }}^* V_{k + 3, \beta + 3}], \\ & & \end{array}\label{eq:spa} \end{equation} where $ k = j$ or $j+1$ and $\beta = \alpha$ or $\alpha+1$, but if $k = j + 1$, then $\beta \neq \alpha + 1$ and similarly, if $\beta = \alpha + 1$ then $ k \neq j + 1$.\footnote{An example of a matrix which has elements containing the phase variable $e^{i \delta}$ to second order, i.e. elements with a phase variable $e^{2i \delta}$ is given at the end of this section.} There are only 162 quark mixing matrices using these parameters which are to first order in the phase variable $e^{i \delta}$ as is the case for the Jarlskog parametrizations, and for which J is not identically zero. It should be noted that these are physically identical and form just one true parametrization. \bea T & = & Im[V_{11} {V_{12}}^* {V_{21}}^* V_{22}] \nonumber \\ & & + Im[V_{12} {V_{13}}^* {V_{22}}^* V_{23}] \nonumber \\ & & - Im[V_{33} {V_{31}}^* {V_{13}}^* V_{11}]. \label{eq:sp} \eea \begin{figure} \rule{5cm}{0.2mm}\hfill\rule{5cm}{0.2mm} \vskip 2.5cm \rule{5cm}{0.2mm}\hfill\rule{5cm}{0.2mm} %\psfig{figure=filename.ps,height=1.5in} \caption{Radiative (off-shell, off-page and out-to-lunch) SUSY Higglets. \label{fig:radish}} \end{figure} \section*{Acknowledgments} This is where one places acknowledgments for funding bodies etc. Note that there are no section numbers for the Acknowledgments, Appendix or References. \section*{Appendix} We can insert an appendix here and place equations so that they are given numbers such as Eq.~\ref{eq:app}. \be x = y. \label{eq:app} \ee \section*{References} \begin{thebibliography}{99} \bibitem{ja}C Jarlskog in {\em CP Violation}, ed. C Jarlskog (World Scientific, Singapore, 1988). \bibitem{ma}L. Maiani, \Journal{\PLB}{62}{183}{1976}. \bibitem{bu}J.D. Bjorken and I. Dunietz, \Journal{\PRD}{36}{2109}{1987}. \bibitem{bd}C.D. Buchanan {\it et al}, \Journal{\PRD}{45}{4088}{1992}. \end{thebibliography} \end{document} %%%%%%%%%%%%%%%%%%%%%% % End of moriond.tex % %%%%%%%%%%%%%%%%%%%%%%

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\documentclass[twocolumn,twoside]{article} \makeatletter\if@twocolumn\PassOptionsToPackage{switch}{lineno}\else\fi\makeatother \usepackage{amsfonts,amssymb,amsbsy,latexsym,amsmath,tabulary,graphicx,times,xcolor} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Following additional macros are required to function some % functions which are not available in the class used. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{url,multirow,morefloats,floatflt,cancel,tfrupee} \makeatletter \AtBeginDocument{\@ifpackageloaded{textcomp}{}{\usepackage{textcomp}}} \makeatother \usepackage{colortbl} \usepackage{xcolor} \usepackage{pifont} \usepackage[nointegrals]{wasysym} \urlstyle{rm} \makeatletter %%%For Table column width calculation. \def\mcWidth#1{\csname TY@F#1\endcsname+\tabcolsep} %%Hacking center and right align for table \def\cAlignHack{\rightskip\@flushglue\leftskip\@flushglue\parindent\z@\parfillskip\z@skip} 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The spread of resistance in Enterobacteriaceae and non-fermenters to the currently available drugs make the treatment of serious nosocomial infections troublesome. The purpose of the study is to find out the carbapenem resistance among Gram-negative bacilli in a tertiary care hospital. Antibiotic susceptibility pattern of 1913 aerobic Gram-negative bacilli isolated from clinical samples was made for a period of 6 months. All the isolates were tested for susceptibility to antibiotics by the Kirby-Bauer disc diffusion technique according to CLSI guidelines. Carbapenemase production was confirmed by the Modified Hodge Test (MHT). Minimum Inhibitory Concentration (MIC) by Epsilometer (E) test was performed (for Imipenem and Meropenem) for carbapenem-resistant strains. A total of 1731 clinical samples, 1913 Gram-negative bacilli were isolated. 1476 (77.1\%) were Enterobacteriaceae and 433 (22.6\%) were non-fermenters. 54 were carbapenemase-producing Gram-negative bacilli. Meropenem E test was done for carbapenemase-producing Gram-negative bacilli. The minimum inhibitory concentration for Meropenem ranged from 0.002\ensuremath{\mu }g/ml to 32\ensuremath{\mu }g/ml. To overcome the problem of emerging resistance, combined interaction and cooperation of microbiologists, clinicians and the infection control team is needed. \end{abstract}\def\keywordstitle{Keywords} \begin{keywords}Carbapenem,\newline E Test,\newline Gram-negative bacilli,\newline Modified Hodge Test,\newline Resistance \end{keywords} \twocolumn[ \maketitle {\printKwdAbsBox}] \makeatletter\textsuperscript{*}Corresponding Author\par Name:\ Pooja~Nair~\\ Phone:\ +91-9500015564~\\ Email:\ poojanair.smc@gmail.com \par\vspace*{-11pt}\hrulefill\par{\fontsize{12}{14}\selectfont ISSN: 0975-7538}\par% \textsc{DOI:}\ \href{https://doi.org/10.26452/\@journalDoi}{\textcolor{blue}{\underline{\smash{https://doi.org/10.26452/\@journalDoi}}}}\par% \vspace*{-11pt}\hrulefill\\{\fontsize{9.12}{10.12}\selectfont Production and Hosted by}\par{\fontsize{12}{14}\selectfont Pharmascope.org}\par% \vspace*{-7pt}{\fontsize{9.12}{10.12}\selectfont\textcopyright\ \@copyrightYear\ $|$ All rights reserved.}\par% \vspace*{-11pt}\rule{\linewidth}{1.2pt} \makeatother \section{Introduction} One of the major burdens in the health care system is the emergence of antibiotic resistance. The spread of resistance among Enterobacteriaceae and non-fermenters to the currently available drugs makes the treatment of severe nosocomial infections complicated \unskip~\citep{701931:16622840}. Carbapenemase has high hydrolytic activity against penicillins, cephalosporins and carbapenems \unskip~\citep{701931:16622839}. Acquired resistance has been reported in \textit{E.coli}, \textit{Klebsiella pneumoniae}, Pseudomonas spp, Acinetobacter spp and various other non-fermenter Gram-negative bacilli \unskip~\citep{701931:16622836}. Carbapenemase gene detection by a molecular method is the gold standard but is available in only a few reference laboratories and phenotypic tests have therefore been developed. The Modified Hodge Test (MHT) is the phenotypic test recommended by the Clinical and Laboratory Standards Institute \unskip~\citep{701931:16622841} for carbapenemase screening method \unskip~\citep{701931:16622829}. The purpose of this study was to determine the carbapenem resistance among Gram-negative bacilli isolated from clinical samples and to confirm the carbapenemase production by Modified Hodge Test (MHT) and Minimum Inhibitory Concentration (MIC) by E test for carbapenem-resistant strains. \section{Materials and Methods} The study was performed in a tertiary care hospital in Tamil Nadu for a period of 6 months. 1913 aerobic gram-negative bacilli were isolated in the clinical microbiology laboratory from various samples. The study was reviewed and approved by the Institutional Ethical Committee. All the isolates have been tested for susceptibility to antibiotics by the Kirby-Bauer disc diffusion technique according to CLSI guidelines (Wayne). Antibiotics (1\ensuremath{^{st}} and 2\ensuremath{^{nd}} line ) used for the susceptibility testing in gram-negative bacilli other than Pseudomonas species were Ampicillin(A), Gentamicin(G), Cephalexin(Cn), Ciprofloxacin(Cip), Ceftazidime(Caz), Cefotaxime(Ctx), Ceftazidime-Clavulanic acid(Cac), Cotrimoxazole(Cot), Cefuroxime(Cxm), Amikacin(Ak), Norfloxacin(Nx), Nitrofurantoin(Nit), Cefaperazone-sublactam(Cfs), Ofloxacin(Of), Piperacillin-tazobactam(Pit), Cefepime(Cpm) and Imipenem(Imp). Antibiotics used for susceptibility testing for Pseudomonas species were Gentamicin(G), Ciprofloxacin(Cip), Ceftazidime(Caz), Amikacin(Ak), Ofloxacin(Of), Cefaperazone-sulbactam(Cfs), Piperacillin-tazobactam(Pit), Imipenem(Imp) and Cefepime(Cpm). \textbf{Detection of Carbapenemase Production\ensuremath{^{}}} \textbf{Modified Hodge Test (MHT)\ensuremath{^{}}} The imipenem resistant strains were subjected to the Modified Hodge test for the detection of carbapenemases. A 0.5 McFarland dilution of the \textit{Escherichia coli} ATCC 25922 was inoculated by lawn culture on the surface of Mueller-Hinton agar (MHA). After drying, 10\ensuremath{\mu }g imipenem disc was placed at the center of the plate and the 0.5 McFarland dilution of the test strain was streaked from the edge of the disc to the periphery of the plate in four different directions. The plates were incubated overnight at 37\ensuremath{^\circ}C. The presence of a 'clover-leaf shaped' zone of inhibition due to the production of carbapenemase production by the test strain was considered as positive \unskip~\citep{701931:16622842}. \textbf{Minimum Inhibitory Concentration (MIC) by E} \textbf{psilometer test } MIC to Imipenem and Meropenem of isolates which are positive for carbapenemase activity were tested by using E strips and inhibition ellipses around the strip were measured \unskip~\citep{701931:16622834}. \section{Results and Discussion} In the present study, an attempt was made to know the rate of carbapenemase-producing aerobic Gram-negative bacilli and to know their antibiogram in a tertiary care hospital. A total number of Gram-negative bacilli isolated from 1731 clinical samples during the study period of 6 months was 1913. Out of the 1731 clinical samples, 1088 (62.8\%) isolates from urine samples, 517 (29.9\%) isolates from exudates samples, 92 (5.3\%) isolates from respiratory samples and 34 (2\%) isolates were from blood samples. Among these 1913, \textit{Escherichia coli} was the commonest followed by Klebsiella spp and Pseudomonas spp (Figure~\ref{f-288ab9adbcf3}). In this study, it was found that about 77.1\% of Gram-negative bacterial isolates belonged to Enterobacteriaceae, which was almost similar to that of the study done in Pakistan \unskip~\citep{701931:16622833} with 63\%. \begin{table}[!htbp] \caption{\boldmath {Distribution of carbapenem-resistant organisms} } \label{tw-ed3de8c557bc} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.4757\linewidth-2\tabcolsep}p{\dimexpr.5243\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}Organisms & Percentage\\ \tblmidrule Pseudomonas spp & 20 (37\%)\\ Acinetobacter spp & 18 (33.3\%)\\ Klebsiella spp & 9 (16.7\%)\\ Escherichia coli & 5 (9.3\%)\\ Proteus spp & 2 (3.7\%)\\ Total & 54 \\ \tblbottomrule \end{tabulary}\par \end{table} \begin{table*}[!htbp] \caption{\boldmath {MIC of meropenem for carbapenemase-producing Gram-negative bacilli} } \label{tw-d71c1dcb0aa9} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.295\linewidth-2\tabcolsep}p{\dimexpr.1617\linewidth-2\tabcolsep}p{\dimexpr.2933\linewidth-2\tabcolsep}p{\dimexpr.25\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}Organism & No. & MIC value (\ensuremath{\mu }g/ml) & Interpretation\\ \tblmidrule Acinetobacter spp & 4 & 0.75 & Sensitive\\ Proteus spp & 2 & 2 & Intermediate\\ Escherichia coli & 10 & {\textgreater}32 & Resistant\\ Acinetobacter spp & 15 & {\textgreater}32 & Resistant\\ Pseudomonas spp & 19 & {\textgreater}32 & Resistant\\ Klebsiella spp & 4 & {\textgreater}32 & Resistant\\ \tblbottomrule \end{tabulary}\par \end{table*} \begin{table*}[!htbp] \caption{\boldmath {Percentage of carbapenem resistance among different organisms from various literature.} } \label{tw-42c5ed48e2f2} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.2362\linewidth-2\tabcolsep}p{\dimexpr.2342000000000001\linewidth-2\tabcolsep}p{\dimexpr.20680000000000007\linewidth-2\tabcolsep}p{\dimexpr.3228\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}Organisms & Percentage of carbapenem resistance & Place & Author\\ \tblmidrule Non-fermenters & 28/50 (56\%) & Vellore & \unskip~\citep{701931:16622838}\\ Acinetobacter spp & 21/150 (14\%) & Bangalore & \unskip~\citep{701931:16622831}\\ Pseudomonas spp & 39/140 (27.9\%) & \multicolumn{1}{p{\dimexpr(.20680000000000007\linewidth-2\tabcolsep)}}{\multirow{2}{\linewidth}{Pondicherry}} & \multicolumn{1}{p{\dimexpr(.3228\linewidth-2\tabcolsep)}}{\multirow{2}{\linewidth}{\unskip~\citep{701931:16622832}}}\\ Acinetobacter spp & 53/100 (53\%) & & \\ Acinetobacter baumannii & 43/130 (33.1\%) & Vellore & \unskip~\citep{701931:16622830}\\ Acinetobacter spp & 28/140 (20\%) & Uttar Pradesh & \unskip~\citep{701931:16622835}\\ Enterobacteriaceae & 57/465 (12.3\%) & Mumbai & \unskip~\citep{701931:16622834}\\ \tblbottomrule \end{tabulary}\par \end{table*} \bgroup \fixFloatSize{images/b834fa9d-bf8f-479a-ae1f-96d14dc4ac17-upicture1.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/b834fa9d-bf8f-479a-ae1f-96d14dc4ac17-upicture1.png}{\includegraphics{images/b834fa9d-bf8f-479a-ae1f-96d14dc4ac17-upicture1.png}}{} \makeatother \caption{\boldmath {Percentage of different GNB isolated}} \label{f-288ab9adbcf3} \end{figure} \egroup \bgroup \fixFloatSize{images/ad6ed729-02be-433a-93c8-b754c83534ff-upicture2.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/ad6ed729-02be-433a-93c8-b754c83534ff-upicture2.png}{\includegraphics{images/ad6ed729-02be-433a-93c8-b754c83534ff-upicture2.png}}{} \makeatother \caption{\boldmath {Distribution of Carbapenemase producers in various clinical samples }} \label{f-f31af16ca9ae} \end{figure} \egroup \bgroup \fixFloatSize{images/43552f1d-4cf5-4f05-b340-0f2816fcb15e-upicture4.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/43552f1d-4cf5-4f05-b340-0f2816fcb15e-upicture4.png}{\includegraphics{images/43552f1d-4cf5-4f05-b340-0f2816fcb15e-upicture4.png}}{} \makeatother \caption{\boldmath {Modified Hodge Test showing indentation towards Imipenem disc for the confirmation of Carbapenemase production}} \label{f-c57e16850fa7} \end{figure} \egroup \bgroup \fixFloatSize{images/1faa5c0e-e6bf-4cbd-a1be-da45a4b406b7-upicture5.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/1faa5c0e-e6bf-4cbd-a1be-da45a4b406b7-upicture5.png}{\includegraphics{images/1faa5c0e-e6bf-4cbd-a1be-da45a4b406b7-upicture5.png}}{} \makeatother \caption{\boldmath {Minimum Inhibitory Concentration (MIC) of Meropenem by E test}} \label{f-9159682b912d} \end{figure} \egroup Out of 1913 isolates, 54 (2.82\%) were found to be carbapenem-resistant by Kirby-Bauer disc diffusion method for 30\ensuremath{\mu }g of imipenem and their distribution in various clinical samples are elucidated in Figure~\ref{f-f31af16ca9ae}. Carbapenemase production was confirmed for all the 54 isolates by the Modified Hodge test (Figure~\ref{f-c57e16850fa7}). Among the 54 clinical samples from which carbapenem-resistant organisms were isolated, 13 were from the age group 41-50 years. The least number of samples collected were 1, from each of both the age group 0-10 years and 11-20 years. In our study, among the carbapenemase producers, Pseudomonas spp (37\%) was the predominant one followed by Acinetobacter spp (33.3\%), as shown in Table~\ref{tw-ed3de8c557bc}. But in a study for simple screening for carbapenemase, 25.64\% of Pseudomonas spp were found to be carbapenemase producers \unskip~\citep{701931:16622832}. The percentage of carbapenem resistance from different literatures is outlined below in Table~\ref{tw-42c5ed48e2f2}. Minimum inhibitory concentration for Meropenem ranged from 0.002\ensuremath{\mu }g/ml to 32\ensuremath{\mu }g/ml (Figure~\ref{f-9159682b912d}). Meropenem E test was done for all the 54 carbapenemases producing Gram-negative bacilli [Table~\ref{tw-d71c1dcb0aa9}]. The MIC of Meropenem for resistant strains of Pseudomonas spp and Acinetobacter spp is {\textgreater} 16\ensuremath{\mu }g/ml. The MIC value of meropenem for resistant strains of members of the Enterobacteriaceae is {\textgreater}4\ensuremath{\mu }g/ml. The strains of Acinetobacter spp with MIC of 0.75\ensuremath{\mu }g/ml for meropenem were sensitive to aminoglycosides, nitrofurantoin and combination of beta-lactamase inhibitors with cephalosporins. These strains were resistant to third-generation cephalosporins and imipenem only. All Meropenem resistant isolates were resistant to Imipenem, but not all Imipenem resistant organisms were resistant to Meropenem. Some of the imipenem resistant strains of Acinetobacter spp showed MIC \textless\ 4\ensuremath{\mu }g/ml (sensitive). This could be because the mechanisms of resistance to these two drugs are different \unskip~\citep{701931:16622837}. In another study, among the 21 carbapenemases producing \textit{Klebsiella pneumoniae}, 7 strains were found to have 0.5\ensuremath{\mu }g/ml MIC for meropenem, which is sensitive \unskip~\citep{701931:16622842}. In a similar study, out of 36 multidrug-resistant Acinetobacter spp, 5 strains that were resistant to meropenem by the disk diffusion method were found to have MICs to meropenem in the sensitive zone \unskip~\citep{701931:16622839}.\ensuremath{^{}} \section{Conclusion} In this study, the Modified Hodge Test and test for Minimum Inhibitory Concentration were used for detecting carbapenemase production and confirming resistance to carbapenem. Modified Hodge Test proved to be a good screening test for the detection of carbapenemase production as the results obtained with this study correlates with other studies. To overcome the problem of emerging resistance, combined interaction and cooperation of microbiologists, clinicians and infection control teams are needed. \bibliographystyle{pharmascope_apa-custom} \bibliography{\jobname} \end{document}

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%% %% Ein Beispiel der DANTE-Edition %% %% 7. Auflage %% %% Beispiel 25-02-20 auf Seite 546. %% %% Copyright (C) 2016 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% %% %% ==== % Show page(s) 1 %% %% \documentclass[]{exaarticle} \pagestyle{empty} \setlength\textwidth{169.16928pt} \setlength\parindent{0pt} %StartShownPreambleCommands \usepackage{pst-barcode} %StopShownPreambleCommands \begin{document} \begin{pspicture}(2in,.3in) \psbarcode{(01)24012345678905}% {format=truncated includetext height=0.3}% {databaromni} \end{pspicture} \end{document}

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% \LaTeX-Main\ %% The LaTeX package tcolorbox - version 4.21 (2019/09/19) %% tcolorbox-tutorial-poster.tex: a tutorial for poster creation with tcolorbox %% %% ------------------------------------------------------------------------------------------- %% Copyright (c) 2006-2019 by Prof. Dr. Dr. Thomas F. Sturm <thomas dot sturm at unibw dot de> %% ------------------------------------------------------------------------------------------- %% %% This work may be distributed and/or modified under the %% conditions of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% The latest version of this license is in %% http://www.latex-project.org/lppl.txt %% and version 1.3 or later is part of all distributions of LaTeX %% version 2005/12/01 or later. %% %% This work has the LPPL maintenance status `author-maintained'. %% %% This work consists of all files listed in README %% % arara: pdflatex: { shell: yes } % arara: pdflatex: { shell: yes } \documentclass[12pt]{article} \usepackage[a3paper,landscape]{geometry} \usepackage{lipsum} \usepackage{lmodern} \usepackage{enumerate} \usepackage[poster]{tcolorbox} \tcbuselibrary{minted} % <- replace by \tcbuselibrary{listings}, if minted does not work for you \pagestyle{empty} \newtcolorbox[auto counter]{guide}[1][]{enhanced jigsaw,inherit height, colback=red!5,opacityback=0.9,colframe=red,title=Poster Tutorial \#\thetcbcounter, grow to left by=8mm,grow to right by=8mm, arc is angular,arc=3mm, fonttitle=\bfseries\large, fuzzy halo=4mm with blue!50!red,#1 } \tcbset{ mylisting/.style={enhanced jigsaw,size=minimal,toprule=0.5mm,bottomrule=0.5mm,boxsep=2mm,oversize, colback=white,opacityback=0.75,listing only} } \newtcblisting{guidelisting}[1]{mylisting,#1} \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = {spread}, poster = {showframe,columns=4,rows=5}, ] \begin{posterboxenv}[blankest]{column=2,span=2,at=middle} \begin{guide}[toptitle=3mm,before title={\begin{center} Thomas F.~Sturm\\ \Large A Tutorial for Poster Creation with Tcolorbox \end{center}}] Welcome to the poster tutorial! \tcbline We start at the very begin with an empty poster.\par\medskip In this tutorial, we use A3 sized paper in landscape format which can be set up with the \texttt{geometry} package. Naturally, we need the \texttt{tcolorbox} package with at least the \texttt{poster} library loaded.\par At begin, we only choose the number of columns (4) and rows (5) and we display a help grid.\par\medskip \begin{guidelisting}{} \documentclass[12pt]{article} \usepackage[a3paper,landscape]{geometry} \usepackage[poster]{tcolorbox} \pagestyle{empty} \begin{document} \begin{tcbposter}[ coverage = {spread}, poster = {showframe,columns=4,rows=5}, ] % Here, we insert the poster content later \end{tcbposter} \end{document} \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe,columns=4,rows=5}, ] \begin{posterboxenv}[blankest]{column=2,span=2,above=bottom} \begin{guide} Now, we put in some fancy settings to the poster \texttt{coverage}.\par Also, some more packages are loaded for the future poster content. \par\medskip \begin{guidelisting}{} \documentclass[12pt]{article} \usepackage[a3paper,landscape]{geometry} \usepackage{lipsum} \usepackage{lmodern} \usepackage{enumerate} \usepackage[poster]{tcolorbox} \tcbuselibrary{minted} % <- replace by \tcbuselibrary{listings}, if minted does not work for you \pagestyle{empty} \begin{document} \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe,columns=4,rows=5}, ] % Here, we insert the poster content later \end{tcbposter} \end{document} \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe,columns=4,rows=5}, ] %---- \posterbox{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ } %---- \posterbox[adjusted title=Process]{name=process,column=2,span=2,above=references}{ } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=3,span=2,at=middle} \begin{guide} It is time to fill boxes into the \texttt{poster} environment. This is the most crucial part of your poster creation, because you have to decide about the general contents and the base design.\par But, as you can see in the listing below, the boxes are placed with relative positions to each other and the sizes are able to change automatically. \par\medskip \begin{guidelisting}{} %... \posterbox{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{} \posterbox[adjusted title=Process]{name=process,column=2,span=2,above=references}{} \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{} \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} \posterbox[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references}{} \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{} %... \end{guidelisting} \medskip The \texttt{project} box is made breakable. Note the two parts \texttt{project1} and \texttt{project2} where the second part is denoted by a placeholder. \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ } %---- \posterbox[adjusted title=Process]{name=process,column=2,span=2,above=references}{ } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=3,span=2,at=middle} \begin{guide} As next step, we choose some nice settings for all the boxes. These global settings are applied using the \texttt{boxes} option of the poster.\par Also, we do not need the auxiliary frame lines anymore and we set \texttt{showframe=false}. \par\medskip \begin{guidelisting}{} %... \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %... \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ } %---- \posterbox[adjusted title=Process]{name=process,column=2,span=2,above=references}{ } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=2,span=2,below=title,yshift=-5mm} \begin{guide}[grow to left by=8mm,grow to right by=8mm,] We make the \texttt{title} box different from the other boxes by removing everything except the background. Also, two pictures are added left and right which should be seen as logos or similar things. \par\medskip \begin{guidelisting}{} %... \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %... \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process]{name=process,column=2,span=2,above=references}{ } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=2,span=2,above=references,yshift=5mm} \begin{guide} The \texttt{references} box is filled with a simple \texttt{enumerate} list.\par You may insert a more fancier and \LaTeX ier bibliography for your real project \ldots \par\medskip \begin{guidelisting}{} %... \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %... \end{guidelisting} \medskip Surely, you noted that all boxes adapt to the grown height of our \texttt{references} box. Maybe, you want to get some pages back to see how the box placements were done for this example. \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=2,span=2,above=process,yshift=5mm} \begin{guide} We go on with the \texttt{process} which gets some example \texttt{tikzpicture}.\par Note that you always can insert additional \texttt{tcolorbox} options like \texttt{halign=center} to a \texttt{posterbox}. \par\medskip \begin{guidelisting}{} %... \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %... \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %---- \posterbox[adjusted title=Central Picture] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=3,span=2,at=middle} \begin{guide} The \texttt{project} is a breakable box with two parts. Nevertheless, you can fill the box like any other box. The information on how to break was already given by the placement options. \par\medskip \begin{guidelisting}{} %... \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %... \end{guidelisting} \medskip The two boxes have a \emph{closed} appearance, because we used \texttt{enhanced standard jigsaw} as global style for all boxes. For an \emph{open} appearance, just use \texttt{enhanced jigsaw} instead:\par\medskip \begin{guidelisting}{} %... \begin{tcbposter}[ %... boxes = { enhanced jigsaw,% <----------- sharp corners=downhill,arc=3mm,boxrule=1mm, %... } ] %... \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %---- \posterbox[adjusted title=Central Picture, interior style={fill overzoom image=blueshade.png}] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm] {name=algorithm,column=4,between=top and references} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=2,span=2,below=picture,yshift=-5mm} \begin{guide} In our example, the whole space of the \texttt{picture} box should be filled with a given picture. This is a piece of cake using a special \texttt{interior style}: \par\medskip \begin{guidelisting}{} %... \posterbox[adjusted title=Central Picture, interior style={fill overzoom image=blueshade.png}] {name=picture,column=3,between=title and process}{} %... \end{guidelisting} \end{guide} \end{posterboxenv} \end{tcbposter} \begin{tcbverbatimwrite}{\jobname.mylist} %... \begin{posterboxenv}[adjusted title=Core Algorithm,leftupper=0pt,rightupper=0pt] {name=algorithm,column=4,between=top and references} \begin{tcblisting}{blankest,listing only} \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} %... \end{tikzpicture} \end{tcblisting} \end{posterboxenv} %... \end{tcbverbatimwrite} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %---- \posterbox[adjusted title=Central Picture, interior style={fill overzoom image=blueshade.png}] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm,leftupper=0pt,rightupper=0pt] {name=algorithm,column=4,between=top and references} \begin{tcblisting}{blankest,listing only} \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \begin{tikzpicture}[very thick,radius=1cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \end{tcblisting} \end{posterboxenv} %---- \posterbox[adjusted title=Contact] {name=contact,column*=4,span=1.5,between=process and bottom}{ } \begin{posterboxenv}[blankest]{column=2,span=2,below=picture,at=middle} \begin{guide} For the Algorithm, we need a \texttt{verbatim} environment. Here, \texttt{tcblisting} is used.\par Therefore, we cannot use a \texttt{posterbox} as usual, but we can a \texttt{posterboxenv} environment instead.\par Note that you would get some weird errors, if \texttt{posterbox} would have been applied. \par\medskip \tcbinputlisting{mylisting,listing file=\jobname.mylist} \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %---- \posterbox[adjusted title=Central Picture, interior style={fill overzoom image=blueshade.png}] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm,leftupper=0pt,rightupper=0pt] {name=algorithm,column=4,between=top and references} \begin{tcblisting}{blankest,listing only} \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \begin{tikzpicture}[very thick,radius=1cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \end{tcblisting} \end{posterboxenv} %---- \posterbox[adjusted title=Contact,fit,fit basedim=12pt] {name=contact,column*=4,span=1.5,between=process and bottom}{ \lipsum[2] } \begin{posterboxenv}[blankest]{column=2,span=2,above=contact,yshift=5mm} \begin{guide} Finally, the \texttt{contact} box is filled. But, in our example case, there is not much space for a lot of contact text.\par Therefore, we add \texttt{fit} to fit in the text automatically. \par\medskip \begin{guidelisting}{} %... \posterbox[adjusted title=Contact,fit,fit basedim=12pt] {name=contact,column*=4,span=1.5,between=process and bottom}{ \lipsum[2] } %... \end{guidelisting} \par\medskip Our poster is finished now. Just go to the next page to see the final result. \end{guide} \end{posterboxenv} \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=4,rows=5}, boxes = { enhanced standard jigsaw,sharp corners=downhill,arc=3mm,boxrule=1mm, colback=white,opacityback=0.75,colframe=blue, title style={left color=black,right color=cyan}, fonttitle=\bfseries\Large\scshape } ] %---- \posterbox[blankest,interior engine=path,height=3cm, halign=center,valign=center,fontupper=\bfseries\large,colupper=red!25!black, underlay={ \node[right,inner sep=0pt,outer sep=0pt] at (frame.west) {\includegraphics[height=3cm]{pink_marble.png}}; \node[left,inner sep=0pt,outer sep=0pt] at (frame.east) {\includegraphics[height=3cm]{crinklepaper.png}}; }, ]{name=title,column=1,span=3,below=top}{ \resizebox{18cm}{!}{\bfseries\Huge My Important Project}\\[3mm] Hans.Mustermann@deepthought.university } %---- \posterbox[adjusted title=References]{name=references,column=2,span=1.5,above=bottom}{ \begin{enumerate}[{[1]}] \item\label{litA} Important Authors, \textit{Important Title} \item\label{litB} More Important Authors, \textit{More Important Title} \item\label{litC} Less Important Authors, \textit{Less Important Title} \end{enumerate} } %---- \posterbox[adjusted title=Process,halign=center]{name=process,column=2,span=2,above=references}{ \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} } %---- \posterbox[adjusted title=Project Description]{name=project, sequence=1 between title and bottom then 2 between title and process}{ See [\ref{litA}]: \lipsum[1] \begin{center} \tikz \draw[thick,rounded corners=8pt] (0,0)--(0,2)--(1,3.25)--(2,2)--(2,0)--(0,2)--(2,2)--(0,0)--(2,0); \quad by [\ref{litB}] \end{center} \lipsum[2-3]\par See [\ref{litC}]: \lipsum[4] \begin{center} \tikz \shadedraw [left color=red,right color=blue] (0,0) rectangle (2,2); \end{center} That's all. } %---- \posterbox[adjusted title=Central Picture, interior style={fill overzoom image=blueshade.png}] {name=picture,column=3,between=title and process}{} %---- \begin{posterboxenv}[adjusted title=Core Algorithm,leftupper=0pt,rightupper=0pt] {name=algorithm,column=4,between=top and references} \begin{tcblisting}{blankest,listing only} \begin{tikzpicture}[very thick,radius=2cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \begin{tikzpicture}[very thick,radius=1cm] \begin{scope} \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=30]; \end{scope} \begin{scope}[xshift=5cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=70]; \end{scope} \begin{scope}[xshift=10cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=110]; \end{scope} \begin{scope}[xshift=15cm] \path[draw=black,fill=white] (0,0) circle; \path[fill=red] (0,0) -- (2,0) arc [start angle=0, end angle=240]; \end{scope} \end{tikzpicture} \end{tcblisting} \end{posterboxenv} %---- \posterbox[adjusted title=Contact,fit,fit basedim=12pt] {name=contact,column*=4,span=1.5,between=process and bottom}{ \lipsum[2] } \end{tcbposter} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{tcbposter}[ coverage = { spread, interior style={top color=yellow,bottom color=yellow!50!red}, watermark text={\LaTeX\ Poster}, watermark color=yellow, }, poster = {showframe=false,columns=3,rows=5}, ] %---- \posterbox[blankest]{name=title,column=1,span=1,below=top}{ \begin{guide}[grow to left by=0mm,grow to right by=-16mm] Source code for the example poster \end{guide} } \posterbox[blankest,posterset/fontsize=11pt]{name=source, sequence=1 between title and bottom then 2 between top and bottom then 3 between top and bottom }{% \tcbinputlisting{standard jigsaw,size=minimal,toprule=0.5mm,bottomrule=0.5mm,boxsep=2mm, colback=white,opacityback=0.75,listing only, enforce breakable,tcb@poster@boxheight,before skip=-\interlineskip,height fixed for=all, minted options={tabsize=2,fontsize=\small,breaklines,breakafter={,]-}}, listing file=tcolorbox-example-poster.tex}% } \end{tcbposter} \end{document}

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\documentclass[twocolumn,twoside]{article} \makeatletter\if@twocolumn\PassOptionsToPackage{switch}{lineno}\else\fi\makeatother \usepackage{amsfonts,amssymb,amsbsy,latexsym,amsmath,tabulary,graphicx,times,xcolor} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Following additional macros are required to function some % functions which are not available in the class used. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{url,multirow,morefloats,floatflt,cancel,tfrupee} \makeatletter \AtBeginDocument{\@ifpackageloaded{textcomp}{}{\usepackage{textcomp}}} \makeatother \usepackage{colortbl} \usepackage{xcolor} \usepackage{pifont} \usepackage[nointegrals]{wasysym} \urlstyle{rm} \makeatletter %%%For Table column width calculation. \def\mcWidth#1{\csname TY@F#1\endcsname+\tabcolsep} %%Hacking center and right align for table \def\cAlignHack{\rightskip\@flushglue\leftskip\@flushglue\parindent\z@\parfillskip\z@skip} 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Sci.} \fancypagestyle{headings}{% \renewcommand{\headrulewidth}{0pt}% \renewcommand{\footrulewidth}{0.3pt} \fancyhf{}% \fancyhead[R]{% \fontsize{9.12}{11}\selectfont\RunningAuthor,\ \abbrvJournalTitle,\ \ifx\@journalVolume\@empty X\else\@journalVolume\fi% \ifx\@journalIssue\@empty\else(\@journalIssue)\fi% ,\ \ifx\@firstPage\@empty 1\else\@firstPage\fi-\pageref*{LastPage}% }% \fancyfoot[LO,RE]{\fontsize{9.12}{11}\selectfont\textcopyright\ International Journal of Research in Pharmaceutical Sciences}% \fancyfoot[RO,LE]{\fontsize{9.12}{11}\selectfont\thepage} }\pagestyle{headings} \fancypagestyle{plain}{% \renewcommand{\headrulewidth}{0pt}% \renewcommand{\footrulewidth}{0.3pt}% \fancyhf{}% \fancyhead[R]{% \fontsize{9.12}{11}\selectfont\RunningAuthor,\ \abbrvJournalTitle,\ \ifx\@journalVolume\@empty X\else\@journalVolume\fi% \ifx\@journalIssue\@empty\else(\@journalIssue)\fi% ,\ \ifx\@firstPage\@empty 1\else\@firstPage\fi-\pageref*{LastPage}% }% \fancyfoot[LO,RE]{\fontsize{9.12}{11}\selectfont\textcopyright\ International Journal of Research in Pharmaceutical Sciences}% \fancyfoot[RO,LE]{\fontsize{9.12}{11}\selectfont\thepage} \ifx\@firstPage\@empty\else\setcounter{page}{\@firstPage}\fi } \def\NormalBaseline{\def\baselinestretch{1.1}} \usepackage{textcase} \setcounter{secnumdepth}{0} \titleformat{\section}[block]{\bfseries\boldmath\NormalBaseline\filright\fontsize{10.5}{13}\selectfont} {\thesection} {6pt} {\MakeTextUppercase{#1}} [] \titleformat{\subsection}[block]{\bfseries\boldmath\NormalBaseline\filright\fontsize{10.5}{12}\selectfont} {\thesubsection} {6pt} {#1} [] \titleformat{\subsubsection}[block]{\NormalBaseline\filright\fontsize{10.5}{12}\selectfont} {\thesubsubsection} {6pt} {#1} [] \titleformat{\paragraph}[block]{\NormalBaseline\filright\fontsize{10.5}{10}\selectfont} {\theparagraph} {6pt} {#1} [] \titleformat{\subparagraph}[block]{\NormalBaseline\filright\fontsize{10.5}{12}\selectfont} {\thesubparagraph} {6pt} {#1} [] \titlespacing{\section}{0pt}{.5\baselineskip}{.5\baselineskip} \titlespacing{\subsection}{0pt}{.5\baselineskip}{.5\baselineskip} \titlespacing{\subsubsection}{0pt}{.5\baselineskip}{.5\baselineskip} \titlespacing{\paragraph}{0pt}{.5\baselineskip}{.5\baselineskip} \titlespacing{\subparagraph}{0pt}{.5\baselineskip}{.5\baselineskip} \captionsetup[figure]{skip=1.4pt,font=bf,labelsep=colon,justification=raggedright,singlelinecheck=false} \captionsetup[table]{skip=1.4pt,font=bf,labelsep=colon,justification=raggedright,singlelinecheck=false} \def\bibyear#1{#1} \def\bibjtitle#1{#1} \def\bibauand{} \setlength\bibsep{3pt} \setlength\bibhang{8pt} \makeatother \date{} \usepackage{float} \newfloat{scheme}{tbp}{Scheme} \floatname{scheme}{Scheme} \makeatletter \@ifpackageloaded{endfloat}{\@ifpackagewith{endfloat}{figuresonly}{\DeclareDelayedFloat{scheme}{Scheme}}{\@ifpackagewith{endfloat}{tablesonly}{}{\DeclareDelayedFloat{scheme}{Scheme}}}}{}\makeatother \begin{document} \def\RunningAuthor{Reem Mohsen Khalaf Al-Uobody et al.} \firstPage{717} \articleType{Original Article} \receivedDate{20.08.2019} \acceptedDate{26.11.2019} \revisedDate{21.11.2019} \journalVolume{2020, 11} \journalIssue{1} \journalDoi{ijrps.v11i1.1884} \copyrightYear{2020} \def\authorCount{5} \def\affCount{3} \def\journalTitle{International Journal of Research in Pharmaceutical Sciences} \title{\textbf{Synthesize and Characterization of New Polydimethylsiloxane Derivatives with Evaluation of Biological Activities}} \author{Reem~Mohsen~Khalaf~Al-Uobody\textsuperscript{*}\textsuperscript{1}, Raheem~Jameel~Mheesn\textsuperscript{1}, Hatam~Ahmed~Jassim\textsuperscript{1}, Eiman~A.~Saeed\textsuperscript{2}, Alaa~A.~Ibrahim~Al~Dirawi\textsuperscript{3}~\\[5pt]{\textsuperscript{1}Department of Pharmaceutical Chemistry, College of Pharmacy, University of Basrah, Iraq}~\\{\textsuperscript{2}Department of Clinical Laboratory Science College of Pharmacy, University of Basrah, Iraq}~\\{\textsuperscript{3}Department of Veterinary Surgery and Obstetric, Collage of Veterinary Medicine, University of Basrah, Iraq}} \begin{abstract} New polymers of silicone derivatives were prepared. The polymers were characterized by IR, NMR spectrophotometry. The biological activity against Streptococcus, E-Coli, Pseudomonas, Staphylococcus, Klebsiella were studied. The new polymers have shown more activity against Pseudomonas, Staphylococcus aureus, Klebsiella. The wound dressing studied on New Zealand White Rabbits (5 groups) each group contained 6 rabbits (3 male and 3 female), each animal had made 2 wounds,one for control (povidone-iodine, silicone gel) and other for our compounds, all products showed good activity on open wounds more than drugs in market. Benzaldehyde is consists of benzene bearing a single formyl substituent; the simplest aromatic aldehyde and parent of the class of benzaldehydes. It has a role as a flavoring agent, a fragrance, an odorant receptor agonist. Polyvinylpyrrolidone has disinfectant properties, so we used it in our compound to become more potent. \end{abstract}\def\keywordstitle{Keywords} \begin{keywords}wound dressing,\newline open wound,\newline polyvinyl pyrrolidone,\newline benzaldehyde,\newline vinyl trimethyl silane,\newline paraflurobenzaldehyde,\newline param ethoxy benzaldehyde,\newline parahydroxybenzaldehyde \end{keywords} \twocolumn[ \maketitle {\printKwdAbsBox}] \makeatletter\textsuperscript{*}Corresponding Author\par Name:\ Reem~Mohsen~Khalaf~Al-Uobody~\\ Phone:\ +96477032196107~\\ Email:\ reem.muhsin83@gmail.com \par\vspace*{-11pt}\hrulefill\par{\fontsize{12}{14}\selectfont ISSN: 0975-7538}\par% \textsc{DOI:}\ \href{https://doi.org/10.26452/\@journalDoi}{\textcolor{blue}{\underline{\smash{https://doi.org/10.26452/\@journalDoi}}}}\par% \vspace*{-11pt}\hrulefill\\{\fontsize{9.12}{10.12}\selectfont Production and Hosted by}\par{\fontsize{12}{14}\selectfont Pharmascope.org}\par% \vspace*{-7pt}{\fontsize{9.12}{10.12}\selectfont\textcopyright\ \@copyrightYear\ $|$ All rights reserved.}\par% \vspace*{-11pt}\rule{\linewidth}{1.2pt} \makeatother \section{Introduction} Multiple biological, non-natural, and hybrid polymers are used for multiple medical applications. A wide range of different polymers is existing, and they have further the benefit to be tunable in physical, chemical, and biological properties in a varied range to match the desires of specific applications\unskip~\citep{643432:15101305} Synthetic polymers gained high attractiveness for technical as well as for medical applications for various reasons. A wide range of physical and chemical properties can be accomplished based on the monomer units, polymerization reaction, and formation of copolymers containing different components at regulating concentrations\unskip~\citep{643432:15101303}. One of the most significant synthetic polymers is silicone.\ensuremath{_{}} Silicones consist of an {\textendash}Si{\textendash}O{\textendash} backbone with different chain lengths and crosslinks, which conclude mechanical properties from liquid oil via a gel construction to rubber elastomer. The side chains may be improved, but in the most communal poly(dimethylsiloxane) (PDMS), they are methyl groups.\unskip~\citep{643432:15101307} Polydimethylsiloxane (PDMS) is the best-known organosilicon rubbery polymer. Thermal stability, Good resistance to UV radiation. Exceptional release properties and surface activity. High permeability to gases. Good damping activities, antifriction, and lubricity. Hydrophobic and physiological inertness. High inertness in physiological surroundings makes it likely to use this material in altered biomedical uses, including soft matrix for drug delivery, cosmetics, wound dressing.\unskip~\citep{643432:15101300} Benzaldehyde is involved benzene bearing a single formyl substituent, the simplest aromatic aldehyde and parent of the class of benzaldehydes. It has a role as a flavoring agent, a fragrance, an odorant receptor agonist. Benzaldehyde seems like a clear colorless to yellow liquid; it odors a little like almond and has a hot, aromatic taste. Benzaldehyde is very soluble in water. Benzaldehyde happens naturally in plants. It can be produced in the atmosphere from the reaction of certain chemicals with sunlight. It is used as a preservative in cosmetics, personal care products, as a solvent for oils, flavoring, and unnatural perfumes. It may be a tobacco additive. It was previously used as an insecticide. Because Benzaldehyde quickly metabolizes to Benzoic Acid in the skin, the obtainable dermal irritation and sensitization data demonstrating no undesirable reactions to Benzoic Acid were regard as supportive of the safety of Benzaldehyde. Benzaldehyde is absorbed within the skin and by the lungs, allocates to all well-perfused organs, but does not store in any specific tissue type.\unskip~\citep{643432:15101301}\textit{.} Polyvinylpyrrolidone (PVP), also generally called polyvidone or povidone, is a water-soluble polymer prepared from the monomer \textit{\space }-vinylpyrrolidone.\textit{\unskip~\citep{643432:15101302}} \textit{\space } PVP added to iodine forms a complex called povidone-iodine that possesses disinfectant properties. This complex is used in different products, similar solutions, ointment, pessaries, liquid soaps, and surgical scrubs.\unskip~\citep{643432:15101296}\textit{.} \section{Materials and Methods} \textbf{Chemicals} The chemical compounds and agars used in an experimental will be mentioned in Table~\ref{tw-73e1adbaf6eb}. \begin{table*}[!htbp] \caption{\boldmath {Chemicals, Agars, and their suppliers} } \label{tw-73e1adbaf6eb} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.17259999999999998\linewidth-2\tabcolsep}p{\dimexpr.46839999999999996\linewidth-2\tabcolsep}p{\dimexpr.359\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}\cAlignHack No & \cAlignHack Chemicals and Agars & \cAlignHack Origin \\ \tblmidrule \cAlignHack 1 & Vinyltrimethylsilane VTMS & Sigma Aldrich - Germany \\ \cAlignHack 2 & Absolute ethanol & Sigma Aldrich - Germany\\ \cAlignHack 3 & Polyvinylpyrrolidone PVP & Sigma Aldrich - Germany\\ \cAlignHack 4 & Benzaldehyde BD & Sigma Aldrich - Germany\\ \cAlignHack 5 & Parafluro benzaldehyde para F.BD & Merk - Germany \\ \cAlignHack 6 & Parahydroxy benzaldehyde para OH.BD & ALPHA - India \\ \cAlignHack 7 & para methoxy benzaldehyde para OCH3.BD & Merk - Germany\\ \cAlignHack 8 & Potassium hydroxide KOH & Schariab - Spain\\ \cAlignHack 9 & Nutrient agar & OXOID - England\\ \cAlignHack 10 & Nutrient broth & OXOID {\textendash} England\\ \cAlignHack 11 & Silicone gel & Philadelphia {\textendash} Jordan\\ \cAlignHack 12 & Povidone-iodine & Jou pharm. - Egypt\\ \tblbottomrule \end{tabulary}\par \end{table*} \begin{table*}[!htbp] \caption{\boldmath {The synthesized compounds} } \label{tw-1bb72d853a50} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.1811333333333333\linewidth-2\tabcolsep}p{\dimexpr.5749\linewidth-2\tabcolsep}p{\dimexpr.24396666666666672\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}\cAlignHack NO & \cAlignHack Name of compounds & \cAlignHack Symbol \\ \tblmidrule \cAlignHack 1 & Polyvinyl pyrrolidone \_ Benzyldehyde & PVB \\ \cAlignHack 2 & polyvinyl pyrrolidon\_Benzaldehyde\_VinylTrimethylSilane & VS.PVB\\ \cAlignHack 3 & Polyvinyl pyrrolidone \_Paraflurobenzyldehyde & F.PVB\\ \cAlignHack 4 & Polyvinyl pyrrolidone \_Paraomethoxyobenzyldehyde & OCH3.PVB\\ \cAlignHack 5 & Polyvinyl pyrrolidone \_Parahydroxybenzyldehyde & OH.PVB\\ \tblbottomrule \end{tabulary}\par \end{table*} \textbf{Synthesis of the compounds} The new products are prepared by the following methods, as shown in Table~\ref{tw-1bb72d853a50} \textbf{Preparation of Polyvinyl pyrrolidone \_ Benzyldehyde PVB} Dissolve 10 moles (1.1g) of PVP in 10 ml ethanol in 60c \ensuremath{{}^{\circ}} with stirring then add 5ml of alcoholic KOH; the colour became yellow, last added 10mmole of B. D (1g) immediately the colour change to obtain on the yellow liquid product and reflux for 2hrs with stirring. Neutralized the solution with 10\% HCL till the PH became 7, filtered the product to remove the precipitate, and evaporate the solvent in 70c\ensuremath{{}^{\circ}} for about 3 hr to give the viscous oily yellowish product. As shown in Scheme~\ref{f-55522759cd5c}. \unskip~\citep{643432:15101306}.\textbf{\space } \bgroup \fixFloatSize{images/bc48c68c-7ee6-4bda-8116-a73fb605d391-uscheme1.png} \begin{scheme}[!htbp] \centering \makeatletter\IfFileExists{images/bc48c68c-7ee6-4bda-8116-a73fb605d391-uscheme1.png}{\includegraphics{images/bc48c68c-7ee6-4bda-8116-a73fb605d391-uscheme1.png}}{} \makeatother \caption{\boldmath {PVB}} \label{f-55522759cd5c} \end{scheme} \egroup \textbf{Preparation of polyvinyl pyrrolidone \_Benzaldeh\_VinylTrimethylSilane VS.PVB} TMS vinyl terminated 5.3 ml (25 mmoles) added to 100mmole (22g )of PVB that prepared in step 3 in sealed round bottom flask (25ml)and reflux about \ensuremath{\frac12} hrs in 70 c\ensuremath{{}^{\circ}} then evaporate the solvent on 50c\ensuremath{{}^{\circ}} for about 1 hr to obtained on pale yellow gel product. As shown in Scheme~\ref{f-35bcc70e6336}. \bgroup \fixFloatSize{images/0afcc4f8-d8c4-45a0-a8f9-6f21909c36f6-uscheme2.png} \begin{scheme}[!htbp] \centering \makeatletter\IfFileExists{images/0afcc4f8-d8c4-45a0-a8f9-6f21909c36f6-uscheme2.png}{\includegraphics{images/0afcc4f8-d8c4-45a0-a8f9-6f21909c36f6-uscheme2.png}}{} \makeatother \caption{\boldmath {VS.PVB}} \label{f-35bcc70e6336} \end{scheme} \egroup \textbf{Preparation of Polyvinyl pyrrolidone \_Paraflurobenzyldehyde F.PVB} Take 10 mmoles (1.1g) of PVP in 10ml ethanol in 60c\ensuremath{{}^{\circ}} with steering then add 5ml of alcoholic KOH the colour became yellow, last added 10mmole of para fluoro B.D (1.24g) immediately the color change to obtained on yellow liquid product and reflux for 2hrs with steering. Neutralized the solution with 10\% HCL till the PH became 7, filtered the product to remove the precipitate, and evaporate the solvent in 70c\ensuremath{{}^{\circ}} for about 3hr to give a yellowish viscous oily product. As shown in Scheme~\ref{f-c8c1cb83c004} \bgroup \fixFloatSize{images/90694273-0ef4-4286-9629-db2ed612a1e0-uscheme3.png} \begin{scheme}[!htbp] \centering \makeatletter\IfFileExists{images/90694273-0ef4-4286-9629-db2ed612a1e0-uscheme3.png}{\includegraphics{images/90694273-0ef4-4286-9629-db2ed612a1e0-uscheme3.png}}{} \makeatother \caption{\boldmath {F.PVB}} \label{f-c8c1cb83c004} \end{scheme} \egroup \textbf{Preparation of Polyvinyl pyrrolidone \_Paraomethoxyobenzyldehyde OCH\ensuremath{_{3}}.PVB} Ten mmoles (1.1g) of PVP dissolved in 10ml ethanol in 60c \ensuremath{{}^{\circ}} with steering then add 5ml of alcoholic KOH the colour became yellow, last added 10mmole of para methoxy B. D (1.36g) immediately the colour change to obtained on yellow liquid product and reflux for 2hrs with steering. Neutralized the solution with 10\% HCL till the PH became 7, filtered the product to remove the precipitate, and evaporate the solvent in 70c\ensuremath{{}^{\circ}} for about 3 hr. To give a viscous oily brownish product. As shown in Scheme~\ref{f-5e68a9be3c95}. \bgroup \fixFloatSize{images/67636f72-b734-45e4-b3b2-3fc96bb5e19e-uscheme4.png} \begin{scheme}[!htbp] \centering \makeatletter\IfFileExists{images/67636f72-b734-45e4-b3b2-3fc96bb5e19e-uscheme4.png}{\includegraphics{images/67636f72-b734-45e4-b3b2-3fc96bb5e19e-uscheme4.png}}{} \makeatother \caption{\boldmath {OCH\ensuremath{_{3}}.PVB}} \label{f-5e68a9be3c95} \end{scheme} \egroup \textbf{Preparation of Polyvinyl pyrrolidone \_Parahydroxybenzyldehyde OH.PVB} Five mmoles (0.65g) of PVP melt in 5ml ethanol in 60c \ensuremath{{}^{\circ}} with steering then add 3ml of alcoholic KOH the colour became yellow, last added 5mmole of para hydroxy B. D (6.1g) immediately the colour change to obtained on the pink liquid product and reflux for 2hrs with steering. Neutralized the solution with 10\% HCL till the PH became 7, filtered the product to remove the precipitate, and evaporate the solvent in 70c\ensuremath{{}^{\circ}} for about 3 hr. To give a viscous oily orange products. As shown in Scheme~\ref{f-48c3f3fd2141}. \bgroup \fixFloatSize{images/a6407521-fa6f-45d1-b470-2c82d682ca58-uscheme5.png} \begin{scheme}[!htbp] \centering \makeatletter\IfFileExists{images/a6407521-fa6f-45d1-b470-2c82d682ca58-uscheme5.png}{\includegraphics{images/a6407521-fa6f-45d1-b470-2c82d682ca58-uscheme5.png}}{} \makeatother \caption{\boldmath {OH.PVB}} \label{f-48c3f3fd2141} \end{scheme} \egroup \textbf{Analytical Techniques} \textbf{FT.IR Spectra} FT.IR spectra for all studied compounds were calculated as KBr disks using FT.IR 8400S SHIMADZU (Japan), in the technique Laboratory of Pharmaceutical Chemistry Department / College of Pharmacy / Basrah University.\unskip~\citep{643432:15101299} \ensuremath{^{\textbf{1}}} \textbf{H-NMR Spectra} The studied compounds were achieved at the analytical Laboratory of Tehran University/College of sciences /Chemistry department, using 500MHz NMR (INOVA Switzerland). DMSO-d\ensuremath{_{6}} was used as a solvent and TMS as an internal standard.\unskip~\citep{643432:15101304} \section{Results and Discussion} The involved study synthesis of the new compound from polyvinylpyrrolidone and benzaldehyde which followed by prepared new compound of polydimethylsiloxane derivatives which predicted by the following, \textbf{FT-IR Spectrum of PVB} The compound PVB show strong absorption band at 3452 cm\ensuremath{^{-1}} refer to O-H stretching, the medium band 2881-2951 cm\ensuremath{^{-1}} attributed C-H stretching of aliphatic alkyl, medium band at 1427cm\ensuremath{^{-1}} refer to C-H bending, strong band at 1670 cm\ensuremath{^{-1}} attributed to N-C=O stretching, 1168cm\ensuremath{^{-1}} medium band attributed C-N stretching, at 1496cm\ensuremath{^{-1}}refer to C=C aromatic, medium band at 1604 cm\ensuremath{^{-1}} refer to C=C stretching (-C=C-OH) \textbf{FT-IR Spectrum of F.PVB} The more characteristic band in IR spectrum of F.PVB Figure~\ref{f-d272fa021c2b} compound is C-F show medium absorption band at 1041cm\ensuremath{^{-1 }}stretching, strong band at 3448 cm\ensuremath{^{-1}} refer to O-H stretching, the medium band 2881-2951 cm\ensuremath{^{-1}} attributed C-H stretching of aliphatic alkyl, medium band at 1427 cm\ensuremath{^{-1}} refer to C-H bending , strong band at 1678 cm\ensuremath{^{-1}} attributed to N-C=O stretching, 1161cm\ensuremath{^{-1}} medium band attributed C-N stretching, medium band at 1600 cm\ensuremath{^{-1}} refer to C=C stretching (-C=C-OH), medium band 1508cm\ensuremath{^{-1}}attributed to C=C aromatic at 1041cm\ensuremath{^{-1}} medium band related to C-F stretching. \bgroup \fixFloatSize{images/2761e29c-4541-4227-b246-6604982aa79b-upicture1.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/2761e29c-4541-4227-b246-6604982aa79b-upicture1.png}{\includegraphics{images/2761e29c-4541-4227-b246-6604982aa79b-upicture1.png}}{} \makeatother \caption{\boldmath {F.PVB}} \label{f-d272fa021c2b} \end{figure} \egroup \bgroup \fixFloatSize{images/a6c7ca6b-9b91-4496-8b7b-db3a85d706ee-upicture2.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/a6c7ca6b-9b91-4496-8b7b-db3a85d706ee-upicture2.png}{\includegraphics{images/a6c7ca6b-9b91-4496-8b7b-db3a85d706ee-upicture2.png}}{} \makeatother \caption{\boldmath {OCH\ensuremath{_{3}} PVB}} \label{f-e3e437e4916d} \end{figure} \egroup \bgroup \fixFloatSize{images/d0a0de7b-b41e-4695-b3fe-d4c163667bc1-ucapture.png} \begin{figure}[!htbp] \centering \makeatletter\IfFileExists{images/d0a0de7b-b41e-4695-b3fe-d4c163667bc1-ucapture.png}{\includegraphics{images/d0a0de7b-b41e-4695-b3fe-d4c163667bc1-ucapture.png}}{} \makeatother \caption{\boldmath {VS.PVB}} \label{f-857244c91fb8} \end{figure} \egroup \begin{table*}[!htbp] \caption{\boldmath {Inhibition zone of tested compounds and standard drugs} } \label{tw-9bdab74b8509} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.1666666666666667\linewidth-2\tabcolsep}p{\dimexpr.1666666666666667\linewidth-2\tabcolsep}p{\dimexpr.1666666666666667\linewidth-2\tabcolsep}p{\dimexpr.1666666666666667\linewidth-2\tabcolsep}p{\dimexpr.1666666666666667\linewidth-2\tabcolsep}p{\dimexpr.16666666666666664\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor} S.aureus compounds & P.aeruginosa & E.coli & Klebsiella & Conc. (\ensuremath{\mu}g/ml) & \\ \tblmidrule \cAlignHack 0 & \cAlignHack 5 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 100 & \cAlignHack PVB\\ \cAlignHack 3 & \cAlignHack 6 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 250 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 7 & \cAlignHack 6 & \cAlignHack 0 & \cAlignHack 500 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 7 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 750 & \cAlignHack \\ \cAlignHack 5 & \cAlignHack 8 & \cAlignHack 7 & \cAlignHack 0 & \cAlignHack 1000 & \cAlignHack \\ \cAlignHack 10 & \cAlignHack 10 & \cAlignHack 10 & \cAlignHack 14 & \cAlignHack 5000 & \cAlignHack \\ & & & & & \\ \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 100 & \cAlignHack F.PVB\\ \cAlignHack 0 & \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 250 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 500 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 750 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 10 & \cAlignHack 0 & \cAlignHack 1000 & \cAlignHack \\ \cAlignHack 7 & \cAlignHack 9 & \cAlignHack 8 & \cAlignHack 15 & \cAlignHack 5000 & \cAlignHack \\ & & & & & \\ \cAlignHack 3 & \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 100 & \cAlignHack OH.PVB\\ \cAlignHack 3 & \cAlignHack 4 & \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 250 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 4 & \cAlignHack 4 & \cAlignHack 0 & \cAlignHack 500 & \cAlignHack \\ \cAlignHack 4 & \cAlignHack 4 & \cAlignHack 4 & \cAlignHack 0 & \cAlignHack 750 & \cAlignHack \\ \cAlignHack 0 & \cAlignHack 4 & \cAlignHack 4 & \cAlignHack 0 & \cAlignHack 1000 & \cAlignHack \\ \cAlignHack 0 & \cAlignHack 4 & \cAlignHack 4 & \cAlignHack 0 & \cAlignHack 5000 & \cAlignHack \\ & & & & & \\ \cAlignHack 3 & \cAlignHack 4 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 100 & \cAlignHack OCH\ensuremath{_{3}}PVB\\ \cAlignHack 3 & \cAlignHack 5 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 250 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 5 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 500 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 5 & \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 750 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 5 & \cAlignHack 7 & \cAlignHack 0 & \cAlignHack 1000 & \cAlignHack \\ \cAlignHack 8 & \cAlignHack 8 & \cAlignHack 8 & \cAlignHack 9 & \cAlignHack 5000 & \\ & & & & & \\ \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 100 & \cAlignHack VS.PVB\\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 250 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 500 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 750 & \cAlignHack \\ \cAlignHack 3 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 0 & \cAlignHack 1000 & \cAlignHack \\ \cAlignHack 8 & \cAlignHack 8 & \cAlignHack 13 & \cAlignHack 14 & \cAlignHack 5000 & \cAlignHack \\ \tblbottomrule \end{tabulary}\par \end{table*} \begin{table*}[!htbp] \caption{\boldmath {Groups of animals treated with products} } \label{tw-4ed0cfb898e8} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.29189999999999998\linewidth-2\tabcolsep}p{\dimexpr.3318\linewidth-2\tabcolsep}p{\dimexpr.3763\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}No. of group & Product at site A & Control at site B\\ \tblmidrule Group 1 & PVB & Povidone-iodine\\ Group 2 & F.PVB & Povidone-iodine\\ Group 3 & OCH\ensuremath{_{3}}PVB & Povidone-iodine\\ Group 4 & OH.PVB & Povidone-iodine\\ Group 5 & VS.PVB & Silicone gel\\ \tblbottomrule \end{tabulary}\par \end{table*} \textbf{FT-IR Spectrum of OH.PVB} The IR spectrum of OH.PVB compound show weak absorption band at 3498cm\ensuremath{^{-1}} refer to O-H stretching, the weak band 2823-2955 cm\ensuremath{^{-1}} attributed C-H stretching of aliphatic alkyl, medium band at 1438 cm\ensuremath{^{-1}} refer to C-H bending, strong band at 1674 cm\ensuremath{^{-1}} attributed to N-C=O stretching, 1288cm\ensuremath{^{-1}} medium band attributed C-N stretching, medium band at 1581 cm\ensuremath{^{-1}} refer to C=C stretching (-C=C-OH), medium band 1500cm\ensuremath{^{-1}}attributed to C=C aromatic at 1149cm\ensuremath{^{-1}} medium band related to C-O stretching. \textbf{FT-IR Spectrum of OCH\ensuremath{_{3}} PVB} The compound OCH\ensuremath{_{3}}PVB show weak absorption band at 3479 cm\ensuremath{^{-1}} refer to O-H stretching , the medium band 2843-2951 cm\ensuremath{^{-1}} attributed C-H stretching of aliphatic alkyl, medium band at 1427cm\ensuremath{^{-1}} refer to C-H bending, strong band at 1678 cm\ensuremath{^{-1}} attributed to N-C=O stretching, 1161cm\ensuremath{^{-1}} medium band attributed C-N stretching, at 1512cm\ensuremath{^{-1}}refer to C=C aromatic, medium band at 1600 cm\ensuremath{^{-1}} refer to C=C stretching (-C=C-OH), medium band at 1022cm\ensuremath{^{-1}} related to C-O in (C-OCH\ensuremath{_{3}}) Figure~\ref{f-e3e437e4916d} \textbf{FT- IR Spectrum of VS.PVB} The medium absorption band at 3448 cm\ensuremath{^{-1}} showed in the IR spectrum of VS. PVB compound refer to O-H stretching, the medium band 2881-2955 cm\ensuremath{^{-1}} attributed C-H stretching of aliphatic alkyl, medium band at 1458 cm\ensuremath{^{-1}} refer to C-H bending, strong band at 1670 cm\ensuremath{^{-1}} attributed to N-C=O stretching, medium band at 1597 cm\ensuremath{^{-1}} refer to C=C stretching, medium band at 1168cm\ensuremath{^{-1}} refer to C-N stretching, strong band at 1693cm\ensuremath{^{-1}} refer to C=C of VTMS polymer stretching, medium band at 1145cm\ensuremath{^{-1}} attributed to Si-(CH\ensuremath{_{3}})\ensuremath{_{3}} stretching. Figure~\ref{f-857244c91fb8} \ensuremath{^{\textbf{1}}} \textbf{H-NMR Spectrum PVB} The \ensuremath{^{1}}H-NMR spectrum of compound PVB displayed characteristic aliphatic signals of alkyl chain protons represented by the following, triplet signal at 1.0 ppm related to protons of -CH\ensuremath{_{2}}- group, 3.4 ppm patent related to -CH- (-CH-CH\ensuremath{_{2}}-), another signal at 7.5-8.0 ppm related to aromatic ring, at 10.0 ppm related to OH group, as shown as in Scheme~\ref{f-55522759cd5c} \ensuremath{^{\textbf{1}}} \textbf{H-NMR Spectrum F.PVB} The \ensuremath{^{1}}H-NMR spectrum of compound F.PVB exhibited specific aliphatic signals of alkyl chain protons signified by the following, triplet signal at 1.0 ppm related to protons of -CH\ensuremath{_{2}}- group, 3.4 ppm patent related to -CH- (-CH-CH\ensuremath{_{2}}-), another signal at 7.5-8.0 ppm related to aromatic ring, at 10.0,9.9 ppm two singular signal related to OH group due to geometric isomer (cis and trans), as shown as in Scheme~\ref{f-c8c1cb83c004} \ensuremath{^{\textbf{1}}} \textbf{H-NMR Spectrum OCH\ensuremath{_{3}}PVB} The compound OCH\ensuremath{_{3}}.PVB presented triplet signal at 1.0 ppm linked to protons of -CH\ensuremath{_{2}}- group, 3.4 ppm patent related to -CH- (-CH-CH\ensuremath{_{2}}-), another signal at 7.5-8.0 ppm related to aromatic ring , at 10.0 ppm correlated to OH group, singular signal shown at 3.8ppm related to CH\ensuremath{_{3}} (OCH\ensuremath{_{3}}) as shown as in Scheme~\ref{f-5e68a9be3c95} \ensuremath{^{\textbf{1}}} \textbf{H-NMR Spectrum OH.PVB} The \ensuremath{^{1}}H-NMR spectrum of compound 0H.PVB showed triplet signal at 1.0 ppm referred to protons of -CH\ensuremath{_{2}}- group, 3.4 ppm patent related to -CH- (-CH-CH\ensuremath{_{2}}-), another signal at 6.7 and 7.6ppm doublet related to C-H aromatic due to presence of OH group (in ionized form)on position no.4 of aromatic ring, at 10.0 ppm related to OH group, as shown as in Scheme~\ref{f-48c3f3fd2141} \textbf{\ensuremath{^{1}}} \textbf{H-NMR Spectrum VS.PVB} The more characteristic signals of VS.PVB compound showed as the following, triplet signal at 1.0 ppm related to protons of -CH\ensuremath{_{2}}- group, 3.4 ppm patent related to -CH- (-CH-CH\ensuremath{_{2}}-), another signal at 7.5-8.0 ppm related to aromatic ring, at 10.0 ppm related to OH group, and showed singular signal at 1.8 ppm related to Si-(CH\ensuremath{_{3}})\ensuremath{_{3.}}Scheme~\ref{f-35bcc70e6336} \textbf{Antibacterial activity} All synthesized compounds were evaluated against certain kinds of Gram-positive bacteria (S. aureus) for their antibacterial activity, and Gram-negative bacteria (E. coli) and Klebsiella used the diffusion technique of the filter paper disk, measuring the diameter of the inhibition area after 24 hours. The preliminary findings showed that there were some active compounds against E. coli or and S. aureus, as shown in Table~\ref{tw-9bdab74b8509}.\textbf{\space } Most compounds prepared showed bacterial activity against Gram-negative and Gram-positive bacteria. Compounds PVB, VS.PVB, F.PVB, OCH\ensuremath{_{3}}.PVB and OH.PVB show good bacterial activity against (Staphylococcus aureus), and also had good activity against resistant bacteria Pseudomonas aeruginosa. The compounds showed good bacterial activity at high concertation against Gram-negative (E. coli), Klebsiella, and Gram-positive (S. aureus). Table~\ref{tw-9bdab74b8509}. \unskip~\citep{643432:15101295} \textbf{Wound Dressing} New Zealand white rabbits were used in the study as 5 groups; each group consists of 6 animals (males 3) and (females 3). Animals were individually housed and were maintained at 19 \ensuremath{\pm} 3 \text{\textordmasculine}C with relative humidity at 30- 70\%, a minimum of 10 to 13 complete air exchange per hour, and 12 hrs. Light/ dark cycle using full-spectrum fluorescent lights. The test and the control sites were prepared by clipping the skin of the trunk free of hair. Two application site on each animal was abraded by making open wound 8mm through the epidermis. One site (A) was applying with the prepared compounds. The second (B) covered with controls. Animals were observed for signs of erythema and edema at 24 and 72 hours post-application of products. The animals in 4 groups were treated by introducing a thin film of the viscous oily PVB, F.PVB, OCH\ensuremath{_{3}}.PVB, OH.PVB at site A and povidone-iodine 10\% at another site. The last group treated with VS.PVB at A site and silicone gel as control at B site. As shown in Table~\ref{tw-4ed0cfb898e8}. \unskip~\citep{643432:15101298} Animals were observed daily for clinical manifestations. The erythema and edema for intact skin and abraded skin were observed as a function of time. The signs and symptoms were observed after 24 hrs and 72 hrs. No erythema, no edema notes at the site of application of our compounds in the first 4 groups while the control site with povidone-iodine showed erythema and slightly edema during the first 24 hrs without edema. The fifth group treated with VS.PVB, notes erythema slightly but not observed any signs at the site of control applied with silicone gel. After 1 week from the application (twice daily), the healing was obtained completely for open wounds from PVB and VS.PVB compounds and without scare rather than the povidone-iodine and silicone gel, while the healing with other compounds occurs after 10 days without any scar.\unskip~\citep{643432:15101297} \section{Conclusion} New derivatives from polyvinylpyrrolidone and polydimethylsiloxane polymers were prepared as wound dressing has good antibacterial activity against gram-positive and gram-negative bacteria and very good effects in the treatment of open wounds during the short duration in comparison with commercial products. \bibliographystyle{pharmascope_apa-custom} \bibliography{\jobname} \end{document}

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% Examination structure in 2015 % (LaTeX macros: Markus Kuhn) \documentclass[12pt,a4paper]{article} \usepackage[width=180mm,vmargin=25mm]{geometry} \usepackage{color} \usepackage{parskip} \pagestyle{empty} \newcommand\tripoyr {2015} %%%% CHANGE EACH YEAR (ALSO CHECK PAPER DATES!) %%%% \newif\ifdraft %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \drafttrue = show additional internal planning information (in red) % \draftfalse = produce the final published version % Change the line below as required: \draftfalse %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % reduce font size by two, simplified version of \relsize{-2} from relsize.sty \makeatletter \newcommand{\absize}{% \ifx\@currsize\normalsize\footnotesize\else % test more likely sizes first \ifx\@currsize\small\scriptsize\else \ifx\@currsize\footnotesize\tiny\else \ifx\@currsize\large\small\else \ifx\@currsize\Large\normalsize\else \ifx\@currsize\LARGE\large\else \ifx\@currsize\scriptsize\tiny\else \ifx\@currsize\huge\Large\else \ifx\@currsize\Huge\LARGE \fi\fi\fi\fi\fi\fi\fi\fi\fi } \makeatother \newcommand{\partia}{Part~I{\absize A}} \newcommand{\partib}{Part~I{\absize B}} \newcommand{\partii}{Part~II} \definecolor{draft}{rgb}{0.9,0,0} \newcommand{\heading}[1]{ \clearpage \begin{minipage}[b][0pt][b]{\linewidth} \begin{center} \large{\color{draft}\ifdraft DRAFT -- Teaching Management Committee -- DRAFT\fi} \end{center} \end{minipage} \begin{center} \large\bfseries UNIVERSITY OF CAMBRIDGE COMPUTER LABORATORY\\[14pt] \Large #1 \end{center} \bigskip } \newcounter{question} \newcounter{hours} \newenvironment{paper}[2]{ \setcounter{question}{0}% \setcounter{hours}{0}% \begin{minipage}[t]{88mm} \begin{center} \large\textbf{\strut Paper #1} \ifdraft\color{draft} \\[\smallskipamount] \footnotesize (#2) \fi \end{center}\medskip\par }{ \end{minipage} } \newcommand\mystrut{\vrule width 0pt height 12pt depth 4pt} \renewcommand{\section}[2]{ \bigskip \leftline{\textbf{\strut Section #1}} \smallskip \emph{\strut #2}\par \medskip } \newcommand{\q}[3]{\stepcounter{question}% \addtocounter{hours}{#1}% \leftline{\vrule height 8pt depth 4pt width 0pt {\small \ifdraft \hspace*{-16pt}\makebox[16pt][r]{\color{draft}#1h}% \fi \makebox[16pt][r]{\arabic{question}.} ~#3 \ifdraft\color{draft}(#2)\fi}}} \newcommand{\draftnote}[1]{\ifdraft\centerline{\mystrut\textbf{(#1)}}\fi} \newcommand{\total}[1][]{ \ifdraft \color{draft}\hspace*{-16pt}\vrule height 1pt width \linewidth\\ \hspace*{-16pt}\makebox[16pt][r]{\small\arabic{hours}h}\quad #1 \fi } \newsavebox{\planningbox} \newenvironment{planningnotes}{ \color{draft} \begin{lrbox}{\planningbox}\begin{minipage}{160mm} \setlength{\parskip}{\medskipamount} \textbf{Notes for the Tripos Management Committee:}\par }{ \end{minipage}\end{lrbox}% \ifdraft \bigskip \begin{center} \setlength{\fboxrule}{2pt} \setlength{\fboxsep}{1em} \fbox{\usebox{\planningbox}} \end{center}\fi } \begin{document} % IMPORTANT: This file is used as a database file, e.g. to generate % templates for typesetting exam papers and the web archive of past % exam questions. % % Various software reads the following lines starting with % \begin{paper}, \section, \q and \end{paper}. Therefore, please avoid % clever LaTeX trickery here (or consult Markus Kuhn or Martyn % Johnson). In particular, please write out question topics (= course % names) properly and do not abbreviate. Question topics listed here % are matched against past usage to aggregate past questions by topic % in the web archive, and therefore should not be changed without good % reason. % % While the date of the paper is not typeset in this document, it is % copied from here automatically to the templates for typesetting the % papers. % % The first parameter of \q is the number of lectures (hours) % associated with this question. This number will be printed in % red if \drafttrue has been selected above, to help the % Teaching Committee review whether the allocation of questions is % well balanced. The second parameter is the uppercase acronym of % the one (!) lecturer responsible for setting the question % (no added plus!), and the third parameter is the full question % title (course name), without any abbreviation (should match % syllabus and coursedb.txt). \heading{\partia: Structure of Papers 1 and 2 in \tripoyr} \begin{paper}{1}{Monday 1 June} \section{A}{Attempt 1 question} \q{6}{LCP}{Foundations of Computer Science} \q{6}{LCP}{Foundations of Computer Science} \section{B}{Attempt 1 question} \q{6}{RKH}{Object-Oriented Programming} \q{6}{RKH}{Object-Oriented Programming} \section{C}{Attempt 1 question} \q{5}{DJG}{Numerical Methods} \q{6}{DJG}{Numerical Methods} \section{D}{Attempt 2 questions} \q{6}{FMS}{Algorithms} \q{6}{FMS}{Algorithms} \q{6}{TMS}{Algorithms} \q{6}{TMS}{Algorithms} \total \end{paper} \hspace{\fill}% \begin{paper}{2}{Tuesday 2 June} \section{A}{Attempt 1 question} \q{6}{IJW}{Digital Electronics} \q{6}{IJW}{Digital Electronics} \section{B}{Attempt 1 question} \q{6}{IML}{Operating Systems} \q{6}{IML}{Operating Systems} \section{C}{Attempt 1 question} \q{5}{AFB}{Software and Interface Design} \q{6}{AFB}{Software and Interface Design} \section{D}{Attempt 2 questions} \q{6}{MPF}{Discrete Mathematics} \q{6}{MPF}{Discrete Mathematics} \q{6}{MPF}{Discrete Mathematics} \q{6}{AMP}{Discrete Mathematics} \total \end{paper} \bigskip \emph{Attempt five questions on each paper.} \vfill Students reading \partia\ of the Computer Science Tripos take both Paper~1 and Paper~2. Students reading the Computer Science option in \partia\ of the Natural Sciences Tripos take only Paper~1. Students reading the Introduction to Computer Science option in Part~I of the Psychological and Behavioural Sciences Tripos take only Paper~1. \vfill \begin{planningnotes} Changes from 2014: Discrete maths will have 3 questions set by MPF and 1 by AMP to reflect the number of given lectures. \end{planningnotes} \heading{\partib: Structure of Papers 3 to 6 in \tripoyr} \begin{paper}{3}{Monday 1 June} %\q{6}{FMS}{Algorithms II} %\q{6}{FMS}{Algorithms II} \q{12}{AVSM}{Programming in C and C++} \q{12}{AVSM}{Programming in C and C++} \q{8}{TGG}{Compiler Construction} \q{8}{TGG}{Compiler Construction} \q{8}{AM}{Concepts in Programming Languages} \q{0}{ARB}{Further Java} \q{8}{ACR}{Prolog} \q{6}{RJA}{Software Engineering} \total[Programming] \end{paper} \hspace{\fill}% \begin{paper}{4}{Tuesday 2 June} \q{6}{SBH}{Artificial Intelligence I} \q{6}{SBH}{Artificial Intelligence I} \q{8}{PR}{Computer Graphics and Image Processing} \q{8}{PR}{Computer Graphics and Image Processing} \q{6}{TGG}{Databases} \q{6}{TGG}{Databases} \q{8}{RJA}{Economics, Law and Ethics} \q{6}{MGK}{Security I} \q{6}{MGK}{Security I} \total[Applications and Professionalism] \end{paper} \bigskip \begin{paper}{5}{Wednesday 3 June} \q{6}{SWM}{Computer Design} \q{6}{SWM}{Computer Design} \q{6}{SWM}{Computer Design} \q{8}{AWM}{Computer Networking} \q{8}{AWM}{Computer Networking} \q{8}{AWM}{Computer Networking} \q{5}{RNW}{Concurrent and Distributed Systems} \q{5}{RNW}{Concurrent and Distributed Systems} \q{6}{RNW}{Concurrent and Distributed Systems} \total[Systems] \end{paper} \hspace{\fill}% \begin{paper}{6}{Thursday 4 June} \q{6}{AD}{Complexity Theory} \q{6}{AD}{Complexity Theory} \q{6}{AMP}{Computation Theory} \q{6}{AMP}{Computation Theory} \q{6}{LCP}{Logic and Proof} \q{6}{LCP}{Logic and Proof} \q{6}{JGD}{Mathematical Methods for Computer Science} \q{10}{RJG}{Mathematical Methods for Computer Science} \q{6}{PMS}{Semantics of Programming Languages} \q{6}{PMS}{Semantics of Programming Languages} \total[Theory] \end{paper} \bigskip \emph{Attempt any five questions on each paper.} \begin{planningnotes} Algorithms 1 has been removed as this is now taught in Part IA. Programming in C and C++ has been extended to 10 lectures, 2 practical classes and 2 exam questions. There will be 8 questions on paper 3, 9 questions on papers 4 and 5 and 10 questions on paper 6. \end{planningnotes} \heading{\partii: Structure of Papers 7 to 9 in \tripoyr} \begin{paper}{7}{Tuesday 2 June} \q{8}{PB}{Advanced Graphics} \q{6}{TMS}{Advanced Algorithms} %\q{8}{SBH}{Artificial Intelligence II} \q{6}{PL}{Bioinformatics} \q{8}{JAL}{Business Studies} \q{8}{RDM}{Comparative Architectures} \q{5}{MPF}{Denotational Semantics} \q{8}{MJCG}{Hoare Logic} \q{8}{AFB}{Human--Computer Interaction} \q{6}{JGD}{Information Theory and Coding} \q{6}{AAC}{Natural Language Processing} \q{8}{AM}{Optimising Compilers} %\q{8}{JAC}{Principles of Communications} %\q{8}{AD}{Quantum Computing} \q{8}{FMS}{Security II} %\q{14}{RKH}{Topical Issues} \total \end{paper} \hspace{\fill}% \begin{paper}{8}{Wednesday 3 June} %\q{4}{NAD}{Advanced Graphics} %\q{8}{SBH}{Artificial Intelligence II} \q{8}{RDM}{Comparative Architectures} \q{6}{RJG}{Computer Systems Modelling} \q{8}{JGD}{Computer Vision} \q{6}{MGK}{Digital Signal Processing} \q{8}{JAL}{E-Commerce} \q{8}{MJCG}{Temporal Logic and Model Checking} \q{8}{SHT}{Information Retrieval} %\q{8}{JAC}{Principles of Communications} \q{8}{AD}{Quantum Computing} \q{8}{MGK}{Security II} \q{6}{DJG}{System-on-Chip Design} \q{12}{RKH}{Topical Issues} \q{6}{JMH}{Topics in Concurrency} % \q{4}{AMP}{Types} \total \end{paper} \bigskip \begin{paper}{9}{Thursday 4 June} \q{6}{PL}{Bioinformatics} \q{6}{RJG}{Computer Systems Modelling} \q{8}{JGD}{Computer Vision} \q{5}{MPF}{Denotational Semantics} \q{6}{MGK}{Digital Signal Processing} \q{6}{JGD}{Information Theory and Coding} \q{8}{CM}{Mobile and Sensor Systems} \q{6}{AAC}{Natural Language Processing} \q{8}{AM}{Optimising Compilers} %\q{8}{JAC}{Principles of Communications} \q{6}{DJG}{System-on-Chip Design} %\q{4}{MJCG}{Temporal Logic and Model Checking} \q{6}{RKH}{Topical Issues} \q{6}{JMH}{Topics in Concurrency} \q{8}{AMP}{Types} \total \end{paper} \bigskip \emph{Attempt any five questions on each paper.} \begin{planningnotes} The following regular courses have come back: Quantum Computing, Topics in Concurrency. The following regular courses are not being held in 2014--15: Principles of Communications. Advanced Graphics is reduced to 8 lectures and one exam question. Artificial Intelligence II will be run as a shortened, non-examinable course. In this draft, there are 12 questions on each of papers 7 and 8 and 13 questions on paper 9. \end{planningnotes} \end{document}

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\include{typohead} \begin{document} \papertitle{Vályi Gábor: Közösségek hálózati kommunikációja}{Közösségek hálózati kommunikációja} %\author{ Vályi Gábor%} \rightrunninghead{Vályi: Közösségek hálózati kommunikációja} %\origref{Vályi Gábor (2004) \textit{Közösségek hálózati kommunikációja} %Szociológiai Szemle, Vol.14. No.4. p. 47-60.} \begin{center} \end{center} A közösség fogalmáról és az egyes közösségeket működtető mozgatórugókról való elmélkedés a társadalommal kapcsolatos gondolkodás egész történetén végighúzódó, központi kérdés. E diskurzusban időről időre megszólaltak a közösség felbomlását panaszoló gondolkodók, s olyanok is, akik a közösség átalakulásaként és továbbéléseként interpretálták ugyanazokat a társadalmi jelenségeket.\footnote{A közösség felbomlásáról zajló tudományos -- filozófiai és szociológiai -- diskurzusról jó áttekintést nyújt Barry Wellman cikke. Wellman többek között Sámuel könyvét idézve meggyőzően állítja, hogy e vita már az Ószövetség idején is zajlott. (Wellman 1999a)} Az elmúlt kétszáz évben a közösségek működése -- illetve a társadalomtudományok erről alkotott képe -- gyökeres átalakuláson ment keresztül, s bár e változás egyaránt magyarázható a bürokratizációval, az iparosítással, a közlekedés technológiai fejlődésével vagy az urbanizációval is, kiemelkedően fontos szerepet játszottak benne a média és a távközlés területén megjelent új technológiák / eszközök / termékek. A tizenkilencedik században megjelenő nyomtatott tömegsajtó emelte ki először az egyént saját, lokálisan szerveződő közösségéből, s tette egy nagyobb, ,,elképzelt közösség'', a nemzet tagjává. (Anderson 1983) Bár a nacionalista ideológia által definiált nemzetközösség tagjait valóban összekötötte a nyomtatott sajtó által megjelenített közös értékkészlet, egységes nyelv és kulturális kánon, ez a fajta mesterségesen, ,,felülről'' létrehozott társadalmi ,,szerveződés'' nem sokban emlékeztet a valós, személyközi ismeretségekre és kommunikációra épülő lokális közösségek alulról szerveződő világára.\footnote{Ezért a meglátásért Babarczy Eszternek tartozom köszönettel.} A huszadik század hozott gyökeres változást e személyközi ismeretségekre épülő közösségek mindennapi működésében, különös tekintettel a közösséget konstituáló (Depew és Peters 2001) közösségi kommunikációra. A távközlés robbanásszerű fejlődése és a közlekedés / szállítás gépesítése lehetővé tette, hogy a közösség túllépjen a közösségi interakciót korábban jellemző alapvetően helyi meghatározottságon. A közösségek szerkezete is megváltozott: a helyi közösségekre jellemző erős kötelékek és a tagok között feszülő sűrűszövésű kapcsolathálót felváltották a flexibilis, laza szövésű, gyengébb kötelékekre, illetve közös érdekekre vagy érdeklődésre épülő hálós kapcsolati struktúrák, s ma az egyén általában egyszerre több ilyen laza közösségnek tagja. (Wellman 2001) Az új típusú -- hálózati -- közösségek kommunikációja legalább annyira épül a ,,valós'', mint a telekommunikációs eszközök ,,virtuális terében'' létrejövő találkozásokra. Bár kétségtelen, hogy a telefon és a mobil eszközök kiemelt szerepet játszanak a hálózati közösségek életében, az internet -- elsősorban technikai specifikumainak köszönhetően -- az első olyan médium, amely lehetővé teszi, illetve hatékonyan támogatja a közösségek spontán önszervezését (Rheingold 1994; Castells 2000), illetve a közösségen belüli közvetlen kommunikációt.\footnote{A telefon és mobiltelefon általában csak az egyes egyének közötti társas (\emph{one-to-one}) kommunikáció eszköze, míg az internetes közösségi felületek egyszerre több résztvevő csoportos (\emph{many-to-many}) kommunikációját is támogatják. A mobil eszközök és közösségszerveződés kapcsán Howard Rheingold könyve (2002) fest alapvetően techno-optimista víziót. Ugyanakkor fontos megjegyezni, hogy miközben az új, hálózati kommunikációs technológiák által nyújtott közösségi önszervező potenciál az azokhoz hozzáférő és az azokat kezelni tudó társadalmi rétegek számára óriási előnyöket jelenthet, a ,,digitális szakadék'' túloldalán rekedt kevésbé szerencsések további lemaradását, információáramlásból és közösségi interakcióból való kirekesztődését is okozhatja. Az magyar internet összetett ,,digitális szakadékát'' Rét Zsófia (2003) és Bognár Éva (2003) kutatásai segítenek jobban megérteni. } \textit{Közösségek hálózati kommunikációja} alatt e tanulmányban -- terjedelmi okokból -- most kizárólag az interneten zajló (\textit{computer mediated communication, CMC}) közösségi kommunikációt értem. Írásom célja, hogy egy, a szociológia hagyományos fogalomrendszerét felhasználó / újraértelmező elméleti keretet nyújtson az interneten kommunikáló közösségeket vizsgáló kutatók számára. Bár a számítógépes hálózatok által közvetített tár\-sas / tár\-sa\-dal\-mi kommunikáció vizsgálható az \textit{információs társadalom} elvont és önbeteljesítő próféciájának / ideológiájának fényében, a \textit{tudásmenedzsment} gyakorlati / alkalmazott diskurzusában vagy a kommunikációelmélet, a nyelvészet és a hálózati gazdaságtan partikuláris szempontrendszere alapján, a következő fejezetekben én egy olyan szociológiai megközelítést mutatok be, mely a \textit{virtuális térben kommunikáló}, alapvetően \textit{valós} \textit{közösségekre} fókuszál. Ez, az interneten zajló kommunikációt nem a mindennapi valóságtól elkülönült, virtuális világként, hanem hús-vér emberek nagyon is valós célokat szolgáló társadalmi interakciójaként interpretáló szemlélet főként a Barry Wellman által vezetett kanadai, társadalmi kapcsolathálót kutató szellemi műhely nevéhez köthető. (Castells 2000)\footnote{Ennek megfelelően e tanulmányban gyakrabban hivatkozom Wellman és különböző munkatársainak munkáira, mint egyéb szerzők és iskolák szövegeire. Wellman túlsúlya a felhasznált irodalomban azonban egy konkrét szemléletmód bemutatásának céljával függ össze, s nem jelenti más megközelítések jelentőségének vagy létjogosultságának tagadását. Az internettel kapcsolatos szociológiai szemléletmódok és kutatási irányok kiegyensúlyozott, széles látókörű bemutatását nyújtja Dányi Endre et al (2004), míg az internetes kommunikációval kapcsolatos kommunikációelméleti megfontolásokat Kiss Aranka (2004) dolgozta fel.} Konkrét hipotézisek bizonyítása helyett e tanulmány célja tehát az interneten kommunikáló, ám nagyon is valós közösségek vizsgálatának elméleti áttekintése. Először röviden bemutatom a közösségek működésének és fogalmának átalakulását; majd ismertetem az internetet ideális közösségi kommunikációs / médiaplatformmá tevő műszaki sajátosságokat, illetve az interneten zajló kommunikáció jellegzetességeit, s végül kitérek arra is, hogy milyen hatást gyakorol az interneten zajló kommunikáció a valós, lokális közösségek életére. \section*{A közösségek átalakulása} A társadalomtudományokban közel sincs egyetértés a közösség fogalmának definícióját illetően, s csak a különböző definíciókban említett kifejezések statisztikai elemzése szolgál útmutatóul: a leggyakrabban előforduló attribútumok a kommunikáció, a közös lokalitás és közösségi élmény, illetve a szolidaritás. (Depew és Peters 2001) A latin \emph{communitas} -- közösség -- szó etimológia gyökerei a -- közös érdekeknek, céloknak és normáknak javára a közösség tagjai által önként vállalt -- kölcsönös alávetettségre vezethetők vissza. (Wattson, 1997) A kölcsönös alávetettség -- és kölcsönös szolidaritás -- vállalása a közösség, és így közvetve az egyén túlélését, előbbre jutását segíti. A közösséghez tartozás az egyén számára közvetlen előnyöket is nyújt, hiszen az egyén társadalmi integrációjának puszta tényén túl az identitását is megerősíti, illetve a \textit{hálózati tőke} forrása is. Barry Wellman és Ken Frank definíciója szerint a hálózati tőke a társadalmi tőke olyan formája, amely az egyént személyes kapcsolatain keresztül juttatja segítséghez, illetve erőforrásokhoz. A barátokhoz, rokonokhoz, szomszédokhoz vagy munkatársakhoz fűződő, kölcsönös segítségre épülő kapcsolatok társaságot, közönséget, (anyagi vagy érzelmi) segítséget és támogatást, információt, a csoporthoz tartozás, illetve a megbecsültség érzését nyújthatják. (Wellman és Frank, 2000; Wellman, 2001) A \hspace{1pt} szociológiában\hspace{1pt} Ferdinand\hspace{1pt} Tönnies\hspace{1pt} ,,Közösség\hspace{1pt} és\hspace{1pt} társadalom''\hspace{1pt} című \hspace{1pt} könyvének (Tönnies 1887 / 1983) megjelenése óta zajlik a vita a közösség felbomlásáról, illetve továbbéléséről. A közösség felbomlását panaszolók sem voltak egységes állásponton a változás okát illetően: az iparosítást, az urbanizációt, a bürokratizációt, a kapitalizmust, a szocializmust épp úgy okolták, mint a közlekedés / szállítás és kommunikáció terén zajló technológiai átalakulást. A közösség átalakulása mellett érvelők pedig egyrészt a tönniesi közösségkép idealizált voltára hívták fel a figyelmet, másrészt az elvileg elidegenedett városi társadalmakban mégis fellelhető, átalakult, új formákat öltő közösségi interakció példái kapcsán a közösségfogalom újradefiniálását szorgalmazták. (Wellman 1999a) Ebben a fejezetben előbb a hagyományos közösségdefiníciót mutatom be, majd egy modern, a közösségeket személyes kapcsolathálókként koncipiáló megközelítést. \subsection*{Közösségek hagyományos megközelítésben} A Tönnies által felállított dichotómia a kiveszőfélben lévő tradicionális, falukra és kisvárosokra jellemző, szoros és tartós családi és szomszédsági kötelékekre, szolidaritásra, homogén kultúrára és normarendszerre épülő közösséget (\textit{Gemeinschaft}) a nagyvárosok kulturálisan heterogén, elidegenedett, gyorsan változó, esetleges, érdekekre épülő kapcsolatok által jellemzett társadalmával (\textit{Gesellschaft}) állítja szembe. (Bell és Newby 1971) Tönnies leírása még a társadalomtudományok kialakulásának korai korszakában -- 1887-ben -- született, amikor az egyes elméletek felállításakor nem tartották szükségesnek azokat empirikus kutatásokkal alátámasztani. Az iparosítást megelőző időszakok falusi kultúráját vizsgáló későbbi történeti antropológiai kutatások fényében idealisztikusnak bizonyultak az e közösségről alkotott nézetek: a falvak lakossága kulturálisan sokkal heterogénebb és -- mind fizikailag, mind társadalmilag -- sokkal mobilisabb volt, mint azt Tönnies elképzelte. A Tönnies-féle közösségfogalom megalapozatlansága ellenére a helyi meghatározottság kiemelten hangsúlyos szerepet játszott a közösségekről folyó közbeszéd és a városi közösségekkel foglalkozó szociológusok közösségképében, akik az egyes városnegyedekben (\emph{neighbourhood}) vélték megtalálni a Tönnies által elveszettnek hitt közösséget.\footnote{Ennek okait Wellman (1999a) a következőkben látja: 1) A kutatást valahol el kell kezdeni. Kézenfekvő egy jól behatárolt környék megfigyelése, felmérése. 2) Sok városszociológus a város építőkockáinak látja az egyes negyedeket, s feltételezi, hogy ezek aggregációja kiadja az egészet. 3) A helyi politikusok, adminisztratív szervek is városnegyedek közösségeire apellálnak, illetve a közbeszédben is ez az elfogadott megközelítés. 4) A kutatások alapjául szolgáló adatok is területi alapon szervezett intézmények adatbázisaiból érhetőek el, illetve területi alapon vannak szervezve.} (Wellman 1999a) A területi alapon szerveződő közösségekre -- társasházi lakóközösségekre, falvakra, városnegyedekre és kisvárosokra -- jellemző, hogy az egy\-ütt\-é\-lés által jelentett kölcsönös kiszolgáltatottság és a közös problémák megoldásának feladata kooperációra kényszeríti az eltérő érdeklődésű és érdekű egyéneket. \begin{itemize} \item Ezek a ,,hagyományos'' közösségek meglehetősen zártak: egyrészt erősen védik határaikat, nehezen fogadnak be új tagokat, másrészt nem jellemző az sem, hogy tagjaik elhagynák a közösséget. \item Az egymással kölcsönösen szolidáris viszonyban lévő tagok közötti kapcsolatok erősek, s egyszerre több funkciót\footnote{Egyszerre nyújthatnak társaságot, közönséget, (anyagi vagy érzelmi) segítséget és támogatást, információt, valamint a csoporthoz tartozás illetve a megbecsültség érzését, ellentétben a specializált funkciót betöltő kapcsolattal, amely csak egy vagy néhány funkciót nyújt.} is szolgálnak. \item A kapcsolatháló sűrű szövésű, azaz a közösség tagjai közül sokan ismerik egymást közvetlenül. \item A közösség életében fontos szerepet játszanak a nyilvános terek (kocsmák, kávézók, közterek, parkok), jellemzően itt találkoznak a közösség tagjai, így ezek a közösségi kommunikáció, interakció színterei. (Wellman 1999b, 2001) \end{itemize} A mai nagyvárosi társadalomban valóban nem nagyon találjuk nyomát a fenti ismérvek szerint működő közösségeknek,\footnote{Wellman (1999a) széles szociológiai szakirodalomra támaszkodva hét tényezőt sorol fel -- többek között a megváltozott munkaerőpiachoz köthető nagyobb földrajzi mobilitást, az interakció sűrűségének növekedését, a városok nagy méretét, a termelés bürokratizálódását, illetve a távközlés és közlekedés / szállítás hatékony és olcsó technológiáinak megjelenését --, amelyek szerepet játszottak a közösségek átalakulásában.} ám ez nem feltétlenül jelenti a közösségek megszűnését. Az egyének továbbra is tagjai szolidaritást és közösségi élményt nyújtó, kölcsönös segítségre épülő csoportoknak, s bár ezek nem mindig köthetők konkrét lokalitáshoz, illetve szerkezetük is nagyban különbözik a hagyományos közösségek fent felsorolt ismérveitől, nyugodtan nevezhetők közösségnek, hiszen azonos funkciókat látnak el (Wellman 1999a, 1999b, 2001; Wellman és Frank 2001). \subsection*{Személyes hálózati közösségek} A közösség fogalmának újradefiniálásakor a mai erősen fragmentált, közös érdekek és érdeklődés mentén szerveződő csoportokból felépülő nagyvárosi társadalmak társadalmi interakcióiból érdemes kiindulni. Barry Wellman több évtizeden keresztül végzett, társadalmi kapcsolathálóra vonatkozó elemzéseinek eredményeire támaszkodva érvel a \textit{személyes hálózati közösség} fogalmának bevezetése mellett. (Wellman 1999a) E megközelítés a közös lokalitás helyett a közösség tagjai közötti kölcsönös segítségnyújtásban látja a közösséget konstituáló tényezőt, s így lehetőséget nyújt a közösségi interakció megfigyelésére akkor is, amikor az nem észlelhető a hagyományos, helyileg fókuszált módszertan optikájával. A hálózati megközelítés helyi meghatározottság hiányában a társadalmi kapcsolatok hálózatában számtalan nehezen elhatárolható, egymást átfedő közösséget tételez, melyek leginkább az egyes egyén szemszögéből válnak megfoghatóvá. Az egyén egyszerre általában több, egymást részben átfedő közösség -- baráti társaság, szomszédsági, rokoni, illetve munkahelyi alapon szerveződő csoport -- tagja, s az egyes közösségek specializált funkciót látnak el életében -- más és más típusú hálózati tőkével szolgálnak. Wellman kapcsolatháló-elemzései azt mutatják (Wellman 1999b, 2001), hogy \begin{itemize} \item a hálózati közösségeket általában laza, könnyen változó, erősen specializált funkciókat nyújtó kapcsolatok tartják össze; \item a személyes kapcsolatháló ritka szövésű, azaz az egyén különböző ismerősei ritkán ismerik egymást; \item a lokalitás kevéssé meghatározó, a személyes közösségi hálózatok egyszerre kötődhetnek az egyén lakóhelyéhez és kiterjedhetnek globálisan is (\textit{glokalizáció}); \item a közösségi interakció, kommunikáció ritkán zajlik a nyilvános terekben, és sokkal jellemzőbbek az egyes családok otthonaiban zajló szűk körű találkozók, illetve a telefonon és az interneten zajló kommunikáció (\textit{computer mediated communication, CMC}). \end{itemize} Az interneten zajló kommunikáció, azon kívül, hogy segíti a már létező személyes kapcsolatok hatékony és olcsó fenntartását akár nagy földrajzi távolságok esetén is, lehetővé teszi új, a virtuális térben kötött közösségi kapcsolatok létrehozását és fenntartását olyan egyének között is, akik korábban nem ismerték egymást. A közösségszerveződést teljesen elszakítva a valós térben való találkozások kötöttségeitől, illetve a már létező személyes kapcsolatháló által behatárolt lehetőségektől,\footnote{Fontos azonban hangsúlyozni, hogy csak a kötöttségek szűntek meg, csökkentek, s maguk az egyének és közösségek nem szakadtak el valós beágyazottságuktól. Howard Rheingold (1994) interneten szerveződő közösségekre használt \textit{virtuális közösségek} elnevezése félrevezető lehet, hiszen ezek a közösségek és tagjaik nagyon is valóságosak. (Wellman és Guila 1999)} az interneten zajló kommunikáció a társadalomszerveződés korábban nem látott formáit teszi lehetővé (Rheingold 1994; Castells 2000, 2001). A továbbiakban a közösségek interneten zajló kommunikációjának sajátosságait vizsgálom részletesebben. \section*{Hálózati kommunikáció} Az internet minden korábbi médiumnál alkalmasabb -- mind a specializált közös érdeklődés / érdekek alapján szerveződő laza; mind a bensőséges, segítség széles skáláját nyújtó; valamint a közös lokalitás, nem, etnicitás vagy társadalmi-gazdasági státusz alapján szerveződő -- közösségek kommunikációjának és spontán önszervezésének hatékony és olcsó támogatására. (Wellman és Hampton 1999; Rheingold 1994; Castells 2000) Ebben a fejezetben előbb a hálózati kommunikáció architektúrájának műszaki sajátosságait mutatom be, majd kitérek az internet közösségi interakcióra gyakorolt hatásaira, végül a hálózaton zajló kommunikáció jellegzetességeit ismertetem. \subsection*{Hálózati architektúra és közösségi kommunikáció} Az internetes kommunikáció -- ellentétben korábbi távközlési formákkal\footnote{Postai szolgáltatások, telefon, telefax.} -- ára nem függ a kommunikáló felek távolságától, így lehetővé teszi egymástól nagy távolságra élő egyének részvételét egyazon közösség online életében. Az internet -- a cset szolgáltatások segítségével -- a {valós idejű} (\textit{real-time}, \textit{synchronous}) kommunikáció\footnote{Korábban például a személyes, illetve telefonos beszélgetés sajátossága.} mellett -- például az e-mail és fórumok esetében -- az {időben eltolt} (\textit{delayed, asynchronous}) kommunikációt is megengedi.\footnote{Korábban például az üzenetrögzítő jellemzője.} A hálózati kommunikáció így lehetőséget biztosít a személyes (\textit{face-to-face}) kommunikációhoz hasonló spontán, azonnali interakción alapuló beszélgetésre, de lehetővé teszi a közösségi interakciót olyan egyének között is, akik nem tudnak közös időpontot találni a kommunikációra. Az internet -- például az e-mail segítségével -- lehetőséget ad az {egyes egyének közötti} (\textit{one-to-one}) kommunikációra, de több, különböző lehetőséget -- például levelezőlisták, fórumok, cset -- biztosít {a közösség tagjai között zajló} (\textit{many-to-many}) kommunikációra, amelyet korábban csak a személyes találkozások vagy a költséges konferenciatelefon-rendszerek tettek lehetővé. (van Dijk 1999) Az internetes hírlevelek, weboldalak, weblogok\footnote{Interneten vezetett, esetenként interaktív naplók.} lehetővé teszik {az egyes egyének}nek és közösségeknek, hogy -- a hagyományos tömegkommunikáció \textit{broadcast} modelljének megfelelően -- {egyszerre nagy közönséghez} juttassák el üzeneteiket (\textit{one-to-many}), amely lehetővé teszi a közösségen kívüli társadalom számára történő reprezentációt, illetve a közönségen belüli olcsó és hatékony információáramlást. Az internetet megelőzően -- postán küldött hírlevelek, nyomtatott, illetve elektronikus sajtó segítségével -- ez a fajta kommunikáció túl költséges volt a marginálisabb érdeklődések mentén szerveződő, kisebb vagy anyagilag hátrányos helyzetű közösségek számára, illetve a médiapiac állami szabályozása is korlátozta ennek lehetőségét. (Castells 2000) Az internet lehetőséget ad {multimediális} kommunikációra -- hangok, képek, mozgóképek és adatok egy rendszerben történő továbbítására --, ám a hálózaton folyó közösségi kommunikáció -- levelezőlisták, fórumok, cset -- többnyire {textuális} formában zajlik. Az \emph{world wide webre} felkerült tartalmak -- például weboldalak, webes alapú fórumok, hírlevél archívumok -- \textbf{kereshetőek}, illetve az ezek készítői által elhelyezett, kapcsolatokat jelző linkek által feszített \textbf{hipertextuális} hálón bejárhatóak, ami lehetőséget biztosít az egyénnek, hogy olyan egyénekkel, illetve közösségekkel is felvegye a kapcsolatot, akikkel csak közvetett kapcsolatban áll vagy akikkel korábban semmilyen kapcsolata sem volt.\footnote{,,Nem kaphatod csak úgy fel a telefont, hogy kapcsolatba lépj valakivel, aki az iszlám művészetről vagy a kaliforniai borról akar beszélgetni, vagy valakivel, akinek egy három éves lánya vagy egy negyvenéves Hudsonja van. Ugyanakkor csatlakozhatsz egy ezen témák bármelyikével foglalkozó számítógépes konferenciához, aztán nyilvános vagy magánlevelezést kezdhetsz korábban ismeretlen emberekkel, akikkel ott találkoztál. A régi módszerekhez képest nagyságrendekkel megnőtt az esélyed, hogy hasonló érdeklődésű csoportot találj.'' (Rheingold 1994, 25)} A következőkben részletesen ismertetem az interneten zajló közösségi kommunikáció sajátosságait, majd e kommunikáció hatását a ,,valós'', lokális közösségek életére. \subsection*{Közösségi kommunikáció az interneten} Ahogy az a következő fejezetből majd kiderül, az interneten zajló kommunikáció fellendítheti, segítheti a már létező társadalmi csoportok közösségi életét, ugyanakkor számtalan olyan, közös érdekek / érdeklődés mentén szerveződő közösség működik az interneten, amelyek tagjai nem ismerik egymást személyesen, s a ,,kibertérben'' találkoznak először. Ezeket a virtuális találkozásokat nem ritkán követik személyes találkozások is, ám gyakoriak az olyan közösségek is, ahol az egyes tagok sosem találkoznak az interneten kívül. (Gelléri 2001) A személyes ismeretség hiánya és a kommunikáció meglehetősen -- főként szöveges formára -- korlátozott formája ellenére ezek az on-line csoportok hatékonyan látnak el a személyes találkozásokra épülő közösségekkel megegyező vagy azokhoz nagyon hasonló funkciókat -- társaságot, közönséget, segítséget és támogatást, információt, a csoporthoz tartozás, illetve a megbecsültség érzését nyújthatják. (Rheingold 1994; Watson 1997) Ezeket az internetes fórumok, levelezőlisták és cset-alkalmazások segítségével kommunikáló csoportokat Howard Rheingold virtuális közösségeknek nevezi, ám elnevezése félrevezető lehet, hiszen ezek a közösségek és tagjaik nagyon is valóságosak. (Wellman és Guila 1999) Az internet -- előző fejezetben ismertetett -- műszaki sajátosságai kihatással vannak a hálózati kommunikáció által hordozott információs spektrumra, a kommunikáció összehangolására, a kommunikatív aktusok gyakoriságára és a kommunikációban résztvevő közösség méretére is. E fejezetben előbb a hálózati kommunikáció sajátosságait ismertetem röviden, majd a közösségi kommunikáció e tulajdonságokból fakadó problémáit. Az egymással az interneten kommunikálók jellemzően textuális formában zajló kommunikációja a személyes találkozás kommunikatív spektrumának csak töredékét kínálja. Teljesen hiányoznak belőle a személyes kommunikáció nemverbális rétegei -- testbeszéd, mimika -- és a beszélt nyelv finom, metakommunikatív tartalmai -- hangsúlyok, szünetek. Ezek a kommunikációs korlátok gyakran vezethetnek félreértésekhez, illetve az e félreértések nyomán -- az időben eltolt kommunikáció esetén ezek azonnali tisztázásának híján -- fellángoló konfliktusokhoz. (Wellman és Gulia 1999). Ugyanakkor érdemes megjegyezni, hogy az online közösségek kommunikációjában gyakran találunk az üzeneteket kontextualizáló elemeket. A csupa nagybetűvel írt üzenet általában a kiabálást helyettesíti, az emberi mimikát utánzó rövid karaktersorozatokból álló emotikonok használata pedig az üzenetet az érzelmi, hangulati töltések széles spektrumával ruházhatja fel.\footnote{Az írásos kommunikáció kibővülése emotikonokkal, illetve különböző rövidítésekkel és nem konvencionális írásmódokkal nemcsak az internetes, de az sms-alapú mobilkommunikációban is jól megfigyelhető. (Sándor 2001) A hazai ,,internetes nyelvről'' jó áttekintést ad az ELTE Tanárképző Főiskolai Kar, Magyar Nyelvtudományi Tanszékének szociolingvisztikai kutatása (2003), illetve Gelléri Gábor (2001) antropológus szakdolgozata, ami az Index törzsasztalának fórumrendszerében folyó kommunikációt vizsgálja a résztvevő megfigyelés módszertanával. Gelléri tanulmánya a magyar nyelvű internetes közösségek vizsgálatának egyik úttörő példája, ami a konkrét közösségek viselkedésének, működésének leírásán túl az online etnográfia módszertani kérdéseivel kapcsolatban is hasznos kiindulási pont. Az ,,internetes nyelvet'' Bódi Zoltán (2004) a szóbeliség írásos megjelenéseként ismerteti.} A technológiai környezet kihat a kommunikáció összehangolására is: még a ,,valós idejű'' kommunikáció lehetőségét kínáló online platformok is sokkal korlátozottabb szintű spontaneitást és szinkronitást tesznek lehetővé, mint a beszélgetés.\footnote{Az időben eltolt kommunikáció lehetőségét kínáló platformok (e-mail, fórumok stb.) esetében még hangsúlyosabban így van ez.} Egy chat-alkalmazás felhasználója az általa közölni kívántak begépelése és elküldése után oszthatja meg a többiekkel mondanivalóját, ami nem csak lassítja az interakciót, de lehetetlenné is teszi a többieknek, hogy az aktuálisan begépelendő gondolat kifejtése közben spontán a szavába vágjanak. A személyes találkozás vizuális elemeinek hiánya a több személy közötti ,,valósidejű'' kommunikáció esetén nehézkessé teszi a beszélgetés menetének alakítását, hiszen mivel nem lehet látni, hogy ki készül szólni, könnyen előfordulhat, hogy többen szinte egyszerre teszik közzé a beszélgetést más-más irányba terelő hozzászólásaikat. A hálózati kommunikáció lehetővé teszi az interakciót a kommunikáló felek időbeli és térbeli összehangolása nélkül, ami nyilvánvalóan növelheti a kommunikációs aktusok gyakoriságát, ahogyan az üzenetek küldésének minimális költségei és szinte azonnali célba jutása, illetve az interneten elküldött informális üzenetekkel kapcsolatos formai, terjedelmi és tartalmi elvárások alacsony szintje is.\footnote{Emmanuel F. Koku és Barry Wellman (2002) az egy campuson dolgozó kutatók kommunikációs szokásait vizsgálva figyelte meg, hogy még az egymástól néhány száz méterre dolgozó kollégák is gyakran választják az e-mailt rövid üzenetek váltására. A nagyobb személyes kapcsolathálóval rendelkező kutatók leggyakrabban e-mail segítségével tartják a kapcsolatot ismerőseikkel.} Az időtől és tértől függetlenített hálózati kommunikáció növelheti az egyes közösségekben résztvevő egyének számát is. A \emph{USENET}-et -- a világ legnagyobb elosztott fórumrendszerét -- statisztikai módszerekkel elemző Mark Smith (1999) a személyes interakcióra épülő közösségek maximális csoportméretének -- körülbelül 150 fő -- három-négyszeresére teszi a hatékonyan működő online közösségek felső létszámhatárát. E közösségek kommunikációjának túlnyomó részét jellemzően egy 30--40 fős stabil mag bonyolítja, míg a tagság legnagyobb része csak ritkán szól hozzá,\footnote{A fórumokat csak olvasók (\textit{lurker}-ek) számát nem tudta mérni a vizsgálat, s csak becsülhető, hogy ezek száma általában a fórumokba írók számának többszörösét teszi ki.} s gyorsan cserélődik. Bár az internet a közösségi kommunikáció hatékony eszköze lehet, néhány, a technológiából fakadó tulajdonsága komoly -- a személyes találkozásokra épülő közösségekre nem jellemző -- problémát jelent az online közösségek számára. Peter Kollock (1999, 220) így foglalja össze e problematikát: \begin{quote} ,,Tekintve, hogy az online interakció relatív anonim, nincs központi autoritás, és hogy nehéz, ha nem lehetetlen pénzügyi vagy fizikai szankciók érvényesítése, meglepő, hogy az internet nem mindenki harca mindenki ellen. Egy, a társadalmi renddel foglalkozó kutató számára nem a rengeteg konfliktus, hanem az online közösségekben megfigyelhető (erőforrás) megosztás és együttműködés nagy mértéke szorul magyarázatra.'' \end{quote} A szolgáltatás fenntartói által ellenőrzött tagságú -- zárt, nem publikus -- közösségi platformok kivételével -- és nem kis mértékben a kommunikáció textuális jellegéből fakadóan -- az on-line közösségek felhasználói relatív anonimek. Mivel az online közösség résztvevőjének online identitása -- amit rendszerint valamilyen becenév (\textit{nick}) reprezentál -- a közösség többi tagja számára rendszerint nem kapcsolható össze ,,valós'' offline személyiségével, nem kell megfelelnie a ,,valós életben'' őt körülvevő környezet elvárásainak. Az anonimitás védelme elősegíti, hogy az online közösségek résztvevői mélyebben, őszintébben nyilatkozzanak egészen intim kérdésekben is (Wellman és Guila 1999); ugyanakkor lehetővé teszi a képzelt, virtuális személyiségek eljátszását is. Még a valamiféle központi autoritással rendelkező online közösségek -- például moderátorok által felügyelt fórumok -- is védtelenek az agresszív, destruktív szerepeket játszó egyénekkel szemben. Míg hasonló magatartás valós közösségekben komoly szankciókat -- a társadalmi elszigetelődéstől a polgári pereken keresztül a fizikai erőszakig terjedő spektrumon -- vonna maga után, az online közösség szankciói -- az agresszív tag megrovása a moderátorok, illetve a közösség egyéb tagjai által, üzeneteinek kiszűrése a rendszerből, illetve a tag teljes kizárása -- alól bárki könnyen kivonhatja magát azzal, hogy újabb becenéven jelentkezik be a rendszerbe. Egy-egy ilyen agresszív egyén egész közösségek életét megzavarhatja, s szélsőséges esetben el is lehetetleníti. (Smith 1999) Az anonimitás és a hatékony szankciókat alkalmazni képes autoritás hiánya nem csak a nyílt destruktív magatartással, de a ,,potyázással'' szemben is védtelenné teszi a közösséget. A közgazdaságtan potyautas-jelenségnek hívja azt a helyzetet, amikor az egyének nem vesznek részt a közjavak\footnote{Javak, melyek haszonélvezetéből nem zárható ki senki. Ilyen például egy tűzijáték vagy a közgyógyellátás.} létrehozásában és fenntartásában, de részt vesznek ezek fogyasztásában. Ez a -- rövid távon az egyes egyén számára maximális hasznot hozó -- stratégia hosszabb távon, amennyiben egy közösségben nagyobb teret nyer, a közjavak teljes feléléséhez vezet, s így a közösség minden tagját, még a potyázókat is rosszabb helyzetbe hozza. Peter Kollock szerint (1999) az online közösségek életében az egyes tagok által a közösséggel megosztott információk közjavak, s velük kapcsolatban könnyen előállhat a potyautas-jelenség, hiszen a közösségi felületen mások által közzé tett információk begyűjtése a közösség számára nem látható, ugyanakkor semmi sem kényszeríti az egyént, hogy maga is megossza a rendelkezésre álló információkat a többiekkel -- válaszoljon a mások által feltett kérdésekre, értesítse a többieket a számukra fontos eseményekről, hírekről. Kollock (1999) ugyanakkor számos motivációs tényezőt sorol fel, amelyek magyarázatot adnak arra kérdésre, hogy miért működik sok közösség mégis hatékonyan.\footnote{Az index fórumainak (\emph{http://forum.index.hu}) átböngészésekor ugyanúgy találunk egymást készséggel segítő orrsövényműtétre várókat és azon már túl levőket, mint Porsche 911 tulajdonosokat, kismamákat és hobbikertészeket, hogy csak néhány kiragadott példát említsek. } A kontribúció alacsony költsége mellett motivációs erőt jelenthet többek között: \begin{itemize} \item a kontribúció által elérhető presztízs; \item az az érzés, hogy az egyén kontribúcióján keresztül hatással van -- online -- környezetére; \item statisztikailag bizonyított, hogy a kérdésekre gyakran válaszolók maguk is gyakrabban és gyorsabban kapnak választ kérdéseikre. \end{itemize} Az online közösségekhez való csatlakozás egyszerűsége miatt állandó problémát okoz a közösségen belüli nagy fluktuáció is. A közösség kommunikációját gyakran zavarja meg, hogy az újonnan csatlakozók olyan kérdéseket tesznek fel, amelyeket korábban már megválaszoltak, illetve nem ismerik a közösségben már kialakult kérdéseket. Sok közösség ezért tart fenn egy \emph{Gyakran Ismételt Kérdéseket} (\textit{FAQ -- Frequently Asked Questions}) tartalmazó weboldalt, ahol az újoncok választ kaphatnak kérdéseikre. \subsection*{A hálózati kommunikáció és közösségi interakció} Ahogy az előző fejezetben láttuk, az internet lehetőséget nyújt az egyén számára, hogy részt vegyen online közösségek életében, ám a világháló szélesebb körű elterjedését követően Észak-Amerikában ismét fellángolt a közösség felbomlásáról szóló vita. Az internetet a közösségre nézve veszélyesnek tartók úgy érveltek, hogy az internetezéssel töltött időt az egyén a korábban a családjára, illetve a közösségére fordított időből veszi el. Ezt az elidegenítő hatást igazolta a \emph{Carnegie Mellon University} pszichológusaiból álló kutatócsoport, amely az internet szociális részvételre és mentális egészségre gyakorolt hatását vizsgálta az első egy-két évüket az interneten töltők között. A kutatás a családdal töltött idő és a baráti kör csökkenése mellett növekvő magányt és frusztrációt mutatott ki a kezdő internetezők körében. A kutatás nem vette figyelembe, hogy a vizsgált alanyok az átlagos internetezőknél sokkal több -- nem kis frusztrációt okozó -- időt töltöttek a számítógép és az internet működésének megismerésével, illetve nem vett tudomást az interneten folytatott társas interakcióról -- a barátokkal folytatott e-mailezésről, az online közösségekben történő részvételről -- sem. (Castells 2000) Azóta számos felmérés\footnote{Ezekről jó összefoglalást nyújt például Castells 2001, illetve Wellman és Gulia 1999. Az alábbi megállapítások Castells összegzéséből származnak. } cáfolta az internet elidegenítő hatásáról alkotott elképzeléseket: \begin{itemize} \item nincs bizonyíték arra, hogy az internetezéssel töltött idő csökkentené a családdal, barátokkal, könyv és újságolvasással töltött időt, egyedül a főzéssel töltött idő csökkenése volt kimutatható; \item az internetezés pozitív hatással van a társadalmi interakcióra: az internetezők gyakrabban szerveztek személyes találkozásokat barátaikkal, nagyobb valószínűséggel folytattak otthonaikon kívül társasági életet, mint az internetet nem használók; \item az internetezők politikai és civil aktivitása megegyezett vagy magasabb volt a nem internetezőkével; \item az internetezők egytizede vett részt online közösségekben és szerzett új barátokat a neten; \item a személyes kommunikáció és a közösségi életben való részvétel csökkenése csak az internetet extrém sokat használók igen kis csoportjára volt jellemző. \end{itemize} Különösen érdekes -- és a fentieket megerősítő -- eredményeket hozott a torontói \emph{Netville} projekt (Wellman 2001) az internet helyi közösségre gyakorolt hatásával kapcsolatban: a nagy sávszélességű internetkapcsolattal felszerelt külvárosi városrészben lakók az internetet használták a helyi közösség ügyeinek megvitatására, illetve ismerkedésre és személyes találkozások szervezésére. A hálózati kommunikáció nagymértékben javította a szomszédsági viszonyokat: \begin{itemize} \item az internettel ellátott lakóknak átlagosan huszonöt ismerősük volt a környéken, míg az internet nélkülieknek átlagosan nyolc; \item az internettel ellátottak kapcsolathálója jóval túlnyúlt háztömbjük közvetelen környékén;\footnote{Hogy mennyire volt a kapcsolatháló az internet-előfizetés oka, s mennyiben következménye, annak nem szentelt figyelmet a tanulmány.} \item az internet elősegítette a kollektív cselekvést is, az interneten kommunikálók csoportja gyorsan mobilizálható volt, amikor közös fellépésre volt szükség a betörőkkel, az internetszolgáltatóval, illetve az ingatlan-fejlesztővel szemben. \end{itemize} \section*{Záró gondolatok} Ahogy például a hazai melegeknek otthont adó \emph{http://www.gay.hu}, vagy az underground elektronikus tánczenei színtér közönségének online diskurzusát bonyolító \emph{http://www.impulsecreator.hu} fórumait tanulmányozva láthatjuk: egyes helyi kulturális közösségek életének aktív, valós városi terekben zajló találkozásaikat is befolyásoló, elősegítő színterévé válhat az internet. A bajaiak helyi ügyeinek online megvitatását vizsgáló Kumin Ferenc tanulmánya (2001), illetve az egyes politikai mozgalmak interneten folytatott társadalmi mobilizációs és ügyképviseleti tevékenységét kutató Csicseri Márta és Lőrincz László (2004) elemzése azt mutatja, hogy az internet magyarok által benépesített és látogatott virtuális helyein nem csak -- szűkebb értelemben vett -- kulturális életüket szervezik az egyes közösségek, de ez érdekérvényesítésük, politikai önszervezésük és kommunikációjuk helyszíne is. A közösségek hálózati kommunikációjának tanulmányozása ma már nehezen megkerülhető a társadalom működésének megértéséhez, az e-demokrácia online intézményrendszerének létrehozásához, a területi alapon szerveződő -- kerületi, városi, falusi, regionális -- közösségek életének revitalizálását, a társadalmi szolidaritás növelését, a marginális kulturális csoportok internetes önszervezését vagy az online kutató, és / vagy tanulóközönségek kiszolgálását célzó informatikai fejlesztések specifikációjához. Hiba lenne azonban az interneten zajló közösségi kommunikációt a személyes találkozásokra épülő, illetve egyéb média- vagy távközlési eszközök által közvetített kommunikációtól elkülönült, önálló rendszerként vizsgálni, hiszen ezek összessége ad csak valós képet az egyéni és közösségi információcseréről és társas viselkedésről. \section*{Irodalomjegyzék} \begin{biblio}{} \item Anderson, B. (1983) {\textit {Imagined Communities: Reflections on the Origins and Spread of Nationalism}}, London: Verso. \item Bell, C. és Newby, H. (1971) ,,An Introduction to the Sociology of the local Community,, in Bell, C. és Newby, H. (szerk.) {\textit {Community Studies}}, London: George Allen. \item Bódi Zoltán (2004) ,,A szóbeliség kifejeződése az internetes kommunikációban'', in {\textit {Információs Társadalom}}, Vol. 4. No. 1. \item Bognár Éva (2003) {\textit {A digitális egyenlőtlenségek kulturális vonatkozásai és a sulinet}}. Szakdolgozat az ELTE Szociológia Szak számára. \item Castells, Manuel (2000) {\textit {The Rise of Network Society. New Edition}}, London: Blackwell Publishers \item Castells, Manuel (2001) {\textit {The Internet Galaxy}}, Oxford: Oxford University Press. \item Csicseri Márta és Lőrincz László (2004) {\textit {Társadalmi mozgalmak mobilizációs és ügyképviseleti tevékenysége az interneten}}. Konferencia-előadás a Rajk László Szakkollégium által rendezett 2004. február 20-án Budapesten rendezett \textit{Társadalmi érdekérvényesítés és online közösségek} című konferencián. \item Dányi Endre, Dessewffy Tibor, Galácz Anna, Ságvári Bence (2004) Információs társadalom, Internet, szociológia'', in {\textit {Információs Társadalom}}, Vol. 4. No. 1. \item Depew, D. és Peters, J. D. (2001) ,,Community and Communication: The Conceptual Background'' in Shepher, G. J. és Rothenbuhler, E. W. (szerk.) {\textit {Communication and Community}}, London: Lawrence Erlbaum Associates Publishers. \item ELTE Tanárképző Főiskolai Kar, Magyar Nyelvtudományi Tanszék (2002) ,,Nyelvi megformálás és kivitelezés az interneten --- egy szociolingvisztikai vizsgálat tapasztalatai'' in {\textit {Kutatási jelentés}}, No. 20-21. \item Gelléri Gábor (2001) {\textit {Törzsasztal. Egy cyber-közösség antropológiája}}. Szakdolgozat az ELTE BTK Kulturális Antropológia Szakja számára. Elérhető az interneten:\\ \emph{http://nyil.embe.hu/elte-btk/dip/gelleri\_gabor.doc} (2004.10.22.) \item Kiss Aranka (2004) ,,Kommunikációtudomány és Internet. Internet-kommunikáció'', in {\textit {Információs Társadalom}}, Vol. 4. No. 1. Koku, E. F. és Wellman, B. (2002) `Scholarly Networks as Learning Communities' in Barab, S. és Kling, R. (szerk.) {\textit {Designing Virtual Communities int he Service of Learning}}, Cambridge: Cambridge University Press. \item Kollock, Peter (1999) ,,The Economies of On-line Cooperation: Gifts and Public Goods in Cyberspace'' in Smith, M. A. és Kollock, P. (szerk) {\textit {Communities in Cyberspace}}, London: Routledge. \item Kumin Ferenc (2001) {\textit {Az on-line Baja. Egy város felfedezi magát az interneten}}. A CEU Politológia Szakja számára készült angol-nyelvű szakdolgozat magyar kivonata. Elérhető az interneten:\\ \emph{ http://www.baja.hu/CEU/szakdolg.doc} (2004.10.22.) \item Reid, E. (1999) ,,Hierarchy and Power: Social Control in Cyberspace'' in Smith, M. A. és Kollock, P. (szerk) {\textit {Communities in Cyberspace}}, London: Routledge. \item Rét Zsófia (2003). {\textit {Az internethasználat terjedésének gátjai}}. Szakdolgozat az ELTE Szociológia Szak számára. \item Rheingold, H. (1994) {\textit {The Virtual Community: Homesteading on the Electronic Frontier}}, London: Secker \& Warburg. Rheingold, H. (2000) `Community Development in the Cybersociety of the Future' in Gaunlet, D. (szerk.) {\textit {Web.studies}}, London: Arnold. \item Rheingold, H. (2002) {\textit {Smart Mobs}}, New York: Perseus. \item Sándor Klára (2001) ,,Mobiltársadalom és myelvhasználat: valami új vagy újra a régi?'', in Nyíri Kristóf (szerk.) {\textit {Mobil információs társadalom: Tanulmányok}}, Budapest: MTA Filozófiai Kutatóintézete. Elérhető az interneten:\\ \R2Lurl{}{http://21st.century.phil-inst.hu/2001\_marc/brosura \_htm/}\\\R2Lurl{}{sandor.htm} (2004.10.22.) \item Smith, A. D. V. (1999) `Problems of Conflict Management in Virtual Communities' in Smith, M. A. és Kollock, P. (szerk) {\textit {Communities in Cyberspace}}, London: Routledge. Smith, M. A. (1999) `Invisible Crowds in Cyberspace: Measuring and Mapping the USENET, Communities' in Smith, M. A. és Kollock, P. (szerk) {\textit {Communities in Cyberspace}}, London: Routledge. \item Tönnies, F. (1887/1983) {\textit {Közösség és társadalom}}, Budapest Gondolat. Van Dijk, J. (1999) {\textit {The Network Society}}, London: Sage Publications. \item Watson, N. (1997) `Why We Argue About Virtual Community: A Case Study of the Phish.Net Fan Community' in Jones, S.G. {\textit {Virtual Culture: Identity \& Communication in Cybersociety}}, London: Sage Publications. \item Wellman, B. (1999a) `The Network Community' in Wellman, B. (szerk.) {\textit {Networks in the Global Village}}, Boulder: Westview Press. Elérhető az interneten: \R2Lurl{}{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/}\\\R2Lurl{}{globalvillage/index.htm }%{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications\\/globalvillage/index.htm} (2004.10.22.) \item Wellman, B. (1999b) `From Little Boxes to Loosly-Bounded Networks: The Privatization and Domestication of Community' in Abu-Lughod, J. (szerk.) {\textit {Sociology or the Twenty-First Century: Continuities and Cutting Edges}}, Chicago: University of Chicago Press. Elérhető az interneten:\\ \R2Lurl{}{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/}\\\R2Lurl{}{littleboxes1/littleboxes1.pdf }%{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/\\littleboxes1/littleboxes1.pdf} (2002.10.22.) \item Wellman, B. (2001) {\textit {The Persistence and Transformation of Community: From Neighbourhood Groops to Social Networks.}} Report to the Law Commission of Canada. Elérhető az interneten:\\ \R2Lurl{}{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/}\\\R2Lurl{}{lawcomm/lawcomm7.PDF }%{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/\\lawcomm/lawcomm7.PDF} (2004.10.22.) \item Wellman, B. és Frank, K. (2001) `Network Capital in a Multi-Level World' in Lin, N., Burt, R., és Cook, K. (szerk.) {\textit {Social Capital:}} {\textit {Theory and Research}}, Chicago: Aldine De Gruyter. Elérhető az interneten:\\ \R2Lurl{}{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/}\\\R2Lurl{}{networkcapital/hlmnan10.pdf }%{http://www.chass.utoronto.ca/{\textasciitilde}wellman/\\publications/networkcapital/hlmnan10.pdf} (2002.10.22) \newpage\item Wellman, B. és Guila, M. (1999) `Net Surfers Don't Ride Alone: Virtual Communities as Communities' in Smith, M. A. és Kollock, P. (szerk) {\textit {Communities in Cyberspace}}, London: Routledge. \item Wellman, B. és Hampton, K. (1999) `Living Networked in a Wired World' in {\textit {Contemporary Sociology}}, Vol. 28 No.6. Elérhető az interneten:\\ \R2Lurl{}{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/}\\\R2Lurl{}{livingnetworked/ieee1\%5B1\%5D.4b.PDF }%{http://www.chass.utoronto.ca/{\textasciitilde}wellman/publications/\\livingnetworked/ieee1\%5B1\%5D.4b.PDF} (2004.10.22.) \end{biblio} \end{document}

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\NeedsTeXFormat{LaTeX2e} \ProvidesPackage{simpleicons}[2023/03/17 8.7.0 Simple Icons 8.7.0 Logos] \RequirePackage{ifxetex,ifluatex} \newif\ifsimpleicons@otf\simpleicons@otffalse \ifxetex \simpleicons@otftrue \else \ifluatex \simpleicons@otftrue\fi\fi \newcommand*{\simpleicon}[1]{% {\csname simpleicon@#1\endcsname}} \ifsimpleicons@otf \usepackage{fontspec} \newfontfamily{\simpleiconsmap}{SimpleIcons} \input{simpleiconsglyphs-xeluatex.tex} \else \DeclareRobustCommand\simpleiconsmapOne{\fontencoding{U}\fontfamily{simpleiconsOne}\selectfont} \DeclareRobustCommand\simpleiconsmapTwo{\fontencoding{U}\fontfamily{simpleiconsTwo}\selectfont} \DeclareRobustCommand\simpleiconsmapThree{\fontencoding{U}\fontfamily{simpleiconsThree}\selectfont} \DeclareRobustCommand\simpleiconsmapFour{\fontencoding{U}\fontfamily{simpleiconsFour}\selectfont} \DeclareRobustCommand\simpleiconsmapFive{\fontencoding{U}\fontfamily{simpleiconsFive}\selectfont} \DeclareRobustCommand\simpleiconsmapSix{\fontencoding{U}\fontfamily{simpleiconsSix}\selectfont} \DeclareRobustCommand\simpleiconsmapSeven{\fontencoding{U}\fontfamily{simpleiconsSeven}\selectfont} \DeclareRobustCommand\simpleiconsmapEight{\fontencoding{U}\fontfamily{simpleiconsEight}\selectfont} \DeclareRobustCommand\simpleiconsmapNine{\fontencoding{U}\fontfamily{simpleiconsNine}\selectfont} \DeclareRobustCommand\simpleiconsmapOneZero{\fontencoding{U}\fontfamily{simpleiconsOneZero}\selectfont} \input{simpleiconsglyphs-pdftex.tex} \fi \endinput

http://www.ipm.ac.ir/papers/pdf/abs11679.tex

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\documentclass[12pt]{article} \usepackage{amsmath,amssymb,amsfonts} \begin{document} In their first-principles calculations of the electronic band structure of graphene under uniaxial strain, Gui, Li and Zhong Phys. Rev. B 78 075435 (2008) have found opening of band gaps at the Fermi level. This finding is in conflict with the tight-binding description of graphene which is closed gap for small strains. In this Comment, we present first-principles calculations which refute the claim that strain opens band gaps in graphene. \end{document}

https://bibliography.jewishstudies.pl/show.php?record=1509&submit=Cite&citeType=LaTeX

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%&LaTeX \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \begin{document} \begin{thebibliography}{1} \bibitem{Friedrich2013} Friedrich A., \textit{The Impact of German Anti-Semitic Press on the Polish Weekly {\textquotedblleft}Rola{\textquotedblright}}, [w:] \textit{Five Hundred Years of Jew-Hatred and Anti-Semitism in German Press: Manifestations and Reactions}, red.~Nagel, M., red.~Zimmermann, M., t. 1, Brema, 2013, s. 273--82 \end{thebibliography} \end{document}

https://wolfgang.dautermann.at/vortraege/Linuxday-2012-Latex-fuer-Fortgeschrittene/10-sagetex/sagetex-example.tex

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\documentclass{article} \usepackage[utf8]{inputenc} \usepackage{sagetex} \usepackage{verbatim} \begin{document} \section{Inline-Berechnungen} Einfache Rechnung: $3 \times 3 = \sage{3*3}$ \\ (\LaTeX-Code: \verb+$3 \times 3 = \sage{3*3}$+) \section{Sage-Blöcke} Funktionsdefinition: \begin{sageblock} f(x) = exp(x) * sin(2*x) \end{sageblock} \subsection{Latex-Code:} \begin{verbatim} \begin{sageblock} f(x) = exp(x) * sin(2*x) \end{sageblock} \end{verbatim} \subsection{2. Ableitung von $f$} \[ \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \sage{f(x)} = \sage{diff(f, x, 2)(x)}. \] \subsection{Latex-Code:} \begin{verbatim} \[ \frac{\mathrm{d}^{2}}{\mathrm{d}x^{2}} \sage{f(x)} = \sage{diff(f, x, 2)(x)}. \] \end{verbatim} \section{Sage-Blöcke ohne Anzeige} \begin{sagesilent} f2(x) = 2*x \end{sagesilent} \begin{verbatim} \begin{sagesilent} f2(x) = 2*x \end{sagesilent} \end{verbatim} \[ 2 * 7 = \sage{f2(7)} \] \subsection{Latex-Code:} \begin{verbatim} \[ 2 * 7 = \sage{f2(7)} \] \end{verbatim} \section{Plot von $f$ from $-1$ to $1$} \sageplot[angle=0, width=5cm]{plot(f, -1, 1)} \subsection{Latex-Code:} \begin{verbatim} \sageplot[width=5cm]{plot(f, -1, 1)} \end{verbatim} \end{document}

http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blob_plain;f=simple.tex;hb=410132e37a1f6e95cbfa9792d63b50b9390e59e4

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\section{Simple commit} A simple single-parent forward commit $C$ as made by git-commit. \begin{gather} \tag*{} C \hasparents \{ L \} \\ \tag*{} \patchof{C} = \patchof{L} \\ \tag*{} D \isin C \equiv D \isin L \lor D = C \end{gather} This also covers Topbloke-generated commits on plain git branches: Topbloke strips the metadata when exporting. \subsection{No Replay} Ingredients Prevent Replay applies. $\qed$ \subsection{Unique Base} If $L, C \in \py$ then by Calculation of Ends, $\pendsof{C}{\pn} = \pendsof{L}{\pn}$ so $\baseof{C} = \baseof{L}$. $\qed$ \subsection{Tip Contents} We need to consider only $L, C \in \py$. From Tip Contents for $L$: \[ D \isin L \equiv D \isin \baseof{L} \lor ( D \in \py \land D \le L ) \] Substitute into the contents of $C$: \[ D \isin C \equiv D \isin \baseof{L} \lor ( D \in \py \land D \le L ) \lor D = C \] Since $D = C \implies D \in \py$, and substituting in $\baseof{C}$, from Unique Base above, this gives: \[ D \isin C \equiv D \isin \baseof{C} \lor (D \in \py \land D \le L) \lor (D = C \land D \in \py) \] \[ \equiv D \isin \baseof{C} \lor [ D \in \py \land ( D \le L \lor D = C ) ] \] So by Exact Ancestors: \[ D \isin C \equiv D \isin \baseof{C} \lor ( D \in \py \land D \le C ) \] $\qed$ \subsection{Base Acyclic} Need to consider only $L, C \in \pn$. For $D = C$: $D \in \pn$ so $D \not\in \py$. OK. For $D \neq C$: $D \isin C \equiv D \isin L$, so by Base Acyclic for $L$, $D \isin C \implies D \not\in \py$. $\qed$ \subsection{Coherence and Patch Inclusion} Need to consider $D \in \py$ \subsubsection{For $L \haspatch \p, D = C$:} Ancestors of $C$: $ D \le C $. Contents of $C$: $ D \isin C \equiv \ldots \lor \true \text{ so } D \haspatch C $. \subsubsection{For $L \haspatch \p, D \neq C$:} Ancestors: $ D \le C \equiv D \le L $. Contents: $ D \isin C \equiv D \isin L \lor f $ so $ D \isin C \equiv D \isin L $, i.e. $ C \zhaspatch P $. By $\haspatch$ for $L$, $\exists_{F \in \py} F \le L$ and this $F$ is also $\le C$. So $\haspatch$. So: \[ L \haspatch \p \implies C \haspatch \p \] \subsubsection{For $L \nothaspatch \p$:} Firstly, $C \not\in \py$ since if it were, $L \in \py$. Thus $D \neq C$. Now by contents of $L$, $D \notin L$, so $D \notin C$. So: \[ L \nothaspatch \p \implies C \nothaspatch \p \] $\qed$ \subsection{Foreign Inclusion:} Simple Foreign Inclusion applies. $\qed$ \subsection{Foreign Contents:} Only relevant if $\patchof{C} = \bot$, and in that case Totally Foreign Contents applies. $\qed$

https://doc.libelektra.org/api/0.8.21/latex/md_doc_help_kdb-restore.tex

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{\ttfamily kdb restore $<$timestamp$>$} \subsection*{D\+E\+S\+C\+R\+I\+P\+T\+I\+ON} This command will restore everything backed up by {\ttfamily kdb backup} (or stashed by {\ttfamily kdb stash}) where {\ttfamily timestamp} is the timestamp returned by {\ttfamily kdb backup} (or {\ttfamily kdb stash}). \subsection*{E\+X\+M\+A\+P\+L\+ES} \begin{DoxyCode} kdb restore 1500000000 \end{DoxyCode} \subsection*{S\+EE A\+L\+SO} \begin{DoxyItemize} \item \hyperlink{md_doc_help_kdb-backup_doc_help_kdb-backup_md}{kdb-\/backup(7)} \item \hyperlink{md_doc_help_kdb-stash_doc_help_kdb-stash_md}{kdb-\/stash(7)} \end{DoxyItemize}

https://dlmf.nist.gov/17.7.E11.tex

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\[{{}_{4}\phi_{3}}\left({q^{-n},q^{n+1},c,-c\atop e,c^{2}q/e,-q};q,q\right)=% \frac{\left(eq^{-n},eq^{n+1},c^{2}q^{1-n}/e,c^{2}q^{n+2}/e;q^{2}\right)_{% \infty}}{\left(e,c^{2}q/e;q\right)_{\infty}}.\]

http://build.openvpn.net/doxygen/latex/dir_78d5dec77f3d0beddd03e217d9f2a1fe.tex

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\hypertarget{dir_78d5dec77f3d0beddd03e217d9f2a1fe}{\subsection{/root/openvpn/src/ Directory Reference} \label{dir_78d5dec77f3d0beddd03e217d9f2a1fe}\index{/root/openvpn/src/ Directory Reference@{/root/openvpn/src/ Directory Reference}} } Directory dependency graph for /root/openvpn/src/\-:\nopagebreak \begin{figure}[H] \begin{center} \leavevmode \includegraphics[width=350pt]{dir_78d5dec77f3d0beddd03e217d9f2a1fe_dep} \end{center} \end{figure} \subsubsection*{Directories} \begin{DoxyCompactItemize} \item directory \hyperlink{dir_b5370af1cd0a844ed977612dc0b00820}{compat} \item directory \hyperlink{dir_c4bdb439cdb9478c537074abfa9e3ecd}{openvpn} \item directory \hyperlink{dir_9d1e5b4b0ccc49bb854cf75652eff1a3}{openvpnserv} \item directory \hyperlink{dir_bc5e476ce157a2262c953f31b13766f9}{plugins} \end{DoxyCompactItemize}

https://anarhija.info/library/wp-202-import.tex

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\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=10pt,% oneside,% paper=210mm:11in]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{CMU Serif} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{croatian} % global style \pagestyle{plain} \usepackage{microtype} % you need an *updated* texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand*\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % continuous numbering across the document. Defaults to resetting at chapter. Unclear % \usepackage{chngcntr} % \counterwithout{footnote}{chapter} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand*{\captionformat}{} \renewcommand*{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand*{\forcelinebreak}{\strut\\*{}} \newcommand*{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment*{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment*{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand*{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{ČILE: VIJESTI O UHAPŠENIM DRUGOVIMA NATALY I JUANU} \date{} \author{} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={ČILE: VIJESTI O UHAPŠENIM DRUGOVIMA NATALY I JUANU},% pdfauthor={},% pdfsubject={},% pdfkeywords={Čile; zatvorenici}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge ČILE: VIJESTI O UHAPŠENIM DRUGOVIMA NATALY I JUANU\par}}% \vskip 1em \vskip 2em \vskip 1.5em \vskip 3em \includegraphics[keepaspectratio=true,height=0.5\textheight,width=1\textwidth]{w-2-wp-202-import-1.png} \vfill \strut\par \end{center} \end{titlepage} \cleardoublepage Advokati drugova Juana Floresa i drugarice Nataly Casanova uputilu su žalbu na pritvor tražeći kućni pritvor. 2. oktobra 2014. Žalbeni sud u San Miguelu odbacio je žalbu. Premještaji: Istog dana Juan je imao ročište na kojem je obrana zatražila premještaj iz zatvora Empresa Santiago 1 u Zatvor Maksimalne Sigurnosti (CAS). Zahtjev se temelji na prijetnjama kojima je podvrgnut Juan, a uputili su ih zatvorenici koje su organizirali stražari. Terorističko tužiteljstvo Sur iz Francisca Brava nastavilo je svojim planom kompliciranja i otežavanja zatočeništva drugova i zatražilo odbacivanje premještaja. Na koncu je sudac Rene Cerda odbio Juanov zahtjev, tražeći od žandarmerije da više nadzire optuženog. \textbf{Solidarnost s Nataly i Juanom!} \textbf{Ne napuštamo naše drugove u zatvoru!} Izvor: \href{http://publicacionrefractario.wordpress.com/2014/10/07/se-mantiene-la-prision-preventiva-contra-juan-y-nataly-y-es-rechazado-el-traslado-al-cas/\#more-6957}{publicacion refractario} via \href{https://radioazione.org/2014/10/cile-aggiornamenti-sugli-arresti-di-natalie-e-juan/}{RadioAzione} % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarhija.info \strut \end{center} \strut \vfill \begin{center} ČILE: VIJESTI O UHAPŠENIM DRUGOVIMA NATALY I JUANU \bigskip \bigskip \textbf{anarhija.info} \end{center} % end final page with colophon \end{document}

https://lib.anarhija.net/library/a-j-p-taylor-economic-imperialism.tex

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\documentclass[DIV=12,% BCOR=0mm,% headinclude=false,% footinclude=false,% fontsize=10pt,% oneside,% paper=a5]% {scrartcl} \usepackage{fontspec} \setmainfont[Script=Latin]{Alegreya} \setsansfont[Script=Latin,Scale=MatchLowercase]{Alegreya Sans} \setmonofont[Script=Latin,Scale=MatchLowercase]{Space Mono} \let\chapter\section % global style \pagestyle{plain} \usepackage{microtype} % you need an *updated* texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand*{\captionformat}{} \renewcommand*{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \usepackage{polyglossia} \setmainlanguage{english} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand*\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand*{\forcelinebreak}{\strut\\*{}} \newcommand*{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment*{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment*{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand*{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Economic Imperialism} \date{1952} \author{A. J. P. Taylor} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Economic Imperialism},% pdfauthor={A. J. P. Taylor},% pdfsubject={},% pdfkeywords={anti-capitalist; economics; history}% } \begin{document} \thispagestyle{empty} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Economic Imperialism\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{A. J. P. Taylor\par}}% \vskip 1.5em {\usekomafont{date}{1952\par}}% \end{center} \vskip 3em \par Ideas live longer than men, and the writer who can attach his name to an idea is safe for immortality. Darwin will live as long as Evolution, Marx be forgotten only when there are no class-struggles. In the same way, no survey of the international history of the twentieth century can be complete without the name of J A Hobson. He it was who found an economic motive for Imperialism. Lenin took over Hobson’s explanation, which thus became the basis for Communist foreign policy to the present day. Non-Marxists were equally convinced, and contemporary history has been written largely in the light of Hobson’s discovery. This discovery was an off-shoot from his general doctrine of under-consumption. The capitalists cannot spend their share of the national production. Saving makes their predicament worse. They demand openings for investment outside their saturated national market, and they find these openings in the undeveloped parts of the world. This is Imperialism. In Hobson’s words, ‘the modern foreign policy of Great Britain has been primarily a struggle for profitable markets of investment’ — and what applied to Great Britain was equally true of France or Germany. Brailsford put it a few years later in a sharper way: \begin{quote} Working men may proceed to slay each other in order to decide whether it shall be French or German financiers who shall export the surplus capital (saved from their own wages bill) to subdue and exploit the peasants of Morocco. \end{quote} This idea is now so embedded in our thought that we cannot imagine a time when it did not exist. Yet the earlier Radical opponents of Imperialism knew nothing of it. They supposed that Imperialism sprang from a primitive greed for territory or a lust for conquest. The more sophisticated held that it was designed to provide jobs for the younger sons of the governing classes (a theory which James Mill invented and himself practised and which Hobson did not discard). Marx had no theory of Imperialism. In classical Marxist theory, the state exists solely to oppress the working classes — to silence their grievances, destroy their trade unions and force them ever nearer to the point of absolute starvation. Marx jeered at the ‘night-watchman’ theory of the state, but the only difference in his conception was that it stayed awake in the day-time. Hobson added a true Marxist refinement. Marx had demonstrated that the capitalist, however benevolent personally, was condemned by economic law to rob the worker at the point of production. Similarly Hobson showed that the capitalist, however pacific, must seek foreign investment and therefore be driven into imperialist rivalry with the capitalists of other states. Previously Marxists had condemned capitalism as being pacific and particularly for preventing the great war of liberation against Russia. Now all wars became ‘capitalistic’, and war the inevitable outcome of the capitalist system. It is not surprising that, when the first world war had broken out, Lenin seized on Hobson’s ‘bourgeois-pacifist’ theory and made it the cornerstone of neo-Marxism. Like most prophets he boasted of his foresight only when his visions had become facts. Hobson wrote his book immediately after the partition of Africa and when the experiences of the Boer war were fresh in everyone’s mind. For him, Imperialism was mainly acquisition of tropical lands, and what he foresaw next was the partition, or perhaps the joint exploitation, of China. In the spring of 1914 Brailsford applied similar doctrines to a wider field. The War of Steel and Gold (1914) is a more brilliant book than Hobson’s, written with a more trenchant pen and with a deeper knowledge of international affairs. Though less remembered now, it had probably a stronger influence on its own generation, and American historians between the wars, in particular, could hardly have got on without it. Our own thought is still unconsciously shaped by it. Brailsford speaks more to our condition. The aggressive, self-confident Imperialism of the Boer war seems remote to us; the competition of great armaments is ever-present in our lives. Both writers wrote with Radical passion. The first sensation in re-reading them is to cry out: ‘Would that we had such writers nowadays!’ Take Hobson’s peroration: \begin{quote} Imperialism is a depraved choice of national life, imposed by self-seeking interests which appeal to the lusts of quantitative acquisition and of forceful domination surviving in a nation from early centuries of animal struggle for existence\dots{} It is the besetting sin of all successful States, and its penalty is unalterable in the order of nature. \end{quote} Or Brailsford’s \begin{quote} Let a people once perceive for what purposes its patriotism is prostituted, and its resources misused, and the end is already in sight. When that illumination comes to the masses of the three Western Powers, the fears which fill their barracks and stoke their furnaces will have lost the power to drive. A clear-sighted generation will scan the horizon and find no enemy. It will drop its armour, and walk the world’s highways safe. \end{quote} These are heavyweights of political combat. The intellectual diet of the mid twentieth century cannot nourish such stamina. But we must stay the flood of our admiration with some doubting questions. Was the Hobsonian-Leninist analysis of international capitalism a true picture either then or now? Has the struggle for overseas investments ever been the mainspring of international politics? The export of capital was certainly a striking feature of British economic life in the fifty years before 1914. But its greatest periods were before and after the time of ostensible Imperialism. What is more, there was little correspondence between the areas of capitalist investment and political annexation. Hobson cheats on this, and Lenin after him. They show, in one table, that there has been a great increase in British investments overseas; in another that there has been a great increase in the territory of the British Empire. Therefore, they say, the one caused the other. But did it? Might not both have been independent products of British confidence and strength? If openings for investment were motive of British Imperialism, we should surely find evidence for this in the speeches of British imperialists, or, if not in their public statements, at any rate in their private letters and opinions. We don’t. They talked, no doubt quite mistakenly, about securing new markets and even more mistakenly, about new openings for emigration; they regarded investment as a casual instrument. Their measuring-stick was Power, not Profit. When they disputed over tropical African territory or scrambled for railway concessions in China, their aim was to strengthen their respective empires, not to benefit the financiers of the City. Hobson showed that Imperialism did not pay the nation. With longer experience, we can even say that it does not pay the investors. But the proof, even if convincing, would not have deterred the advocates of Imperialism. They were thinking in different terms. The economic analysis breaks down in almost every which has been examined in detail. Morocco has often been treated as a classical case of finance imperialism, by Brailsford himself and in more detail by E D Morel. In fact, the French financiers were forced to invest in Morocco much against their will, in order to prepare the way for French political control. They knew they would lose their money, and they did. But Morocco became a French protectorate. Again, Brailsford made much play with the British investment in Egypt, which Cromer had promoted. But Cromer promoted these investments in order to strengthen British political control, and not the other way round. The British held on to Egypt for the sake of their empire; they did not hold their empire for the sake of Egypt. Even the Boer war was not purely a war for financial gain. British policy in South Africa would have been exactly the same if there had been no gold-mines. The only difference is that, without the profits from the dynamite-monopoly, the Boers would have been unable to put up much resistance. Rhodes was a great scoundrel in Radical eyes, and quite rightly. But not for the reasons that they supposed. Rhodes wanted wealth for the power that it brought, not for its own sake. Hence he understood the realities of politics better than they did. Those who explained Imperialism in terms of economics were rationalists themselves and therefore sought a rational explanation for the behaviour of others. If capitalists and politicians were as rational as Hobson and Brailsford, this is how they would behave. And of course a minority did. They took their profits, agreed with their enemy in the way and died quietly in their beds. But they did not set the pattern of events. It is disturbing that, while Hobson and Brailsford were so penetrating about the present, they were wrong about the future. Hobson ignored Europe altogether — rightly, since he was discussing colonial affairs. He expected the international capitalists to join in the exploitation of China and even to recruit Chinese armies with which to hold down the workers of Europe. Brailsford looked to Europe only to reject it. He wrote — this in March 1914: ‘the dangers which forced our ancestors into European coalitions and Continental wars have gone never to return’. And again, ‘it is as certain as anything in politics can be, that the frontiers of our modern national states are finally drawn. My own belief is that there will be no more wars among the six Great Powers.’ Even if there were a war, ‘it is hard to believe that \dots{} German Socialists would show any ardour in shooting down French workmen. The spirit which marched through Sedan to Paris could not be revived in our generation.’ It may be unfair to judge any writer in the light of what came after. Yet men with far less of Brailsford’s knowledge and intellectual equipment foresaw the conflict of 1914, and even the shape that it would take. The true vision of the future was with Robert Blatchford, when he wrote his pamphlet, Germany and England, for the Daily Mail. This is a sad confession. Hobson and Brailsford are our sort. We think like them, judge like them, admire their style and their moral values. We should be ashamed to write like Blatchford, though he was in fact the greatest popular journalist since Cobbett. Yet he was right, and they were wrong. Their virtues were their undoing. They expected reason to triumph. He knew that men love Power above all else. This, not Imperialism, is the besetting sin. Lenin knew it also. Hence, though a rationalist by origin, he turned himself into a wielder of power. Thanks to him, there is nothing to choose between Rhodes and a Soviet commissar. Nothing except this: the capitalist may be sometimes corrupted and softened by his wealth; the Soviet dictators have nothing to wear them down. If the evils which Hobson and Brailsford discovered in capitalism had been in fact the greatest of public vices, we should now be living in an easier world. It is the high-minded and inspired, the missionaries not the capitalists, who cause most of the trouble. Worst of all the men of Power who are missionaries as well. % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Library.Anarhija.Net \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} A. J. P. Taylor Economic Imperialism 1952 \bigskip Retreived on April 30\textsuperscript{th}, 2009 from \href{http://www.panarchy.org/taylor/imperialism.1952.html}{www.panarchy.org} \bigskip \textbf{lib.anarhija.net} \end{center} % end final page with colophon \end{document}

https://tr.anarchistlibraries.net/library/meydan-gazetesi-yasadigimiz-topraklardaki-halklarin-mayasidir-isyan.tex

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Bu topraklarda yaşayanlar, iktidarın sarsılmaz olmadığını, polisin dost olmadığını ve sokakların kendilerine ait olduğunu hatırladılar. Hatırladılar diyoruz, çünkü Baba İshak “dünya malı halkındır” diyen değil, bozguncu; Celaliler, halkın kendisi değil bir avuç çapulcu ve eşkıya; Şeyh Bedreddin adalet için mücadele veren bir devrimci değil iktidar meraklısı bir devlet adamı olarak anlatılmıştı tarih kitaplarında. Efendiler ve resmi tarih öğreticileri bozguncunun bozguna uğratılacağını, biat edenin huzur ve refah içinde yaşayacağını adeta beynimize kazımıştı. Ancak bu toprakların geleneği biat değil, isyandır! O isyanın adı, kimi zaman Bizans’a kafa tutan özgür Pavlakiler, kimi zaman Selçuklu’ya diz çöktüren Babailer, kimi zaman ellerinde sadece kazma kürekler olmasına rağmen defalarca Osmanlı ordusunu geri püskürten Ortaklar olmuştur. Dehaq’lara karşı isyan ateşini yakan Kawa’lar, ulus-devlet uğruna katledilen Şeyh Sait’ler, onca oyuna ve kırıma rağmen baş eğmeyen Seyit Rıza ile Dersimliler ve daha niceleri\dots{} \section{\textbf{Pavlakiler: Devletin Dinine Baş Kaldıranlar!}} Pavlakiler, 7. yy.de Sivas, Malatya ve Erzurum’da yaşayan Ermenilerdir. Resmi dini Hristiyanlık olan Bizans Devleti’nin egemenliği altında olan bu bölgede, kilise ve iktidar yanlısı Hristiyanlığın otoritesini reddederek, Alevilik, İran Manihaizm’i ve Binyılcı Hristiyanlık gibi görece daha özgür ve halkçı anlayışları birleştirmeleri; onları egemen dinin saldırısına maruz bırakmıştır. Nihayetinde Bizans’ın ve kilisenin baskılarına başkaldıran Pavlakiler, Arap Müslümanların ve daha birçok ezilenin katılımıyla 9. yy’de büyük bir isyana kalkışmışlardır. İsyancılar Ankara’ya kadar gelmiş, fakat burada Bizans ordusu tarafından durdurulmuşlardır. Sonrasında Bizans ordusu, isyancıları akıl almayacak işkencelerle katletmiş, (Bizans kayıtlarına göre 100.000 kişi) geri kalanları da sürgüne göndermiştir. Sonraki süreçte, Pavlakiler sürüldükleri yerleri Bektaşiliğin merkezi haline getirmişler, Babai ve Şeyh Bedreddin İsyanı gibi halk isyanlarına hem esin kaynağı olmuş, hem de doğrudan katılmışlardı. \section{\textbf{Babai İsyanları: “Dünya Mülkü Halkındır.”}} Babai İsyanı, Anadolu halklarının adalet ve özgürlük arayışlarının belirginleştiği, sonrasında da bu topraklarda, devlete ve efendilere karşı girişilecek olan isyanlara esin kaynağı olan bir hareket olmuştur. Anadolu’daki hemen hemen tüm halkları devletin iktidarına karşı birleştiren Babai İsyanları, döneminde bu toprakların çehresini değiştirerek uzun yılar Babailik olarak bilinen bir isyan geleneğini yeşertmişlerdir. 1240 yılında başlayan Babailer Hareketi, diğer öncüllerinde de olduğu gibi dinci, ayrılıkçı, Sünni-Şii çatışması şeklinde resmi tarihin tanımladığı gibi değil; örgütlü, politik bir çabayı ve devrimci zihniyeti gerçekleştirmenin bir başka örneğidir. “Dünya mülkü halkındır.” diyen Baba İlyas’ın adalet anlayışı ve Baba İshak’ın halkın arasındaki çalışmalarıyla gittikçe büyüyen isyan, Müslümanından Hristiyanına, Türkmeninden Rumuna, konarından göçerine bütün bir halkın sırtında, başkent Konya kapılarına kadar gelmiş Selçuklu Devleti’ni yıkamadıysa bile sarsmıştır. İsyan bastırıldıktan sonra, çoluk çocuk demeden bütün Babaileri kılıçtan geçiren Selçuklular, ne devletlerinin yıkılmasını engelleyebilmişler, ne de yanmakta olan isyan ateşini söndürebilmişlerdir. O gün bir Selçuklu askeri tarafından başı vurulan bir Babai, bir kaç yüzyıl sonra Osmanlı’nın karşısına bir Celali olarak dikilmeye devam etmiştir. \section{\textbf{Celali İsyanları: Osmanlı’ya Kıyama Kalkanlar}} 16. yy.’ın ilk yarısında, Osmanlı›ya karşı başlayan ve neredeyse yüzyılı aşkın bir süre Osmanlı devlet geleneğine ve onun, baskılarla, vergilerle, askerleriyle “dirlik ve düzen” içinde tutmak istediği Anadolu topraklarında çıkan isyanlardır. Bunlardan bazıları; 1517 yılında Yozgat-Tokat bölgesinde Bozoklu Celal, 1525 yılında Süklün Koca ve Baba Zünnun Bozok’ da, 1527 yılında Tokat ve yöresinde Zünnünoğlu Halil ve Hubyar Baba, 1526 yılında Kırşehir-Ankara yöresinde Kalender Çelebi, 16 yy. ortalarında Sivas›ta Pir Sultan Abdal\dots{} Bunların tümü Celali İsyanları olarak anılmış, bu topraklarda yaşayanların adalet için mücadeleleri olarak görülmüştür. Bu isyanlar her zaman olduğu gibi, çok ağır bir şekilde bastırılarak, isyancılar katledilmiş; hatta isyana katılanlar, çapulcu eşkıya diye anılarak hiçleştirilmeye çalışılmıştır. Fakat bugün, ne isyan değerinden bir şey yitirmiş, ne de Celaliler’in yeniden harladığı isyan ateşinin bugünü aydınlatması engellenebilmiştir. \section{\textbf{Şeyh Bedreddin ve Börklüce Mustafa: Yarin Yanağından Gayri Her Şeyi Paylaşmak İçin!}} Şeyh Bedreddin İsyanı, hem ortaklaşacılığın ete kemiğe bürünmüş hali, hem de 16. yy.›da Osmanlı Devleti’ne karşı örgütlenmiş bir devrim girişimiydi. Şeyh Bedreddin ile onun ortakçıları Börklüce Mustafa ve Torlak Kemal’in çalışmaları ile büyüyen isyan, ağır vergiler altında ezilen, yok sayılan, savaşlarla, sürgünlerle talan edilen köylülerde, ahi birliklerinde, Müslümanlarda ve Gayri Müslimlerde; kısacası toplumun ezilen tüm kesimlerinde karşılık bulmuştu. İsyan, özellikle Ege bölgesinde, İzmir ve Manisa çevresinde, köylülerin, devlete haraç olarak verdiği ürünleri vermeyip, toprağı ortak işleyip, topraktan geleni ortakça tüketmeleriyle; daha doğrusu öşürcüleri başlarından kovup, devleti ve özel mülkiyeti hayatlarından çıkartarak, hayatlarını paylaşma ve dayanışma ekseninde kurmak istemeleriyle iyice büyüdü. Köylüler artık devlete haraç vermiyor, toprakların beraber işleyip beraber tüketiyor, her şeye beraber karar veriyor, yemekler köy meydanlarında büyük kazanlarda pişirilip beraber yeniliyordu. Devlet, tabi ki buna daha fazla müsaade edemezdi. Osmanlı, bu komünlere defalarca saldırdı ama her seferinde geri püskürtüldü. Binlerce insan Karaburun’a çekilerek hem ortakçılıklarına devam ettiler, hem de Osmanlı ile savaşmaya\dots{} Fakat bu isyan da çok sert bastırıldı. Şeyh Bedreddin’in ortakçıları, katledilerek bugün “ölüm kuyuları” diye bilinen yerlere atıldılar. İsyanın sona erdiği haberini alan Bedreddin, sürgünde olduğu İznik’ten kalkıp Serez’e geldi, fakat onun ölüm fermanını hiçbir ulema imzalayamadı. Kendi ölüm fermanını yazdı ve boğazına ilmiği kendi geçirip, idam sehpasını tekmeledi. \section{\textbf{Demirci Kawa Destanı: Dehaq’lara Karşı, Hepimiz Kawa’yız!}} Bundan 2.500 sene önce, Mezopotamya’da hüküm süren Asurlu Kral Dehaq’a karşı ayaklanan Kürtleri anlatır bu destan. Zalim kral Dehaq, hem baharın gelişini engelliyor, hem de yakalandığı ölümcül bir hastalıktan kurtulmak için, her gün bölgeden yakalanan iki genci öldürüp, beyinlerini yiyordu. Gençler katledilirken, sıra daha önce bu şekilde 17 oğlunu kaybetmiş olan Kawa adındaki demircinin en küçük oğluna gelmişti. Her gün, gençler Dehak’ın askerleri tarafından başları kesilmek üzere götürülürken, Kawa’nın aklına başkaldırı fikri gelir ve bu konuyu etrafında güvendiği birkaç kişiye açıklar. Demirci dükkânında, demirden savaş malzemeleri olarak Gürz û Kember, Kêr gibi araçlar yapar ve bir taraftan da başkaldırı için etrafındakileri eğitir. Bu hareket, yavaş yavaş yayılmaya başlar. Mart ayının 20’sini 21’ine bağlayan gece, zalim Dehak’a karşı direniş başlar. O gece Demirci Kawa, kralın sarayına doğru yürür. Zalim Kral Dehaq’ı öldürerek, hem Kürtleri özgürlüğüne kavuşturmuş olur, hem de yeniden gelen baharın müjdecisi olur. \section{\textbf{Şeyh Sait İsyanı: “Torunlarımızın Bizden Dolayı Utanç Duymaması Bizim İçin Yeterlidir!”}} 5 Şubat 1925, Osmanlı Devleti yıkılmış; ulus temelli T.C’nin kurulması için adımlar atılmaya başlanmıştır. Bu adımlardan biri, tabi ki Kürtlerden kurtulmak, olmazsa onları etkisiz hale getirmektir. İlk önce 2 Mart 1925‘te dönemin başbakanı Fethi Okyar: “Elimi kana bulamak istemiyorum.” der ve ardından görevden alınır, yerine İsmet İnönü atanır. Takrir-i Sükun Kanunu çıkartılır, İstiklal Mahkemeleri kurulur. Hâlihazırda bir isyan hazırlığında olan Kürtler, bir provokasyonla savaşın içine çekilir. Sonrasında Kürt halkıyla T.C Devleti arasında amansız bir savaş başlar. İstanbul ve Ankara’da gazeteler adeta sağır ve dilsizdir. Onlara göre bir mesele yoktur. Yaşanan küçük bir zabıta vakasıdır. Kürt isyanı bastırılır\dots{} Şeyh Sait ve arkadaşları İstiklal Mahkemeleri’nde yargılanıp apar topar idam edilirler. Şeyh Sait’in son sözü şu olur: “Torunlarımızın Bizden Dolayı Utanç Duymaması Bizim İçin Yeterlidir!” \section{\textbf{Seyit Rıza (Dersim İsyanı): “Ben Sizin Yalan ve Hilelerinizle Baş Edemedim Bu Bana Dert Oldu Ama Ben de Sizin Önünüzde Eğilmedim Bu da Size Dert Olsun”}} 1935 yılında İsmet İnönü’nün hazırladığı Kürt Raporu’nda aynen şunlar yazıyordu: “Dersim Türklük için kanayan bir çıbandır, derhal kesilip atılması gerekir.” Bu mesaj, gerekli mecralara ulaşır. Dersim’e devletin tunçtan eli dokunmalı, bölge acilen Türkleştirilmelidir. Fakat TC’nin orduları hangi bahaneyle gelirse gelsin, Seyit Rıza ve arkadaşlarının yani Dersimlilerin isyanıyla karşılaşırlar. Mustafa Kemal’in manevi kızı, pilot Sabiha Gökçen, 1937’de devlet töreniyle bölgeye gönderilir. Hazırlıklar tamamlandıktan sonra, 21 Mart 1937’de, yani Newroz sabahında Seyit Rıza’nın evi bombalanır. Ertesi gün gazeteler, Sabiha Gökçen’i “Türk amazonu” diye manşetlerine taşırlar. İsyanın bastırıldığı 1938’e gelindiğinde, 40.000 kişi öldürülmüş, bir o kadar kişi de sürgün edilmiştir. Seyit Rıza yakalanmış, idama mahkûm edilmiştir. İdam sehpasından şöyle seslenir Seyit Rıza: ”Ben sizin yalan ve hilelerinizle baş edemedim bu bana dert oldu ama ben de sizin önünüzde eğilmedim bu da size dert olsun.” \textbf{Buraya sığdıramadığımız yüzlerce isyanda belirgin olan şuydu: özgürlüğün üzerindeki her baskı karşısında halkların isyanını bulmuştur. Bunu bilmenin gerçekliğiyle telaşlanan günümüz iktidarıysa yeni bir halk isyanıyla karşılaşmanın korkusunu yaşamakta ve yok olmanın telaşıyla saldırmaktadır. İsyanı başlatanların ateşini elden ele taşıyan bizler unutmayalım ki bir isyanı başlatmak o isyanı kazanmaktır. Ve biz kazanıyoruz.} % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} Anarşist Kütüphane \bigskip \includegraphics[width=0.25\textwidth]{logo-en.pdf} \bigskip \end{center} \strut \vfill \begin{center} Meydan Gazetesi Yaşadığımız Topraklardaki Halkların Mayasıdır İsyan 07.08.2013 \bigskip Bu yazı Meydan Gazetesi’nin 11. sayısında yayımlanmıştır. \bigskip \textbf{tr.anarchistlibraries.net} \end{center} % end final page with colophon \end{document} % No format ID passed.

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\documentclass[12pt]{article} \input{Preambule.tex} \usepackage{gfsartemisia} % pour la fonte \geometry{a4paper,hmargin=2cm,vmargin=2cm} \begin{document} \pagestyle{empty} \begin{empfile} % Tout doit être inclus dans cet environnement % qui a un paramètre facultatif : le nom du fichier .mp % par défaut, c'est le nom du fichier .tex (plus simple) \input{ComonDefMetaPost.tex} \devpers{Devoir n\up{o} 3 : Test limite de suites (15 min)}{}{T\up{ale} }{30 septembre 2021.} \setlength{\columnseprule}{.5pt} \setlength{\columnsep}{30pt} \setcounter{exercice}{0} \begin{exercice} Complétez par le résultat ou bien par indéterminé le cas échéant. \begin{enumerate}[itemsep=0.5cm, label=\ding{93}] \item Si $\limite{n}{\pI} u_n = \pI$ et $\limite{n}{\pI} v_n = -2 $ alors $\limite{n}{\pI} \dfrac{u_n}{v_n} = \dotfill$ \item Si $\limite{n}{\pI} u_n = \pI$ et $\limite{n}{\pI} v_n = 0 $ alors $\limite{n}{\pI} {u_n}{v_n} = \dotfill$ \item Si $\limite{n}{\pI} u_n = 0$ et $\limite{n}{\pI} v_n = 0 $ alors $\limite{n}{\pI} \dfrac{u_n}{v_n} = \dotfill$ \item Si $\limite{n}{\pI} u_n = \E$ et $\limite{n}{\pI} v_n = \pI $ alors $\limite{n}{\pI} {u_n}+{v_n} = \dotfill$ \item Si $\limite{n}{\pI} u_n = 0$ et $\limite{n}{\pI} v_n = \pI $ alors $\limite{n}{\pI} \dfrac{u_n}{v_n} = \dotfill$ \end{enumerate} \end{exercice} \begin{exercice} Déterminer les limites des suites suivantes : \begin{enumerate}[itemsep=0.5cm] \item $u_n=(1-n^3)(4+n^2)$ ; $n \in \N$. \item $v_n=\dfrac{n^3-n}{4n^2-3n^3}$ ; $n \in \N^\star$. \end{enumerate} \end{exercice} \end{empfile} \end{document}

https://uubu.fr/tex/pwck.tex

uubu.fr

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\documentclass{report} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{textcomp} \usepackage{geometry} \geometry{top=15mm, bottom=15mm, left=1cm, right=1cm} \usepackage[french]{babel} \usepackage{pslatex} \usepackage[colorlinks=true,urlcolor=black]{hyperref} \usepackage{graphicx} \usepackage{fancyhdr} \pagestyle{fancy} \renewcommand{\footrulewidth}{0.4pt} \fancyfoot[L]{Uubu.fr} \fancyfoot[R]{jeu. nov. 3 09:28:59 CET 2011} \lfoot{\Large \textit{Uubu.fr}} \hypersetup{pdfinfo={ Title={pwck}, Author={Sylvain Girod}, Creator={Bash script from uubu.fr's format version 1}, Producer={Bash script and PDFLaTeX}, Subject={Vérifier l’intégrité des fichiers de mots de passe}, CreationDate={D:20111103092859}, ModDate={D:20111103092859}, Keywords={Linux} }} \begin{document} \begin{center} {\Huge pwck } \end{center} \vspace{1cm} \begin{flushleft} {\large Vérifier l’intégrité des fichiers de mots de passe} \vspace{10mm} \hspace{1mm} Toutes les entrées de \textbf{/etc/shadow} et \textbf{/etc/passwd} sont vérifiées afin de s’assurer qu’elles ont le bon format et qu’elles contiennent des données valables dans chaque champ. Une confirmation est demandé pour détruire les entrées mal formatées ou ayant des erreurs irrécupérables. \vspace{5mm} \\ \vspace{1cm}{\huge Vérifications effectuées } \ \begin{description} \normalsize \item[\hspace{6mm} ]{Nombre correcte de champs} \item[\hspace{6mm} ]{Unicité des noms d’utilisateurs} \item[\hspace{6mm} ]{Validité des UID et GID} \item[\hspace{6mm} ]{Validité des groupes primaires} \item[\hspace{6mm} ]{Validité du répertoire personnel} \item[\hspace{6mm} ]{Validité du shell initial} \end{description} \hspace{1mm} Les vérifications dans \textbf{shadow} sont effectuées quand un second paramètre de fichier est spécifié ou quand \textbf{/etc/shadow} existe sur le système. Les vérifications sont : \vspace{5mm} \\ \begin{description} \normalsize \item[\hspace{6mm} ]{Chaque mot de passe correspond à une entrée shadow, et chaque shadow a une entrée dans passwd} \item[\hspace{6mm} ]{Les mots de passe sont indiqués dans le fichier des mots de passe cachés} \item[\hspace{6mm} ]{Nombre correct de champs} \item[\hspace{6mm} ]{Le dernier changement de mot de passe n’est pas dans le future.} \end{description} \vspace{1cm}{\huge OPTIONS } \ \begin{description} \normalsize \item[\hspace{1mm} -q]{Les avertissements qui ne nécessitent pas une action de l’utilisateur ne sont pas affichés} \item[\hspace{1mm} -r]{Mode lecture seule} \item[\hspace{1mm} -s]{Trie les entrées de /etc/passwd et /etc/shadow par UID} \end{description} \hspace{1mm} \textbf{pwck} utilise des variables dans login.defs \vspace{5mm} \\ \vspace{1cm}{\huge Valeurs de retour } \ \begin{description} \normalsize \item[\hspace{1mm} 0]{succès} \item[\hspace{1mm} 1]{erreur de syntaxe} \item[\hspace{1mm} 2]{une entrée de mot de passe est incorrecte} \item[\hspace{1mm} 3]{impossible d’ouvrir les fichiers de mots de passe} \item[\hspace{1mm} 4]{impossible de verrouiller les fichiers de mots de passe} \item[\hspace{1mm} 5]{impossible de mettre à jours les fichiers de mots de passe} \item[\hspace{1mm} 6]{impossible de trier les fichiers de mots de passe} \end{description} \end{flushleft} \end{document}

http://wicky-math.fr.nf/pdf/2011/207/C1_Generalites_Fct.tex

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\documentclass[4apaper,11pt,french]{article} \linespread{1} \newcommand{\ch}{Chapitre 1} \newcommand{\Ch}{Exprimer une quantit\'e \linebreak[2] en \textbf{\textit{fonction}} d'une autre %\linebreak[2] en math\'ematiques } \newcommand{\Cl}{Seconde} \newcommand{\Annee}{2011-2012} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Package \input macro_final.tex \geometry{hmargin=2cm,vmargin=2.5cm} \setcounter{NumLecon}{1} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Premiere page \begin{document} %\setcounter{NumLecon}{1} \debutCha{Degas_Toilette2.eps}{Autoportrait (1863) \fg \, et \og Le Tub (1885)}{Edgar Degas} % Image + titre + Auteur {Quand quelqu'un paye un tableau $3\,000$ francs, c'est qu'il lui plaît. \linebreak[4] Quand il le paye $300\,000$ francs, c'est qu'il plaît aux autres. }{Edgar Degas} % Citation + Auteur {Edgar Degas (1834-1917) est un peintre français, en général rattaché au mouvement impressionniste, formé à la fin du XIXe siècle, en réaction à la peinture académique de l’époque. \\ Sa carrière fut dès le départ influencée par les danseuses. En 1874, il commence à se faire connaître, les critiques louant ou dénigrant le réalisme de son travail. Il explore des thèmes comme les repasseuses ou les femmes à leur toilette, multipliant les points de vue audacieux, recherchant des effets lumineux et colorés. Il dit d’ailleurs à propos de ses nus : \og Jusqu’à présent, le nu avait toujours été représenté dans des poses qui supposent un public. Mais mes femmes sont des gens simples... Je les montre sans coquetterie, à l’état de bêtes qui se nettoient. \fg \\ A partir des années 1880, Degas va aussi poser la question d'une sculpture « impressionniste », réalisant des modèles en cire peints au naturel, qu'il accessoirise ensuite. Seule \textit{La Grande Danseuse} (cf première page) fut présenté de son vivant, les autres modèles l'aidant surtout dans ses peintures. Cette incarnation de la grâce et de l'innocence trahit en réalité la fascination de Degas pour la criminalité. En effet, avec son visage est sculpté sur le modèle des physionomies de criminels définies à l'époque, et la danseuse était un parfait \og petit rat \fg , transmettant la syphilis aux bourgeois venant la voir ... } % Présentation auteur {1.1} % Ratio portrait {0.31} % Ratio Image \setcounter{NumLecon}{1} \TITRE{Degas_Petite_Danseuse_de_14_ans(1881).eps}{0.28} % Image 1ere page + ratio %\begin{abstract} \begin{flushright} \textit{Petite Danseuse de 14 ans} \\ ou \textit{La Grande danseuse} (1879-1881) \end{flushright} \begin{Intro}{Au fil du temps}{ \noindent Le concept de fonction a mis des siècles à s'établir en math\'ematiques. La notion intuitive comme relation entre plusieurs quantités est assez ancienne, mais il faut attendre le $XVII^e$ siècle pour qu'elle soit formalisée. Découvrir les fonctions, apprendre à les représenter et à étudier certaines de leurs propriétés représente une partie importante du programme de seconde. \begin{itemize} \item C'est le français Pierre de Fermat (16010-1665) qui met en place la notion fondamentale d'équation d'une courbe, associant donc ainsi les fonctions à une courbe du plan, et s'intéresse aux extrema de fonctions.\\ \textit{Fermat est essentiellement connu pour ses théorèmes en arithmétique, notamment pour son grand théorème, qu'il prétendit avoir démontré dans une note de bas de page, mais dont la preuve ne fut trouvée qu'en 1994.} \item En 1673, l'allemand Gottfried von Leibniz (1646-1716), à la fois philosophe et math\'ematicien, utilise pour la première fois le mot \og fonction \fg \, et introduit le vocabulaire.\\ \textit{Leibniz est essentiellement connu en sciences pour avoir d\'ecouvert conjointement avec Newton le calcul infinit\'esimal, c'est-\`a-dire dans l'infiniment petit.} \item En $1698$, le suisse Jean Bernoulli (1667-1748) reprit le terme et en donne une première définition. Il proposa alors la notation $f(x)$.\\ \textit{Bernoulli développa le calcul exponentiel et la théorie des probabilités.} \item Euler, math\'ematicien form\'e par Bernoulli, adopte cette notation en $1734$ et d\'efinit en $1748$ une fonction d'une variable comme combinaison d'opérations à partir de cette variable et de nombres constants. \\ \textit{Euler travailla essentiellement sur le calcul infinit\'esimal lui aussi et sur la th\'eorie des graphes (utiliser pour les GPS) } \end{itemize} En fait, le lien entre l'expression algébrique d'une fonction et sa courbe représentative en permet une étude plus approfondie. Le concept de fonction et l'étude de leur propriété a révolutionné la recherche mathématique. jusqu'\`a aujourd'hui.\\ Compte tenu du nombre incroyable d'applications en physique, en économie et dans quasiment tous les domaines, l'étude des fonctions est l'un des objectifs majeurs du lycée en mathématiques. \\ Dans ce chapitre, nous allons essentiellement découvrir le vocabulaire, travailler les calculs et l'approche graphique. Cependant, tout cela nous permettra également de réfléchir aux différents types de nombres et ensembles les désignant, ainsi qu'à la pertinence d'une écriture d'expression algébrique plutôt qu'une autre. } \end{Intro} \newpage \section{Notion de fonction} \subsection{Activité découverte} %\Act{ %Dans un récipient de forme cylindrique et de rayon $4$ cm, on verse de l'eau jusqu'à une hauteur de $5,25$ cm. %On veut alors placer une bille dans le récipient de façon à ce que le liquide la recouvre exactement. %Le problème consiste à déterminer le rayon de la bille. %} %\textbf{Objectifs :} Introduire les notions d'inconnue, de dépendance entre deux quantités, %mettre en équation d'un problème, montrer l'utilité d'un tableau de valeur et/ou %représentation graphique, discuter de la comparaison de valeurs approchées, vérifier qu'un nombre est solution %d'une équation. %\textbf{Transversalement : rappels des volumes du cylindre et de la sphère, calcul littéral} \Act{}\begin{multicols}{2} \noindent Rom\'eo souhaite au plus vite offrir une rose fraîchement cueillie \`a Juliette. \\\\ La situation est sch\'ematis\'ee de la façon ci-contre.\\\\ Quel chemin doit prendre Roméo pour rejoindre Juliette le plus tôt possible ?\\\\ \begin{center} \psset{xunit=1cm , yunit=1cm} \begin{pspicture*}(-2,-1.7)(7,3.6) \def\xmin{-1.5} \def\xmax{8} \def\ymin{-2} \def\ymax{3.6} \def\pshlabel#1{\psframebox*[framesep=1pt]{\small #1}} \def\psvlabel#1{\psframebox*[framesep=1pt]{\small #1}} \psclip{% \psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax) } \psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4} \psline(-2.0000,0.0000)(8.0000,0.0000) \psline{<->}(0.0000,-1.0000)(5.0000,-1.0000) %\uput{0.3000}[-90.0000](0.0000,0.0000){H} %\uput{0.3000}[-90.0000](5.0000,0.0000){K} \uput{0.3000}[-130.0000](3.90000,0.0000){Allée des roses} \uput{0.3000}[-130.0000](3.000,-0.4000){$10$ m} \uput{1.0000}[100.0000](-0.50000,0.0000){5 m} \psline{<->}(0.0000,0.0000)(0.0000,2.0000) \psline{<->}(5.0000,3.0000)(5.0000,0.0000) \psline[linestyle=dashed](0.0000,-1.0000)(0.0000,0.0000) \psline[linestyle=dashed](5.0000,0.0000)(5.0000,-1.0000) \uput{1.0000}[80.0000](5.5000,0.0000){7 m} \uput{0.3000}[90.0000](0.0000,2.0000){Romeo} \uput{0.3000}[90.0000](5.0000,3.0000){Juliette} \uput{0.3000}[100.0000](3.5000,0.0000){?} \psline(0.0000,2.0000)(3.5000,0.0000) \psline(3.5000,0.0000)(5.0000,3.0000) \endpsclip \end{pspicture*} \end{center} \end{multicols} \textbf{\textit{Objectifs} :} modéliser d'un problème, introduire la notion de variable, faire le lien entre deux quantités, introduire la notion de fonction, constater la pertinence de représenter une fonction et/ou de faire un tableau de valeurs, discuter des valeurs approchées, introduire la notation d'intervalles.\\ \textbf{\textit{Prérequis} :} Pythagore.\\ \Rq{Le problème possède également une réponse géométrique (par symétrie).} \Defc{ Une \textbf{fonction} est une relation qui associe un élément d'un ensemble de d\'epart $E$ \`a \underline{au plus} un \'el\'ement d'un ensemble d'arriv\'ee $F$ (donc à 0 ou 1 élément de $F$). } \Expls{Vous connaissez d\'ej\`a quelques fonctions en g\'eom\'etrie : \begin{itemize} \item La formule du p\'erim\`etre d'un cercle est la fonction qui \`a tout nombre positif $R$ associe le nombre $ 2\pi R$. \item La formule de l'aire d'un triangle est la fonction qui à tout couple de nombres positifs $(b;h)$ associe le nombre $\dfrac{b\times h}{2}$\\ \end{itemize} } \noindent \Rq{ Une fonction peut associer autres choses que des nombres entre eux. \\ Par exemple, à un segment on peut associer son milieu.\\ Cette année, nous n'étudierons cependant que les fonctions qui transforment un seul nombre en un autre. %\\ On parle de fonction \textbf{num\'erique \`a une variable}.\\ En général, on nous donnera l'expression algébrique d'une fonction, sans préciser ce qu'elle représente concrètement.\\ } \Expl{ La fonction qui \`a un nombre $x$ associe le nombre $2x-1$. } 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\psline[linewidth=0.04cm](11.403747,-0.4301821)(11.503747,-0.6301821) \psline[linewidth=0.04cm](11.503747,-0.6301821)(11.303747,-0.7301821) \psline[linewidth=0.04cm](11.303747,0.5698179)(11.503747,0.4698179) \psline[linewidth=0.04cm](11.503747,0.4698179)(11.403747,0.2698179) \psline[linewidth=0.04cm](12.403747,2.369818)(12.503747,2.069818) \psline[linewidth=0.04cm](12.503747,2.069818)(12.103746,2.069818) \psline[linewidth=0.04cm](12.103746,1.9698179)(12.503747,2.069818) \psline[linewidth=0.04cm](12.503747,2.069818)(12.303747,1.8698179) \uput{1.50000}[-90.0000](2.5000,-2.0000){\textbf{Ensemble de d\'epart $E$}} \uput{1.5000}[-90.0000](13.0000,-2.0000){\textbf{Ensemble d'arriv\'ee $F$}} \uput{1.5000}[-90.0000](8.30000,4.50000){\textbf{Fonction $f$}} \end{pspicture} } \end{center} \vspace{5mm} \Rqs{ \item On note souvent une fonction $f$ (mais on peut les appeler comme on veut). \item Un élément de $E$ n'est pas forcément associé à un élément de $F$. On l'appelle alors \textbf{valeur interdite} de la fonction. \\ Ici, $d$ est une valeur interdite de $f$ (mais pas $e$ !). \item Un élément de $E$ ne peut pas être associé à plusieurs éléments de $F$.\\ Ici, il ne peut pas y avoir une deuxième flèche partant de $x$. \item Plusieurs éléments de $E$ peuvent étre associés au même élément de $F$. \\ Ici $a$ et $b$ sont tous les deux reliés à $c$. } \Defc{Si un élément $x$ de $E$ est associé par une fonction $f$ à un élément $y$ de $F$, alors $y$ s'appelle l'\textbf{image de $x$} par la fonction $f$ et on le note $f(x)$. On pourra également noter $f \, : \, x \mapsto y$\\ De plus, on dit que $x$ est un \textbf{antécédent de $y$} par la fonction $f$.\\ L'ensemble des éléments $x$ de $E$ auxquels une fonction $f$ fait correspondre un élément $y$ de $F$ est appelé \textbf{l'ensemble de défintion} de $f$ et est noté $D_f$.\\ } \Rqs{ \item Un élément de $E$ possède 0 ou 1 image par $f$.\\ Ici, $a$ possède une image par $f$, c'est $c$. On note $f(a)=c$ ou encore $f \, x \mapsto c$. \\ Tandis que $d$ ne possède pas d'image par $f$. \item Un élément de $F$ peut ne pas avoir d'antécédent par $f$, comme en avoir un seul, ou plusieurs.\\ Ici, $e$ ne possède pas d'antécédent par $f$. \\ Par contre, $y$ en possède 1, c'est $x$. On a donc $f(x)=y$.\\ De plus, $c$ possède 2 antécédents par $f$, il s'agit de $a$ et $b$. On a donc $f(a)=f(b)=c$ \item L'ensemble de définition d'une fonction $f$ est en fait l'ensemble des éléments de $E$, sauf les valeurs interdites. } \Exos{n$^{\circ}$ 5-6 p 46} \Expls{ \begin{itemize} \item Soit $g$ la fonction qui à un nombre $x$ associe le nombre $g(x)=5-3x$.\\ L'image de $0$ est $g(0)=5-3 \times 0 = 5$.\\ Chercher de même l'image de $\dfrac{4}{9}$ et celle de $-2$.\\ En fait, on peut toujours calculer l'image d'un nombre par la fonction $g$. Il n'y a donc pas de valeurs interdites.\\ L'ensemble de définition de $g$ est donc l'ensemble des nombres que vous connaissez. On le note $\R$ et on appelle ces nombres, les nombres réels. \\ On a donc $ D_g=\R$.\\ On peut également chercher les éventuels antécédents de nombres de l'ensemble d'arrivée. \\ Pour cela, on résout toujours une équation.\\ L'éventuel antécédent de $0$ est le nombre $x$ tel que $g(x)=0$. On doit donc résoudre : \begin{eqnarray*} && 5-3x=0 \\ &\stackrel{-5}{\iff} & -3x=-5 \\ & \stackrel{\times (-1)}{\iff} & 3x = 5 \\ & \stackrel{/3}{\iff} & x = \dfrac{5}{3} \end{eqnarray*} L'antécédent de $0$ est $\dfrac53$.\\ Chercher de même les éventuels antécédents de $4$ et de $-2$.\\ \item Soit $l$ la fonction qui \`a un nombre $x$ associe le nombre $l(x)=\dfrac{3}{6-2x}$. \\ L'image de $1$ par $l$ est le nombre $l(1)=\dfrac{3}{6-2 \times 1 }= \dfrac{3}{4} $. \\ Quelle est l'image de $0$ ? de $-4$ ? \\ En fait, on peut toujours calculer $l(x)$ sauf si l'on est amené à diviser par $0$, ie si et seulement si $6-2x = 0 \Longleftrightarrow x = 3$. \\ La seule valeur interdite est donc $3$. \\ L'ensemble de définition de $l$ est donc tous les nombres sauf $3$. On le note $ D_l=\R \setminus \{3\}$\\ L'éventuel antécédent de $1$ est le nombre tel que $l(x)=1$. On doit donc résoudre \begin{eqnarray*} && \dfrac{3}{6-2x}=1 \\ & \iff & 3=6-2x \quad \text{ et } x \neq 3 \\ & \stackrel{-6}{\iff} & -3 = -2 x \quad \text{ et } x \neq 3 \\ & \stackrel{\times (-1)}{\iff} & 3 = 2 x \quad \text{ et } x \neq 3 \\ & \stackrel{/2}{\iff} & x = \dfrac32 \end{eqnarray*} L'antécédent de $1$ est donc $\dfrac32$.\\ Quels sont les éventuels antécédents de $0$ ? \end{itemize} } \Expl{ Soit la fonction $f$ qui \`a tout r\'eel $x$ associe le r\'eel $f(x)=3\sqrt{x+2}+\sqrt{11-x} \,$ quand il existe. \\ L'image de $7$ par $f$ est le nombre $f(7)=3 \sqrt{7+2}+\sqrt{11-7}=3\sqrt{9}+\sqrt{4}=3 \times 3 + 2 = 11$.\\ Calculer l'image de $4.5$, puis celle de $16$.\\ En fait, on peut toujours calculer $f(x)$ à partir du moment où les valeurs sous les racines sont des quantités positives. On doit donc avoir $x \geq -2$ \textbf{et} $x\leq 11$, ie $-2 \leq x \leq 11$.\\ On note $[-2;11]$ l'ensemble des nombres compris entre $-2$ et $11$ inclus et on appelle cet ensemble un intervalle. \\ On a donc $ D_f=[-2;11]$.\\ On sait que $7$ est un antécédent de $11$ par $f$, mais il en existe en fait un deuxième proche de $10.97$. Pour trouver le trouver exactement, on doit résoudre l'équation $3\sqrt{x+2}+\sqrt{11-x}=11$, qui est trop compliquée en seconde.\\ } \Cadre[Méthodes]{ \begin{enumerate} \item Pour trouver l'image d'un nombre $x$ par une fonction $f$, on remplace $x$ par sa valeur dans l'expression algébrique de $f$ et on compte. \item On trouve les éventuels antécédents d'un nombre $y$ par une fonction $f$ en résolvant l'équation $f(x)=y$. \item On trouve l'ensemble de définition d'une fonction $f$ en cherchant les valeurs interdites. Pour cela, on applique les deux r\`egles suivantes : \begin{enumerate} \item On ne divise pas par z\'ero. \item On ne prend pas la racine d'un nombre strictement n\'egatif. \end{enumerate} \end{enumerate} } \Exop{Soit la fonction $f$ d\'efinie qui à tout réel $x$ associe le réel $f(x)=x^2-\dfrac{6}{x}$ quand il existe. \begin{enumerate} \item Calculer $f(-2)$. \item Calculer l'image de $3$. \item Pourquoi l'image de $0$ par $f$ n'existe-t-elle pas ? En déduire l'ensemble de définition de $f$. \end{enumerate} } \Exop{Soit $f$ la fonction définie sur $\R$ par :$$f(x)=x^2-2x+3$$ \begin{enumerate} \item La fonction $f$ admet-elle des valeurs interdites ? En déduire sont ensemble de définition $D_f$. \item Déterminer l'image par $f$ des réels $0$ ; $-\dfrac{3}{2}$ et $ \sqrt{2}$. \item Déterminer les éventuels antécédents de $3$ par $f$. \item Montrer que pour tout $ x\in\R$ on a $f(x)=(x-1)^2+2$. \item En utilisant cette dernière écriture, déterminer les éventuels antécédents de $2$ et de $-4$ par $f$. \end{enumerate}} \Exop{Soit la fonction $g$ qui à tout réel $x$ associe le réel $g(x)=2x^2-3$\\ D\'eterminer l'image de 3, puis celle de $-1$ par la fonction $g$. \newline D\'eterminer les ant\'ec\'edents \'eventuels de $7$, de $-3$ et de $-4$ par la fonction $g$. } \Exos{n$^{\circ}$ 7-9 p 46 + 55 p 54 (basiques)\\ + n$^{\circ}$ 18 à 27 p 48 + 44 p 52 (révisions développement/factorisation à faire en \textbf{\textit{module}})\\ + n$^{\circ}$ 28-30 p 48 (choix d'une écriture)\\ + n$^{\circ}$ 33-35-40-41 p 50 (approfondissement)} \section{Ensembles de nombres} \subsection{Divers type de nombres} \Cadre[Un peu d'histoire]{ \noindent Aujourd'hui, on connait beaucoup de nombres, regroupés en ensembles en fonction de leurs propriétés, mais il n'en a pas toujours été ainsi. \\ Les entiers positifs (ou \textbf{\textit{naturels}}) sont connus depuis la préhistoire (au moins $-35\,000$), excepté pour le zéro découvert et formalisé bien plus tard. Les nombres pouvant s'écrirent comme quotient d'entiers (ou \textbf{\textit{rationnels}}) furent également assez vite découverts, car ils renvoient à la notion de partage.\\ Rapidement (au moins $-2000$), on s'intéresse à certains nombres \textit{\textbf{irrationnels}} particuliers (réels ne pouvant pas s'écrire comme le quotient de deux entiers), tels que $\sqrt{2}$ ou $\pi$.\\ On manipule les 4 opérations depuis fort longtemps, dont la soustraction. Cependant, il faudra attendre le VIII$^e$ siècle pour que les nombres négatifs soient découverts, suite à l'introduction de la numération positionnelle, des chiffres arabes et du fameux zéro.\\ Cette découverte est probablement la plus importante de l'algèbre. Elle arriva avec la mise en place d'une méthode générale de résolution d'équation. On constata alors qu'une équation n'ayant que des paramètres entier positifs pouvait avoir des solutions qui ne l'étaient pas (comme $2x+5=3$)... On fut donc contraint de s'int\'eresser \`a la nature des nombres, et d'en introduire de nouveaux, comme les négatifs. } On a vu précédemment de nouvelles notations pour désigner un ensemble de nombres. Il en existe d'autres, résumées dans cette partie.\\ \Defc{ Rappelons déjà que $\R$ désigne l'ensemble des nombres que vous connaissez, appelés \textbf{nombres réels}.\\ $\Q$ désigne l'ensemble des nombres pouvant s'écrire sous forme d'une fraction (quotient de deux entiers et de dénominateurs non nul), appelés \textbf{nombres rationnels}.\\ $\Z$ désigne l'ensemble des nombres entiers, appelés \textbf{nombres entiers relatifs}.\\ $\N$ désigne l'ensemble des nombres entiers positifs ou nul, appelés \textbf{nombres entiers naturels}. } \Expls{A faire trouver} \Rq{ On remarquera que tout entier naturel est également un entier relatif.\\ De même tout entier relatif peut s'écrire comme une fraction de dénominateur 1, c'est donc également un rationnel.\\ Enfin tout rationnel est un nombre que vous connaissez, c'est donc un réel.\\ Nous utiliserons peu les autres notations que $\R$ dans ce chapitre. } \subsection{Intervalles de $\R$} Il est souvent utile de ne désigner qu'une partie de $\R$, notamment pour les ensembles de définition. En particulier, on s'intéressera souvent à l'ensemble des nombres compris entre deux autres fixés, appelés \textbf{intervalle}.\\ Les tableaux ci-dessous résument les diverses situations.\\ Soient $a$ et $b$ deux r\'eels tels que $a<b$. \begin{center} \begin{tabular}{|c|c|c|c|} \hline In\'egalit\'e & Repr\'esentation graphique & Intervalle born\'e & D\'enomination \\ \hline $a \leq x \leq b$ & & & \\ &&&\\\hline & & & Intervalle ouvert \\&&&\\\hline & & & Intervalle semi-ouvert \\ & & & \`a droite \\\hline & & & Intervalle semi-ouvert \\ & & & \`a gauche \\\hline \end{tabular} \vspace{0.5cm} \begin{tabular}{|c|c|c|c|} \hline In\'egalit\'e & Repr\'esentation graphique & Intervalle & D\'enomination \\ \hline $x \geq a$ & & $[a;+\infty [$ & Intervalle ferm\'e \\&&&\\ \hline & & $]a;+\infty [$ & \\&&&\\\hline & & & \\&&&\\\hline & & & \\&&&\\\hline \end{tabular} \end{center} \Rq{ On note :\begin{multicols}{3} \begin{itemize} \item $\R^+=[0;+\infty[$ \item $\R^-=]-\infty;0]$ \item $\R^*=\R\smallsetminus \{0\}$ \item $\R^{+*}=]0;+\infty[$ \item $\R^{-*}=]-\infty;0[$ \item $\R=]-\infty;+\infty[$ \end{itemize} \end{multicols} } \Expls{\begin{enumerate} \item Donner les intervalles correspondant aux in\'egalit\'es suivantes: $$-6\leq x \leq 7 \qquad\qquad -5<x \qquad\qquad x\leq 3 $$ \item Donner les in\'egalit\'es correspondant aux intervalles suivants : $$\left] \dfrac{1}{3} ; \sqrt{7} \right] \qquad \qquad \left[ -\sqrt{5};+\infty\right[ $$ \end{enumerate} } \Exos{n$^{\circ}$ 1-2 p 46 + 50-52-53 p 53} \section{Algorithmie} \Cadre[Un peu d'histoire]{ \noindent Dans l'antiquit\'e, les math\'ematiques sont utilis\'ees pour les besoins quotidiens, tels que des calculs d'aires de champs, d'imp\^ots lors des crues du Nil, de constructions. Elles servent aussi \`a r\'esoudre des probl\`emes dans lesquels figure une (ou plusieurs) quantit\'e inconnue \`a trouver. \\ Vers 1800-1500 avant JC, les Babyloniens savent déjà résoudre des équations du $1^{er}$ et du $2^{nd}$ degré. On parle de ''chose'' à trouver et on suit un discours logique phrasé (peu clair pour nous aujourd'hui) pour arriver à une solution.\\ Ce n'est qu'au VIII$^e$ si\`ecle, avec l'introduction de la num\'eration positionnelle, des chiffres arabes et du z\'ero, que la th\'eorie générale prend place peu \`a peu. Le point de d\'epart est de d\'esigner dans des calculs l'inconnue par un symbole (aujourd'hui souvent la lettre $x$) puis de mettre en \'equation les probl\`emes. \\ Rapidement, on comprend l'int\'er\^et d'une telle m\'ethode. C'est \textit{Al-Khawarizmi} qui le premier s'int\'eresse \`a cela et classifie les différents types d'équations, afin que dans chaque problème, on n'ait plus qu'à reconnaitre le type d'équation et suivre la méthode générale appropriée, menant à la solution. Le mot \textit{\textbf{algorithme}} découle de son nom et d\'esigne aujourd'hui \textbf{\textit{une proc\'edure \`a suivre, \`a partir d'un \'el\'ement donn\'e, pour arriver \`a une solution unique}}. \\ \noindent Jusqu'au d\'ebut du XIX$^e$, trouver des algorithmes de r\'esolutions d'\'equations constituent la pr\'eoccupation principale des alg\'ebristes. Ils d\'eveloppent la notation symbolique et la conventionnent : au XVI$^e$ Viete s\'epare l'alphabet en deux, le d\'ebut d\'esignant plut\^ot les param\`etres, la fin les inconnues, ce qui est encore utilisé de nos jours. On cat\'egorise les \'equations suivants leurs param\`etres, leur degr\'e et leur nombre d'inconnues, afin de g\'en\'eraliser le plus possible leur r\'esolution.Parallèlement, la notion de fonction prend forme.\\ Les équations de degré 3 sont résolues par les italiens Tartaglia et Cardan au XVI$^e$ si\`ecle, et celles de degré 4 par l'élève de ce dernier, Ferrari. L'histoire des formules de résolution s'arrête là, car le français Evariste Galois (1811-1832) montre au XIX$^e$ qu'il est impossible de trouver des formules de résolution pour les équations de degré supérieur ou égal à 5.\\ }\\ \Defc{ Un \textbf{algorithme} est une suite d'instructions, qui, une fois ex\'ecut\'ee correctement, conduit \`a un unique résultat. } \Expls{Indiquer un itinéraire allant d'un lieu à un autre, une recette de cuisine, télécharger un ficher, compresser des données, les jeux vidéos, les feux tricolores, les lumières de la tour Eifel, le pilote automatique des avions, la cryptographie (codage de messages) ...\\ En mathématiques, vous connaissez déjà l'algorithme d'Euclide qui permet de trouver le pgcd de deux nombres entiers positifs. \\ Les Babyloniens suivaient un algorithme très performant pour trouver une valeur approchée de la racine carré d'un nombre.\\ Dans ce chapitre, nous allons écrire un algorithme pour calculer les images d'une fonction donnée.} \Expl[Vocabulaire, démarche et rédaction]{ Dans certains magasins, en période de soldes, le prix figurant sur un article correspond au prix sans la remise et une étiquette précise $-20\%$, $-30\%$ ...\\ On voudrait écrire un algorithme, puis un programme sur Algobox, qui détermine le montant de la remise ainsi que le prix à payer. } \begin{enumerate} \item \textbf{Détermination des variables : analyse préliminaire} \begin{enumerate} \item Quelles sont les informations initiales dont nous avons besoin ?\\ On les appelle les \textit{entrées} de l'algorithme. \item Que doit-on calculer ?\\ % \item Que doit-on obtenir à la fin ?\\ On prendra l'habitude de faire afficher le(s) résultat(s) de l'algorithme, que l'on appelle \textit{sortie(s)}.\\ L'ensemble des données de l'algorithme pouvant variées (entrées-sorties) sont les \textit{variables}. \end{enumerate} \item \textbf{Rédaction du processus français : l'algorithme}\\ On commence toujours un algorithme en énonçant les variables mise en jeu (désignées par des lettres), et en précisant leur nature (nombre, mots ...)\\ \textit{Saisir} une donnée permet à l'utilisateur d'attribuer une valeur à une variable (ce sont les entrées).\\ \textit{Affecter} une donnée permet à l'algorithme d'attribuer une valeur à une variable (on peut aussi utiliser le symbole $\to$ )\\ \textit{Afficher} permet à l'utilisateur de voir un texte (entre guillemets) ou la valeur d'une variable à l'écran. Compléter l'algorithme suivant : \Algo[Calcul d'une remise et d'un nouveau montant]{12cm}{ \Var{ ...., ...., ...., .... sont des nombres réels } \Deb{ Saisir ...\\ Saisir ...\\ Affecter à ... la valeur .........\\ ...... $\to$ ...\\ Afficher " Le montant de la remise est " ...\\ Afficher " Le prix à payer est " ...\\ } } \item \textbf{La programmation : sur Algobox et sur TI}\\ Trouver comment programmer cet algorithme sur Algobox et sur votre calculatrice.\\ \end{enumerate} \Rqs{ \item Pour fonctionner, un algorithme doit contenir uniquement des instructions compr\'ehensibles par celui qui devra l'ex\'ecuter %(sinon il suffirait de dire pour indiquer un chemin d'aller de l\`a o\`u l'on est \`a l'endroit d\'esir\'e !).\\ \item En math\'ematiques, les algorithmes consistent par exemple en des suites d'op\'erations \`a effectuer (pour les fonctions notamment), ou des suites de manipulations \`a faire (pour construire une figure g\'eom\'etrique). \\ On consid\`ere pour acquises les connaissances du coll\`ege, et l'on pourra donc les utiliser comme instructions. \item On peut alors voir une fonction numérique comme une machine, dans laquelle on introduit un nombre et en ressort un nombre transform\'e ou modifi\'e, suivant un algorithme de calcul donné. \begin{center} \psset{xunit=1cm , yunit=1cm} \begin{pspicture*}(-1,-2)(11.9,1) \def\xmin{-4} \def\xmax{12} \def\ymin{-4} \def\ymax{1} %\psframe[linewidth=0.3pt,linecolor=gray](-4.2,-3.2)(12.2,1.2) \def\pshlabel#1{\psframebox*[framesep=1pt]{\small #1}} \def\psvlabel#1{\psframebox*[framesep=1pt]{\small #1}} \psclip{% \psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax) } \psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4} \pspolygon(3.0000,1.0000)(3.0000,-1.0000)(5.0000,-1.0000)(5.0000,1.0000) \psline(0.0000,0.0000)(3.0000,0.0000) \psline(5.0000,0.0000)(8.0000,0.0000) \uput{0.30000}[-180.0000](0.0000,0.0000){Nombre} \uput{0.3000}[0.0000](3.0000,0.0000){Machine} \uput{0.3000}[0.0000](8.0000,0.0000){Nombre transform\'e} \uput{0.3000}[-180.0000](-0.5000,-0.50000){$x$} \uput{0.300}[0.0000](3.5000,-0.5000){$f$} \uput{0.300}[0.0000](8.5000,-0.50000){$f(x)$} \uput{2.0000}[-122.0000](1.0000,0.5000){Ant\'ec\'edent} \uput{2.0000}[-70.0000](3.0000,0.5000){Fonction} \uput{2.2000}[-57.0000](8.0000,0.50000){Image} \endpsclip \end{pspicture*} \end{center} } \Expl{ Consid\'erons la machine $f$ qui retranche 3 et \'el\`eve au carr\'e. \begin{itemize} \item Si on rentre le nombre 0, il en ressort 9, ou encore l'image de 0 par $f$ est $9$, ou encore $f(0)=9$ \item Si on rentre 3, il en ressort 0, ie l'image de $3$ par $f$ vaut $0$, ie $f(3)=0$. \item Si on rentre le nombre $-4$, il en ressort 49, ou encore l'image de $-4$ par $f$ est $49$, ou encore $f(-4)=49$ \item Si on rentre $\sqrt{2}$, il en ressort $(\sqrt{2}-3)^2$, ie $f(\sqrt{2})=(\sqrt{2}-3)^2$. \item Si on rentre $x$, il en ressort $(x-3)^2$, ie $f(x)=(x-3)^2$. \end{itemize} Ici, on a décrit la fonction numérique $f: x \longmapsto (x-3)^2 $ dont l'ensemble de définition est $\R$, par l'algorithme calculatoire : $$x \longmapsto x-3 \longmapsto(x-3)^2$$ L'algorithme détaillant les étapes de calcul et donnant en sortie l'image d'un nombre est le suivant :} \begin{center} %\begin{multicols}{2} \begin{minipage}[c]{7cm} \Algo[Fonction]{6.5cm}{ \Var{$x$, $y$, $a$ sont des nombres réels } \Deb{ Saisir $x$\\ Affecter à $a$ la valeur $x-3$\\ $a^2 \to y$ \\ Afficher $y$ } } \end{minipage} \qquad ou encore \qquad \begin{minipage}[c]{7cm} \Algo[Fonction]{6.5cm}{ \Var{$x$, $y$ sont des nombres réels } \Deb{ Saisir $x$\\ Affecter à $y$ la valeur $x-3$\\ $y^2 \to y$ \\ Afficher $y$ } } \end{minipage} %\end{multicols} \end{center} On aimerait désormais écrire un algorithme donnant les éventuels antécédent d'un nombre par la fonction $f$.\\ Par exemple, un antécédent de $9$ par $f$ est $0$, car on a vu précédemment que $f(0)=9$. Mais il en existe peut-être d'autres.\\ Pour tous les trouver, on doit résoudre $f(x)=9$. Or \begin{eqnarray*} (x-3)^2=9 & \Longleftrightarrow & x-3 = 3 \textrm{ ou } x-3 = -3\\ & \Longleftrightarrow & x = 6 \textrm{ ou } x = 0 \end{eqnarray*} Donc les antécédents de $9$ par $f$ sont $0$ et $6$.\\ Un antécédent de $0$ par $f$ est $3$. On peut vérifier que c'est le seul en résolvant l'équation $(x-3)^2 = 0$.\\ Par contre, $-1$ n'a pas d'antécédent par $f$, car l'équation $(x-3)^2=-1$ n'a pas de solutions.\\ L'algorithme cherché est : \Algo[Antécédents]{12cm}{ \Var{$x_1$, $x_2$, $y$, $a$, $b$ sont des nombres réels } \Deb{ Saisir $y$\\ \IfThenElse{$y < 0$} {Afficher $y$ "n'a pas d'antécédent par $f$"} {Affecter à $a$ la valeur $\sqrt{y}$\\ Affecter à $b$ la valeur $-\sqrt{y}$\\ Affecter à $x_1$ la valeur $a+3$\\ Affecteur à $x_2$ la valeur $b+3$\\ Afficher "Les antécédents de" $y$ "sont" $x_1$ "et" $x_2$ } } } \Exop{ On choisit un nombre, on lui ajoute 4, on \'el\`eve le r\'esultat au carr\'e, on retranche 16 et on divise le tout par le nombre de d\'epart. \\ Quelle est la fonction $blop$ décrite par cet algorithme ? Quelle est l'image de 4 ? Que vaut $blop(0)$ ? } \begin{multicols}{2} \Exop{ Décrire la fonction associée à l'algorithme ci-contre et donner son ensemble de définition.} \Algo{8cm}{ \Var{$x$ et $y$ sont des nombres réels} \Deb{ Saisir $x$\\ Affecter à $y$ la valeur $\sqrt{2x}+5$\\ Afficher $y$ } } \end{multicols} \Exop{Ecrire un algorithme permettant de déterminer les antécédents de n'importe quel nombre réel $y$ par la fonction $f$ définie sur $\R$ par $ f(x)=3x+1$ } \Exos{n$^{\circ}$ 4 p 46 + 45 p 52} \Exop{ Déterminer \textbf{toutes} les bonnes réponses.\\ On donne le programme de calcul suivant et l'algorithme correspondant : } \begin{multicols}{2} \begin{enumerate} \item Une expression algébrique de la fonction $f$ définie sur $\R$ par cet algorithme est : %\begin{multicols}{3} \begin{enumerate} \item $f(x)=x^2-2x+2$ \item $(x-1)^2 + 1 $ \item $f(x)=x^2+2$ \end{enumerate} %\end{multicols} \item L'image de $2$ par $f$ est : \begin{multicols}{3} \begin{enumerate} \item $0$ \item $2$ \item $10$ \end{enumerate} \end{multicols} \item L'image de $-1$ par $f$ est : \begin{multicols}{3} \begin{enumerate} \item $-1$ \item $-3$ \item $5$ \end{enumerate} \end{multicols} \item Les antécédents de $10$ par $f$ sont : \begin{multicols}{3} \begin{enumerate} \item $4$ \item $-2$ \item $0$ \end{enumerate} \end{multicols} \item Les antécédents de $17$ par $f$ sont : \begin{multicols}{3} \begin{enumerate} \item $5$ \item $2$ \item $-3$ \end{enumerate} \end{multicols} \end{enumerate} \fbox{ \begin{minipage}{7cm} \begin{center} \textbf{ Programme de calcul} \end{center} \begin{itemize} \item Choisir un nombre \item Mettre le nombre au carré \item Calculer le double du nombre \item Soustraire le deuxième résultat au premier \item Ajouter 2. \end{itemize} \end{minipage} } \Algo{7cm}{ \Var{$x$, $a$, $b$, $c$ sont des nombres réels} \Deb{ Entrer $x$ $a \leftarrow x^2 $ \\ $b \leftarrow 2 \times x $ \\ $c \leftarrow a-b + 2 $\\ Afficher $c$ } } \end{multicols} \begin{multicols}{2} \Exop{ Donner \textbf{toutes} les bonnes réponses. On donne l'algorithme ci-contre : \begin{enumerate} \item Le nombre obtenu avec l'entrée $-2$ est : \begin{multicols}{3} \begin{enumerate} \item $0$ \item $-4$ \item $12$ \end{enumerate} \end{multicols} \item Le nombre obtenu avec l'entrée $1$ est : \begin{multicols}{3} \begin{enumerate} \item $5$ \item $2$ \item $13$ \end{enumerate} \end{multicols} \item Si on veut obtenir $0$, on peut entrer : \begin{multicols}{3} \begin{enumerate} \item $0$ \item $-2$ \item $-4$ \end{enumerate} \end{multicols} \item Si on veut obtenir $-4$, on peut entrer : \begin{multicols}{3} \begin{enumerate} \item $0$ \item $2$ \item $-2$ \end{enumerate} \end{multicols} \item Une expression algébrique de la fonction $f$ définie sur $\R$ par cet algorithme est : %\begin{multicols}{3} \begin{enumerate} \item $f(x)=x^2-2$ \item $f(x)=(x+2)^2-4$ \item $f(x)=x^2+4x$ \end{enumerate} %\end{multicols} \end{enumerate} } \Algo{7cm}{ \Var{ $x$, $a$ et $b$ sont des nombres réels } \Deb{ Entrer $x$ \\ $a \leftarrow x+2 $\\ $b \leftarrow a^2 - 4 $ \\ Afficher $b$ } } \end{multicols} \Exop{ Un consommateur a la possibilité de choisir entre deux formules de location d'un studio pour ses vacances : \begin{itemize} \item Formule A : location fixe de $205\euro + 10 \euro$ de charges par jour \item Formule B : location fixe de $300\euro + 5 \euro$ de charges par jour. \end{itemize} \begin{enumerate} \item Quelle est la formule la plus avantageuse pour une location d'une semaine ? de 12 jours ? \item Pour chaque formule, exprimer le montant à régler en fonction du nombre $N$ de jours de location. \item D'une façon plus générale, le consommateur souhaite connaître la formule la plus avantageuse en fonction du nombre de jours de location.\\ On lui propose les algorithmes suivants.\\ Quel(s) est (sont) le(s) algorithme(s) correct(s) ? \end{enumerate} } \begin{multicols}{3} \Algo{6cm}{ \Var{ $N$, $A$, $B$ sont des nombres entiers} \Deb{ Entree $N$\\ $A \leftarrow 250 + 10 N$ \\ $B \leftarrow 300+5N$\\ \IfThenElse{$A<B$}{Afficher $\og B \fg $} {\IfThenElse{$A=B$}{Afficher $\og A $ ou $B \fg$}{Afficher $\og A \fg $ }} } } \Algo{6cm}{ \Var{ $N$, $A$, $B$ sont des nombres entiers} \Deb{ Entree $N$\\ $A \leftarrow 250 + 10 N$ \\ $B \leftarrow 300+5N$\\ \IfThenElse{$A<B$}{Afficher $\og A \fg $} {\IfThenElse{$A=B$}{Afficher $\og A $ ou $B \fg$}{Afficher $\og B \fg $ }} } } \Algo{6cm}{ \Var{ $N$, $D$ sont des nombres entiers} \Deb{ Entree $N$\\ $D \leftarrow 5N-50$ \\ \IfThenElse{$D>0$}{Afficher $\og B \fg $} {\IfThenElse{$D=0$}{Afficher $\og A $ ou $B \fg$}{Afficher $\og A \fg $ }} } } \end{multicols} \section{Représentation graphique d'une fonction} \subsection{Définition} On peut associer \`a une fonction un tableau de valeurs (que l'on trouve à la calculatrice). Il comporte deux lignes, la premi\`ere regroupe les ant\'ec\'edents $x$ et la seconde les images $f(x)$ correspondantes.\\ On peut alors placer les points de coordonnées $(x;f(x))$ dans un repère $(O; I ; J )$ du plan.\\ \Defc{ La \textbf{courbe représentative} $\mathscr C_f$ (ou encore \textbf{représentation graphique}) d'une fonction $f$ d\'efinie sur $D_f$ est l'ensemble des points de coordonn\'ees $\left(x;f(x)\right)$ o\`u $x$ parcourt $D_f$.\\ Autrement dit : $M(x;y) \in \mathscr C_f $ si et seulement si $\left\{\begin{array}{cc} x\in D_f \\ f(x)=y. \end{array} \right.$\\ On dit que la courbe $\mathscr C_f$ a pour équation $y=f(x)$ dans le repère choisi. } \Expl{Soit $f$ la fonction d\'efinie sur $\R$ par $f(x)=x^2-1$. Compléter le tableau de valeurs suivant grâce à la calculatrice: \begin{center} \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ & -2 & -1 & $-0.5$ & 0 & 1 & 2 & 3 \\\hline $f(x)$ & & & & & & & \\\hline \end{tabular} \end{center} Repr\'esenter dans un rep\`ere orthonorm\'e les points de coordonn\'ees $\left(x;f(x)\right)$. \\ Imaginer alors l'allure de la courbe repr\'esentative $\mathscr C_f$ de la fonction $f$.\\ Le point $A(1.5;1.25)$ appartient-il à $\mathscr C_f$ ? Et le point $B(0.5;-0.7)$? } \begin{center} \psset{xunit=1cm , yunit=0.5cm} \begin{pspicture*}(-3,-2)(3,6) \def\xmin{-3} \def\xmax{3} \def\ymin{-2} \def\ymax{6} \psframe[linewidth=0.3pt,linecolor=gray](-3.1,-2.1)(3.1,6.1) \def\pshlabel#1{\psframebox*[framesep=1pt]{\footnotesize #1}} \def\psvlabel#1{\psframebox*[framesep=1pt]{\footnotesize #1}} \psset{xunit=0.25cm,yunit=0.25cm} \psgrid[gridlabels=0pt,gridwidth=.3pt, gridcolor=lightgray, subgridwidth=.3pt, subgridcolor=gray, subgriddiv=1](0,0)(-15,-10)(15,30) \psset{xunit=1cm , yunit=1cm} \psaxes[labels=all,labelsep=1pt, Dx=1,Dy=1,Ox=0,Oy=0]{-}(0,0)(\xmin,\ymin)(\xmax,\ymax) \uput[u](0.9,0){I} \uput[r](0,1){J} \psclip{% \psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax) } \newrgbcolor{couleur1}{0.6549 0.6549 0} \newrgbcolor{couleur2}{0 0.3176 0.4745} \newrgbcolor{couleur3}{0.0941 0.647 0.0196} \def\F{x 2 exp 1 sub} \psplot[linecolor=blue,linestyle=solid,plotpoints=1000]{-3}{3}{\F} \endpsclip \end{pspicture*} \end{center} \noindent \Rq{ Pour tracer la courbe repr\'esentative d'une fonction, on relie les points du tableau de valeurs avec le plus de coh\'erence possible. On prendra toujours un tableau avec \textbf{\textit{au moins 10 valeurs}} et on consultera le trac\'e de la courbe sur la calculatrice pour s'aider.\\ N\'eanmoins, on ne sait pas exactement comment varie la fonction entre deux points de la courbe, ni en dehors du graphique. } \Cadre[Utilisation de la calculatrice]{Pour obtenir un tableau de valeurs (et la courbe repr\'esentative d'une fonction) \`a la calculatrice graphique : \begin{itemize} \item On rentre la fonction consid\'er\'ee dans \fbox{Y=} \textbf{ou} dans \fbox{f(x)} \textbf{ou} dans \fbox{Menu} + \fbox{Graph}. \item On r\`egle les param\`etres du tableau de valeurs (premi\`ere, derni\`ere valeur de $x$ et pas) dans le menu \fbox{Table} + \fbox{Tblset} (jaune + F4) \textbf{ou} dans \fbox{Déf table} (jaune + F2) \textbf{ou} dans \fbox{Menu} + \fbox{Table} + \fbox{F5} : \begin{center} \begin{multicols}{2} \textbf{CASIO}\\ Start=... \\ End=... \\ Pitch=... \\ \textbf{TI}\\ TblStart=... \\ $\Delta$Tbl=... \\ \end{multicols} \end{center} \item On règle les param\`etres de la fenêtre graphique (début et fin du $x$, début et fin du $y$, échelle) dans le menu \fbox{Graphe} + \fbox{windowset} (jaune + F?) \textbf{ou} dans \fbox{fenêtre} \textbf{ou} dans \fbox{Menu} + \fbox{graphe} + \fbox{F5} : \begin{center} \begin{multicols}{2} \textbf{CASIO}\\ Start=... \\ End=... \\ Pitch=... \\ \textbf{TI}\\ TblStart=... \\ $\Delta$Tbl=... \\ \end{multicols} \end{center} \item On affiche le tableau de valeurs dans le menu \fbox{Table} (jaune + F5) \item On affiche la courbe repr\'esentative dans le menu \fbox{Graphe}. \end{itemize} } \begin{multicols}{2} \Rq{\\ Toutes les courbes ne repr\'esentent pas des fonctions. \\ On s'appuie sur la d\'efinition pour le comprendre. \\ En effet, un \'el\'ement ne peut avoir plusieurs images.\\ Ci-contre, on constate que le nombre $4$ possède deux images : $-1$ et $4$.\\ La courbe ci-contre n'est donc pas représentative d'une fonction. \begin{center} \psset{xunit=0.8cm , yunit=0.8cm} \begin{pspicture*}(-3,-3)(6.8,6) \def\xmin{-3} \def\xmax{7} \def\ymin{-3} \def\ymax{6} \psframe[linewidth=0.3pt,linecolor=gray](-3.2,-3.2)(7.2,6.2) \def\pshlabel#1{\psframebox*[framesep=1pt]{\small #1}} \def\psvlabel#1{\psframebox*[framesep=1pt]{\small #1}} \psclip{% \psframe[linestyle=none](\xmin,\ymin)(\xmax,\ymax) } \psset{linecolor=black, linewidth=.5pt, arrowsize=2pt 4} \pscircle(1.5000,1.5000){2.85} \psline[linestyle=dashed](4.0000,-3.0000)(4.0000,6.0000) %\uput{0.5000}[-120.0000](4.0000,0.0000){$x$} \psline[linestyle=dashed](-3.0000,4.0000)(7.0000,4.0000) \psline[linestyle=dashed](-3.0000,-1.0000)(7.0000,-1.0000) %\uput{0.3000}[-50.0000](0.0000,-1.0000){$y_1$} %\uput{0.3000}[50.0000](0.0000,4.0000){$y_2$} \endpsclip \psaxes[labels=all,labelsep=1pt, Dx=1,Dy=1]{-}(0,0)(\xmin,\ymin)(\xmax,\ymax) \uput[dl](0,0){0} \uput[u](0.9,0){I} \uput[r](0,1){J} \end{pspicture*} \end{center} } \end{multicols} \Expls{Tracer les courbes représentatives des fonctions $f$, $g$ et $h$ définies sur $\R$ par $$f(x)=3 \qquad g(x)=2x+1 \qquad \text{et} \qquad h(x)=-2x+1$$ } \Exos{n$^{\circ}$ 10 à 12 p 47 + 62 p 55} \subsection{Lecture graphique} \Act{Reprendre l'une des courbes tracées précédemment et répondre à des questions de lecture graphique, telles que ensemble de définition, image, antécédents, signes ... } \Cadre[Méthodes pour déterminer graphiquement ]{ \begin{itemize} \item \textbf{Un ensemble de définition} : On détermine l'ensemble des abscisses de tous les points de la courbe représentative.\\ Puis on le décrit sous la forme d'un intervalle ou d'une réunion d'intervalles, en faisant attention aux bornes (crochets ouverts ou fermés). \item \textbf{L'image $f(a)$ d'un réel $a$} : On place sur la courbe le point d'abscisse $a$ et on lit son ordonnée. \item \textbf{Les éventuels antécédents d'un réel $b$} : On place sur la courbe tous les points éventuels d'ordonnées $b$ (on peut les mettre en évidence en traçant la droite parallèle à l'axe des abcisses passant par le point $(0;b)$ d'équation $y=b$) et on lit leur abscisses. \end{itemize} } \Expl{Dessin Déclic p 18 (méthodes) + n$^{\circ}$ 26 à 29 p 29 (basiques) + 38 à 41 p 31 (classiques)} \Exos{n$^{\circ}$ 3 + 13 + 17 p 46 (classiques) + 48 p 52 (critique) + 54-57 p 54} \setcounter{algor}{1} \begin{multicols}{2} \Exop{ On considère les fonctions $f$ et $g$ définies par $$f(x)=2x^2-x+1 \text{ et } g(x)=\dfrac{3x+1}{2x-1}$$ \begin{enumerate} \item Quel est l'ensemble de définition de $f$ ? \\ Celui de $g$ ? \item \textbf{Boucle Si}. \begin{enumerate} \item Que fait l'algorithme 1 ? \item Ecrire un algorithme similaire pour la fonction $g$ (en prenant soin de traiter à part le cas de la valeur interdite) \end{enumerate} \item \textbf{Boucle Pour.} \begin{enumerate} \item Que fait l'algorithme 2 ? \item Ecrire un algorithme qui donne un tableau de valeurs de $g$, pour $x$ allant de $-2$ à $3$, avec un pas de $0.5$ (avec pour réponse \og valeur interdite \fg\, quand nécessaire). \end{enumerate} \end{enumerate} } \Algo{9cm}{ \Var{ $x$, $y$ et $a$ sont des nombres réels } \Deb{ Entrer $x$ et $y$ \\ $a$ prend la valeur $2x^2-x+1$\\ \IfThenElse{$y==a$}{Afficher \og Le point $(x;y)$ appartient à la courbe représentative de $f$\fg}{ Afficher \og Le point $(x;y)$ n'appartient pas à la courbe représentative de $f$\fg} } } \end{multicols} \Algo{7cm}{ \Var{ $x$, $y$ et $i$ sont des nombres réels } \Deb{ Entrer $x$ \\ \For{$i=-3$ \textbf{à} $5$}{ $y$ prend la valeur $2x^2-x+1$\\ Afficher $(x;y)$\\ $i$ prend la valeur $i+1$ } } } \Exop{ On considère la fonction $f$ définie sur $[-2;4]$ par : $$f(x)=\left\{\begin{array}{lll} x+1 & \text{si} & x\in[-2;1] \\ -x^2+1 & \text{si} & x\in]1;4] \end{array}\right.$$ \begin{enumerate} \item Ecrire un algorithme qui permette de calculer l'image par $f$ d'un nombre $x$. \item Construire la courbe représentative de $f$. \end{enumerate} } \begin{multicols}{2} \Exop{On considère l'algorithme 3 : \begin{enumerate} \item Faire fonctionner cet algorithme pour $x=-2$, $x=1$ et $x=3$. \item Cet algorithme définit une fonction $f$. \begin{enumerate} \item Donner l'ensemble de définition de $f$. \item Exprimer $f(x)$ en fonction de $x$. \item Représenter graphiquement la fonction $f$. \end{enumerate} \end{enumerate} } \Algo{7cm}{ \Var{ $x$ et $y$ sont des nombres réels } \Deb{ Entrer $x$ \\ \IfThenElse{$x< 1$}{$y \leftarrow x^2 $}{$y \leftarrow 2x $} \\ Afficher $y$ } } \end{multicols} \textit{\textbf{Approfondissement possible : établir graphiquement le signe d'une fonction, réfléchir à la cohérence entre un tableau (de valeurs ou de signe) et une courbe représentative... }} %\vspace{20mm} \begin{epigraphe} {Le dessin n'est pas la forme, il est la manière de voir la forme.}{Degas}{Edgar} \end{epigraphe} \end{document}

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\[\tan z=\frac{\sin\left(2x\right)+\mathrm{i}\sinh\left(2y\right)}{\cos\left(2x% \right)+\cosh\left(2y\right)},\]

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\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{*3}{*1} \titlespacing{\subsection}{0pt}{*2}{*0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[ngerman,english]{babel} \usepackage{float} \begin{document} \title{AVR in patients with anomalous course of the circumflex artery without prosthetic downsizing} \author[1]{Luca Botta}% \author[1]{Ciro Amodio}% \author[1]{Vincenzo Pagano}% \author[2]{Luca Di Marco}% \author[1]{Alessandro Leone}% \author[1]{Antonino Loforte}% \author[1]{Sofia Martin-Suarez}% \author[1]{Carlo Savini}% \author[3]{Davide Pacini}% \affil[1]{S. Orsola Hospital}% \affil[2]{s'Orsola Malpighi Hospital}% \affil[3]{University of Bologna}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} An anomalous origin of the left circumflex coronary artery that arises as a side branch of the right coronary artery and encircles the aortic annulus is usually an incidental finding. However, in patients undergoing aortic valve/root procedures, its existence can significantly complicate the surgical treatment. We report our operative strategy with three different prostheses without valve downsizing.% \end{abstract}% \sloppy \textbf{Surgical Technique} Pre-operative evaluation for suspected coronary artery disease (CAD) with invasive coronary angiography should be performed when surgery or an intervention is planned to determine if concomitant coronary revascularization is indicated {[}1{]}. Coronary angiography is recommended before valve surgery in men \textgreater{}40 years and post-menopausal women, in patients with history of cardiovascular disease, symptoms of angina, objective evidence or suspected myocardial ischemia, decreased left ventricular systolic function and in case of cardiovascular/coronary risk factors {[}1{]}. Alternatively, coronary computed tomography (CT) can be used to rule out CAD in patients at low risk {[}2{]}. These imaging techniques can provide more information than the simple presence of CAD, such as coronary anatomy, origin, course and spatial relationships {[}1,2{]}. Nevertheless, coronary angiography and/or CT-scan are not always performed before aortic valve (AV) surgery (young patients without risk factors or urgent cases like endocarditis) or can be undervalued when stenotic lesions are excluded. Coronary anomalies such as anomalous~left~circumflex~coronary~artery (LCA)~arising from the right sinus of Valsalva, strictly leaning on the aortic annulus, can have serious consequences in aortic valve/root surgery, particularly if unrecognized or underestimated {[}3,4{]}. In this paper, we present three patients with an anomalous course of the LCA undergoing AV replacement (AVR) with three different prostheses, without prosthetic downsizing. Coronary angiography was performed in two patients. All patients underwent a preoperative CT-scan (Fig.1A). Chest was opened by median sternotomy and mild hypothermic cardiopulmonary bypass (32--34\selectlanguage{ngerman}°C) was initiated with ascending-aortic and right-atrial cannulation. After cross-clamping and infusion of antegrade crystalloid cardioplegia, aortotomy was performed with a transverse incision just above the sinotubular-junction avoiding the oblique incision towards the non-coronary sinus. Aortic valve was explored, leaving the native cusps in situ in presence of severe leaflet/annular calcifications to avoid any damage to the LCA during excision. A 1.0/1.5-mm coronary probe was placed into the assumed anomalous LCA to verify the anomalous course between the aortic root/annulus and the left atrial roof. A careful and complete dissection of the LCA was performed to free the artery from the aortic wall along its course, initially on the anterior and right side of the root, then posterior to the aorta at the level of the annulus until the atrio-ventricular groove (Fig.1B). Once the LCA was completely free from the surrounding tissues, we proceeded with native cusps excision. A meticulous attention was paid to the mobilized anomalous LCA when placing annular sutures (Fig.1C) using standard 2-0 U-stiches with small/soft pledgets on the ventricular side. Three different prostheses were used: a mechanical valve (On-X 23mm) in a 31 years-old male with bicuspid aortic valve and severe regurgitation due to active endocarditis (E. Faecalis), a stented bioprosthesis (Carpentier Edwards magna Ease 23mm) and a rapid deployment sutureless valve (Perceval-S Size-M) in two ladies of 67 and 79 years with severe aortic stenosis, respectively. A complete LCA scheletonization allowed us to avoid prosthetic downsize, implanting valves of sizes exactly corresponding to every single annulus. Once the prosthesis was deployed, we verified the absence of compression on the LCA by the sewing-ring for stented prostheses (Fig.1D) or by the inflow-ring/sinusoidal struts for the sutureless valve. Aortotomy was closed in the standard fashion, avoiding the use of pledgets on the right side. After deairing and clamp removal, careful attention must be paid to LCA verifying its mobility with a blood-full root and the absence of hematoma, minor bleeding or compression by the surrounding structures. No sealants/hemostatic products were used. The patients were weaned from cardiopulmonary bypass in sinus rhythm without ischemic signs. Postoperative course was good in all cases without signs/symptoms of perioperative ischemia. Postoperative CT-scan confirmed the absence of LCA compression (Fig.2) in all patients, currently in good clinical conditions at last FU. Anomalous origin of the coronary arteries is usually an incidental finding in patients undergoing cardiac catheterization. Coronary anomalies were found in 99 patients among 3,233 coronary angiograms by Sidhu and coll. {[}5{]}, with an incidence of 3.06\%. Patients' mean age was 56.2years (range: 20-86). Ectopic origin of LCA from the right sinus or right coronary artery was noted in 13 patients (0.40\%), usually with a benign clinical course {[}5{]}. Appropriate imaging is crucial to understand the spatial relationship between the anomalous coronary arteries and the aortic valve/root before surgery but in the real life is not always performed, particularly in younger patients or in absence of coronary risk factors. In addition, the low incidence of this anomaly in clinical practice could reduce the proper attention of surgeons, particularly when critical stenoses are not reported. Anomalous LCA with a retro-aortic trajectory has major implications during AV surgery, particularly when unrecognized or underestimated {[}3-5{]}. Injury to the LCA may occur in isolated AVR by compression from the prosthesis (sewing ring) or ligation by annular sutures while resection of the non-coronary sinus or suturing could complicate aortic root/sinus repair. A careful surgical planning and management is mandatory and every step requires a strong attention as well as the choice of the right prosthesis. Implanting a smaller-sized prosthesis with the aim to avoid coronary artery distortion or compression has been reported {[}3,6{]}, although patient-prosthesis-mismatch can occur with serious complications in small aortic annuli. In this small series, we have avoided this problem through the complete LCA skeletonization. When preoperative echocardiography shows a small aortic annulus and a standard stented prosthesis is not suitable, we suggest to use a sutureless aortic valve as reported by Cerillo and coll. {[}7{]}. In alternative, transcatheter aortic valve implantation has been described with success, using when necessary, a coronary guidewire before deploying TAVI to prevent coronary occlusion/stenosis {[}8{]}. Whenever postoperative ischemia should be detected after AVR with anomalous LCA, compression or surgical ligation must be immediately suspected and ruled out. If there is high suspicion of compression as the mechanism of ischemia, percutaneous coronary intervention can be a reasonable treatment option {[}6{]}. Coronary anatomy should always be evaluated in elective or urgent AVR. Careful and complete arterial skeletonization is recommended in presence of anomalous LCA to avoid prosthetic downsize and patient-prosthetic mismatch with every type of prosthesis. \textbf{Figure Legend} \textbf{Fig.1} The yellow-arrow shows the anomalous LCA, originating from the right coronary artery (white-arrow) at multiplanar CT-scan (Fig.1A; Blu: aortic root; Red: coronary arteries). The LCA (black-arrow) was completely skeletonized and surrounded by a yellow vessel-loop before cusp removal (Fig.1B). U-stiches with soft-pledgets on the ventricular side were used, paying attention to avoid any LCA involvement (Fig.1C). After valve replacement, accurate evaluation of the field to verify the absence of LCA (black-arrow) compression (Fig.1D). \textbf{Fig.2} Postoperative CT-scan after a mechanical valve replacement (white-arrow, Fig.2A) and after a sutureless implantation (red-arrow, Fig.2B). The yellow arrow shows the anomalous LCA, not compressed by the sewing/basal rings nor by the left atrium (L.A.). \textbf{References} \begin{enumerate} \tightlist \item Baumgartner H, Falk V, Bax JJ, et al. 2017~ESC/EACTS~Guidelines~for the management of~valvular~heart disease. Eur Heart J. 2017;38:2739-2791. \item Opolski MP, Staruch AD, Jakubczyk M, et al. CT angiography for the detection of coronary artery stenoses in patients referred for cardiac valve surgery: systematic review and meta- analysis. J Am Coll Cardiol Img 2016;9:1059-70. \item Liebrich M,~Tzanavaros I,~Scheid M,~et al. Aortic valve/root procedures in patients with an~anomalous~left~circumflex~coronary~artery~and a bicuspid~aortic valve: anatomical and technical implications. Interact Cardiovasc Thorac Surg.~2015;21:114-6. \item Harky A,~Hof A,~Ahmad MU,~et al. Incidental finding of~anomalous~circumflex~coronary~artery~from right coronary sinus prior to~aortic valve~surgery. BMJ Case Rep.~2017Mar 31;2017. \item Sidhu NS, Wander GS, MongaA, et al. Incidence,~Characteristics~and~Atherosclerotic~Involvement~of~Coronary~Artery~Anomalies~in Adult Population~Undergoing~Catheter~Coronary~Angiography. Cardiol Res.~2019;10(6):358-368. \item Castillo JG, Sanz J, Fischer GW, et al. Management of anomalous left circumflex artery encircling the aortic annulus in a patient undergoing multivalvular surgery. J Card Surg 2009;24:667--9. \item Cerillo GA,~Haxhiademi D,~Berti S,~et al. Sutureless~Aortic Valve~Replacement: An Easy and Safe Approach for Patients with~Anomalous Left~Circumflex~Coronary~Artery. J Heart~Valve~Dis.~2016;25:145-148. \item Ujihira K,~Raval AN,~Wolff MR,~et al. Transcatheter~aortic valve~replacement~in patients with~anomalous~left~circumflex~coronary~artery. J Card Surg.~2019;34:503-505. \end{enumerate}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig1-new/Fig1-new} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig-2def/Fig-2def} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}

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\documentclass[DIV=12,% BCOR=10mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% twoside,% paper=210mm:11in]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{Linux Libertine O} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{english} % global style \pagestyle{plain} \usepackage{microtype} % you need an *updated* texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand*\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand*{\captionformat}{} \renewcommand*{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand*{\forcelinebreak}{\strut\\*{}} \newcommand*{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment*{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment*{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand*{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{50 Ways to Prepare for Revolution} \date{2011} \author{Stephanie McMillan} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={50 Ways to Prepare for Revolution},% pdfauthor={Stephanie McMillan},% pdfsubject={},% pdfkeywords={preparation; Revolution; strategy}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge 50 Ways to Prepare for Revolution\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Stephanie McMillan\par}}% \vskip 1.5em \vfill {\usekomafont{date}{2011\par}}% \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage The people of the United States are currently unprepared to seize a revolutionary moment. We must fix that. How can we raise our levels of revolutionary consciousness, organization and struggle? \section{Raise consciousness} 1) Raise consciousness with the purpose of building organization and raising the level of struggle. 2) Investigate before forming opinions. Research how the world and the system function. 3) Read foundational and historical works about revolution, by those who have participated in and led them. 4) Analyze the system’s current condition and trajectory. 5) Learn about the resistance, uprisings and revolutions going on in the world today. 6) Read the material that currently active groups are issuing and discussing. 7) Continuously develop, elaborate upon and refine principles, theories and strategies for our movement. 8. Raise our voices. Articulate revolutionary ideas, and give them a public presence. 9) Listen and speak in the spirit of mutual clarification. 10) Participate in discussion, to develop our ideas and hone our skills in expressing them, and to help others do so. 11) Figure out how to use all our various talents, positions, energy and resources as effectively as possible, to expose the system’s evil, irredeemable and unreformable nature. 12) Analyze and explain the many ways the system dominates and exploits. 13) Stand with the dominated, exploited, invaded, colonized, threatened and oppressed. 14) Display a revolutionary spirit and celebrate it in others. 15) Exercise patience in winning over reluctant potential allies and supporters. 16) Ridicule and discredit the enemy. 17) Create revolutionary culture. Make videos and art, speak, sing, and write blogs, books, comments, leaflets, rhymes, stories, and articles about the enemy’s crimes and the people’s resistance. 18) Exchange ideas locally, nationally and (within the law or safe channels) globally. 19) Encourage others to participate in the revolutionary process. \section{Organize} 20) Organize as a way to raise consciousness more broadly and to build struggle. 21) Start with people we know. 22) If our friends discourage us, make new friends. 23) Network sensibly with people online. Find local people online who express similar ideas, and meet with them. 24) Find a group that we basically agree with. Work with it. 25) If there’s no local group we want to work with, start one. 26) Write a leaflet with contact info. Pass it out in public to find potential comrades. 27) When we meet people, assess our points of agreement. If we agree on basic essentials, decide how to work together. If not, say goodbye for now. 28) Build strong ties locally and nationally, and build solidarity globally. 29) Define allies according to overall outlook and goals. 30) Don’t let secondary differences prevent cooperation. Handle differences between allies non-antagonistically. 31) Do not tolerate oppressive (sexist, racist, homophobic etc.) dynamics within the movement. Confront their expression and put a stop to it. 32) Refrain from saying anything aloud, on the phone or electronically that we wouldn’t want to hear played back in court. 33) Keep illegal drugs away from our political life. 34) Research and practice good security culture. 35) Prioritize the wellbeing of our organizations over personal benefit. 36) Ready our ranks to seize on any breaks in the legitimacy of the system. \section{Struggle} 37) Use struggle to spread revolutionary consciousness and build organization. 38) Collectively determine what we want, and declare our demands. 39) Act as far as possible within our capacity, not either beyond or below our capacity. 40) Continuously strive to expand and consolidate our capacity and strength. 41) Assert our rights and our responsibilities. 42) Bring our revolutionary perspective into struggles already occurring. 43) Defend, support, and encourage our allies. 44) As opportunities arise, weaken the enemy and its ability to rule. 45) Obey the small laws. Don’t get taken out of the game for something unworthy. 46) For illegal acts, make sure you can trust your comrades with your life and the lives of everyone connected to you. 47) Avoid being distracted and diverted into symbolic action-for-action’s sake. 48) Don’t expect the enemy to act against its nature. It has no mercy and can not be reasoned with. 49) Turn every attack by the enemy into an opportunity to speak out, organize, and grow more powerful. 50) Be willing to work hard. Be smart. Be brave. Remember we are all in this together. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} Anarchist library \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-yu.pdf} \bigskip \end{center} \strut \vfill \begin{center} Stephanie McMillan 50 Ways to Prepare for Revolution 2011 \bigskip Retrieved on May 23, 2011 from \href{http://stephaniemcmillan.org/2011/05/09/50-ways-to-prepare-for-revolution-2/}{stephaniemcmillan.org} May 09, 2011 \bigskip \textbf{en.anarchistlibraries.net} \end{center} % end final page with colophon \end{document}

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% mcolenum.sty % from http://www.jokr.de/stefan/ % File created by Stefan Krause -- version 1.0. % Creates an enumerate or an itemize environment within a multicols environment, % aligning items in one row at the same height. % You may access % \begin{mcolenum}{}{} % \end{mcolenum} % \begin{mcolitem}{}{} % \end{mcolitem} % from this document. \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{mcolenum}[2010/11/16] \RequirePackage{multicol} \newenvironment{mcolenum}[2]{% \begin{multicols}{#1}\begin{enumerate}\def\makelabel##1{\hss\llap{\vphantom{#2}##1}}% }{% \end{enumerate}\end{multicols}% } \newenvironment{mcolitem}[2]{% \begin{multicols}{#1}\begin{itemize}\def\makelabel##1{\hss\llap{\vphantom{#2}##1}}% }{% \end{itemize}\end{multicols}% }

https://melusine.eu.org/syracuse/B/BaseCollege/Evaluation/a2001/exo35.tex?enregistrement=ok

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Une école achète 5 dictionnaires à 29,97~\textgreek{\euro} l'un.\par Donne un ordre de grandeur de la dépense totale. \par \hbox to10cm{La dépense totale est proche de \dotfill~\textgreek{\euro}}

https://dk.archive.ubuntu.com/pub/ctan/biblio/bibtex/contrib/bestpapers/bestpapers-guide.tex

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\documentclass{article} \usepackage[numbers]{natbib} \usepackage{hyperref,alltt} \usepackage[resetlabels]{multibib} \newcommand{\BibTeX}{\textsc{Bib}\TeX} \newcites{tex}{Books and articles about \TeX} \newcites{typography}{Books and articles about typography} \begin{document} \title{User Guide for \texttt{bestpapers.bst} Bibliography Style} \author{Boris Veytsman\thanks{This work was commissioned by Consumer Financial Protection Bureau, United States Treasury. This file and the package are in the public domain}} \date{October 2014} \maketitle \section{Introduction} \label{sec:intro} Many people preparing their r\'esum\'es find the requirement ``please list five (or six, or ten) papers authored by you''. The same requirement is often stated for reports prepared by professional teams. The creation of such lists may be a cumbersome task. Even more difficult is to support the lists over the time, when one adds new papers. The style \texttt{bestpapers.bst} is intended to make this task simpler. It is based on the idea that it is easier to score than to sort: we can assign a score to a paper, and then let the computer to select the papers with highest scores. \section{Simple Usage} \label{sec:simple} The use of the package is simple. We assume that you keep all your publications in a \BibTeX\ file (or files). Then, \begin{enumerate} \item Add to each bibliographic entry in the file the field \begin{alltt} score = \itshape SCORE \end{alltt} where \texttt{\itshape SCORE} is an non-negative integer. The higher the score is, the more you think about the paper. Since only the relation between scores matter, you may limit yourself to scores between, say, $0$ and $100$. An absent score is equivalent to \texttt{score=0}. \item Add to the preamble of your r\'esum\'e \begin{verbatim} \usepackage[numbers]{natbib} \end{verbatim} and to the document itself \begin{verbatim} \renewcommand{\refname}{My Best Works} \nocite{*} \bibliography{myworks} \bibliographystyle{bestpapers} \end{verbatim} \item You document will get the list of five~best works, sorted by decreasing scores. \end{enumerate} \section{Customization} \label{sec:custom} Sometimes you need to change the number of best papers displayed. The package introduces a new entry type \verb|@SETUP| with the field \verb|max.best.papers|, for example, \begin{verbatim} @SETUP{setup, max.best.papers = 6, } \end{verbatim} Normally the score of the papers is not printed. However, for debug purposes you can change this: just define the command \verb|\PrintScore|, for example \begin{verbatim} \newcommand{\PrintScore}[1]{Score: #1} \end{verbatim} \section{Bibexport} \label{sec:bibexport} Sometimes you need to extract your best works from \texttt{.bib} files rather than typeset the list of them. You can use for this the program \textsl{bibexport} (\url{http://www.ctan.org/pkg/bibexport}), a handy tool for the manipulation of \BibTeX\ databases. The package provides the style \texttt{bestpapers-export.bst} intended for this task. To extract the best works from the files \texttt{myworks.bib} and \texttt{ourworks.bib} into the file \texttt{result.bib}, \begin{enumerate} \item Create the file \texttt{extract.aux} with the following content: \begin{verbatim} \citation{*} \bibdata{myworks,ourworks} \bibstyle{bestpapers-export} \end{verbatim} \item If necessary, add to any of these files \texttt{@SETUP} entry as described in Section~\ref{sec:custom}. \item Run \begin{verbatim} bibexport -b bestpapers-export -o result.bib export.aux \end{verbatim} \end{enumerate} \section{Multiple Bibliographies} \label{sec:multiple} Sometimes you need to have collective report and provide several best papers for each person in the group. The package \texttt{multibib} allows you to do this: \begin{verbatim} \usepackage{multibib} \newcites{chico,harpo,groucho,zeppo}{Chico's Papers,% Harpo's Papers,% Groucho's Papers,% Zeppo's Papers} ... \nocitechico{*} \bibliographychico{chico.bib} \bibliographystylechico{bestpapers} \nociteharpo{*} \bibliographyharpo{harpo.bib} \bibliographystyleharpo{bestpapers} \nocitegroucho{*} \bibliographygroucho{groucho.bib} \bibliographystylegroucho{bestpapers} \nocitezeppo{*} \bibliographyzeppo{zeppo.bib} \bibliographystylezeppo{bestpapers} \end{verbatim} Note that you may want to use \texttt{resetlabels} option of the \texttt{multibib} package if you want all the lists to start from~1. An example of this usage is the source code of this file, which lists 6~books about \TeX\ and 5~books about typography separately. \nocitetex{*} \nocitetypography{*} \bibliographytex{tex} \bibliographystyletex{bestpapers} \bibliographytypography{typography} \bibliographystyletypography{bestpapers} \end{document}

https://wiki.horde.org/GroupwarePEAR?actionID=export&format=tex

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\documentclass{article} \usepackage{ulem} \pagestyle{headings} \begin{document} \part{How to install or update PEAR packages with Horde Groupware (Webmail Edition)} From version 1.2.4 on, Horde Groupware and Horde Groupware Webmail Edition ship with a complete, working PEAR installation. This means that you can update the PEAR packages bundled with Horde Groupware, for example to get bug or security fixes directly from PEAR. You can also install new PEAR package that might be necessary for any additional Horde applications that you plan to install. To get the local PEAR installation working, you have to run the \texttt{setup.php} script and pick the menu item "Update PEAR for a new or changed location". This is also necessary each time you rename or move the directory of Horde Groupware. Then you can manage the bundled PEAR installation by calling the PEAR command like so: \begin{verbatim} ./pear/pear -c pear/horde.ini install Text_Wiki \end{verbatim} This example assumes that you are inside the Horde Groupware directory, but you can call the \texttt{pear} command from anywhere. Just make sure that you use the \texttt{pear} command from inside the Groupware's \texttt{pear/} directory, and the \texttt{-c} flag with the \texttt{horde.ini} file from the same directory. See http://pear.php.net/manual/en/guide.users.commandline.cli.php\footnote{http://pear.php.net/manual/en/guide.users.commandline.cli.php} for further documentation of the \texttt{pear} command. \end{document}

https://ejde.math.txstate.edu/Volumes/2017/70/ducomet.tex

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\documentclass[reqno]{amsart} \usepackage{hyperref} \usepackage{graphicx} \AtBeginDocument{{\noindent\small \emph{Electronic Journal of Differential Equations}, Vol. 2017 (2017), No. 70, pp. 1--13.\newline ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu} \thanks{\copyright 2017 Texas State University.} \vspace{8mm}} \begin{document} \title[\hfilneg EJDE-2017/70\hfil Lifetime of localized states] {Lifetime of localized states for a generalized Schr\"odinger operator appearing in nuclear physics} \author[B. Ducomet \hfil EJDE-2017/70\hfilneg] {Bernard Ducomet} \address{Bernard Ducomet \newline Bruy\`eres le Ch\^atel, CEA, DAM, DIF, 91297 Arpajon, France} \email{bernard.ducomet@cea.fr} \dedicatory{Communicated by Pavel Drabek} \thanks{Submitted January 30, 2016. Published March 14, 2017.} \subjclass[2010]{35Q40, 35J10, 35P10} \keywords{Schr\"odinger; lifetime; uncertainty inequality} \begin{abstract} We apply time-energy uncertainty inequalities introduced by Pfeifer and Fr\"ohlich \cite{PF} to estimate the lifetime of quasistationary mixed states for a variable coefficients Schr\"odinger operator, without using directly resonance theory. \end{abstract} \maketitle \numberwithin{equation}{section} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \allowdisplaybreaks \section{Introduction}\label{intro} In various phenomena of quantum physics one is interested in the dynamics of quantum states driven by Schr\"odinger operators with variable coefficients and made unstable due to tunneling. The first example comes from quantum field theory on curved spaces (Riemanian manifolds) where barrier penetration may justify the decay of ``false vacua" \cite{C,CC,GS}. Just mention that in cosmology, tunelling of such false vacua could explain nucleation processes during the formation of the early universe \cite{SST,TSY}. A second example comes from low-energy nuclear physics \cite{CBGW,Ho1,Ho2,RMR} where the study of large collective motions of a heavy nucleus made of $N$ nucleons (protons and neutrons) is investigated by the so called Generator Coordinate Method (GCM) \cite{RS}. Namely taking weighted superpositions of collective coordinates as trial functions for deformed states and applying a minimization precedure, one gets the Hill and Wheeler non-local integral equation \cite{HW}, which in turn, after solving in the so-called Gaussian Overlap Approximation (GOA) \cite{VL}, reduces to a 1 body problem described by a Schr\"odinger equation in $\mathbb{R}^d$ with variable coefficients ($d$ is the number of collective degrees of freedom which, in the present status of computations \cite{GBCG}, is currently in the range 1-5). The simplest paradigm for quantifying these decay phenomena is the so called ``puits dans l'isle" problem introduced by Helffer and Sj\"ostrand in \cite{HSj} which reads as follows: `` given a potential with a local minimum and decaying at large distance, try to estimate the ``life time" $T$ of an unstable state escaping from the well surrounding the local minimum". In a physical (formal) setting, functional integral formalism \cite{ZJ} gives a formula for such a lifetime $T$, of the type \begin{equation} T= A\ e^{\frac{B}{\hbar}}, \label{LT} \end{equation} where $A,B$ are positive constants partially computable in some specific situations (see \cite{C,CC}) and the exponential is expected to be large due to the presence of the small parameter $\hbar$ (Planck's constant). From a mathematical point of view the main strategy invoked to make \eqref{LT} rigorous is to identify the lifetime $T$ as the inverse of the imaginary part of a resonance $\Gamma$ as in \cite{CS,KRW,MS,SW} in a time-dependent process and to estimate the width $\Gamma$ by using the now well-developed semiclassical resonance theory based on complex deformations (see \cite{CFKS,DZ,HSj,HS} for detailed expositions). In fact an equality such that \eqref{LT} is out of reach, at least in the multidimensional case ($d>1$) and only upper (and sometimes lower) bounds for $\Gamma$ have been proved by Helffer and Sj\"ostrand \cite{HSj} (see also \cite{M}) for arbitrary $d\geq 1$. Alternatively, another possible definition of lifetime can be derived from first principles through a direct estimate of the probability $p(t)=\operatorname{Trace}(P\rho(t))$ for a quantum system described by the density operator $\rho(t)$ at time $t$ to remain in a given subspace of the state space ${\mathcal H}$ defined by the projector $P$ on suitable subspaces. This last approach has been introduced by Pfeifer and Fr\"ohlich \cite{PF} and applied in \cite{ASF} to adiabatic evolutions, with the advantage that it does not rely directly on resonance theory and avoid technical assumptions on operators in the (non physical) complex domain. In \cite{BD} we considered an extension of the first method to a Schr\"odinger operator with variable coefficients and then evaluated the lifetime as the inverse of the imaginary part of the associated resonance. In the present note, we focus on the second method and we show that the robust estimates of Pfeifer and Fr\"ohlich in \cite{PF}, relying on suitable time-uncertainty relations, can also be adapted to the generalized (variable coefficients) Schr\"odinger case to recover an upper bound of the type \eqref{LT} for some (in principle calculable) positive numbers $A$ and $B$ depending on the geometry of the problem. The plan of the paper is as follows: in Section \ref{m} we define the model, in Section \ref{comp} we introduce a comparison dynamics and derive necessary estimates for the various operators involved, then in Section \ref{lt} we give and prove our main result by applying a time-energy uncertainty relation proposed in \cite{PF} and recalled for the reader's convenience in the Appendix. In the whole paper we shall use the Einstein's summation convention on repeated indices. \section{Physical model} \label{m} As presented in the introduction, our model is issued from low-energy nuclear physics and the Generator Coordinate Method leads to a Schr\"odinger operator with variable coefficients in $\mathbb{R}^d$, where $d$ is the number of degrees of freedom so we define the hamiltonian of the system by \begin{equation} H(\lambda):=-g^{-1/2}(x) \partial_j(g^{1/2}(x)g^{jk}(x)\partial_k) +V_{\lambda}(x), \label{hamil} \end{equation} where $V_{\lambda}(x):=\lambda^2 V(x)$. In \eqref{hamil} $\lambda$ is a large positive parameter (in the semiclassical context, one can think to $\lambda=\frac{1}{\hbar}$), $x=(x_1,\dots, x_d)\in {\mathbb R}^d$ represents collective variables (physically: multipolar momenta) with $\partial_k=\frac{\partial}{\partial x_k}$, $k=1, \dots , d$ and $g_{ij}(x)$ is the collective ``mass tensor" with $g_{ij}g^{jk}=\delta_i^k$ (Kronecker's index), $i,k=1, \dots , d$ and $g(x)=\det \{g^{jk}(x)\}$. In fact from a computational point of view the functions $V(x_a)$ and $g_{ij}(x_a)$ are obtained from a finite number of (constrained) mean field calculations based on Hartree-Fock-Bogoliubov approximation \cite{RS}, for each $x_a$ in a finite set $F\subset \mathbb{R}^d$ (see \cite{CBGW} for a brief description of such a computation). However we will assume in the following that $V(x)$ and $g_{ij}(x)$ are smooth functions defined for any $x\in \mathbb{R}^d$, even for large $x$ where the approximation is questionable. Supposing that the function $V$ has a local minimum corresponding to a metastable collective state of the nucleus and that the barrier separating this local minimum from the exterior world is large and high enough (observe that the height of the barrier is ${\mathcal O}(\lambda^2)$ and that its diameter and width are ${\mathcal O}(\lambda)$) one expects that any quantum collective states initially trapped in the local well will spend a long time in it and will ultimately escape outside by tunnelling through the barrier. In the nuclear context the local minimum may correspond to an unstable nucleus decaying into several fragments through a fission barrier \cite{Ho2,RMR} or it can also correspond to a state of spherical shape of the nucleus (unstable for a large class of heavy nuclei) tunelling through the barrier toward a (super-)deformed state \cite{CBGW}. After definition \eqref{hamil}, it is natural to think of the previous quantum dynamics as taking place on a Riemannian manifold $(X,g)$ \cite{Sh} provided with the Riemannian metric $g$ given in local coordinates by $g^{ij}\in C^{\infty}(X)$ and associated distance $d_g$. Setting $g(x)=\det (g^{ij}(x))$ and $g_{ij}g^{jk}=\delta_i^k$ with (Kronecker's index), $i,k=1, \dots , d$, where the summation convention is used, the (generalized) Schr\"odinger operator $H$ in \eqref{hamil} is \begin{equation} H(\lambda)=-\frac{1}{2} \Delta_g + V_{\lambda}, \label{hamilbis} \end{equation} where $\Delta_g$ is the Laplace-Beltrami operator locally defined for any $u\in C^{\infty}(X)$ by \begin{equation} \Delta_g u:=g^{-1/2} \partial_j( g^{1/2}g^{jk}\ \partial_ku). \label{LB} \end{equation} This geometric framework has been used in the ``resonance" point of view by De Bi\`evre-Hislop \cite{dBH} and Froese-Hislop \cite{FH}, however in the present note we do not focus on the global geometrical aspects of the problem and concentrate on the variable coefficient framework so we will suppose in all the sequel that $X\equiv \mathbb{R}^d$ and $H(\lambda)$ is the variable coefficient elliptic operator defined globally on $X\equiv \mathbb{R}^d$ by \eqref{hamilbis} and \eqref{LB}. Accordingly we denote by $L^2(X)$ the weighted space $L^2(\mathbb{R}^d,dV_g)$ with $dV_g(x)=g(x)\,dx$ and by $H^s$ for $s\in \mathbb{R}$ the associated Sobolev spaces built on $L^2(\mathbb{R}^d,dV_g)$. \section{Comparison dynamics} \label{comp} \subsection{Comparison dynamics and spectral properties} According to the previous presentation we suppose that $g^{ij}(x)\sim \delta^{ij}$ (Kronecker symbol) for $|x|$ large (``$X\equiv (\mathbb{R}^d,g)$ is euclidean at large distance") and we note $|x|=d_g(0,x)$ for any $x\in X$. For a multiindex $\alpha\in {\mathbb N}^d$ with $|\alpha|:=\sum_{j=1}^d\alpha_j$, we note $D^{\alpha}_x=\partial^{\alpha_1}_{x_1}\partial^{\alpha_2}_{x_2}\dots \partial^{\alpha_d}_{x_d}$. More precisely we suppose that there exist positive constants $R$, $C_{\alpha}$, $C_{R,\alpha}$ and $\varepsilon$ such that \begin{itemize} \item[(A1)] The matrix $\{g^{ij}\}$ is positive definite and smooth: $g^{ij}\in C^\infty(X)$. Moreover \begin{equation} |D_x^{\alpha}g^{ij}(x)| \leq C_{\alpha}, \label{ater} \end{equation} for $|\alpha|=0,1,2$ and $i,j=1,\dots ,d$, \item[(A2)] The matrix $\{g^{ij}\}$ decays toward identity at large distance \begin{equation} |D_x^{\alpha}(g^{ij}(x)-\delta^{ij}) | \leq C_{\alpha,R}\langle x\rangle^{-|\alpha|-\varepsilon}, \label{a} \end{equation} for any $|x|\geq R$, for $|\alpha|=0,1,2$ and $i,j=1,\dots ,d$, with $\langle x\rangle:=(1+|x|^2)^{-1/2}$ and a possibly small $\varepsilon>0$ (long range case). \end{itemize} We also suppose that the potential $V$ is smooth, of shape-resonance type (``le puits dans l'isle" in the terminology of Helffer and Sj\"ostrand \cite{HSj}) and is small at large distance. Namely there exist positive constants $R$ and $C'_{R,\alpha}$ such that \begin{itemize} \item[(A3)] $V\in C^\infty(X)$,\ $ V\geq 0$. \item[(A4)] $\ \ V$ has a positive non degenerate local minimum $V_0$ at the origin: $V_0=V(0)>0$. \item[(A5)] $\ \ $ $V$ goes to zero at large distance: \[ |D_x^{\alpha}V | \leq C'_{R,\alpha}\langle x\rangle^{-|\alpha|-\varepsilon} \quad \text{for } |x|>R \text{ and } |\alpha|=0,1,2, \] for a possibly small $\varepsilon>0$ (long range potential). \item[(A6)] For a small $w>0$ precised below, the classically forbidden region (see \cite{HS} Chap. 20) \[ \mathcal{F}(V_0+w):=\{x\in\mathbb{R}^d:\ V(x)>V_0+w\}, \] is a relatively compact region bounded by two smooth hypersurfaces $S^-(V_0+w)$ and $S^+(V_0+w)$ (turning surfaces) such that the interior region ${\mathcal W}(V_0+w)$ (the well) is bounded by $S^-(V_0+w)$ and the exterior (unbounded) region $\mathcal{E}(V_0+w)$ admits $S^+(V_0+w)$ as boundary. \end{itemize} Provided $\lambda$ is large enough, one expects that the well $\{|x|\ll R\}$ and the exterior region $\{|x|\gg R\}$ are almost decoupled, and we define a comparison potential \[ \widetilde V(x)= \begin{cases} V_0+w &\text{for } x\in \mathcal{E}(V_0+w),\\ V(x) &\text{for } X\backslash \mathcal{E}(V_0+w), \end{cases} \] where we suppose that $w$ is small enough in order that $\tilde V$ has a ground state $E_0$ such that $V_0<E_0<V_0+w$. \begin{figure}[ht] \begin{center} \includegraphics[width=0.7\textwidth]{fig1} \end{center} \caption{Comparison potential $\widetilde{V}(x)$.} \label{fig_contour} \end{figure} The corresponding comparison hamiltonian is then defined as \begin{equation} H_0(\lambda):= - g^{-1/2}(x) \partial_j(g^{1/2}(x)g^{jk}(x)\partial_k) + \widetilde V_{\lambda}(x) \equiv-\frac{1}{2}\ \Delta_g+\lambda^2 \widetilde V(x), \label{hamilzero} \end{equation} and we denote by $W_{\lambda}$ the perturbation \begin{equation} W_{\lambda}(x)= V_{\lambda}(x)-\widetilde V_{\lambda}(x). \label{W} \end{equation} It is well known \cite{Sh} that $H(\lambda)$ and $H_0(\lambda)$ are well defined as selfadjoint operators on $L^2(X)$ with domain $H^2(X)$ and we first briefly describe their spectra. \begin{lemma} \label{lem1} Under assumption {\rm (A3)} on the potential $V$, $H(\lambda)$ and $H_{0}(\lambda)$ are bounded below. Moreover \begin{enumerate} \item For each $\alpha<w$: $\sigma_d(H_0)\equiv\sigma(H_0)\cap (-\infty,\alpha))$ consists of a finite number of eigenvalues $e_n$ of finite multiplicity. \item $\sigma_{\rm ess}(H_0(\lambda))= [\lambda^2(V_0+w),\infty)$. \item $\sigma(H(\lambda))=\sigma_{\rm ess}(H(\lambda))= [0,\infty)$. \item Singular continuous spectra $\sigma_c(H(\lambda))$ and $\sigma_c(H_0(\lambda))$ are empty. \end{enumerate} \end{lemma} \begin{proof} 1. Given any energy $E$ such that $V_0<E<V_0+w$, there is a finite set $\mathcal{E}_E$ of eigenvalues $e_n$ of $H_0$ such that \[ e_n<E\quad \text{for } |n|\leq N_E:=\operatorname{card}(\mathcal{E}_E). \] Moreover using a generalization of the Cwikel-Lieb-Rosenblum estimate \cite{OP}, one has the ``explicit" bound for $N_E$, namely \begin{equation} N_E\leq \frac{1}{g(1)}\int_0^{\infty}\int_X p(t;x,x)G(\lambda^2t(\widetilde{V}-E)_-) dV_g(x) \frac{dt}{t}, \label{CLR} \end{equation} where $G$ is any arbitrary non trivial convex function on $[0,\infty)$ polynomially bounded and such that $s\to s^{-1}G(s)$ is integrable near $0$, $g(1)$ is the Laplace transform of $s\to s^{-1}G(s)$ and $p(t;x,y)$ is the heat kernel for $\Delta_g$ defined by $e^{-t\Delta_g}f(x)=\int_X p(t;x,y)f(y) dV_g(y)$. As the integral is convergent, $N_E$ is finite. 2. It will be convenient to shift the potential to fix it at 0 at infinity. So we put $\widehat{V}(x):=\widetilde V(x)-\lambda^2(V_0+w)$ and the shifted comparison hamiltonian is then $\widehat H_0=-\frac{1}{2}\Delta_g+\widehat V$. After Step $1$. we know that $\sigma_{\rm ess}(\widehat H_0(\lambda))\cap (-\infty,0)=\emptyset$, so we have just to prove that $[0,\infty)\subset \sigma(\widehat H_0)$. We know that $\lambda\geq 0$ belongs to $\sigma(\widehat H_0)$ if and only if (Weyl's criterion) there is a sequence $\phi_n\in D(\widehat H_0),\ n\in {\mathbb N}^d$ such that \begin{equation} \lim_{n\to \infty}\ \frac{\|(\widehat H_0-\lambda I)\phi_n\|}{\| \phi_n\|}=0. \label{weyl} \end{equation} To construct such a sequence, one observes that \[ -\Delta_g e^{ik\cdot x} =(-ik_j\partial_i g^{ij}+k_ik_jg^{ij} -\frac{i}{2}\ k_j\partial_i(\log g) g^{ij} )e^{ik\cdot x}, \] so as $\widehat{V}(x)\to 0$ at infinity, \[ \lim_{|x|\to\infty}\big[ -\frac{1}{2}\Delta_g+\widehat V+ik_j\partial_i g^{ij}-k_ik_jg^{ij} +\frac{i}{2}\ k_j\partial_i(\log g) g^{ij}\big]e^{ik\cdot x}=0. \] Let us pick a cut off $\chi\in C^{\infty}_0(X)$ such that $\chi(x)\geq 0$, $\chi(x)=1$ for $|x|\leq 1/2$ and $\chi(x)=0$ for $|x|\geq 2$ and set $\chi_n(x):=\chi(|n|^{-1/2}(x-n))$ for $n\in {\mathbb Z}^d$. Of course $\operatorname{supp} \chi_n\subset\{ x\in X:\ |x-n|\leq|n|^{1/2}\}$ therefore \[ \lim_{|n|\to\infty} \sup_{x\in \operatorname{supp} \chi_n}|\widehat{V}|=0. \] It is easy to check that the sequence $\{\phi_n\}_n$ such that $\phi_n(x)=\chi_n(x)e^{ik\cdot x}$, with $k$ such that $\lambda=\sup_{x\in X}g^{ij}(x)k_ik_j$, satisfies \eqref{weyl}. 3. As $V> 0$, $\sigma_{pp}(H(\lambda)$ is empty after the Cwikel-Lieb-Rosenblum bound on the number of eigenvalues, moreover for $\sigma_{\rm ess}(H(\lambda))$ the same proof as that given in Step $2$. (with $w=0$) applies. 4. Let $H=H(\lambda)$ or $\widehat H_0(\lambda)$. After \cite[Theorem XIII.19]{ReSi} it is sufficient to show that for any interval $(\mu_1,\mu_2)\in \mathbb{R}_+$ the bound $\sup_{\varepsilon>0}\sup_{\mu \in (\mu_1,\mu_2)} | \langle f, \Im m (H-\mu-i\varepsilon)^{-1} f\rangle |\leq C(f)<\infty$ holds for $f$ in a dense set of $ L^2(X)$ but after the decay property (A2) assumed above for $g^{ij}$, for positive energies, this estimate follows from \cite[Proposition 1.1]{R} and for small non negative energies, after \cite[Theorem 12]{B2}. \end{proof} \begin{remark} \label{rmk1}\rm It can also be checked that embedded eigenvalues are absent from $\sigma_{\rm ess}(H(\lambda))$ and from $\sigma_{\rm ess}(H_0(\lambda))$. In fact after the decay properties (A2) and ($V_3$), one can directly use a result of Koch and Tataru \cite{KT} (indeed the original argument of \cite{KT} involving the hamiltonian ${ -\partial_j (g^{jk} \partial_k u)+V}$ extends without modification to $-\Delta_g u+Vu$). Namely, let us denote $L:=\frac{1}{2}\Delta_g$ and $V:=V_{\lambda}+E$ for a positive $E$. We assume that for a $\delta>0$ small enough: \[ \limsup_{|x|\to\infty} |x||Dg^{ij}(x)|\leq\delta,\quad \liminf_{|x|\to\infty}V>0, \quad \tau_0:=-\liminf_{|x|\to\infty}\frac{x\cdot\nabla V}{4V}<1/2. \] So supposing that $u\in H^1_{\rm loc}$ is a solution of $Lu+Vu=0$ with $|u|^{\tau_1-1/2}\in L^2$ for a $\tau_1>\tau_0$, we conclude from \cite[Theorem 12]{KT} that $u\equiv 0$, which of course excludes that $E$ is an eigenvalue. \end{remark} \subsection{Exponential decay of eigenfunctions of $H_0$} In the sequel, we use the simplified notation: $V$ for $V_{\lambda}$ and $\widetilde V$ for $\widetilde V_{\lambda}$. Following Agmon \cite{A} we denote by $\rho_A(x,y;V,E)$ the Agmon's distance in $X$ at energy $E>0$ corresponding to the potential $V$, associated to the Riemannian metric $ds^2=(V(x)-E)_+ g_{ij}(x)\,dx_i\,dx_j$, where $\{g_{ij}\}:=\{g^{ij}\}^{-1}$, given for any pair $x,y\in X$ by \begin{equation} \begin{aligned} &\rho_A(x,y;V,E)\\ &:= \inf_{\{\gamma\in AC[0,1]:\gamma(0)=x,\gamma(1)=y\} } \int_0^1 [ V(\gamma(t))-E)_+]^{1/2} [g_{ij}(\gamma(t)) \dot\gamma_i(t)\dot\gamma_j(t)]^{1/2}dt. \end{aligned} \label{agmonV} \end{equation} Assuming that the classically forbidden region $\mathcal{F}_V(E):=\{x\in X: V(x)>E\}$ at energy $E$ separates $X$ into two disjoint connected sets: the (bounded) well ${\mathcal W}_V(E)$ with boundary $S^-_V(E)$ and the (unbounded) exterior region $\mathcal{E}_V(E)$ with boundary $S^+_V(E)$, the associated distance from $S^-_V(E)$ to $S^+_V(E)$ is defined by \begin{equation} \rho_A(V;E)=\inf_{x\in S^-_V(E),y\in S^+_V(E)}\rho_A(x,y;V,E). \label{agV} \end{equation} Of course one defines as well the analogous quantities corresponding to the approximate potential $\widetilde V$, and in this case we will omit in the sequel the argument $\widetilde V$. Then we write $\rho_A(x,y;E)$ for $\rho_A(x,y;\widetilde V,E)$, ${\mathcal W}(E)$ for ${\mathcal W}_{\widetilde V}(E)$, $S^-(E)$ for $S^-_{\widetilde V}(E)$ and $\mathcal{F}(E)$ for $\mathcal{F}_{\widetilde V}(E)$. We also use the notation $\rho_A(x;V,E):=\rho_A(x,0; V,E)$. Suppose now that $n$ is such that the classically forbidden region $\mathcal{F}(e_n)$ at energy $e_n:=e_n(\lambda)\in\sigma(H_0)$ is not empty and that $\partial B(0,R)\subset \mathcal{F}(e_n)$ for any $\lambda$ large enough. \begin{theorem} \label{thm1} Suppose that $\psi$ is an eigenfunction of $H_0$ associated to the eigenvalue $e_n$and let $\varepsilon> 0$ be arbitrary small. There exists a constant $C_n>0$ independent of $\lambda$ such that for any $\lambda$ large enough, \[ \|e^{(1-\varepsilon)\rho_A(\cdot ;\widetilde V,e_n)}\ \psi\|_{L^2(X)}\leq C_n. \] \label{Agmon} \end{theorem} \begin{proof} As the proof can be easily adapted from Hislop-Sigal \cite{HS}, using complementary arguments of Agmon \cite{A} in the variable coefficient case (see also Helffer \cite{H}) we just sketch the main points. (1) The mapping $x\to\rho_A(x,y;\widetilde V,e_n)$ is locally Lipschitz continuous and then differentiable almost everywhere in each variable. Moreover at any point $x$ where it is differentiable, the Eikonal inequality holds $|(\nabla_g)_x\rho_A(x ,y;\widetilde V,e_n)|^2\leq (\widetilde V(x)-e_n)_+$, for any $y\in X$ and $e_n\in\sigma(H_0)$. Moreover the function $E\to\rho_A(x,y;\widetilde V,E)$ is increasing. (2) For any fixed $\epsilon,\delta>0$ small enough, let $E:=e_n$ and $f(x):=(1-\epsilon)\rho_A(x;\widetilde V,E)$ and let $\phi\in D(\widetilde V)\cap H^1(X)$ compactly supported in the set $ \mathcal{F}_{E<\delta}\equiv \{x\in X:\widetilde V(x)-E>\delta\}$. Then, using Step $1$, there exists a positive constant $\delta_1$ such that \begin{equation} \operatorname{Re} \langle e^f\phi,(H_0-E)e^{-f}\phi\rangle\geq \delta_1 \|\phi\|^2. \label{ineg1} \end{equation} (3) Let $\alpha>0$, $E:=e_n$ and $f_{\alpha}=f(1+\alpha f)^{-1}$ and let $\theta$ be a smooth bounded function such that $ |\nabla_g\theta|$ is compactly supported. Defining $\phi\equiv \theta e^{f_{\alpha}}\psi$, where $H_0\psi=E\psi$, one checks that \begin{equation} \operatorname{Re} \langle e^{f_{\alpha}}\phi,(H_0-E)e^{-f_{\alpha}}\phi\rangle = \langle \xi e^{2f_{\alpha}}\psi,\psi\rangle, \label{ineg2} \end{equation} where $\xi= |\nabla_g\theta|^2+2\theta \nabla_g\theta\cdot\nabla_g f_{\alpha}$. (4) Let us consider for $E:=e_n$ the sets $$ \mathcal{F}_{E,2\delta}:=\{x\in X : \widetilde V(x)-E>2\delta\}, \quad \mathcal{A}_{E,\delta}:=\{x\in X : \widetilde V(x)-E<\delta\}, $$ associated to $E\in \sigma_d(H_0)$ and let $\theta\in C^{\infty}(X)$ be such that \[ \theta(x)=\begin{cases} 1 & \text{if } x\in \mathcal{F}_{E,2\delta},\\ 0 & \text{if } x\in \mathcal{A}_{E,\delta}. \end{cases} \] After the construction of $\widetilde V$, $\nabla_g\theta$ is compactly supported. Let $f=(1-\epsilon)\rho_A(E)$ and $f_{\alpha}=f(1+\alpha f)^{-1}$ as before. Then $\phi=\theta e^{f_{\alpha}}\psi$ meets the hypotheses of Step 2. so using \eqref{ineg1} there exists a positive $\delta_1$ such that \begin{equation} \delta_1 \|\phi\|^2 \leq \operatorname{Re} \langle e^{f_{\alpha}}\phi,(H_0-E)e^{-f_{\alpha}}\phi\rangle \leq |\langle \xi e^{f_{\alpha}}\psi,\psi\rangle| \leq \sup_{x\in \operatorname{supp} |\nabla_g\theta|}|\xi e^{2f_{\alpha}}|\|\psi\|^2, \label{IN} \end{equation} where we used \eqref{ineg2}. As $\nabla_g\theta$ is compactly supported, we can take $\alpha=0$ in the right hand side of \eqref{IN}. If $f_0\equiv \sup_{x\in \operatorname{supp} |\nabla_g\theta|}|f(x)|$ and for a normalized $\psi$ \begin{equation} \|e^{f_{\alpha}}\theta\psi\|^2\leq C, \label{IN2} \end{equation} for a $C>0$ independent of $\alpha$. So we can take $\alpha=0$ in the left hand side of \eqref{IN2}. Now as $S_{\delta}:=\operatorname{supp} |\nabla_g\theta|\cup \overline{\mathcal{A}}_{E,\delta}$ is compact, $e^{2f(x)}$ is bounded on this set and $\int_S e^{2f}|\psi|^2\,dV_g(x)<\infty$. Then finally there exists $C_{\varepsilon,n}\in (0,\infty)$ such that \begin{align*} &\int e^{2(1-\epsilon)\rho_A(x,E)}|\psi(x)|^2\,dV_g(x)\\ &=\int_{ \{x:\theta(x)=1\}} e^{2f}|\psi(x)|^2\,dV_g(x) + \int_{S_{\delta}} e^{2f}|\psi(x)|^2\,dV_g(x) \leq C_{\varepsilon,n}, \end{align*} which completes the proof by taking the best constant $C_{\varepsilon,n}$. \end{proof} \section{Lifetime of a quasi-localized state}\label{lt} In the sequel, we note $H$ and $H_0$ for $H({\lambda})$ and $H_0(\lambda)$. After Lemma \ref{lem1}, given any energy $E$ such that $V_0<E<V_0+w$, there is a finite set $\mathcal{E}_E$ of eigenvalues $e_n$ of $H_0$ such that $e_n<E$ for $|n|\leq N_E:=\operatorname{card}(\mathcal{E}_E)$. Denoting by $\psi_n$ the associated eigenfunctions and ${\mathcal H}_E$ the subspace of ${\mathcal H}$ spanned by the set $\{\psi_n;|n|<N_E\}$, let us define a closed complex contour $\gamma_E\in \mathbb{C}$ such that its interior $\Delta_E$ contains the discrete set $\sigma_0\cap [0,E]$ where $\sigma_0$ is the spectrum of $H_0$, and such that the distance from $\gamma_E$ to $\sigma_0$ satisfies \begin{equation} \operatorname{dist}(\gamma_E,\sigma_0):=\delta_E=\frac{1}{2} \min_{|n|,|n'|\leq N_E}|e_n-e_{n'}|>0. \label{dE} \end{equation} The spectral projector of $H_0$ on the subspace ${\mathcal H}_E$ is the Riesz integral \begin{equation} P_{\lambda,E}=\frac{1}{2\pi i}\int_{\gamma_E}(z-H_0)^{-1}dz, \label{proj} \end{equation} with $\operatorname{tr}(P_{\lambda,E})=N_E$. \begin{lemma} \label{lem2} For any $\phi\in \operatorname{Ran}( P_{\lambda,E})$ there exists a real positive constant $C_{E}$ such that \begin{equation} \|e^{(1-\varepsilon)\rho_A(\cdot;\widetilde V,e_N)}\phi\|_{L^2(X)} \leq C_{E}\|\phi\|_{L^2(X)}. \label{asym} \end{equation} \end{lemma} \begin{proof} Let $\Phi_E(x):= e^{(1-\varepsilon)\rho_A(\cdot;\widetilde V,e_N)}$ and $\phi\in{\mathcal H}_E$ with ${ \phi:=\sum_{n=1}^{N_E}\lambda_n\psi_n}$. One has \begin{align*} \int_X |\Phi_E\phi|^2dV_g(x) &=\int_X |\Phi_E|^2|\sum_{n=1}^{N_E}\lambda_n\psi_n|^2dV_g(x)\\ &\leq \|\phi\|_{L^2(X)}^2\int_X |\Phi_E|^2\sum_{n=1}^{N_E}|\psi_n|^2\,dV_g(x), \end{align*} and \eqref{asym} follows from Theorem \ref{thm1}. \end{proof} Recall that the density operator $\rho_t$ associated to $H$ is solution of the Liouville equation $i\lambda\partial_t\rho_t=[H,\rho_t]$ with $\rho_t|_{t=0}=\rho_0$. Our main result is the following. \begin{theorem} \label{thm2} Suppose that $P_{\lambda,E}$ is the projector defined by \eqref{proj} and suppose that we prepare the initial density operator $\rho_0$ of the system according \[ \operatorname{tr}(\rho_0P_{\lambda,E})\geq (1-\boldsymbol{\epsilon})^2, \] for a small $\boldsymbol{\epsilon}>0$. Then the probability $p_t:=\operatorname{tr}(\rho_tP_{\lambda,E})$ for the density operator $\rho_t$ to remain in the range of the projector $P_{\lambda,E}$ is bounded as follows \begin{equation} \sin_*^2\big(\frac{\pi}{2}-\sqrt{2\boldsymbol{\epsilon}}-\frac{t}{\tau}\big) \leq p_t \leq \sin_*^2 \big( \frac{\pi}{2}-\sqrt{\frac{\boldsymbol{\epsilon}}{2}}+\frac{t}{\tau}\big), \label{ineq} \end{equation} where $\sin_*$ is defined by \eqref{sin*} and $\tau$ is a positive constant given by \begin{equation} \tau=\sqrt{2}\lambda_E^{-1/2} e^{(1-\varepsilon)\rho_A(V;e_N)}, \label{tau} \end{equation} with $\lambda_E=C_{E}^2(V_0+w)\lambda^4$. \end{theorem} \begin{remark} \rm In other words the result reads as follows: a state prepared at $t=0$ in a state well localized in the potential well, does not escape from it with high probability $p_t$ for any time $t$ such that $t\ll \tau$. Namely as $\epsilon$ is small, the lower and upper bounds are near to $1$ provided that the ratio $\frac{t}{\tau}$ is small. \end{remark} \begin{proof}[Proof of Theorem \ref{thm2}] It relies on a generalized time-energy uncertainty relation due to Pfeifer and Fr\"ohlich (see Proposition \ref{propA.1}). Let us consider the unitary groups $U_t:=e^{-i\lambda t H}$ and $U^{(0)}_t:=e^{-i\lambda t H_0}$ together with the projector $\bar P_t:={U^{(0)}_t}^*P_{\lambda,E}U^{(0)}_t\equiv P_{\lambda,E}$ and the conjugate dynamics \[ \bar H_t:={U^{(0)}_t}^*[H-i\lambda\partial_t]U^{(0)}_t ={U^{(0)}_t}^*(H-H_{0} )U^{(0)}_t={U^{(0)}_t}^* W_{\lambda}U^{(0)}_t. \] From Proposition \ref{propA.1} in the Appendix , taking $R=P_{\lambda,E}=P_{\lambda,E}^*=P_{\lambda,E}^2$ in \eqref{fRA}, we obtain \[ f(\bar P_t,\bar H_s) =f\big( {U^{(1)}_{t-s}}^*P_{\lambda,E}{U^{(1)}_{t-s}}\ ,W_{\lambda}\big) =f(P_{\lambda,E},W_{\lambda}), \] and using cyclicity of the trace in \eqref{fRA} we end with \begin{equation} f^2(P_{\lambda,E},W_{\lambda}) =\frac{1}{2}\ \operatorname{tr}(-[P_{\lambda,E}\ ,W_{\lambda}]^2). \label{trace} \end{equation} Denoting by $K_{\lambda,E}(x,y)$ the kernel of the operator $P_{\lambda,E}$ in $L^2(X)$, we first observe after \eqref{asym} that \begin{equation} \int_{X\times X}|K_{\lambda,E}(x,y)|^2 \Phi^2_E(x)\Phi^2_E(y)\,dV_g(x)\,dV_g(y)\leq C_E^2, \label{asymbis} \end{equation} for a constant $C_E$. We compute the trace in \eqref{trace} as follows \begin{equation} \begin{aligned} &\frac{1}{2}\ \operatorname{tr}(-[P_{\lambda,E}\ ,W_{\lambda}]^2)\\ &=\frac{1}{4} \int_{X\times X} |K_{\lambda,E}(x,y)[W_{\lambda}(x)-W_{\lambda}(y)] |^2dV_g(x)\,dV_g(y) \\ &\leq \int_{X\times X} |K_{\lambda,E}(x,y)|^2 \Phi^2_E(x)\Phi^2_E(y) e^{-2(1-\varepsilon)(\rho_A(x;\widetilde V,e_N)+\rho_A(y;\widetilde V,e_N))}\\ &\quad\times [W_{\lambda}(x)-W_{\lambda}(y)]^2\,dV_g(x)\,dV_g(y). \end{aligned} \label{rhs} \end{equation} Using \eqref{asymbis} and \eqref{asym} we can bound the integral in the right-hand side of \eqref{rhs} and we end with \begin{equation} \operatorname{tr}(-[P_{\lambda,E}\ ,W_{\lambda}]^2) \leq \lambda_E e^{-2(1-\varepsilon)\rho_A(V,e_N)}, \label{trace3} \end{equation} for a positive constant $\lambda_E=C_E^2(V_0+w)^2\lambda^4$. Defining now $\rho_t:=U_t\rho_0U_t^*$ and $p_t:=\operatorname{tr}(\rho_tP_{\lambda,E})$, we are in position to apply the second result of Pfeifer and Fr\"ohlich (see Propostion \ref{propA.2}). Let $U_t$ and $U_t^{(1)}$ be the unitary groups defined above and given by \[ U_t:=e^{-i\lambda t H},\quad U^{(0)}_t:=e^{-i\lambda t H_0}, \] together with the projector \[ \bar P_t:={U^{(0)}_t}^*P_{\lambda,E}U^{(0)}_t\equiv P_{\lambda,E}. \] Consider the conjugate dynamics \[ \bar H_t:={U^{(0)}_t}^*[H-i\lambda\partial_t]U^{(0)}_t ={U^{(0)}_t}^*(H-H_{0} )U^{(0)}_t. \] Then we have the bounds from above and from below for the probability $p_t$, \begin{align*} &\sin_*^2 \Big( \arcsin\sqrt{\operatorname{tr}(\bar P_{\lambda,E}\rho_0)} -\min\Big\{\int_0^t f(\bar P_{\lambda,E},\bar H_s)\,ds, \int_0^t f(\rho_0,\bar H_s)\,ds\Big\}\Big)\\ &\leq p_t\\ &\leq \sin_*^2\Big(\arcsin \sqrt{\operatorname{tr}(\bar P_{\lambda,E})\rho_0} +\min\Big\{\int_0^t f(\bar P_{\lambda,E},\bar H_s)\,ds, \int_0^t f(\rho_0,\bar H_s)\,ds\Big\}\Big), \end{align*} where $f(R,A)$ is defined by \eqref{fRA} and the continuous function $\sin_*$ is defined by \eqref{sin*}. Supposing that we prepare the initial density according $\operatorname{tr}(\rho_0P_{\lambda,E})\geq (1-\boldsymbol{\epsilon})^2$ for a small $\boldsymbol{\epsilon}>0$, we obtain the estimate \begin{align*} &\sin_*^2 \Big(\arcsin(1-\boldsymbol{\epsilon}) -\int_0^t f( P_{\lambda,E},\bar H_s)\,ds \Big)\\ &\leq p_t \leq \sin_*^2 \Big(\arcsin(1-\boldsymbol{\epsilon}) +\int_0^t f( P_{\lambda,E},\bar H_s)\,ds\Big). \end{align*} After \eqref{trace} and \eqref{trace3} we see that $0\leq f( P_{\lambda,E},\bar H_s)\leq \frac{\lambda_E^{1/2}}{\sqrt{2}} e^{-(1-\varepsilon)\rho_A(V,e_N)}$, and that $\frac{\pi}{2}-\sqrt{2\boldsymbol{\epsilon}} \leq \arcsin(1-\varepsilon) \leq \frac{\pi}{2}-\sqrt{\frac{\boldsymbol{\epsilon}}{2}}$, so we obtain \eqref{ineq} and we conclude that the density operator $\rho_t$ of the system remains in the range of the projector $P_{\lambda,E}$ with probability $p_t$ for all times $t\ll \tau$ where $\tau$ is given by \eqref{tau}. \end{proof} \begin{remark} \label{rmk2} \rm To recover formula \eqref{LT}, we observe that $V$ and $e_n$ are of order $\lambda^2$ so we see that ${ \rho_A(V,e_N):= \lambda (1-\varepsilon)b}$ with (see \ref{agV}) \begin{align*} b&:= \inf_{x\in S^-_V(E),y\in S^+_V(E)} \Big(\inf_{\{\gamma\in AC[0,1]:\gamma(0)=x,\gamma(1)=y\} } \int_0^1 \Big[ \Big(\frac{V(\gamma(t))}{\lambda^2} -\frac{e_N}{\lambda^2}\Big)_+\Big]^{1/2} \\ &\quad\times [g_{ij}(\gamma(t)) \dot\gamma_i(t)\dot\gamma_j(t)]^{1/2}dt\Big). \end{align*} Then the lifetime $\tau$ is as expected of the form \eqref{LT} with computable constants $\lambda=\frac{1}{\hbar}$, $B=(1-\varepsilon)b$ and $A=\sqrt{2}\lambda_E^{-1/2}$. \end{remark} \section{Appendix: Uncertainty relations after Pfeifer and Fr\"ohlich \cite{PF}} \label{appB} The first result is an uncertainty relation for subspaces and the second one is a generalized time-energy uncertainty relation. Both of them are proved in \cite{PF}. \begin{proposition} \label{propA.1} For a positive operator $R$ with pure point spectrum with eigenvalues $\{\lambda_n\}_{n=1,\dots ,N}$ and eigenprojectors $\{P_n\}_{n=1,\dots ,N}$, and for two selfadjoint operators $A$ and $B$, let us define the function $f$ by \begin{equation} f(R,A)=\Big(\sum_{n=1}^N \lambda_n \operatorname{tr}(P_nA^2-P_nAP_nA)\Big)^{1/2}. \label{fRA} \end{equation} Then \[ |\operatorname{tr}(R[A,B])|^2\leq 4f^2(R,A)f^2(R,B). \] \end{proposition} \begin{proposition} \label{propA.2} Let $U_{t,s}$ be the unitary group defining the evolution from time $s$ to $t$ for a system described by the (possibly $t$-dependent) Hamiltonian $H_t$, solution of the equation \begin{equation} U_{t,s}=1-\frac{i}{\hbar}\int_s^t H_\tau U_{\tau,s}\,d\tau, \label{eqU} \end{equation} for all $s,t\in \mathbb{R}$. Let $\rho_0$ an initial density operator and $P$ a projector. Define \begin{equation} \rho_{t,s}:= U_{t,s}\rho_0U^*_{t,s},\quad p_{t,s}:= \operatorname{tr} (P\rho_{t,s}). \label{eqro} \end{equation} Then we have the following bounds from above and from below for the probability $p_t=\operatorname{tr}(\rho_t P)$, \begin{equation} \begin{aligned} &\sin_*^2\Big(\arcsin\sqrt{\operatorname{tr}( P\rho_0)} -\hbar^{-1}\min\Big\{\int_s^t f( P, H_\tau)\,d\tau,\int_s^t f(\rho_0, H_\tau) \,d\tau\Big\}\Big) \\ &\leq p_{t,s} \\ &\leq \sin_*^2 \Big( \arcsin\sqrt{\operatorname{tr}( P\rho_0)} +\hbar^{-1}\min\Big\{\int_s^t f( P, H_\tau)\,d\tau, \int_s^t f(\rho_0, H_\tau)\,d\tau\Big\} \Big), \end{aligned} \label{Llbound} \end{equation} where $f$ is defined for any $A$ self-adjoint by $f(P,A)=\sqrt{\operatorname{tr}(PA^*(1-P)A)}$ and the continuous function $\sin_*:\mathbb{R}\to\mathbb{R}_+$ is given by \begin{equation} \sin_*(x) = \begin{cases} 0 &\text{if } x<0,\\ \sin(x) &\text{if } 0\leq x\leq \frac{\pi}{2},\\ 1 &\text{if } x>\frac{\pi}{2}. \end{cases} \label{sin*} \end{equation} \end{proposition} \subsection*{Acknowledgements} The author would like to express his warm thanks to F. 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\set@arabfont \test@token }% \putwordb@x {#1}\a@spacetrue \vfootnote {#1}} %%%%%%%%%%%%%%%%%% \marginpar in an arabic environment %%%%%%%%%%%%%%% \def \a@c@marginpar {% for Arabic environments only \setbox0 \vtop \bgroup \unarab@codes \a@@marginpar } \long \def \a@@marginpar #1{% get text of note \hsize \marginparwidth \parskip 0pt \raggedright \noindent \rm \strut #1\vss \egroup \dp0 \z@ \setbox\lineb@x \hbox {\unhbox\lineb@x \rlap {\hskip \marginparsep \box0 \hss }}\test@token } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \all@w@ne \settrans \def \a@c@tracingmacros {\afterassignment \test@token \tracingmacros=} \def \a@c@test #1{\csname test@#1true\endcsname \test@token } \def \a@c@untest #1{\csname test@#1false\endcsname \test@token } \a@spec@def \<{\a@get@ins } \def \a@get@ins #1>{\test@token #1 } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \endinput %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EOF %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\begin{PROFILE} \HavePortraittrue% \DEF{所属}{\所属P{120481}{University Hospital 先端医療開発研究プロジェクト }\所属S{148006}{University Hospital Clinical Division Department of Ophthalmology, Otolaryngology, Dermatology, Orthopedics, and Plastic Surgery Orthopedic Surgery }\所属S{201840}{Faculty of Medicine School of Medicine Course of Pathologic Medicine for Senso-motoric System Orthopedics }}% \DEF{EID}{346379}% \DEF{肩書}{Assistant Professor}% \DEF{名前}{Toki, Shun-ichi}% \DEF{名前:日}{土岐 俊一}% \DEF{名前:読}{とき しゅんいち}% \DEF{名前:英}{Toki, Shun-ichi}% \DEF{職名}{Assistant Professor}% \DEF{性別}{Male}% \DEF{生年}{1983}% \DEF{電話}{{\NONE}}% \DEF{電子メール}{{\NONE}}% \DEF{学歴}{% {\NONE}}% \DEF{学位}{学士 (日本大学)}% \DEF{職歴}{% \履歴{2018.{\EdbZSp}10.}{Designated Assistant Professor at Tokushima University, Institute of Biomedical Sciences (-2019.12.)}% % \履歴{2020.{\EdbZSp}1.}{Assistant Professor at Tokushima University, University Hospital}% % }% \DEF{担当授業科目}{% \BULLET{}{\bfseries Orthopedics} (Bachelor Course) % }% \DEF{専門分野}{% {\NONE}}% \DEF{研究概要}{% {\NONE}}% \DEF{著書・論文:数}{% \著作件数{Academic Paper (Judged Full Paper)}{5}\著作件数{Proceeding of Domestic Conference}{4}}% \DEF{著書・論文}{% }% \DEF{所属学会(役職):数}{0}% \DEF{社会・学内活動等:数}{0}% \DEF{受賞等:数}{2}% \DEF{所属学会(役職)}{% {\NONE}}% \DEF{社会・学内活動等}{% {\NONE}}% \DEF{受賞等}{\BULLET{}\年月{2018.{\EdbZSp}7.} 第51回日本整形外科学会骨・軟部腫瘍外科学会(2018年7月12日-13日):優秀ポスター賞 % \BULLET{}\年月{2019.{\EdbZSp}3.} 徳島大学:優秀大学院表彰 % }% \end{PROFILE} \endinput

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% IEEEtran howto: % http://ftp.univie.ac.at/packages/tex/macros/latex/contrib/IEEEtran/IEEEtran_HOWTO.pdf \documentclass[9pt,technote,a4paper]{IEEEtran} \usepackage[T1]{fontenc} % required for luximono! \usepackage[scaled=0.8]{inconsolata} % typewriter font with bold face % To install the luximono font files: % getnonfreefonts-sys --all or % getnonfreefonts-sys luximono % % when there are trouble you might need to: % - Create /etc/texmf/updmap.d/99local-luximono.cfg % containing the single line: Map ul9.map % - Run update-updmap followed by mktexlsr and updmap-sys % % This commands must be executed as root with a root environment % (i.e. run "sudo su" and then execute the commands in the root % shell, don't just prefix the commands with "sudo"). \usepackage[unicode,bookmarks=false]{hyperref} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{units} \usepackage{nicefrac} \usepackage{eurosym} \usepackage{graphicx} \usepackage{verbatim} \usepackage{algpseudocode} \usepackage{scalefnt} \usepackage{xspace} \usepackage{color} \usepackage{colortbl} \usepackage{multirow} \usepackage{hhline} \usepackage{listings} \usepackage{float} \usepackage{tikz} \usetikzlibrary{calc} \usetikzlibrary{arrows} \usetikzlibrary{scopes} \usetikzlibrary{through} \usetikzlibrary{shapes.geometric} \def\FIXME{{\color{red}\bf FIXME}} \lstset{basicstyle=\ttfamily,frame=trBL,xleftmargin=0.7cm,xrightmargin=0.2cm,numbers=left} \begin{document} \title{Yosys Application Note 011: \\ Interactive Design Investigation} \author{Clifford Wolf \\ Original Version December 2013} \maketitle \begin{abstract} Yosys \cite{yosys} can be a great environment for building custom synthesis flows. It can also be an excellent tool for teaching and learning Verilog based RTL synthesis. In both applications it is of great importance to be able to analyze the designs it produces easily. This Yosys application note covers the generation of circuit diagrams with the Yosys {\tt show} command, the selection of interesting parts of the circuit using the {\tt select} command, and briefly discusses advanced investigation commands for evaluating circuits and solving SAT problems. \end{abstract} \section{Installation and Prerequisites} This Application Note is based on the Yosys \cite{yosys} GIT Rev. {\tt 2b90ba1} from 2013-12-08. The {\tt README} file covers how to install Yosys. The {\tt show} command requires a working installation of GraphViz \cite{graphviz} and \cite{xdot} for generating the actual circuit diagrams. \section{Overview} This application note is structured as follows: Sec.~\ref{intro_show} introduces the {\tt show} command and explains the symbols used in the circuit diagrams generated by it. Sec.~\ref{navigate} introduces additional commands used to navigate in the design, select portions of the design, and print additional information on the elements in the design that are not contained in the circuit diagrams. Sec.~\ref{poke} introduces commands to evaluate the design and solve SAT problems within the design. Sec.~\ref{conclusion} concludes the document and summarizes the key points. \section{Introduction to the {\tt show} command} \label{intro_show} \begin{figure}[b] \begin{lstlisting} $ cat example.ys read_verilog example.v show -pause proc show -pause opt show -pause $ cat example.v module example(input clk, a, b, c, output reg [1:0] y); always @(posedge clk) if (c) y <= c ? a + b : 2'd0; endmodule \end{lstlisting} \caption{Yosys script with {\tt show} commands and example design} \label{example_src} \end{figure} \begin{figure}[b!] \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/example_00.pdf} \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/example_01.pdf} \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/example_02.pdf} \caption{Output of the three {\tt show} commands from Fig.~\ref{example_src}} \label{example_out} \end{figure} The {\tt show} command generates a circuit diagram for the design in its current state. Various options can be used to change the appearance of the circuit diagram, set the name and format for the output file, and so forth. When called without any special options, it saves the circuit diagram in a temporary file and launches {\tt xdot} to display the diagram. Subsequent calls to {\tt show} re-use the {\tt xdot} instance (if still running). \subsection{A simple circuit} Fig.~\ref{example_src} shows a simple synthesis script and a Verilog file that demonstrate the usage of {\tt show} in a simple setting. Note that {\tt show} is called with the {\tt -pause} option, that halts execution of the Yosys script until the user presses the Enter key. The {\tt show -pause} command also allows the user to enter an interactive shell to further investigate the circuit before continuing synthesis. So this script, when executed, will show the design after each of the three synthesis commands. The generated circuit diagrams are shown in Fig.~\ref{example_out}. The first diagram (from top to bottom) shows the design directly after being read by the Verilog front-end. Input and output ports are displayed as octagonal shapes. Cells are displayed as rectangles with inputs on the left and outputs on the right side. The cell labels are two lines long: The first line contains a unique identifier for the cell and the second line contains the cell type. Internal cell types are prefixed with a dollar sign. The Yosys manual contains a chapter on the internal cell library used in Yosys. Constants are shown as ellipses with the constant value as label. The syntax {\tt <bit\_width>'<bits>} is used for for constants that are not 32-bit wide and/or contain bits that are not 0 or 1 (i.e. {\tt x} or {\tt z}). Ordinary 32-bit constants are written using decimal numbers. Single-bit signals are shown as thin arrows pointing from the driver to the load. Signals that are multiple bits wide are shown as think arrows. Finally {\it processes\/} are shown in boxes with round corners. Processes are Yosys' internal representation of the decision-trees and synchronization events modelled in a Verilog {\tt always}-block. The label reads {\tt PROC} followed by a unique identifier in the first line and contains the source code location of the original {\tt always}-block in the 2nd line. Note how the multiplexer from the {\tt ?:}-expression is represented as a {\tt \$mux} cell but the multiplexer from the {\tt if}-statement is yet still hidden within the process. \medskip The {\tt proc} command transforms the process from the first diagram into a multiplexer and a d-type flip-flip, which brings us to the 2nd diagram. The Rhombus shape to the right is a dangling wire. (Wire nodes are only shown if they are dangling or have ``public'' names, for example names assigned from the Verilog input.) Also note that the design now contains two instances of a {\tt BUF}-node. This are artefacts left behind by the {\tt proc}-command. It is quite usual to see such artefacts after calling commands that perform changes in the design, as most commands only care about doing the transformation in the least complicated way, not about cleaning up after them. The next call to {\tt clean} (or {\tt opt}, which includes {\tt clean} as one of its operations) will clean up this artefacts. This operation is so common in Yosys scripts that it can simply be abbreviated with the {\tt ;;} token, which doubles as separator for commands. Unless one wants to specifically analyze this artefacts left behind some operations, it is therefore recommended to always call {\tt clean} before calling {\tt show}. \medskip In this script we directly call {\tt opt} as next step, which finally leads us to the 3rd diagram in Fig.~\ref{example_out}. Here we see that the {\tt opt} command not only has removed the artifacts left behind by {\tt proc}, but also determined correctly that it can remove the first {\tt \$mux} cell without changing the behavior of the circuit. \begin{figure}[b!] \includegraphics[width=\linewidth,trim=0 2cm 0 0]{APPNOTE_011_Design_Investigation/splice.pdf} \caption{Output of {\tt yosys -p 'proc; opt; show' splice.v}} \label{splice_dia} \end{figure} \begin{figure}[b!] \lstinputlisting{APPNOTE_011_Design_Investigation/splice.v} \caption{\tt splice.v} \label{splice_src} \end{figure} \begin{figure}[t!] \includegraphics[height=\linewidth]{APPNOTE_011_Design_Investigation/cmos_00.pdf} \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/cmos_01.pdf} \caption{Effects of {\tt splitnets} command and of providing a cell library. (The circuit is a half-adder built from simple CMOS gates.)} \label{splitnets_libfile} \end{figure} \subsection{Break-out boxes for signal vectors} As has been indicated by the last example, Yosys is can manage signal vectors (aka. multi-bit wires or buses) as native objects. This provides great advantages when analyzing circuits that operate on wide integers. But it also introduces some additional complexity when the individual bits of of a signal vector are accessed. The example show in Fig.~\ref{splice_dia} and \ref{splice_src} demonstrates how such circuits are visualized by the {\tt show} command. The key elements in understanding this circuit diagram are of course the boxes with round corners and rows labeled {\tt <MSB\_LEFT>:<LSB\_LEFT> -- <MSB\_RIGHT>:<LSB\_RIGHT>}. Each of this boxes has one signal per row on one side and a common signal for all rows on the other side. The {\tt <MSB>:<LSB>} tuples specify which bits of the signals are broken out and connected. So the top row of the box connecting the signals {\tt a} and {\tt x} indicates that the bit 0 (i.e. the range 0:0) from signal {\tt a} is connected to bit 1 (i.e. the range 1:1) of signal {\tt x}. Lines connecting such boxes together and lines connecting such boxes to cell ports have a slightly different look to emphasise that they are not actual signal wires but a necessity of the graphical representation. This distinction seems like a technicality, until one wants to debug a problem related to the way Yosys internally represents signal vectors, for example when writing custom Yosys commands. \subsection{Gate level netlists} Finally Fig.~\ref{splitnets_libfile} shows two common pitfalls when working with designs mapped to a cell library. The top figure has two problems: First Yosys did not have access to the cell library when this diagram was generated, resulting in all cell ports defaulting to being inputs. This is why all ports are drawn on the left side the cells are awkwardly arranged in a large column. Secondly the two-bit vector {\tt y} requires breakout-boxes for its individual bits, resulting in an unnecessary complex diagram. For the 2nd diagram Yosys has been given a description of the cell library as Verilog file containing blackbox modules. There are two ways to load cell descriptions into Yosys: First the Verilog file for the cell library can be passed directly to the {\tt show} command using the {\tt -lib <filename>} option. Secondly it is possible to load cell libraries into the design with the {\tt read\_verilog -lib <filename>} command. The 2nd method has the great advantage that the library only needs to be loaded once and can then be used in all subsequent calls to the {\tt show} command. In addition to that, the 2nd diagram was generated after {\tt splitnet -ports} was run on the design. This command splits all signal vectors into individual signal bits, which is often desirable when looking at gate-level circuits. The {\tt -ports} option is required to also split module ports. Per default the command only operates on interior signals. \subsection{Miscellaneous notes} Per default the {\tt show} command outputs a temporary {\tt dot} file and launches {\tt xdot} to display it. The options {\tt -format}, {\tt -viewer} and {\tt -prefix} can be used to change format, viewer and filename prefix. Note that the {\tt pdf} and {\tt ps} format are the only formats that support plotting multiple modules in one run. In densely connected circuits it is sometimes hard to keep track of the individual signal wires. For this cases it can be useful to call {\tt show} with the {\tt -colors <integer>} argument, which randomly assigns colors to the nets. The integer (> 0) is used as seed value for the random color assignments. Sometimes it is necessary it try some values to find an assignment of colors that looks good. The command {\tt help show} prints a complete listing of all options supported by the {\tt show} command. \section{Navigating the design} \label{navigate} Plotting circuit diagrams for entire modules in the design brings us only helps in simple cases. For complex modules the generated circuit diagrams are just stupidly big and are no help at all. In such cases one first has to select the relevant portions of the circuit. In addition to {\it what\/} to display one also needs to carefully decide {\it when\/} to display it, with respect to the synthesis flow. In general it is a good idea to troubleshoot a circuit in the earliest state in which a problem can be reproduced. So if, for example, the internal state before calling the {\tt techmap} command already fails to verify, it is better to troubleshoot the coarse-grain version of the circuit before {\tt techmap} than the gate-level circuit after {\tt techmap}. \medskip Note: It is generally recommended to verify the internal state of a design by writing it to a Verilog file using {\tt write\_verilog -noexpr} and using the simulation models from {\tt simlib.v} and {\tt simcells.v} from the Yosys data directory (as printed by {\tt yosys-config -{}-datdir}). \subsection{Interactive Navigation} \begin{figure} \begin{lstlisting} yosys> ls 1 modules: example yosys> cd example yosys [example]> ls 7 wires: $0\y[1:0] $add$example.v:5$2_Y a b c clk y 3 cells: $add$example.v:5$2 $procdff$7 $procmux$5 \end{lstlisting} \caption{Demonstration of {\tt ls} and {\tt cd} using {\tt example.v} from Fig.~\ref{example_src}} \label{lscd} \end{figure} \begin{figure}[b] \begin{lstlisting} attribute \src "example.v:5" cell $add $add$example.v:5$2 parameter \A_SIGNED 0 parameter \A_WIDTH 1 parameter \B_SIGNED 0 parameter \B_WIDTH 1 parameter \Y_WIDTH 2 connect \A \a connect \B \b connect \Y $add$example.v:5$2_Y end \end{lstlisting} \caption{Output of {\tt dump \$2} using the design from Fig.~\ref{example_src} and Fig.~\ref{example_out}} \label{dump2} \end{figure} Once the right state within the synthesis flow for debugging the circuit has been identified, it is recommended to simply add the {\tt shell} command to the matching place in the synthesis script. This command will stop the synthesis at the specified moment and go to shell mode, where the user can interactively enter commands. For most cases, the shell will start with the whole design selected (i.e. when the synthesis script does not already narrow the selection). The command {\tt ls} can now be used to create a list of all modules. The command {\tt cd} can be used to switch to one of the modules (type {\tt cd ..} to switch back). Now the {\tt ls} command lists the objects within that module. Fig.~\ref{lscd} demonstrates this using the design from Fig.~\ref{example_src}. There is a thing to note in Fig.~\ref{lscd}: We can see that the cell names from Fig.~\ref{example_out} are just abbreviations of the actual cell names, namely the part after the last dollar-sign. Most auto-generated names (the ones starting with a dollar sign) are rather long and contains some additional information on the origin of the named object. But in most cases those names can simply be abbreviated using the last part. Usually all interactive work is done with one module selected using the {\tt cd} command. But it is also possible to work from the design-context ({\tt cd ..}). In this case all object names must be prefixed with {\tt <module\_name>/}. For example {\tt a*/b*} would refer to all objects whose names start with {\tt b} from all modules whose names start with {\tt a}. The {\tt dump} command can be used to print all information about an object. For example {\tt dump \$2} will print Fig.~\ref{dump2}. This can for example be useful to determine the names of nets connected to cells, as the net-names are usually suppressed in the circuit diagram if they are auto-generated. For the remainder of this document we will assume that the commands are run from module-context and not design-context. \subsection{Working with selections} \begin{figure}[t] \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/example_03.pdf} \caption{Output of {\tt show} after {\tt select \$2} or {\tt select t:\$add} (see also Fig.~\ref{example_out})} \label{seladd} \end{figure} When a module is selected using the {\tt cd} command, all commands (with a few exceptions, such as the {\tt read\_*} and {\tt write\_*} commands) operate only on the selected module. This can also be useful for synthesis scripts where different synthesis strategies should be applied to different modules in the design. But for most interactive work we want to further narrow the set of selected objects. This can be done using the {\tt select} command. For example, if the command {\tt select \$2} is executed, a subsequent {\tt show} command will yield the diagram shown in Fig.~\ref{seladd}. Note that the nets are now displayed in ellipses. This indicates that they are not selected, but only shown because the diagram contains a cell that is connected to the net. This of course makes no difference for the circuit that is shown, but it can be a useful information when manipulating selections. Objects can not only be selected by their name but also by other properties. For example {\tt select t:\$add} will select all cells of type {\tt \$add}. In this case this is also yields the diagram shown in Fig.~\ref{seladd}. \begin{figure}[b] \lstinputlisting{APPNOTE_011_Design_Investigation/foobaraddsub.v} \caption{Test module for operations on selections} \label{foobaraddsub} \end{figure} The output of {\tt help select} contains a complete syntax reference for matching different properties. Many commands can operate on explicit selections. For example the command {\tt dump t:\$add} will print information on all {\tt \$add} cells in the active module. Whenever a command has {\tt [selection]} as last argument in its usage help, this means that it will use the engine behind the {\tt select} command to evaluate additional arguments and use the resulting selection instead of the selection created by the last {\tt select} command. Normally the {\tt select} command overwrites a previous selection. The commands {\tt select -add} and {\tt select -del} can be used to add or remove objects from the current selection. The command {\tt select -clear} can be used to reset the selection to the default, which is a complete selection of everything in the current module. \subsection{Operations on selections} \begin{figure}[t] \lstinputlisting{APPNOTE_011_Design_Investigation/sumprod.v} \caption{Another test module for operations on selections} \label{sumprod} \end{figure} \begin{figure}[b] \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/sumprod_00.pdf} \caption{Output of {\tt show a:sumstuff} on Fig.~\ref{sumprod}} \label{sumprod_00} \end{figure} The {\tt select} command is actually much more powerful than it might seem on the first glimpse. When it is called with multiple arguments, each argument is evaluated and pushed separately on a stack. After all arguments have been processed it simply creates the union of all elements on the stack. So the following command will select all {\tt \$add} cells and all objects with the {\tt foo} attribute set: \begin{verbatim} select t:$add a:foo \end{verbatim} (Try this with the design shown in Fig.~\ref{foobaraddsub}. Use the {\tt select -list} command to list the current selection.) In many cases simply adding more and more stuff to the selection is an ineffective way of selecting the interesting part of the design. Special arguments can be used to combine the elements on the stack. For example the {\tt \%i} arguments pops the last two elements from the stack, intersects them, and pushes the result back on the stack. So the following command will select all {\$add} cells that have the {\tt foo} attribute set: \begin{verbatim} select t:$add a:foo %i \end{verbatim} The listing in Fig.~\ref{sumprod} uses the Yosys non-standard {\tt \{* ... *\}} syntax to set the attribute {\tt sumstuff} on all cells generated by the first assign statement. (This works on arbitrary large blocks of Verilog code an can be used to mark portions of code for analysis.) Selecting {\tt a:sumstuff} in this module will yield the circuit diagram shown in Fig.~\ref{sumprod_00}. As only the cells themselves are selected, but not the temporary wire {\tt \$1\_Y}, the two adders are shown as two disjunct parts. This can be very useful for global signals like clock and reset signals: just unselect them using a command such as {\tt select -del clk rst} and each cell using them will get its own net label. In this case however we would like to see the cells connected properly. This can be achieved using the {\tt \%x} action, that broadens the selection, i.e. for each selected wire it selects all cells connected to the wire and vice versa. So {\tt show a:sumstuff \%x} yields the diagram shown in Fig.~\ref{sumprod_01}. \begin{figure}[t] \includegraphics[width=\linewidth]{APPNOTE_011_Design_Investigation/sumprod_01.pdf} \caption{Output of {\tt show a:sumstuff \%x} on Fig.~\ref{sumprod}} \label{sumprod_01} \end{figure} \subsection{Selecting logic cones} Fig.~\ref{sumprod_01} shows what is called the {\it input cone\/} of {\tt sum}, i.e. all cells and signals that are used to generate the signal {\tt sum}. The {\tt \%ci} action can be used to select the input cones of all object in the top selection in the stack maintained by the {\tt select} command. As the {\tt \%x} action, this commands broadens the selection by one ``step''. But this time the operation only works against the direction of data flow. That means, wires only select cells via output ports and cells only select wires via input ports. Fig.~\ref{select_prod} show the sequence of diagrams generated by the following commands: \begin{verbatim} show prod show prod %ci show prod %ci %ci show prod %ci %ci %ci \end{verbatim} When selecting many levels of logic, repeating {\tt \%ci} over and over again can be a bit dull. So there is a shortcut for that: the number of iterations can be appended to the action. So for example the action {\tt \%ci3} is identical to performing the {\tt \%ci} action three times. The action {\tt \%ci*} performs the {\tt \%ci} action over and over again until it has no effect anymore. \begin{figure}[t] \hfill \includegraphics[width=4cm,trim=0 1cm 0 1cm]{APPNOTE_011_Design_Investigation/sumprod_02.pdf} \\ \includegraphics[width=\linewidth,trim=0 0cm 0 1cm]{APPNOTE_011_Design_Investigation/sumprod_03.pdf} \\ \includegraphics[width=\linewidth,trim=0 0cm 0 1cm]{APPNOTE_011_Design_Investigation/sumprod_04.pdf} \\ \includegraphics[width=\linewidth,trim=0 2cm 0 1cm]{APPNOTE_011_Design_Investigation/sumprod_05.pdf} \\ \caption{Objects selected by {\tt select prod \%ci...}} \label{select_prod} \end{figure} \medskip In most cases there are certain cell types and/or ports that should not be considered for the {\tt \%ci} action, or we only want to follow certain cell types and/or ports. This can be achieved using additional patterns that can be appended to the {\tt \%ci} action. Lets consider the design from Fig.~\ref{memdemo_src}. It serves no purpose other than being a non-trivial circuit for demonstrating some of the advanced Yosys features. We synthesize the circuit using {\tt proc; opt; memory; opt} and change to the {\tt memdemo} module with {\tt cd memdemo}. If we type {\tt show} now we see the diagram shown in Fig.~\ref{memdemo_00}. \begin{figure}[b!] \lstinputlisting{APPNOTE_011_Design_Investigation/memdemo.v} \caption{Demo circuit for demonstrating some advanced Yosys features} \label{memdemo_src} \end{figure} \begin{figure*}[t] \includegraphics[width=\linewidth,trim=0 0cm 0 0cm]{APPNOTE_011_Design_Investigation/memdemo_00.pdf} \\ \caption{Complete circuit diagram for the design shown in Fig.~\ref{memdemo_src}} \label{memdemo_00} \end{figure*} But maybe we are only interested in the tree of multiplexers that select the output value. In order to get there, we would start by just showing the output signal and its immediate predecessors: \begin{verbatim} show y %ci2 \end{verbatim} From this we would learn that {\tt y} is driven by a {\tt \$dff cell}, that {\tt y} is connected to the output port {\tt Q}, that the {\tt clk} signal goes into the {\tt CLK} input port of the cell, and that the data comes from a auto-generated wire into the input {\tt D} of the flip-flop cell. As we are not interested in the clock signal we add an additional pattern to the {\tt \%ci} action, that tells it to only follow ports {\tt Q} and {\tt D} of {\tt \$dff} cells: \begin{verbatim} show y %ci2:+$dff[Q,D] \end{verbatim} To add a pattern we add a colon followed by the pattern to the {\tt \%ci} action. The pattern it self starts with {\tt -} or {\tt +}, indicating if it is an include or exclude pattern, followed by an optional comma separated list of cell types, followed by an optional comma separated list of port names in square brackets. Since we know that the only cell considered in this case is a {\tt \$dff} cell, we could as well only specify the port names: \begin{verbatim} show y %ci2:+[Q,D] \end{verbatim} Or we could decide to tell the {\tt \%ci} action to not follow the {\tt CLK} input: \begin{verbatim} show y %ci2:-[CLK] \end{verbatim} \begin{figure}[b] \includegraphics[width=\linewidth,trim=0 0cm 0 0cm]{APPNOTE_011_Design_Investigation/memdemo_01.pdf} \\ \caption{Output of {\tt show y \%ci2:+\$dff[Q,D] \%ci*:-\$mux[S]:-\$dff}} \label{memdemo_01} \end{figure} Next we would investigate the next logic level by adding another {\tt \%ci2} to the command: \begin{verbatim} show y %ci2:-[CLK] %ci2 \end{verbatim} From this we would learn that the next cell is a {\tt \$mux} cell and we would add additional pattern to narrow the selection on the path we are interested. In the end we would end up with a command such as \begin{verbatim} show y %ci2:+$dff[Q,D] %ci*:-$mux[S]:-$dff \end{verbatim} in which the first {\tt \%ci} jumps over the initial d-type flip-flop and the 2nd action selects the entire input cone without going over multiplexer select inputs and flip-flop cells. The diagram produces by this command is shown in Fig.~\ref{memdemo_01}. \medskip Similar to {\tt \%ci} exists an action {\tt \%co} to select output cones that accepts the same syntax for pattern and repetition. The {\tt \%x} action mentioned previously also accepts this advanced syntax. This actions for traversing the circuit graph, combined with the actions for boolean operations such as intersection ({\tt \%i}) and difference ({\tt \%d}) are powerful tools for extracting the relevant portions of the circuit under investigation. See {\tt help select} for a complete list of actions available in selections. \subsection{Storing and recalling selections} The current selection can be stored in memory with the command {\tt select -set <name>}. It can later be recalled using {\tt select @<name>}. In fact, the {\tt @<name>} expression pushes the stored selection on the stack maintained by the {\tt select} command. So for example \begin{verbatim} select @foo @bar %i \end{verbatim} will select the intersection between the stored selections {\tt foo} and {\tt bar}. \medskip In larger investigation efforts it is highly recommended to maintain a script that sets up relevant selections, so they can easily be recalled, for example when Yosys needs to be re-run after a design or source code change. The {\tt history} command can be used to list all recent interactive commands. This feature can be useful for creating such a script from the commands used in an interactive session. \section{Advanced investigation techniques} \label{poke} When working with very large modules, it is often not enough to just select the interesting part of the module. Instead it can be useful to extract the interesting part of the circuit into a separate module. This can for example be useful if one wants to run a series of synthesis commands on the critical part of the module and wants to carefully read all the debug output created by the commands in order to spot a problem. This kind of troubleshooting is much easier if the circuit under investigation is encapsulated in a separate module. Fig.~\ref{submod} shows how the {\tt submod} command can be used to split the circuit from Fig.~\ref{memdemo_src} and \ref{memdemo_00} into its components. The {\tt -name} option is used to specify the name of the new module and also the name of the new cell in the current module. \begin{figure}[t] \includegraphics[width=\linewidth,trim=0 1.3cm 0 0cm]{APPNOTE_011_Design_Investigation/submod_00.pdf} \\ \centerline{\tt memdemo} \vskip1em\par \includegraphics[width=\linewidth,trim=0 1.3cm 0 0cm]{APPNOTE_011_Design_Investigation/submod_01.pdf} \\ \centerline{\tt scramble} \vskip1em\par \includegraphics[width=\linewidth,trim=0 1.3cm 0 0cm]{APPNOTE_011_Design_Investigation/submod_02.pdf} \\ \centerline{\tt outstage} \vskip1em\par \includegraphics[width=\linewidth,trim=0 1.3cm 0 0cm]{APPNOTE_011_Design_Investigation/submod_03.pdf} \\ \centerline{\tt selstage} \vskip1em\par \begin{lstlisting}[basicstyle=\ttfamily\scriptsize] select -set outstage y %ci2:+$dff[Q,D] %ci*:-$mux[S]:-$dff select -set selstage y %ci2:+$dff[Q,D] %ci*:-$dff @outstage %d select -set scramble mem* %ci2 %ci*:-$dff mem* %d @selstage %d submod -name scramble @scramble submod -name outstage @outstage submod -name selstage @selstage \end{lstlisting} \caption{The circuit from Fig.~\ref{memdemo_src} and \ref{memdemo_00} broken up using {\tt submod}} \label{submod} \end{figure} \subsection{Evaluation of combinatorial circuits} The {\tt eval} command can be used to evaluate combinatorial circuits. For example (see Fig.~\ref{submod} for the circuit diagram of {\tt selstage}): {\scriptsize \begin{verbatim} yosys [selstage]> eval -set s2,s1 4'b1001 -set d 4'hc -show n2 -show n1 9. Executing EVAL pass (evaluate the circuit given an input). Full command line: eval -set s2,s1 4'b1001 -set d 4'hc -show n2 -show n1 Eval result: \n2 = 2'10. Eval result: \n1 = 2'10. \end{verbatim} \par} So the {\tt -set} option is used to set input values and the {\tt -show} option is used to specify the nets to evaluate. If no {\tt -show} option is specified, all selected output ports are used per default. If a necessary input value is not given, an error is produced. The option {\tt -set-undef} can be used to instead set all unspecified input nets to undef ({\tt x}). The {\tt -table} option can be used to create a truth table. For example: {\scriptsize \begin{verbatim} yosys [selstage]> eval -set-undef -set d[3:1] 0 -table s1,d[0] 10. Executing EVAL pass (evaluate the circuit given an input). Full command line: eval -set-undef -set d[3:1] 0 -table s1,d[0] \s1 \d [0] | \n1 \n2 ---- ------ | ---- ---- 2'00 1'0 | 2'00 2'00 2'00 1'1 | 2'xx 2'00 2'01 1'0 | 2'00 2'00 2'01 1'1 | 2'xx 2'01 2'10 1'0 | 2'00 2'00 2'10 1'1 | 2'xx 2'10 2'11 1'0 | 2'00 2'00 2'11 1'1 | 2'xx 2'11 Assumed undef (x) value for the following signals: \s2 \end{verbatim} } Note that the {\tt eval} command (as well as the {\tt sat} command discussed in the next sections) does only operate on flattened modules. It can not analyze signals that are passed through design hierarchy levels. So the {\tt flatten} command must be used on modules that instantiate other modules before this commands can be applied. \subsection{Solving combinatorial SAT problems} \begin{figure}[b] \lstinputlisting{APPNOTE_011_Design_Investigation/primetest.v} \caption{A simple miter circuit for testing if a number is prime. But it has a problem (see main text and Fig.~\ref{primesat}).} \label{primetest} \end{figure} \begin{figure*}[!t] \begin{lstlisting}[basicstyle=\ttfamily\small] yosys [primetest]> sat -prove ok 1 -set p 31 8. Executing SAT pass (solving SAT problems in the circuit). Full command line: sat -prove ok 1 -set p 31 Setting up SAT problem: Import set-constraint: \p = 16'0000000000011111 Final constraint equation: \p = 16'0000000000011111 Imported 6 cells to SAT database. Import proof-constraint: \ok = 1'1 Final proof equation: \ok = 1'1 Solving problem with 2790 variables and 8241 clauses.. SAT proof finished - model found: FAIL! ______ ___ ___ _ _ _ _ (_____ \ / __) / __) (_) | | | | _____) )___ ___ ___ _| |__ _| |__ _____ _| | _____ __| | | | ____/ ___) _ \ / _ (_ __) (_ __|____ | | || ___ |/ _ |_| | | | | | |_| | |_| || | | | / ___ | | || ____( (_| |_ |_| |_| \___/ \___/ |_| |_| \_____|_|\_)_____)\____|_| Signal Name Dec Hex Bin -------------------- ---------- ---------- --------------------- \a 15029 3ab5 0011101010110101 \b 4099 1003 0001000000000011 \ok 0 0 0 \p 31 1f 0000000000011111 yosys [primetest]> sat -prove ok 1 -set p 31 -set a[15:8],b[15:8] 0 9. Executing SAT pass (solving SAT problems in the circuit). Full command line: sat -prove ok 1 -set p 31 -set a[15:8],b[15:8] 0 Setting up SAT problem: Import set-constraint: \p = 16'0000000000011111 Import set-constraint: { \a [15:8] \b [15:8] } = 16'0000000000000000 Final constraint equation: { \a [15:8] \b [15:8] \p } = { 16'0000000000000000 16'0000000000011111 } Imported 6 cells to SAT database. Import proof-constraint: \ok = 1'1 Final proof equation: \ok = 1'1 Solving problem with 2790 variables and 8257 clauses.. SAT proof finished - no model found: SUCCESS! /$$$$$$ /$$$$$$$$ /$$$$$$$ /$$__ $$ | $$_____/ | $$__ $$ | $$ \ $$ | $$ | $$ \ $$ | $$ | $$ | $$$$$ | $$ | $$ | $$ | $$ | $$__/ | $$ | $$ | $$/$$ $$ | $$ | $$ | $$ | $$$$$$/ /$$| $$$$$$$$ /$$| $$$$$$$//$$ \____ $$$|__/|________/|__/|_______/|__/ \__/ \end{lstlisting} \caption{Experiments with the miter circuit from Fig.~\ref{primetest}. The first attempt of proving that 31 is prime failed because the SAT solver found a creative way of factorizing 31 using integer overflow.} \label{primesat} \end{figure*} Often the opposite of the {\tt eval} command is needed, i.e. the circuits output is given and we want to find the matching input signals. For small circuits with only a few input bits this can be accomplished by trying all possible input combinations, as it is done by the {\tt eval -table} command. For larger circuits however, Yosys provides the {\tt sat} command that uses a SAT \cite{CircuitSAT} solver \cite{MiniSAT} to solve this kind of problems. The {\tt sat} command works very similar to the {\tt eval} command. The main difference is that it is now also possible to set output values and find the corresponding input values. For Example: {\scriptsize \begin{verbatim} yosys [selstage]> sat -show s1,s2,d -set s1 s2 -set n2,n1 4'b1001 11. Executing SAT pass (solving SAT problems in the circuit). Full command line: sat -show s1,s2,d -set s1 s2 -set n2,n1 4'b1001 Setting up SAT problem: Import set-constraint: \s1 = \s2 Import set-constraint: { \n2 \n1 } = 4'1001 Final constraint equation: { \n2 \n1 \s1 } = { 4'1001 \s2 } Imported 3 cells to SAT database. Import show expression: { \s1 \s2 \d } Solving problem with 81 variables and 207 clauses.. SAT solving finished - model found: Signal Name Dec Hex Bin -------------------- ---------- ---------- --------------- \d 9 9 1001 \s1 0 0 00 \s2 0 0 00 \end{verbatim} } Note that the {\tt sat} command supports signal names in both arguments to the {\tt -set} option. In the above example we used {\tt -set s1 s2} to constraint {\tt s1} and {\tt s2} to be equal. When more complex constraints are needed, a wrapper circuit must be constructed that checks the constraints and signals if the constraint was met using an extra output port, which then can be forced to a value using the {\tt -set} option. (Such a circuit that contains the circuit under test plus additional constraint checking circuitry is called a {\it miter\/} circuit.) Fig.~\ref{primetest} shows a miter circuit that is supposed to be used as a prime number test. If {\tt ok} is 1 for all input values {\tt a} and {\tt b} for a given {\tt p}, then {\tt p} is prime, or at least that is the idea. The Yosys shell session shown in Fig.~\ref{primesat} demonstrates that SAT solvers can even find the unexpected solutions to a problem: Using integer overflow there actually is a way of ``factorizing'' 31. The clean solution would of course be to perform the test in 32 bits, for example by replacing {\tt p != a*b} in the miter with {\tt p != \{16'd0,a\}*b}, or by using a temporary variable for the 32 bit product {\tt a*b}. But as 31 fits well into 8 bits (and as the purpose of this document is to show off Yosys features) we can also simply force the upper 8 bits of {\tt a} and {\tt b} to zero for the {\tt sat} call, as is done in the second command in Fig.~\ref{primesat} (line 31). The {\tt -prove} option used in this example works similar to {\tt -set}, but tries to find a case in which the two arguments are not equal. If such a case is not found, the property is proven to hold for all inputs that satisfy the other constraints. It might be worth noting, that SAT solvers are not particularly efficient at factorizing large numbers. But if a small factorization problem occurs as part of a larger circuit problem, the Yosys SAT solver is perfectly capable of solving it. \subsection{Solving sequential SAT problems} \begin{figure}[t!] \begin{lstlisting}[basicstyle=\ttfamily\scriptsize] yosys [memdemo]> sat -seq 6 -show y -show d -set-init-undef \ -max_undef -set-at 4 y 1 -set-at 5 y 2 -set-at 6 y 3 6. Executing SAT pass (solving SAT problems in the circuit). Full command line: sat -seq 6 -show y -show d -set-init-undef -max_undef -set-at 4 y 1 -set-at 5 y 2 -set-at 6 y 3 Setting up time step 1: Final constraint equation: { } = { } Imported 29 cells to SAT database. Setting up time step 2: Final constraint equation: { } = { } Imported 29 cells to SAT database. Setting up time step 3: Final constraint equation: { } = { } Imported 29 cells to SAT database. Setting up time step 4: Import set-constraint for timestep: \y = 4'0001 Final constraint equation: \y = 4'0001 Imported 29 cells to SAT database. Setting up time step 5: Import set-constraint for timestep: \y = 4'0010 Final constraint equation: \y = 4'0010 Imported 29 cells to SAT database. Setting up time step 6: Import set-constraint for timestep: \y = 4'0011 Final constraint equation: \y = 4'0011 Imported 29 cells to SAT database. Setting up initial state: Final constraint equation: { \y \s2 \s1 \mem[3] \mem[2] \mem[1] \mem[0] } = 24'xxxxxxxxxxxxxxxxxxxxxxxx Import show expression: \y Import show expression: \d Solving problem with 10322 variables and 27881 clauses.. SAT model found. maximizing number of undefs. SAT solving finished - model found: Time Signal Name Dec Hex Bin ---- -------------------- ---------- ---------- --------------- init \mem[0] -- -- xxxx init \mem[1] -- -- xxxx init \mem[2] -- -- xxxx init \mem[3] -- -- xxxx init \s1 -- -- xx init \s2 -- -- xx init \y -- -- xxxx ---- -------------------- ---------- ---------- --------------- 1 \d 0 0 0000 1 \y -- -- xxxx ---- -------------------- ---------- ---------- --------------- 2 \d 1 1 0001 2 \y -- -- xxxx ---- -------------------- ---------- ---------- --------------- 3 \d 2 2 0010 3 \y 0 0 0000 ---- -------------------- ---------- ---------- --------------- 4 \d 3 3 0011 4 \y 1 1 0001 ---- -------------------- ---------- ---------- --------------- 5 \d -- -- 001x 5 \y 2 2 0010 ---- -------------------- ---------- ---------- --------------- 6 \d -- -- xxxx 6 \y 3 3 0011 \end{lstlisting} \caption{Solving a sequential SAT problem in the {\tt memdemo} module from Fig.~\ref{memdemo_src}.} \label{memdemo_sat} \end{figure} The SAT solver functionality in Yosys can not only be used to solve combinatorial problems, but can also solve sequential problems. Let's consider the entire {\tt memdemo} module from Fig.~\ref{memdemo_src} and suppose we want to know which sequence of input values for {\tt d} will cause the output {\tt y} to produce the sequence 1, 2, 3 from any initial state. Fig.~\ref{memdemo_sat} show the solution to this question, as produced by the following command: \begin{verbatim} sat -seq 6 -show y -show d -set-init-undef \ -max_undef -set-at 4 y 1 -set-at 5 y 2 -set-at 6 y 3 \end{verbatim} The {\tt -seq 6} option instructs the {\tt sat} command to solve a sequential problem in 6 time steps. (Experiments with lower number of steps have show that at least 3 cycles are necessary to bring the circuit in a state from which the sequence 1, 2, 3 can be produced.) The {\tt -set-init-undef} option tells the {\tt sat} command to initialize all registers to the undef ({\tt x}) state. The way the {\tt x} state is treated in Verilog will ensure that the solution will work for any initial state. The {\tt -max\_undef} option instructs the {\tt sat} command to find a solution with a maximum number of undefs. This way we can see clearly which inputs bits are relevant to the solution. Finally the three {\tt -set-at} options add constraints for the {\tt y} signal to play the 1, 2, 3 sequence, starting with time step 4. It is not surprising that the solution sets {\tt d = 0} in the first step, as this is the only way of setting the {\tt s1} and {\tt s2} registers to a known value. The input values for the other steps are a bit harder to work out manually, but the SAT solver finds the correct solution in an instant. \medskip There is much more to write about the {\tt sat} command. For example, there is a set of options that can be used to performs sequential proofs using temporal induction \cite{tip}. The command {\tt help sat} can be used to print a list of all options with short descriptions of their functions. \section{Conclusion} \label{conclusion} Yosys provides a wide range of functions to analyze and investigate designs. For many cases it is sufficient to simply display circuit diagrams, maybe use some additional commands to narrow the scope of the circuit diagrams to the interesting parts of the circuit. But some cases require more than that. For this applications Yosys provides commands that can be used to further inspect the behavior of the circuit, either by evaluating which output values are generated from certain input values ({\tt eval}) or by evaluation which input values and initial conditions can result in a certain behavior at the outputs ({\tt sat}). The SAT command can even be used to prove (or disprove) theorems regarding the circuit, in more advanced cases with the additional help of a miter circuit. This features can be powerful tools for the circuit designer using Yosys as a utility for building circuits and the software developer using Yosys as a framework for new algorithms alike. \begin{thebibliography}{9} \bibitem{yosys} Clifford Wolf. The Yosys Open SYnthesis Suite. \url{http://www.clifford.at/yosys/} \bibitem{graphviz} Graphviz - Graph Visualization Software. \url{http://www.graphviz.org/} \bibitem{xdot} xdot.py - an interactive viewer for graphs written in Graphviz's dot language. \url{https://github.com/jrfonseca/xdot.py} \bibitem{CircuitSAT} {\it Circuit satisfiability problem} on Wikipedia \url{http://en.wikipedia.org/wiki/Circuit_satisfiability} \bibitem{MiniSAT} MiniSat: a minimalistic open-source SAT solver. \url{http://minisat.se/} \bibitem{tip} Niklas Een and Niklas S\"orensson (2003). Temporal Induction by Incremental SAT Solving. \url{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.8161} \end{thebibliography} \end{document}

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\documentclass[letter]{article} \usepackage{color, ulem, soul, longtable} \newcommand\temp{\bgroup\color{red}\markoverwith {\color{black}{\rule[-0.5ex]{2pt}{.5pt}}}\ULon} \newcommand\rul[1]{ \temp{#1\hfill}} \title{Underlining colored text with linebreak in \LaTeX} \begin{document} \maketitle \Large \begin{longtable}{p{10cm}} \verb \rul \\ \rul{Xa kitzij xk'oje wi uwinaqirik. Chiwinaqir ulew: --Ulew! Xecha. Lib'aj chi' xwinaqirik: k'eje ri xa ta sutz', xa mayul uwinaqirik, chi k'u pupuje'ik.} \\\\ \verb \uline \\ \uline{Xa kitzij xk'oje wi uwinaqirik. Chiwinaqir ulew: --Ulew! Xecha. Lib'aj chi' xwinaqirik: k'eje ri xa ta sutz', xa mayul uwinaqirik, chi k'u pupuje'ik. \hfill}\\\\ \verb \ul \\ \color{red} \setulcolor{black} \ul{Xa kitzij xk'oje wi uwinaqirik. Chiwinaqir ulew: --Ulew! Xecha. Lib'aj chi' xwinaqirik: k'eje ri xa ta sutz', xa mayul uwinaqirik, chi k'u pupuje'ik. } \end{longtable} \end{document}

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\documentclass[11pt]{article} \usepackage{odonnell} \begin{document} \noindent {\large {\bf Analysis of Boolean Functions}} {\hfill {\bf CMU 18-859S / 21-801A, Fall 2012}} \begin{center} {\sc Problem Set 3} \\ {\bf Due: Monday, Oct.\ 1, beginning of class} \\ \end{center} \hrule \bigskip \noindent {\bf Homework policy}: Please work on the homework by yourself; it isn't intended to be too difficult. Questions about the homework or other course material can be asked on Piazza.\\ \hrule \bigskip \begin{enumerate} \item Let $p \in [1, \infty)$. Given $f \btR$ we define its \emph{$p$-norm} to be $\|f\|_p = \E_{\bx}[|f(\bx)|^p]^{1/p}$ and its \emph{Fourier $p$-norm} to be $\snorm{f}_p = (\sum_{S} |\wh{f}(S)|^p)^{1/p}$. We also define $\|f\|_\infty = \max_x \{|f(x)|\}$ and $\snorm{f}_\infty = \max_S \{|\wh{f}(S)|\}$. \begin{enumerate} \item For $1 \leq p \leq q \leq \infty$, show that $\|f\|_p \leq \|f\|_q$. (Hint: one solution uses the fact that the function $t \mapsto t^{q/p}$ is convex on $[0, \infty)$.) Conversely, show $\snorm{f}_p \geq \snorm{f}_q$. \item Show that $\snorm{f}_\infty \leq \|f\|_1$ and $\|f\|_\infty \leq \snorm{f}_1$. \end{enumerate} \item In this exercise you are asked to prove some fancily-named properties of the noise operator $\T_\rho$. \begin{enumerate} \item Show that $\T_\rho$ is ``positivity-preserving'' for all $\rho \in [-1,1]$, meaning $f \geq 0 \Rightarrow \T_\rho f \geq 0$. Show also that it is ``positivity-improving'' for all $\rho \in (-1,1)$, meaning $f \geq 0, f \not \equiv 0 \Rightarrow \T_\rho f > 0$. \item Show the ``semigroup property'': $\T_{\rho_1} \circ \T_{\rho_2} = \T_{\rho_1 \rho_2}$ for all $\rho_1, \rho_2, \in [0,1]$. (If you like, prove it even for $\rho_1, \rho_2 \in [-1,1]$.) \item Show that $\T_\rho$ is a ``contraction on $L^p$'' for all $p \geq 1$ and $\rho \in [-1,1]$; i.e., $\|\T_\rho f\|_p \leq \|f\|_p$. \end{enumerate} \item For functions $f \co \F_2^n \to \R$, sometimes it is more natural to index the Fourier coefficients not by subsets $S \subseteq [n]$ but by elements $\gamma \in \F_2^n$; here we identify a subset with its indicator vector. In this case we would write the Fourier expansion as \[ f = \sum_{\gamma \in \F_2^n} \wh{f}(S) \chi_\gamma, \qquad \text{where } \chi_\gamma(x) = (-1)^{\gamma \cdot x} \] and $\gamma \cdot x$ is the dot-product of $\gamma$ and $x$ in the vector space $\F_2^n$. Note that for $\beta, \gamma \in \F_2^n$ we have $\chi_{\beta} \chi_{\gamma} = \chi_{\beta + \gamma}$. \begin{enumerate} \item Let $H$ be a vector subspace of $\F_2^n$. Let $H^\perp$ be its ``perpendicular subspace''; i.e., $H^\perp = \{\gamma \in \F_2^n : \gamma \cdot x = 0 \text{ for all } x \in H\}$. Show that the indicator function $1_H \co \F_2^n \to \{0,1\}$ of~$H$ has the Fourier expansion $1_H = \sum_{\gamma \in H^\perp} 2^{-k} \chi_\gamma$, where $k = \dim(H^\perp)$. (Remark: $k = n - \dim(H)$ is sometimes denoted $\codim(H)$.) \item Given the subspace $H$ and also $y \in \F_2^n$, the set $H + y = \{h + y : h \in H\}$ is called an ``affine subspace'' of~$\F_2^n$. Show that the indicator function $1_{H+y} \co \F_2^n \to \{0,1\}$ of this affine subspace has the Fourier expansion $1_{H+y} = \sum_{\gamma \in H^\perp} 2^{-k} \chi_\gamma(y) \chi_\gamma$, where again $k = \dim(H^\perp)$. \end{enumerate} \item Suppose the Fourier spectrum of $f \btR$ is $\eps_1$-concentrated on $\calF$ and that $g \btR$ satisfies $\|f - g\|_2^2 \leq \eps_2$. Show that the Fourier spectrum of $g$ is~$2(\eps_1+\eps_2)$-concentrated on~$\calF$. \item Given $s \in \N^+$, let $\calC$ be the class of all functions $f \btb$ expressible as $f(x) = g(h_1(x), \dots, h_s(x))$, where $h_1, \dots, h_s \btb$ are weighted majority functions and $g \co \bits^s \to \bits$ is any function. Show that $\calC$ is learnable from random examples to error~$\eps$ in time~$n^{O(s^2/\eps^2)}$. You may use Peres's Theorem, that $\NS_\delta[h] \leq 2\sqrt{\delta}$ for all $\delta \in [0,\frac12]$ and all weighted majorities~$h$. (Hint: how can you bound $\NS_\delta[f]$?) \item \begin{enumerate} \item Let $k \in \N^+$ and let $\calC = \{f \btb \mid \deg(f) \leq k\}$. (In particular, $\calC$ contains all functions computable by depth-$k$ decision trees.) Show that $\calC$ is learnable from random examples with error~$0$ in time $n^k \cdot \poly(n, 2^k)$. You may use the following ``Degree/Granularity Fact'': for every $f \in \calC$ and every $S \subseteq [n]$, the Fourier coefficient $\wh{f}(S)$ is an integer multiple of $2^{1-k}$. \item (Bonus.) Prove the Degree/Granularity Fact. \end{enumerate} \end{enumerate} \end{document}

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The \href{https://build.libelektra.org/}{\texttt{ Elektra buildserver}} handles a variety of tasks that reaches from testing Pull Requests (P\+Rs) to deploying new versions of the \href{https://www.libelektra.org}{\texttt{ Elektra website}}. We reworked our build system to use a more modern Jenkinsfile approach with benefits such as \begin{DoxyItemize} \item tracking modifications to our build process in S\+CM \item tracking changes to the build environment \item speeding up builds \end{DoxyItemize} This section aims to give an introduction into this setup. We use the Jenkins Job type called \href{https://jenkins.io/doc/book/pipeline/multibranch/\#creating-a-multibranch-pipeline}{\texttt{ Multibranch Pipeline}} provided by the \href{https://wiki.jenkins.io/display/JENKINS/Pipeline+Multibranch+Plugin}{\texttt{ Pipeline Multibranch Plugin}} for our CI tests called {\ttfamily libelektra}. Simplified a multibranch pipeline job acts as an umbrella job that spawns child jobs for different branches (hence multibranch). The main purpose of the libelektra job is to scan the repository for changes to existing branches or to find new ones (for example branches that are used in PR\textquotesingle{}s). It also contains the information on how to build the jobs in the form of a path that points to a Jenkinsfile containing more detailed instructions. The job also takes care of handling build artifacts that are archived and cleaning them out once the PR\textquotesingle{}s are closed and a grace period has expired. Summarized libelektra\textquotesingle{}s job purpose is to combine the where (our G\+IT repository), with a when (tracking changes via polling or webhooks) with a how (pointing to the Jenkinsfile + configuration). Jenkinsfiles describe what actions the build system should execute on which build slave. Currently Elektra uses two different files. \begin{DoxyItemize} \item Jenkinsfile.daily contains daily maintenance tasks, like cleaning up build servers. \item \href{https://build.libelektra.org/job/libelektra-daily/}{\texttt{ Buildjob\+: libelektra-\/daily}} \item \href{https://master.libelektra.org/scripts/jenkins/Jenkinsfile.daily}{\texttt{ Jenkinsfile.\+daily}} \end{DoxyItemize} \begin{DoxyItemize} \item Triggered on code changes and is for testing changes to the codebase. \item Jenkinsfile contains descriptions how to build, test and deploy Elektra. \item \href{https://build.libelektra.org/job/libelektra/}{\texttt{ Buildjob\+: libelektra}} \item \href{https://master.libelektra.org/scripts/jenkins/Jenkinsfile}{\texttt{ Jenkinsfile}} \end{DoxyItemize} The language used is a groovy based D\+SL described in the \href{https://jenkins.io/doc/book/pipeline/jenkinsfile/}{\texttt{ Jenkinsfile book}}. Most groovy syntax is allowed to describe pipelines in a Jenkinsfile, but it is executed in a sandbox which might block certain calls. Since plugins might extend the pool of available commands or variables a full list of currently available syntax can be seen in \href{https://build.libelektra.org/job/libelektra/pipeline-syntax/}{\texttt{ pipeline syntax}} after a login to the build server. Some functionality is not covered by this page when the responsible plugin is not implementing it. Usually an approach similar to what is described on \href{https://stackoverflow.com/questions/51103359/jenkins-pipeline-return-value-of-build-step}{\texttt{ stackoverflow}} can be used to track down the responsible code inside the providing plugins source code. We also provide a number of helper functions in our Jenkinsfiles that are documented at the function head. Most common use cases, for example adding a new build with certain cmake flags, are easy to add because of them. For example, the configuration that is responsible for the {\ttfamily debian-\/stable-\/full} stage is generated completely by a single helper function called {\ttfamily build\+And\+Test}\+: \begin{DoxyCode}{0} \DoxyCodeLine{tasks << buildAndTest(} \DoxyCodeLine{ "debian-stable-full",} \DoxyCodeLine{ DOCKER\_IMAGES.stretch,} \DoxyCodeLine{ CMAKE\_FLAGS\_BUILD\_ALL +} \DoxyCodeLine{ CMAKE\_FLAGS\_BUILD\_FULL +} \DoxyCodeLine{ CMAKE\_FLAGS\_BUILD\_STATIC +} \DoxyCodeLine{ CMAKE\_FLAGS\_COVERAGE} \DoxyCodeLine{ ,} \DoxyCodeLine{ [TEST.ALL, TEST.MEM, TEST.NOKDB, TEST.INSTALL]} \DoxyCodeLine{)} \end{DoxyCode} When adding new stages to the build chain it is generally a good idea to look up an existing stage which does something similar and adapt it to the new use case. Since a malicious PR could easily destroy the build server and slaves or expose credentials some restrictions are introduced. Only PR authors that have the right to push to libelektra can modify the Jenkinsfile and have those changes be respected for the respective branch. We use Docker containers to provide the various test environments. They are described \href{https://master.libelektra.org/scripts/docker}{\texttt{ in the repository}} and the Jenkinsfile describes how to build them. If a rebuild of the images is needed is determined by the hash of the Dockerfile used to describe it. If it has not changed the build step will be skipped. In the case that an image needed a build it will afterwards be uploaded into a private Docker image registry (on a7) and thus is shared between all Docker capable build slaves. We will use the Docker images build as described earlier to run compilations and tests for Elektra. This allows us to run tests independent of which nodes are available (as the environment is portable). The Jenkinsfile describes the steps used to run tests. Helper functions for easily adding new tests are available ({\ttfamily build\+And\+Test}, {\ttfamily Build\+And\+Test\+Asan}, ...). The {\ttfamily with\+Docker\+Env} helper makes sure to print the following information at the start of a test branch\+: \begin{DoxyItemize} \item branch name \item build machine \item docker image id \end{DoxyItemize} Coverage reports are generated automatically when using the {\ttfamily build\+And\+Test} helper and the appropriate C\+Make flags for coverage generation have been set. They are uploaded to \href{https://doc.libelektra.org/coverage/}{\texttt{ https\+://doc.\+libelektra.\+org/coverage/}}. Artifacts from {\ttfamily ctest} are also preserved automatically when using {\ttfamily build\+And\+Test}. The function also takes care of providing a stage name based path so multiple tests can not overwrite files that share the same name. Tests are executed in order dictated by the Jenkinsfile. In general new tests should be added to the \textquotesingle{}full build stage\textquotesingle{} that will only run after a standard full test run succeeded. This saves execution time on the build server for the most common errors. Since there is no strict way to enforce the way tests are added we encourage you to read the existing configuration and modify existing tests so they suite your needs. For runs of the build job that are run in the master branch we also execute deployment steps after all tests pass. We use it to build Debian packages and move it into the repository on the a7 node. Additionally we recompile the homepage and deploy it on the a7 node. This section describes how to replicate the current Jenkins configuration. The {\ttfamily libelektra} build job is a multibranch pipeline job. It is easiest to add via the Blue\+Ocean interface. Most of the default settings should be ok, however some settings need to be verified or added to build Elektra correctly\+: \begin{DoxyItemize} \item In Branch Sources under Behaviors {\ttfamily Filter by name} should be added to exclude the {\ttfamily debian} branch from being build. The reason for this is that the {\ttfamily debian} branch only differs that it contains build instructions for Debian packages (the {\ttfamily debian} folder). \item {\ttfamily Advanced clone behaviors} should be added and the path to the git mirror needs to be specified\+: {\ttfamily /home/jenkins/git\+\_\+mirrors/libelektra}. This reference repository is created and maintained by our \href{https://build.libelektra.org/job/libelektra-daily/}{\texttt{ daily buildjob}}. \item Under Property strategy you can add {\ttfamily Trigger build on pull request comment}. {\ttfamily jenkins build (libelektra$\vert$all) please} is a good starting point. This functionality is provided by the \href{https://wiki.jenkins-ci.org/display/JENKINS/GitHub+PR+Comment+Build+Plugin}{\texttt{ Git\+Hub PR Comment Build Plugin}}. \item For Build Configuration you want to specify {\ttfamily by Jenkinsfile} and add the script path\+: {\ttfamily scripts/jenkins/\+Jenkinsfile}. \end{DoxyItemize} A node needs to have a J\+RE (Java Runtime Environment) installed. Further it should run an S\+SH (Secure S\+Hell) server. Docker need to be installed as well. A {\ttfamily jenkins} user with 47110\+:47110 ids should be created as this is what is expected in Docker images. {\ttfamily useradd -\/u 47110 jenkins} Additionally a public key authentication should be set up so the jenkins master can establish an ssh connection with the node. If the node should be able to interact with Docker the jenkins user should be added to the {\ttfamily docker} group. Nodes should be set to only build jobs matching their labels and to be online as much as possible. As for labels {\ttfamily gitmirror} should be if you want to cache repositories on this node. If Docker is available the {\ttfamily docker} label should be set. All files and folders in the Node under {\ttfamily /home/jenkins} should be owned by user {\ttfamily jenkins}. Our Jenkins build uses parallel steps inside a single build job to do most of the work. To reliable determine which stages failed it is best to look over the build results in the Jenkins Blue Ocean view. It is the default View opened when accessing the build results from Git\+Hub. For libelektra the U\+R\+Ls are \href{https://build.libelektra.org/job/libelektra/}{\texttt{ https\+://build.\+libelektra.\+org/job/libelektra/}} and \href{https://build.libelektra.org/blue/organizations/jenkins/libelektra/branches/}{\texttt{ https\+://build.\+libelektra.\+org/blue/organizations/jenkins/libelektra/branches/}} Failed stages are marked in red. On selecting a stage you can further expand all steps in the stage. Of interest should be one of the first steps which echos out the Docker image used to run the stage. You also want to look for whatever failed (which should be in a step also marked red to indicate failure). First you have to determine which image is used. This is described above in {\itshape Understanding Jenkins output}. Afterwards you can download it from our registry via {\ttfamily docker pull}. Pay attention that you have to use {\bfseries{hub-\/public.\+libelektra.\+org}} as this subdomain does not require authentication for G\+ET operations used by the Docker client. As an example\+: \begin{DoxyCode}{0} \DoxyCodeLine{docker pull hub-public.libelektra.org/build-elektra-alpine:201809-791f9f388cbdff0db544e02277c882ad6e8220fe280cda67e6ea6358767a065e} \end{DoxyCode} You can also rebuild the images locally, which is useful if you want to test changes you made to the Dockerfiles themselves. Locate which Dockerfile you need by looking up the reference the stage that used it in the Jenkinsfile. For {\itshape alpine} this would be {\ttfamily D\+O\+C\+K\+E\+R\+\_\+\+I\+M\+A\+G\+E\+S.\+alpine}. You can search for this entry in the Jenkinsfile to find that this image is build from the context {\ttfamily ./scripts/docker/alpine/3.8} and uses {\ttfamily ./scripts/docker/alpine/3.8/\+Dockerfile} as a Dockerfile. Now you can build the image as described in \href{https://master.libelektra.org/scripts/docker/README.md\#building-images-locally}{\texttt{ scripts/docker/\+R\+E\+A\+D\+M\+E.\+md}}. You can find more information on how to use our images in \href{https://master.libelektra.org/scripts/docker/README.md\#testing-elektra-via-docker-images}{\texttt{ scripts/docker/\+R\+E\+A\+D\+M\+E.\+md}}. Alternatively, you can follow the \mbox{\hyperlink{doc_tutorials_run_all_tests_with_docker_md}{tutorial}}. You can also modify the test environments (update a dependency, install a new dependency, ...) by editing the Dockerfiles checked into S\+CM. Determine which ones you need to modify by tracing which images are used for what stages via the {\ttfamily D\+O\+C\+K\+E\+R\+\_\+\+I\+M\+A\+G\+ES} map used in our Jenkinsfile. The {\ttfamily docker\+Init} function should be a good start point. Following docker best practises you should try to minimize layer count when possible. Our docker images are quite large and hence take a long time to build so make sure to test any modifications locally first. All Triggers are described in the configuration of the respective build jobs. The \href{https://build.libelektra.org/job/libelektra/}{\texttt{ libelektra}} build is triggered for all branches of the libelektra repository except for {\ttfamily debian}. Additionally all open branches in forks targeting libelektra\textquotesingle{}s repository via P\+Rs are going to be build. Pushes to any of those branches will trigger a new build automatically. The \href{https://build.libelektra.org/job/libelektra-daily/}{\texttt{ daily build}} is executed according to a cron schedule. The following phrases can be used as comments to manually trigger a specific build\+: \begin{DoxyItemize} \item jenkins build \href{https://build.libelektra.org/job/libelektra/}{\texttt{ libelektra}} please \item jenkins build \href{https://build.libelektra.org/job/libelektra-daily/}{\texttt{ daily}} please \item jenkins build \href{https://build.libelektra.org/job/libelektra-monthly/}{\texttt{ monthly}} please \end{DoxyItemize} Additionally {\ttfamily jenkins build all please} can be used to trigger all build jobs relevant for PR\textquotesingle{}s. This is not necessary anymore as all relevant tests have been moved into the libelektra job. If you are not yet authorized, the following question will be asked (by user @markus2330)\+: \begin{DoxyVerb}Can one of the admins verify if this patch should be build? \end{DoxyVerb} Then one of the admins (sorted by activity)\+: \begin{DoxyItemize} \item @sanssecours \item @markus2330 \item @beku \item @\+Bernhard\+Denner \item @fberlakovich \item @manuelm \end{DoxyItemize} need to confirm by saying\+: \begin{DoxyVerb}.*add\W+to\W+whitelist.* \end{DoxyVerb} or if just the pull request should be checked\+: \begin{DoxyVerb}.*build\W+allow.* \end{DoxyVerb} If you have issues that are related to the build system you can open a normal issue and tag it with {\ttfamily build} and {\ttfamily question}. If you feel like your inquiry does not warrant an issue on its own, please use \href{https://issues.libelektra.org/160}{\texttt{ our buildserver issue}}.

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\[P^{(\alpha,\alpha)}_{n}\left(x\right)=\frac{{\left(\alpha+1\right)_{n}}}{{% \left(2\alpha+1\right)_{n}}}C^{(\alpha+\frac{1}{2})}_{n}\left(x\right).\]

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\documentclass[12pt]{book} \usepackage{parskip} \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} %% \usepackage{mathptmx} % times roman %%\usepackage{lucidabr} % lucida bright \usepackage{pos} % generate iTeX page position data \usepackage[pdftex,bookmarks=true,bookmarksopen=true, bookmarksnumbered=true,bookmarksopenlevel=3, colorlinks,urlcolor=blue,linkcolor=blue, pdftitle={Kapteeni Grantia etsimässä}, pdfauthor={Jules Verne}, citecolor=blue]{hyperref} \newcommand{\mdsh}[1]{\mbox{#1}\linebreak[1]} \newcommand{\nodate}{\date{}}\nodate \newcommand{\gutchapter}[1]{% \cleardoublepage \chapter{#1} \markboth{Kapteeni Grantia etsimässä}{#1} } % \setcounter{chapter}{1} \begin{document} \pagenumbering{alph} % bogus, never shown, names don't collide with below \title{Kapteeni Grantia etsimässä} \author{Jules Verne} \maketitle \pagenumbering{roman} \frontmatter The Project Gutenberg EBook of Kapteeni Grantia etsim\"{a}ss\"{a}, by Jules Verne This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org/license Title: Kapteeni Grantia etsim\"{a}ss\"{a} Author: Jules Verne Translator: Eino Voionmaa Release Date: March 5, 2012 [EBook \#39057] Language: Finnish Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK KAPTEENI GRANTIA ETSIM\"{A}SS\"{A} *** Produced by Tapio Riikonen KAPTEENI GRANTIA ETSIM\"{A}SS\"{A} Kirj. Jules Verne Suomentanut Eino Voionmaa Karisto Oy, H\"{a}meenlinna, 1922. This text was converted to LaTeX by means of \textbf{GutenMark} software (version Jul 12 2014). The text has been further processed by software in the iTeX project, by Bill Cheswick. \cleardoublepage \tableofcontents \cleardoublepage \mainmatter \pagenumbering{arabic} \gutchapter{SIS\"{A}LLYS: } Taas laivalla Tristan da Cunha Amsterdamin saari Jacques Paganelin ja majuri MacNabbsin vedonly\"{o}nnit Intian valtameren myrskyt Kap Bernouilli Ayrton L\"{a}ht\"{o} Victorian maakunta Wimerra-joki Burke ja Stuart Rautatie Melbournesta Sandhurstiin Ensimm\"{a}inen palkinto maantieteess\"{a} Mount Alexanderin kaivokset Australian ja Uuden Seelannin Uutiset Majuri v\"{a}itt\"{a}\"{a} alkuasukkaita apinoiksi Upporikkaat karjanomistajat Australian alpit Teatteritemppu Aland --- Zealand Nelj\"{a}n p\"{a}iv\"{a}n tuska Eden Viiteselitykset. \section*{\raggedright TAAS LAIVALLA.} Ensimm\"{a}iset hetket pyhitettiin j\"{a}lleenn\"{a}kemisen onnelle. Lordi Glenarvan ei halunnut, ett\"{a} etsinn\"{a}n ep\"{a}onnistuminen kylment\"{a}isi ilon h\"{a}nen yst\"{a}viens\"{a} syd\"{a}miss\"{a}. Niinp\"{a} h\"{a}nen ensimm\"{a}iset sanansa kuuluivat: --- Luottamusta, yst\"{a}v\"{a}ni, luottamusta! Kapteeni Grant ei ole meid\"{a}n mukanamme, mutta meill\"{a} on varmuus, ett\"{a} l\"{o}yd\"{a}mme h\"{a}net. Tarvittiinkin v\"{a}hint\"{a}\"{a}n t\"{a}llainen vakuutus toivon yll\"{a}pit\"{a}miseksi \textit{Duncanin} matkustajissa. Lady Helena ja Mary Grant olivat tosiaan veneen l\"{a}hestyess\"{a} laivaa t\"{a}hyst\"{a}neet sit\"{a} odotuksen tuhansin tuskin. Korkealta paikaltaan he yrittiv\"{a}t laskea laivalle palaavien lukum\"{a}\"{a}r\"{a}\"{a}. Milloin tuli nuori tytt\"{o} ep\"{a}toivoiseksi, milloin h\"{a}n taas p\"{a}invastoin luuli n\"{a}kev\"{a}ns\"{a} Harry Grantin. H\"{a}nen syd\"{a}mens\"{a} tykytti kovasti; h\"{a}n ei voinut puhua ja pysyi tuskin pystyss\"{a}. Lady Helena kiersi k\"{a}sivartensa h\"{a}nen ymp\"{a}rilleen. John Mangles, joka seisoi h\"{a}nen vieress\"{a}\"{a}n t\"{a}hyst\"{a}m\"{a}ss\"{a}, oli vaiti; h\"{a}nen kauas n\"{a}kem\"{a}\"{a}n tottuneet merimiessilm\"{a}ns\"{a} eiv\"{a}t n\"{a}hneet kapteenia. --- H\"{a}n on mukana! H\"{a}n tulee! Is\"{a}ni! neitonen puhui itsekseen. Mutta veneen l\"{a}hestyess\"{a} t\"{a}m\"{a} kuvitelma k\"{a}vi mahdottomaksi. Tulijat eiv\"{a}t olleet viel\"{a} sadanviidenkymmenen metrin p\"{a}\"{a}ss\"{a} laivasta, kun lady Helena ja John Mangles, viel\"{a}p\"{a} Mary itsekin, silm\"{a}t kyyneliss\"{a}, olivat menett\"{a}neet kaiken toivon. Oli aika, ett\"{a} lordi Glenarvan saapui lausumaan rauhoittavat sanansa. Ensimm\"{a}isten tervehdysten j\"{a}lkeen lady Helenalle, Mary Grantille ja John Manglesille tehtiin selkoa matkan p\"{a}\"{a}vaiheista, ja ennen kaikkea Glenarvan ilmoitti heille uuden tulkinnan asiakirjasta, josta tuli kiitt\"{a}\"{a} Jacques Paganelin ter\"{a}vyytt\"{a}. H\"{a}n ylisti sitten Robertia, josta Mary hyv\"{a}ll\"{a} syyll\"{a} saattoi olla ylpe\"{a}. H\"{a}nen uljuuttaan, uskollisuuttaan, h\"{a}nen kest\"{a}mi\"{a}\"{a}n vaaroja Glenarvan kuvasi siten, ett\"{a} poika ei olisi tiennyt minne piiloutua, ellei h\"{a}nen sisarensa syli olisi ollut h\"{a}nen turvapaikkanaan. --- Sinun ei tarvitse punastua, Robert, John Mangles sanoi, --- sin\"{a} olet k\"{a}ytt\"{a}ytynyt kapteeni Grantin pojan arvoisesti. H\"{a}n puristi Maryn veljen rintaansa vasten ja painoi huulensa t\"{a}m\"{a}n poskille, jotka olivat nuoren tyt\"{o}n kyynelist\"{a} viel\"{a} kosteat. Vain sivumennen mainittakoon t\"{a}ss\"{a} majurin ja maantieteilij\"{a}n osaksi tullut vastaanotto ja se muisto, jolla jalomielist\"{a} Thalcavea kunnioitettiin. Lady Helena pahoitteli, ettei saanut puristaa uljaan intiaanin k\"{a}tt\"{a}. Ensimm\"{a}isten tervehdysten j\"{a}lkeen oli MacNabbs mennyt kajuuttaansa ja ryhtynyt, k\"{a}si tyynen\"{a} ja varmana, ajamaan partaansa. Mit\"{a} Paganeliin tulee, h\"{a}n pyr\"{a}hteli yhden luota toisen luo kuin mehil\"{a}inen imien tervehdysten ja hymyjen hunajaa. H\"{a}n tahtoi syleill\"{a} \textit{Duncanin} koko v\"{a}est\"{o}\"{a}, ja katsoen, ett\"{a} niin hyvin lady Helena kuin my\"{o}s Mary Grant kuuluivat siihen, aloitti t\"{a}m\"{a}n toimituksensa heist\"{a} p\"{a}\"{a}tt\"{a}en sen herra Olbinettiin. Muonamestari arveli ettei voinut paremmin vastata t\"{a}llaiseen kohteliaisuuteen kuin ilmoittamalla, ett\"{a} aamiainen oli valmis. --- Aamiainen! Paganel huudahti. --- Niin, herra Paganel, herra Olbinett vastasi. --- Oikea aamiainenko, oikealla p\"{o}yd\"{a}ll\"{a}, jolla on t\"{a}ysi kalusto ja lautasliinatkin? --- Tietenkin, herra Paganel. --- Eik\"{a} tarjota \textit{charquita}, ei kovia munia eik\"{a} kamelikurkikyljyst\"{a}? --- No no, herra Paganel! muonamestari vastasi ammattinsa puolesta loukkaantuneena. --- Min\"{a} en tahtonut loukata teit\"{a}, yst\"{a}v\"{a}ni, tiedemies sanoi hymyillen. --- Mutta kuukauden p\"{a}iv\"{a}t on meid\"{a}n ruokanamme ollut s\"{a}\"{a}nn\"{o}llisesti sellaista, emmek\"{a} sy\"{o}neet p\"{o}yd\"{a}ss\"{a} istuen, vaan maassa loikoen, ellemme istuneet hajas\"{a}\"{a}rin puiden oksilla. Teid\"{a}n ilmoittamanne aamiainen saattoi siis minusta tuntua unelta, kuvitelmalta, kangastukselta! --- No, menk\"{a}\"{a}mme toteamaan, ett\"{a} se on kouraantuntuvaa todellisuutta, herra Paganel, vastasi lady Helena, joka ei voinut olla nauramatta. --- T\"{a}ss\"{a} k\"{a}sivarteni, kohtelias tiedemies lausui. --- Mit\"{a} ohjeita teill\"{a}, mylord, on antaa minulle \textit{Duncanin} suhteen? John Mangles kysyi. --- Aamiaisen j\"{a}lkeen, rakas John, Glenarvan vastasi, --- keskustelemme yhteisesti uuden retkemme ohjelmasta. Laivan matkustajat ja nuori kapteeni meniv\"{a}t salonkiin. Koneenk\"{a}ytt\"{a}j\"{a}lle annettiin m\"{a}\"{a}r\"{a}ys pit\"{a}\"{a} h\"{o}yry\"{a} yll\"{a}, jotta voitaisiin l\"{a}hte\"{a} milloin tahansa. Kun majuri oli ajanut partansa ja muutkin pikaisesti hiukan siistiytyneet, istuttiin p\"{o}yt\"{a}\"{a}n. Herra Olbinettin aamiaisp\"{o}yd\"{a}lle tehtiin oikeutta. Se julistettiin oivalliseksi, viel\"{a}p\"{a} pampan loistavia juhla-aterioita paremmaksi. Paganel otti jokaista ruokalajia kaksi kertaa, ``hajamielisyydest\"{a}'', kuten h\"{a}n selitti. T\"{a}m\"{a} varomaton sana sai lady Glenarvanin tiedustelemaan, oliko tiedemies joskus sattunut lankeamaan vanhaan perisyntiins\"{a}. Majuri ja lordi Glenarvan katsahtivat toisiinsa hymyillen. Paganel puolestaan purskahti \"{a}\"{a}nekk\"{a}\"{a}seen nauruun ja lupasi ``kautta kunniansa'', ettei h\"{a}n koko matkan aikana en\"{a}\"{a} hairahdu ainoaankaan hajamielisyyteen; sitten h\"{a}n alkoi eritt\"{a}in leikkis\"{a}sti kertoa erehdyksist\"{a}\"{a}n ja perinpohjaisista kieliopinnoistaan Camo\"{e}nsin teoksen johdolla. --- Ja kuitenkin, h\"{a}n sanoi lopuksi, --- on onnettomuudesta aina jollakin tavalla hy\"{o}ty\"{a}kin, enk\"{a} min\"{a} surkuttele erehdyst\"{a}ni. --- Mink\"{a} vuoksi, kelpo yst\"{a}v\"{a}ni? majuri kysyi. --- Kun nyt osaan sek\"{a} espanjan ett\"{a} my\"{o}s portugalin kielt\"{a}. Puhun kahta kielt\"{a} yhden asemesta. --- Kautta kunniani, sit\"{a} en tullut ajatelleeksi! majuri lausui. --- Onnittelen, Paganel, onnittelen vilpitt\"{o}m\"{a}sti. Muutkin onnittelivat Paganelia, joka s\"{o}i rauhassa edelleen. H\"{a}n n\"{a}et s\"{o}i ja jutteli yhtaikaa. Niinp\"{a} h\"{a}n ei huomannut er\"{a}st\"{a} seikkaa, jota Glenarvan ei voinut olla havaitsematta: John Manglesin huomaavaisuutta vieress\"{a}\"{a}n istuvaa Mary Grantia kohtaan. Lady Helenan salainen merkki puolisolleen vahvisti, ett\"{a} ``asia oli niin''. Glenarvan katseli n\"{a}it\"{a} nuoria suopein silmin ja k\"{a}\"{a}ntyi John Manglesin puoleen, mutta aivan toisessa asiassa. --- Ent\"{a} kuinka teid\"{a}n matkanne on sujunut, John? h\"{a}n kysyi. --- Mit\"{a} parhaiten, kapteeni vastasi. --- Minun on vain ilmoitettava teille, mylord, ett\"{a} me emme palanneet Magalh\~{a}esin salmen kautta. --- Ah, Paganel huudahti, --- te olette kulkeneet Kap Hornin ymp\"{a}ri, enk\"{a} min\"{a} ollut mukana! --- Hirtt\"{a}k\"{a}\"{a} itsenne! majuri sanoi. --- Itsek\"{a}s mies! Sen neuvon te annatte minulle vain saadaksenne peri\"{a} k\"{o}yden! maantieteilij\"{a} vastasi. --- Mutta, rakas Paganel, Glenarvan huomautti, --- ellei ihminen ole saanut kyky\"{a} olla kaikkialla, h\"{a}n ei voi olla joka paikassa. Kun nyt olitte vaeltamassa pitkin pampaa, ette voinut samaan aikaan olla Kap Hornia kiert\"{a}m\"{a}ss\"{a}. --- Se ei est\"{a} minua sit\"{a} pahoittelemasta, Paganel vastasi. H\"{a}nt\"{a} ei ahdisteltu enemp\"{a}\"{a}, vaan tyydyttiin t\"{a}h\"{a}n vastaukseen. John Mangles jatkoi sitten kertomustaan \textit{Duncanin} matkasta. Kulkiessaan pitkin Amerikan rannikkoa h\"{a}n oli tarkastanut kaikki l\"{a}ntiset saaristot tapaamatta j\"{a}lke\"{a}k\"{a}\"{a}n \textit{Britanniasta}. Saavuttuaan Kap Pilaresin luo salmen suulla h\"{a}n k\"{a}\"{a}ntyi etel\"{a}\"{a}n, kun tuuli oli vastainen; \textit{Duncan} sivuutti Desolacion-saaret ja eteni 67. asteelle etel\"{a}ist\"{a} leveytt\"{a}, kiersi Kap Hornin, kulki pitkin Tulimaan rantaa ja, sitten purjehdittuaan Lemairen salmen l\"{a}pi, Patagonian rannikkoa my\"{o}ten. Siell\"{a} nousi hirve\"{a} tuuli Kap Corrientesin kohdalla, arvatenkin sama, joka niin ankarasti oli ahdistanut maata pitkin kulkeneita rajuilman aikana. Mutta alus suoriutui hyvin, ja John Mangles oli risteillyt rannikolla kolme p\"{a}iv\"{a}\"{a}, kunnes pyssynlaukaukset ilmoittivat niin hartaasti odotettujen matkamiesten saapuneen. Mit\"{a} lady Glenarvaniin ja miss Grantiin tulee, olisi \textit{Duncanin} kapteeni tehnyt v\"{a}\"{a}ryytt\"{a}, ellei olisi maininnut heid\"{a}n harvinaista pelottomuuttaan. Myrsky ei heit\"{a} huolettanut, ja heid\"{a}n ainoa pelkonsa oli vain, kuinka heid\"{a}n silloin Argentiinan tasangoilla harhailevien yst\"{a}viens\"{a} k\"{a}visi. N\"{a}in p\"{a}\"{a}ttyi John Manglesin kertomus, ja lordi Glenarvan kiitteli kapteenia. Sitten h\"{a}n k\"{a}\"{a}ntyi Mary Grantin puoleen sanoen: --- Rakas neiti, siit\"{a}, mit\"{a} kapteeni John Mangles kertoo teid\"{a}n uljaasta mielest\"{a}nne, huomaan ilokseni, ett\"{a} te viihdytte h\"{a}nen laivallaan. --- Kuinkas muuten voisi olla? Mary vastasi katsahtaen lady Helenaan ja ehk\"{a} hiukan my\"{o}s nuoreen kapteeniin. --- Niin, minun sisareni rakastaa teit\"{a}, herra John, Robert huudahdi, --- niin kuin min\"{a}kin! --- Ja min\"{a} sinua, rakas lapseni! John Mangles vastasi hiukan h\"{a}mill\"{a}\"{a}n Robertin sanoista, jotka olivat nostattaneet hienon punan Mary Grantin otsalle. Sitten k\"{a}\"{a}nt\"{a}en keskustelun v\"{a}hemm\"{a}n polttavalle alalle, John Mangles lis\"{a}si: --- Kun min\"{a} nyt olen kertonut kaiken \textit{Duncanin} matkasta, ehk\"{a}p\"{a} te, mylord, tahdotte kertoa meille muutamia yksityiskohtia matkastanne Amerikan poikki ja nuoren sankarinne urot\"{o}ist\"{a}. Mik\"{a}\"{a}n ei olisi voinut olla lady Helenalle ja neiti Grantille mieluisampaa. Niinp\"{a} lordi Glenarvan kiiruhtikin tyydytt\"{a}m\"{a}\"{a}n heid\"{a}n uteliaisuuttaan. H\"{a}n kertoi kohta kohdalta koko heid\"{a}n matkansa valtamerelt\"{a} toiselle. Kordillieerien ylitys, maanj\"{a}ristys, Robertin katoaminen, kondorin kaappaus, Thalcaven pyssynlaukaus, punaisten susien hy\"{o}kk\"{a}ys, Robertin uljuus siin\"{a}, kersantti Manuel, tulva, pelastautuminen ombu-puuhun, ukonilma, tulipalo, kaimaanit, pilvipatsas, y\"{o} Atlantin rannikolla, kaikki n\"{a}m\"{a} eri kohdat, hauskat ja hirvitt\"{a}v\"{a}t, her\"{a}ttiv\"{a}t vuoron per\"{a}\"{a}n kuuntelijain riemua tai kauhua. Mainittiin monta seikkaa, joista Robert joutui sisarensa ja lady Helenan hyv\"{a}ilt\"{a}v\"{a}ksi. Milloinkaan ei poika ollut saanut niin suurta suosiota, viel\"{a}p\"{a} niin innokkailta yst\"{a}vilt\"{a}. P\"{a}\"{a}tetty\"{a}\"{a}n kertomuksensa lordi Glenarvan lausui lopuksi: --- Nyt, yst\"{a}v\"{a}ni, ajatelkaamme nykyhetke\"{a}; mennyt on mennytt\"{a}, mutta tulevaisuus on edess\"{a}mme; palatkaamme kapteeni Harry Grantiin. Aamiainen oli p\"{a}\"{a}ttynyt; siirryttiin lady Glenarvanin erikoissalonkiin; istuuduttiin kartoilla ja piirroksilla peitetyn p\"{o}yd\"{a}n ymp\"{a}rille, ja keskustelu alkoi heti. --- Rakas Helena, lordi Glenarvan sanoi, --- noustessani laivaan lausuin, ett\"{a} vaikka meill\"{a} ei ollut \textit{Britannian} haaksirikkoisia mukanamme, meill\"{a} kuitenkin oli enemm\"{a}n toivoa kuin milloinkaan l\"{o}yt\"{a}\"{a} heid\"{a}t. Matkamme Amerikan halki on saanut meid\"{a}t vakuuttuneeksi siit\"{a} tai paremminkin antanut varmuuden, ett\"{a} haaksirikko ei ole tapahtunut Tyynen Valtameren eik\"{a} Atlantin rannikolla. Siit\"{a} on luonnollinen johtop\"{a}\"{a}t\"{o}s, ett\"{a} olimme tulkinneet asiakirjan v\"{a}\"{a}rin, mit\"{a} Patagoniaan tulee. Onneksi yst\"{a}v\"{a}mme Paganel keksi erehdyksen \"{a}killisen mielijohteen ansiosta. H\"{a}n on todistanut, ett\"{a} olimme v\"{a}\"{a}rill\"{a} j\"{a}ljill\"{a}, ja tulkinnut asiakirjan tavalla, joka ei j\"{a}t\"{a} mieleemme en\"{a}\"{a} mit\"{a}\"{a}n tilaa ep\"{a}ilylle. T\"{a}ss\"{a} on puhe ranskaksi kirjoitetusta asiakirjasta, ja min\"{a} pyyd\"{a}n Paganelia selitt\"{a}m\"{a}\"{a}n sen, jotta ei kenenk\"{a}\"{a}n mieleen j\"{a}isi pienint\"{a}k\"{a}\"{a}n ep\"{a}ilyst\"{a} t\"{a}ss\"{a} suhteessa. Tiedemies totteli pyynt\"{o}\"{a}; h\"{a}n selitti katkelmat \textit{gonie} ja \textit{indi} mit\"{a} vakuuttavimmalla tavalla; h\"{a}n johti tavuista \textit{austral} ehdottomasti sanan Australia; h\"{a}n osoitti, ett\"{a} kapteeni Grant, l\"{a}hdetty\"{a}\"{a}n Perun rannikolta palatakseen Eurooppaan, oli voinut avuttomaksi k\"{a}yneell\"{a} aluksella joutua Tyynenmeren etel\"{a}isten tuulten viem\"{a}n\"{a} Australian rannikolle saakka; ja lopulta h\"{a}nen nerokkaat olettamuksensa, h\"{a}nen hienoimmat p\"{a}\"{a}telm\"{a}ns\"{a} saavuttivat t\"{a}ydellisen hyv\"{a}ksymisen John Manglesin taholta, joka t\"{a}ll\"{a} alueella oli ehdottoman tarkka eik\"{a} antanut mink\"{a}\"{a}nlaisten kuvittelujen eksytt\"{a}\"{a} itse\"{a}\"{a}n. Kun Paganel oli antanut selityksens\"{a}, ilmoitti Glenarvan \textit{Duncanin} l\"{a}htev\"{a}n suoraa p\"{a}\"{a}t\"{a} matkalle Australiaan. Mutta ennen kuin annettiin k\"{a}sky k\"{a}\"{a}nty\"{a} it\"{a}\"{a}np\"{a}in, majuri pyysi saada tehd\"{a} er\"{a}\"{a}n yksinkertaisen huomautuksen. --- Puhukaa, MacNabbs, Glenarvan vastasi. --- Minun tarkoitukseni, majuri sanoi, --- ei ole heikent\"{a}\"{a} yst\"{a}v\"{a}ni Paganelin todistelua, viel\"{a} v\"{a}hemmin sit\"{a} kiist\"{a}\"{a} v\"{a}\"{a}r\"{a}ksi; minusta h\"{a}nen esitt\"{a}m\"{a}ns\"{a} syyt ovat painavia, j\"{a}rkevi\"{a} ja ansaitsevat kaiken huomiomme; niiden tulee olla tulevien etsiskelyjemme perustana. Mutta min\"{a} haluan, ett\"{a} ne viel\"{a} kerran tarkastetaan, jotta niiden arvoa ei k\"{a}y kumoaminen eik\"{a} kumotakaan. Ei k\"{a}sitetty, mihin j\"{a}rkev\"{a} MacNabbs oikein pyrki, ja h\"{a}nt\"{a} kuunneltiin ep\"{a}m\"{a}\"{a}r\"{a}isen levottomina. --- Jatkakaa, majuri, Paganel sanoi. --- Min\"{a} olen valmis vastaamaan kaikkiin kysymyksiinne. --- Ei mik\"{a}\"{a}n ole yksinkertaisempaa, majuri vastasi. --- Kun me nelj\"{a}tt\"{a} kuukautta sitten Clyden lahdella tutkimme n\"{a}it\"{a} kolmea asiapaperia, niiden tulkinta tuntui meist\"{a} eitt\"{a}m\"{a}tt\"{o}m\"{a}lt\"{a}. Mik\"{a}\"{a}n muu seutu kuin Patagonian l\"{a}nsirannikko ei voinut olla haaksirikon paikkana. Meill\"{a} ei siin\"{a} suhteessa ollut ep\"{a}ilyn varjoakaan. --- Se on aivan totta, Glenarvan vahvisti. --- Sittemmin, majuri jatkoi, --- kun Paganel kaitselmuksen s\"{a}\"{a}t\"{a}m\"{a}ss\"{a} hajamielisyyden puuskassa asettui meid\"{a}n alukseemme, n\"{a}ytettiin asiakirjat h\"{a}nelle, ja h\"{a}n hyv\"{a}ksyi empim\"{a}tt\"{a} etsiskelyn aloittamisen Amerikan rannikolla. --- Min\"{a} my\"{o}nn\"{a}n sen, tiedemies vastasi. --- Ja kuitenkin me olemme erehtyneet, majuri sanoi. --- Me olemme erehtyneet, Paganel toisti. --- Onhan ihminen erehtyv\"{a}inen, MacNabbs, mutta hullu se, joka pit\"{a}\"{a} kiinni erehdyksest\"{a}\"{a}n. --- Odottakaa, Paganel, majuri vastasi, --- \"{a}lk\"{a}\"{a} kiivastuko. Min\"{a} en tahdo sanoa, ett\"{a} meid\"{a}n pit\"{a}isi jatkaa etsiskely\"{a}mme Amerikassa. --- Mutta mit\"{a} te sitten tahdotte? Glenarvan kysyi. --- Yhden tunnustuksen, en mit\"{a}\"{a}n muuta, tunnustuksen, ett\"{a} Australia n\"{a}ytt\"{a}\"{a} nyt olevan \textit{Britannian} haaksirikon tapahtumapaikka yht\"{a} eitt\"{a}m\"{a}tt\"{o}m\"{a}sti kuin taannoin n\"{a}ytti, ett\"{a} se oli Amerikka. --- Sen tunnustamme kernaasti, Paganel lausui. --- Min\"{a} panen sen muistiin, majuri jatkoi, --- ja min\"{a} k\"{a}yt\"{a}n sit\"{a} saadakseni teid\"{a}t ep\"{a}ilem\"{a}\"{a}n n\"{a}it\"{a} per\"{a}kk\"{a}isi\"{a} ja vastakkaisia eitt\"{a}m\"{a}tt\"{o}myyksi\"{a}. Kuka tiet\"{a}\"{a}, eik\"{o} Australian j\"{a}lkeen joku muu maa n\"{a}yt\"{a} meist\"{a} yht\"{a} varmalta ja jos etsiskelymme Australiassa osoittautuu turhaksi, eik\"{o} meist\"{a} n\"{a}yt\"{a} eitt\"{a}m\"{a}tt\"{o}m\"{a}lt\"{a}, ett\"{a} etsiskely on siirrett\"{a}v\"{a} sinne? Glenarvan ja Paganel katsahtivat toisiinsa. Majurin huomautukset olivat t\"{a}ysin oikeita. --- Min\"{a} haluan siis, MacNabbs jatkoi, --- ett\"{a} asia tutkitaan viel\"{a} kerran, ennen kuin l\"{a}hdemme matkalle Australiaan. T\"{a}ss\"{a} ovat asiakirjat, t\"{a}ss\"{a} kartat. Tutkikaamme j\"{a}rjestyksess\"{a} kaikki paikat, joiden kautta 37. leveysaste kulkee, ja katsokaamme, onko mit\"{a}\"{a}n muuta maata, mihin asiakirja voi t\"{a}ysin sopia. --- Se on helposti ja pian tehty, Paganel vastasi, --- sill\"{a} onneksi ei t\"{a}ll\"{a} leveysasteella ole moniakaan maita. --- Katsokaamme, majuri sanoi ja levitti englantilaisen, Mercatorin projektion mukaan laaditun yleiskartan, joka tasapinnalla esitti koko maapalloa. Kartta pantiin lady Helenan eteen, ja jokainen sijoittui niin, ett\"{a} saattoi seurata Paganelin esityst\"{a}. --- Kuten jo olen sanonut, maantieteilij\"{a} lausui, --- koskettaa 37. leveysaste Tristan da Cunhan-saaria kuljettuaan Etel\"{a}-Amerikan poikki. Min\"{a} v\"{a}it\"{a}n, ett\"{a} ainoakaan asiakirjan sana ei voi koskea n\"{a}it\"{a} saaria. Kun oli tarkoin tutkittu asiakirjoja, t\"{a}ytyi my\"{o}nt\"{a}\"{a}, ett\"{a} Paganel oli oikeassa. Tristan da Cunha hyl\"{a}ttiin yksimielisesti. --- Jatkakaamme, maantieteilij\"{a} sanoi. --- Poistuessamme Atlantilta kuljemme kaksi astetta Hyv\"{a}ntoivonniemen etel\"{a}puolitse ja tulemme Intian valtamerelle. Yksi ainoa saariryhm\"{a} on meid\"{a}n matkamme varrella, Amsterdamin saariryhm\"{a}. Tutkikaamme sit\"{a} samalla tavalla kuin Tristan da Cunhaa. Huolellisen tutkimuksen j\"{a}lkeen hyl\"{a}ttiin vuorostaan Amsterdamin saaret. Ei mik\"{a}\"{a}n sana tai sen katkelma, ranskalainen, englantilainen tai saksalainen soveltunut t\"{a}h\"{a}n Intian valtameren saaristoon. --- Me saavumme nyt Australiaan, Paganel jatkoi. --- 37. leveysaste kohtaa t\"{a}m\"{a}n mantereen Kap Bernouillin kohdalla ja j\"{a}tt\"{a}\"{a} sen Twofoldin lahdessa. Te my\"{o}nn\"{a}tte kuten min\"{a}, tekstej\"{a} v\"{a}kivaltaisesti tulkitsematta, ett\"{a} englantilainen tavu \textit{stra} ja ranskalaiset tavut \textit{austra} voivat soveltua sanaan Australia. Asia on siksi selv\"{a}, etten voi olla pit\"{a}m\"{a}tt\"{a} kiinni siit\"{a}. Kaikki hyv\"{a}ksyiv\"{a}t Paganelin p\"{a}\"{a}telm\"{a}n. Kaikki todenn\"{a}k\"{o}isyys oli sen puolella. --- Menk\"{a}\"{a}mme edemm\"{a}ksi, majuri sanoi. --- Menk\"{a}\"{a}mme, maantieteilij\"{a} vastasi, --- matka on helppo. L\"{a}hdetty\"{a}mme Twofoldin poukamasta kuljemme Australian it\"{a}puolella olevan merenhaaran poikki ja kohtaamme Uuden Seelannin. Ensinn\"{a}kin pyyd\"{a}n huomauttaa, ett\"{a} ranskalaisen asiakirjan tavut \textit{contin} viittaavat ep\"{a}\"{a}m\"{a}tt\"{o}m\"{a}ll\"{a} tavalla mantereeseen. Kapteeni Grant ei siis ole voinut pelastua Uuteen Seelantiin, joka on vain saari. Yht\"{a}kaikki, tutkikaa, verratkaa, k\"{a}\"{a}nnelk\"{a}\"{a} sanoja, ja katsokaa, voivatko ne ehk\"{a} sittenkin soveltua t\"{a}h\"{a}n uuteen seutuun. --- Eiv\"{a}t mill\"{a}\"{a}n tavoin, John Mangles vastasi, tarkasteltuaan huolellisesti asiakirjoja ja karttaa. --- Ei, sanoivat Paganelin kuulijat, jopa majurikin, --- ei. Uudesta Seelannista ei voi olla puhe. --- Nyt, maantieteilij\"{a} jatkoi, --- 37. leveysaste koko sill\"{a} laajalla alueella, joka erottaa n\"{a}m\"{a} suuret saaret Amerikan rannikosta, ei kohtaa kuin yhden hedelm\"{a}tt\"{o}m\"{a}n ja aution pikku saaren. --- Jonka nimi on? majuri kysyi. --- Katsokaa karttaa. Se on Maria-Teresia, josta nimest\"{a} en l\"{o}yd\"{a} j\"{a}lke\"{a}k\"{a}\"{a}n miss\"{a}\"{a}n n\"{a}ist\"{a} kolmesta asiakirjasta. --- Oikeassa olette, Glenarvan my\"{o}nsi. --- Min\"{a} j\"{a}t\"{a}n siis teid\"{a}n p\"{a}\"{a}tett\"{a}v\"{a}ksenne, yst\"{a}v\"{a}ni, eik\"{o} kaikki todenn\"{a}k\"{o}isyys, etten sanoisi varmuus, puhu Australian mantereen puolesta. --- Eitt\"{a}m\"{a}tt\"{a}, \textit{Duncanin} matkustajat ja kapteeni vastasivat yksimielisesti. --- John, Glenarvan kysyi nyt, --- onko teill\"{a} riitt\"{a}v\"{a}sti elintarvikkeita ja hiili\"{a}? --- On, mylord, min\"{a} varustauduin runsaasti Talkahuanossa ja muuten voimme hyvin helposti t\"{a}ydent\"{a}\"{a} varastoamme Kapkaupungissa. --- Hyv\"{a} on, siisp\"{a} l\"{a}htek\"{a}\"{a}mme matkaan... --- Viel\"{a} yksi huomautus, majuri sanoi keskeytt\"{a}en yst\"{a}v\"{a}ns\"{a}. --- Tehk\"{a}\"{a} se, MacNabbs. --- Mit\"{a} menestyksen takeita meille Australia antaakin, eik\"{o} kuitenkin olisi syyt\"{a} poiketa p\"{a}iv\"{a}ksi tai kahdeksi Tristan da Cunha- ja Amsterdam-saarille? Ne ovat matkamme varrella eiv\"{a}tk\"{a} sanottavasti hidastuta sit\"{a}. Voimme tiedustella eik\"{o} \textit{Britannia} ole j\"{a}tt\"{a}nyt sinne mit\"{a}\"{a}n j\"{a}lke\"{a} haaksirikostaan. --- Ep\"{a}uskoinen majuri! Paganel huudahti. --- H\"{a}n pit\"{a}\"{a} kiinni ep\"{a}uskostaan! --- Min\"{a} pid\"{a}n kiinni p\"{a}\"{a}asiassa siit\"{a}, ettei tarvitse palata samaa tiet\"{a}, jos Australia sattumalta ei toteuttaisi niit\"{a} toiveita, joita se her\"{a}tt\"{a}\"{a}. --- Varovaisuus voi olla hyv\"{a}ksi, Glenarvan huomautti. --- Enk\"{a} suinkaan min\"{a} varoita sit\"{a} noudattamasta, Paganel sanoi. --- P\"{a}invastoin. --- No niin, John, Glenarvan lausui, --- k\"{a}skek\"{a}\"{a} k\"{a}\"{a}nt\"{a}m\"{a}\"{a}n keula Tristan da Cunhaa kohti. --- Heti, mylord, kapteeni vastasi ja l\"{a}hti kannelle Robertin ja Mary Grantin ryhtyess\"{a} innokkain sanoin kiittelem\"{a}\"{a}n lordi Glenarvania. Amerikan rannikolta poistuen ja it\"{a}\"{a}np\"{a}in kulkien halkoi \textit{Duncanin} nopea keula pian Atlantin valtameren aaltoja. \gutchapter{TRISTAN DA CUNHA.} Jos laiva olisi purjehtinut pitkin p\"{a}iv\"{a}ntasaajaa, olisivat ne satayhdeks\"{a}nkymment\"{a}kuusi astetta, jotka erottavat Australian Amerikasta, tai tarkemmin sanoen Kap Bernouillin Kap Corrientesista, vastanneet noin kahdeksantoistatuhannen yhdeks\"{a}nsadan kilometrin matkaa. Mutta 37. leveysasteella eiv\"{a}t n\"{a}m\"{a} satayhdeks\"{a}nkymment\"{a}kuusi astetta maan pallomuodon vuoksi ole kuin viisitoistatuhatta kaksisataa kilometri\"{a}. Amerikan rannikolta Tristan da Cunhaan lasketaan olevan l\"{a}hes kolmetuhatta nelj\"{a}sataa kilometri\"{a}, jonka taipaleen John Mangles toivoi voivansa suorittaa kymmeness\"{a} p\"{a}iv\"{a}ss\"{a}, elleiv\"{a}t it\"{a}tuulet hidastuttaisi laivan kulkua. H\"{a}nell\"{a} oli siis syyt\"{a} olla tyytyv\"{a}inen, sill\"{a} iltapuolella tuuli tyyntyi tuntuvasti, viel\"{a}p\"{a} k\"{a}\"{a}ntyi, joten \textit{Duncan} saattoi jokseenkin tyynell\"{a} merell\"{a} k\"{a}ytt\"{a}\"{a} kaikkia verrattomia ominaisuuksiaan. Matkustajat olivat viel\"{a} samana p\"{a}iv\"{a}n\"{a} palanneet vanhoihin tapoihinsa laivalla. Ei n\"{a}ytt\"{a}nyt silt\"{a}, ett\"{a} he olivat olleet kokonaisen kuukauden poissa alukselta. Tyynen valtameren aaltojen asemesta levisiv\"{a}t heid\"{a}n silmiens\"{a} eteen Atlantin laineet, ja muutamia vivahteita lukuunottamatta ovat kaikki laineet samanlaisia. Luonnonvoimat, jotka olivat heit\"{a} niin ankarasti koetelleet, liittyiv\"{a}t nyt suosimaan heit\"{a}. Valtameri oli tyyni, tuuli puhalsi hyv\"{a}st\"{a} suunnasta, ja l\"{a}nsituulen pullistamat purjeet auttoivat kattilan v\"{a}sym\"{a}t\"{o}nt\"{a} h\"{o}yry\"{a}. Nopea merimatka suoritettiin siis ilman mink\"{a}\"{a}nlaisia v\"{a}likohtauksia. Odotettiin luottavaisesti Australian rannikkoa. Todenn\"{a}k\"{o}isyys muuttui varmuudeksi. Puhuttiin kapteeni Grantista ik\"{a}\"{a}n kuin laiva olisi menossa noutamaan h\"{a}nt\"{a} m\"{a}\"{a}r\"{a}tyst\"{a} satamasta. H\"{a}nen hyttins\"{a} ja h\"{a}nen kahden kumppaninsa makuusijat pantiin jo kuntoon. Mary Grant tahtoi omin k\"{a}sins\"{a} j\"{a}rjest\"{a}\"{a} ja tehd\"{a} viihtyis\"{a}ksi is\"{a}ns\"{a} hytin. Sen oli h\"{a}nelle luovuttanut herra Olbinett, joka nyt siirtyi rouva Olbinettin hyttiin. T\"{a}m\"{a} hytti oli sen kuuluisan numero kuuden vieress\"{a}, jonka Jacques Paganel oli tilannut \textit{Scotiassa}. Oppinut maantieteilij\"{a} pysytteli melkein koko ajan sinne sulkeutuneena. H\"{a}n kirjoitti aamusta iltaan teosta, jonka nimen\"{a} oli: \textit{Maantieteilij\"{a}n vaikutelmia Argentiinan aavikkotienoilta}. H\"{a}nen kuultiin \"{a}\"{a}ni v\"{a}risten maistelevan siromuotoisia lauseitaan, ennen kuin h\"{a}n uskoi ne muistikirjansa valkoisille lehdille, ja useammin kuin kerran h\"{a}n uskottomana Kliolle, historian hengett\"{a}relle, vetosi jumalaiseen Kalliopeen, joka innoittaa eeppisi\"{a} sankarirunoja. Paganel ei muuten sit\"{a} salannutkaan. Apollon neitseelliset tytt\"{a}ret j\"{a}ttiv\"{a}t mielell\"{a}\"{a}n h\"{a}nelle Parnasson tai Helikonin kukkulat. Lady Helena kiitteli h\"{a}nt\"{a} vilpitt\"{o}m\"{a}sti siit\"{a}. Majuri onnitteli h\"{a}nt\"{a} my\"{o}s n\"{a}ist\"{a} vierailuista mytologian alalle. --- Mutta kuulkaa, h\"{a}n lis\"{a}si, --- ei mit\"{a}\"{a}n hajamielisyyksi\"{a}, rakas Paganel, ja jos mieleenne sattumalta juolahtaa ryhty\"{a} opiskelemaan australian kielt\"{a}, \"{a}lk\"{a}\"{a} ryhtyk\"{o} opettelemaan sit\"{a} kiinalaisesta kieliopista! Laivalla sujui siis kaikki mit\"{a} parhaiten. Lordi ja lady Glenarvan tarkkailivat mielenkiinnolla John Manglesia ja Mary Grantia. Heill\"{a} ei ollut siihen mit\"{a}\"{a}n muistuttamista, ja kun John Mangles ei avannut suutaan, oli tietenkin parasta olla puuttumatta asiaan. --- Mit\"{a}h\"{a}n kapteeni Grant ajattelee siit\"{a}? Glenarvan kysyi er\"{a}\"{a}n\"{a} p\"{a}iv\"{a}n\"{a} lady Helenalta. --- H\"{a}n ajattelee, ett\"{a} John on Maryn arvoinen, rakas Edward, eik\"{a} siin\"{a} erehdy. Sill\"{a} v\"{a}lin laiva kulki nopeasti p\"{a}\"{a}m\"{a}\"{a}r\"{a}\"{a}ns\"{a} kohti. Viisi p\"{a}iv\"{a}\"{a} sen j\"{a}lkeen kun Kap Corrientes oli kadonnut n\"{a}kyvist\"{a}, marraskuun 16:ntena, alkoi tuntua suotuisia l\"{a}nsituulia, joita laivat k\"{a}yttiv\"{a}t hyv\"{a}kseen kiert\"{a}ess\"{a}\"{a}n Afrikan k\"{a}rke\"{a} tavallisia kaakkoistuulia vasten. \textit{Duncan} viritti kaikki purjeensa, ja keulapurje, em\"{a}purje, latvapurje, prammipurje, sivupurje, kahvelipurje ja haruspurje lev\"{a}ll\"{a}\"{a}n se kiiti eteenp\"{a}in huikeaa vauhtia. Potkuri tuskin enn\"{a}tti velloa sen keulan halkomaa pakenevaa vett\"{a}, ja n\"{a}ytti silt\"{a} kuin se olisi kilpailemassa Thamesin kuninkaallisen purjehduskerhon kilpaveneiden kanssa. Seuraavana p\"{a}iv\"{a}n\"{a} meri oli t\"{a}ynn\"{a} suunnattomia ajopuita kuin ruohojen tukkima \"{a}\"{a}ret\"{o}n lampi. Melkein olisi luullut, ett\"{a} kaikki l\"{a}heisten mantereiden pirstotut puut ja muut kasvit olisivat joutuneet t\"{a}nne ja muodostaneet ulapasta toisen Sargassomeren. Kapteeni Maury on erityisesti kiinnitt\"{a}nyt merenkulkijoitten huomiota t\"{a}llaiseen ilmi\"{o}\"{o}n. \textit{Duncan} n\"{a}ytti kulkevan pitkin laajaa ruohikkoa, jota Paganel sattuvasti vertasi Argentiinan tasankoihin, ja sen kulku hidastuikin jonkun verran. Vuorokautta my\"{o}hemmin, p\"{a}iv\"{a}n noustessa, ilmoitti t\"{a}hyst\"{a}j\"{a}matruusi: --- Maata! --- Mill\"{a} suunnalla? kysyi vahdissa oleva Tom Austin. --- Tuulen alla meist\"{a}, matruusi vastasi. T\"{a}m\"{a} aina innostava huuto toi laivan kannelle nopeasti v\"{a}ke\"{a}. Pian ilmestyi per\"{a}hytist\"{a} pitk\"{a} kaukoputki ja heti sen takana Jacques Paganel. Tiedemies kohdisti kapineensa sanottuun suuntaan, mutta ei n\"{a}hnyt maan h\"{a}iv\"{a}\"{a}k\"{a}\"{a}n. --- Katsokaa pilviin, neuvoi h\"{a}nt\"{a} John Mangles. --- Todellakin, Paganel vastasi hetken kuluttua, --- siell\"{a} p\"{a}in on jonkinlainen ep\"{a}m\"{a}\"{a}r\"{a}inen piikki. --- Se on Tristan da Cunha, John Mangles sanoi. --- Niink\"{o}? No, jos oikein muistan, tiedemies vastasi, niin olemme siit\"{a} noin sadanviidenkymmenen kilometrin p\"{a}\"{a}ss\"{a}, sill\"{a} Tristanin huippu on 2325 metri\"{a} korkea ja n\"{a}kyy siis n\"{a}in kauas. --- Aivan oikein, kapteeni John vastasi. Muutamia tunteja my\"{o}hemmin tuli t\"{a}m\"{a} hyvin korkeiden ja jyrkkien saarten ryhm\"{a} selv\"{a}sti n\"{a}kyviin. Tristanin keilamainen huippu piirtyi mustana taivaan kirkasta taustaa vasten, jota nousevan auringon s\"{a}teet kirjasivat. Pian t\"{a}st\"{a} kalliorykelm\"{a}st\"{a} erottautui p\"{a}\"{a}saari koillista kohti suuntautuvan kolmion k\"{a}rjess\"{a}. Tristan da Cunha sijaitsee maantieteellisesti sanoen kohdassa, jossa 37$^{\circ}$ 8' etel\"{a}ist\"{a} leveytt\"{a} ja 10$^{\circ}$ 44' l\"{a}ntist\"{a} pituutta leikkaavat toisiaan. Paitsi p\"{a}\"{a}saarta kuuluu t\"{a}h\"{a}n eristyneeseen Atlantin saariryhm\"{a}\"{a}n viel\"{a} kolmenkymmenenviiden kilometrin p\"{a}\"{a}ss\"{a} lounaaseen sijaitseva saari, nimelt\"{a} Inaccessible --- luoksep\"{a}\"{a}sem\"{a}t\"{o}n --- ja kahdeksantoista kilometrin p\"{a}\"{a}ss\"{a} kaakkoon Nightingalen eli Satakielen saari. Puolenp\"{a}iv\"{a}n aikaan tulivat n\"{a}kyviin molemmat t\"{a}rkeimm\"{a}t maamerkit, jotka ovat merenkulkijoille tienviittoina, nimitt\"{a}in er\"{a}\"{a}ll\"{a} Inaccessiblen niemekkeell\"{a} t\"{a}ysiss\"{a} purjeissa olevaa laivaa t\"{a}ydellisesti muistuttava kallio ja Nightingalen pohjoisp\"{a}\"{a}ss\"{a} kaksi raunioiksi murtuneen linnakkeen n\"{a}k\"{o}ist\"{a} luotoa. Kello kolmen aikaan laski \textit{Duncan} Tristan da Cunhan saaren edustalle Falmouth-poukamaan, jota Help- eli Apuniemi suojaa l\"{a}nsituulilta. Siell\"{a} oli ankkurissa muutamia valaanpyyntilaivoja; ne olivat tulleet pyydyst\"{a}m\"{a}\"{a}n hylkeit\"{a} ja muita meriel\"{a}imi\"{a}, joita n\"{a}ill\"{a} rannikoilla on lukemattomia lajeja. John Mangles ryhtyi etsim\"{a}\"{a}n hyv\"{a}\"{a} ankkuripaikkaa, sill\"{a} n\"{a}m\"{a} avoimet valkamat ovat perin vaarallisia luoteis- ja pohjoistuulien sattuessa, ja juuri t\"{a}ll\"{a} kohtaa hukkui englantilainen priki \textit{Julia} miehist\"{o}ineen p\"{a}ivineen vuonna 1829. \textit{Duncan} laski noin kilometrin p\"{a}\"{a}h\"{a}n rannasta ja ankkuroi kolmisenkymment\"{a} metri\"{a} syv\"{a}ll\"{a} kalliopohjaan. Sen j\"{a}lkeen matkustajat laskeutuivat heti suureen soutuveneeseen ja nousivat maihin hienolle, mustalle hiekalle, joka oli ker\"{a}ytynyt saaren rapautuneiden kallioiden tomuista. Koko Tristan da Cunhan saariryhm\"{a}n keskus on pieni kyl\"{a} poukaman pohjukassa isohkon ja kovasti kohisevan puron varrella. Siin\"{a} oli noin viitisenkymment\"{a} jokseenkin siisti\"{a} taloa; niiden rakentamisessa oli noudatettu sit\"{a} mittausopillista s\"{a}\"{a}nn\"{o}llisyytt\"{a}, joka n\"{a}ytt\"{a}\"{a} olevan englantilaisen rakennustaidon viimeinen sana. T\"{a}m\"{a}n pienoiskaupungin takana oli tuhat viisisataa hehtaaria tasankoa, jota rajoitti valtava laavapenger; siit\"{a} kohosi keilamainen vuorenhuippu 2325 metrin korkeuteen. Lordi Glenarvanin otti vastaan kuvern\"{o}\"{o}ri, joka on Kapkaupungin englantilaisen siirtokunnan alainen. Kun h\"{a}nelt\"{a} kysyttiin Harry Grantia ja \textit{Britanniaa}, k\"{a}vi ilmi, ett\"{a} n\"{a}m\"{a} nimet olivat t\"{a}ysin tuntemattomia. Tristan da Cunha-saaret ovat laivareitin ulkopuolella; siksi siell\"{a} k\"{a}yd\"{a}\"{a}n vain harvoin. \textit{Blendon Hallin} kuulun haaksirikon j\"{a}lkeen Inaccessible-saaren kareilla vuonna 1821 oli \"{a}sken mainitun \textit{Julian} lis\"{a}ksi kaksi laivaa tuhoutunut p\"{a}\"{a}saaren rannikolla, \textit{Primauguet} vuonna 1845 ja amerikkalainen fregatti \textit{Philadelphia} vuonna 1857. da Cunhan haaksirikkotilasto rajoittui n\"{a}ihin nelj\"{a}\"{a}n onnettomuuteen. Glenarvan ei odottanutkaan tarkempia tietoja, vaan oli kysynyt kuvern\"{o}\"{o}rilt\"{a} ainoastaan rauhoittaakseen omaatuntoaan. L\"{a}hettip\"{a} h\"{a}n laivan veneet kiert\"{a}m\"{a}\"{a}n saarta, jonka ymp\"{a}rys on korkeintaan kolmekymment\"{a} kilometri\"{a}. Lontoo tai Pariisi ei mahtuisi sinne, vaikka se olisi kolme kertaa suurempi. T\"{a}m\"{a}n etsinn\"{a}n aikana retkeiliv\"{a}t \textit{Duncanin} matkustajat kyl\"{a}ss\"{a} ja l\"{a}hirannikolla. Tristan da Cunhalla ei ole asukkaita edes sataaviitt\"{a}kymment\"{a} henke\"{a}. He ovat englantilaisia tai amerikkalaisia, naimisissa Kapmaan neekerinaisten tai hottentottien kanssa, joiden rumuudessa ei tosiaan ollut en\"{a}\"{a} lis\"{a}\"{a} toivomista. N\"{a}iden seka-avioliittojen lapset edustivat kovin ep\"{a}miellytt\"{a}v\"{a}\"{a} anglosaksilaisen j\"{a}ykkyyden ja afrikkalaisen mustaihoisuuden yhdistelm\"{a}\"{a}. Matkailijat, joista tuntui hyv\"{a}lt\"{a} polkea vankkaa maata jalkojensa alla, ulottivat k\"{a}velyretkens\"{a} sille rannalle saakka, johon vain t\"{a}ss\"{a} saaren osassa tavattava viljelty peltoalue rajoittuu. Kaikkialla muualla rannikko on jyrkk\"{a}\"{a} ja hedelm\"{a}t\"{o}nt\"{a} laavat\"{o}rm\"{a}\"{a}. Siell\"{a} oli suuria albatrosseja ja tyhmi\"{a} pingviinej\"{a} sadoin tuhansin. Tarkasteltuaan n\"{a}it\"{a} tuliper\"{a}isi\"{a} kallioita matkailijat palasivat tasangolle p\"{a}in; lukuisia vuorikartion ikuisesta lumesta vetens\"{a} saavia puroja kohisi siell\"{a} t\"{a}\"{a}ll\"{a}; vihre\"{a}t pensaat, joissa n\"{a}kyi melkein yht\"{a} paljon varpusia kuin kukkiakin, tekiv\"{a}t maan el\"{a}v\"{a}mm\"{a}ksi; yksi ainoa puu, jonkinlainen \textit{phylica}-laji, kuuden ja puolen metrin korkuinen, ja \textit{tusseh}, j\"{a}ttil\"{a}ism\"{a}inen \textit{arundinacea}-sukuun kuuluva puuvartinen kasvi, kasvoi vihannoivalla laitumella; muuan r\"{o}nsyinen, kitker\"{a}marjainen \textit{acena}-laji, rehev\"{a}t, sotkus\"{a}ikeiset \textit{lomariat}, muutamat monivuotiset pensaskasvit, \textit{ancerinit}, joiden hyv\"{a} tuoksu tuntui tuulenhenk\"{a}yksess\"{a}, sammaleet, villi selleri ja sanajalat olivat harvalajisena, mutta runsaana kasvistona. Ikuinen kev\"{a}t tuhlasi t\"{a}lle luonnon suosimalle saarelle suloista vaikutustaan. Paganel v\"{a}itti innostuneena, ett\"{a} F\'{e}nelonin ylist\"{a}m\"{a} kuuluisa Ogygia oli t\"{a}\"{a}ll\"{a}. H\"{a}n kehotti lady Glenarvania etsim\"{a}\"{a}n jotakin luolaa ryhty\"{a}kseen kauniin Kalypson seuraajaksi eik\"{a} pyyt\"{a}nyt itselleen muuta tointa kuin saada olla ``yksi h\"{a}nt\"{a} palvelevia nymfej\"{a}''. N\"{a}in puhellen ja ihaillen palasivat palvelijat illan tullen laivalle; kyl\"{a}n ymp\"{a}rist\"{o}ss\"{a} oli nauta- ja lammaskarjaa laitumella; vehn\"{a}-, maissi- ja maustekasvipellot, joihin ensimm\"{a}iset siemenet oli tuotu nelj\"{a}kymment\"{a} vuotta sitten, levittiv\"{a}t rikkauksiaan p\"{a}\"{a}kaupungin kaduille saakka. Samaan aikaan kuin lordi Glenarvan palasi laivalleen, saapuivat my\"{o}s \textit{Duncanin} venekunnat takaisin. Ne olivat muutamassa tunnissa kiert\"{a}neet saaren. Matkalla ei ollut tavattu v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n j\"{a}lke\"{a} \textit{Britanniasta}. Niinp\"{a} t\"{a}st\"{a} kierroksesta oli ainoana tuloksena Tristanin saaren lopullinen poistaminen etsiskelyn ohjelmasta. Sen j\"{a}lkeen saattoi \textit{Duncan} j\"{a}tt\"{a}\"{a} t\"{a}m\"{a}n afrikkalaisen saariryhm\"{a}n ja jatkaa matkaansa it\"{a}\"{a}n. Kun kuitenkaan ei matkaan l\"{a}hdetty viel\"{a} samana iltana, se johtui siit\"{a}, ett\"{a} Glenarvan antoi miehist\"{o}lle luvan ryhty\"{a} pyydyst\"{a}m\"{a}\"{a}n hylkeit\"{a} --- merivasikoita, merileijonia, merikarhuja ja merinorsuja --- joita Falmouth-poukaman rannat olivat t\"{a}ynn\"{a}. Muinoin saaren vesill\"{a} uiskenteli oikeita valaskaloja, mutta niin monet pyydyst\"{a}j\"{a}t olivat niit\"{a} ahdistaneet ja keih\"{a}st\"{a}neet, ett\"{a} niit\"{a} tuskin oli ainoatakaan j\"{a}ljell\"{a}. Hylkeit\"{a} sen sijaan oli joukoittain. Laivan miehist\"{o} p\"{a}\"{a}tti k\"{a}ytt\"{a}\"{a} y\"{o}n niiden pyydyst\"{a}miseen ja seuraavan p\"{a}iv\"{a}n taas runsaan \"{o}ljyvaraston kokoamiseen. N\"{a}in ollen lykk\"{a}ytyi \textit{Duncanin} l\"{a}ht\"{o} ylihuomiseen, 20. p\"{a}iv\"{a}ksi marraskuuta. Illallista sy\"{o}dess\"{a} Paganel kertoi Tristanin saarista yht\"{a} ja toista, mik\"{a} her\"{a}tti h\"{a}nen kuulijoidensa mielenkiintoa. Niinp\"{a} he saivat kuulla, ett\"{a} t\"{a}m\"{a} saariryhm\"{a}, jonka vuonna 1506 l\"{o}ysi portugalilainen Tristao da Cunha, muuan Albuquerguen tovereista, pysyi sen j\"{a}lkeen toista vuosisataa t\"{a}ysin tutkimattomana. N\"{a}it\"{a} saaria pidettiin, syyst\"{a} kyll\"{a}kin, myrskypes\"{a}kkein\"{a}, ja ne olivat suunnilleen samassa maineessa kuin Bermudan saaret. Siksi ei niit\"{a} l\"{a}hestytty eik\"{a} yksik\"{a}\"{a}n laiva laskenut sinne muuten kuin Atlantin myrskyjen pakottamana. Vasta vuonna 1697 sinne saapui kolme hollantilaista It\"{a}-Intian kauppayhti\"{o}n laivaa; t\"{a}ll\"{o}in laskettiin niiden maantieteellinen asema, jonka sitten vuonna 1700 kuuluisa t\"{a}htitieteilij\"{a} Halley tarkisti. Vuosien 1712 ja 1767 v\"{a}lill\"{a} sinne poikkesi muutamia ranskalaisia merenkulkijoita ja sitten varsinkin Laperouse, joka ohjeidensa mukaan k\"{a}vi t\"{a}\"{a}ll\"{a}kin kuuluisalla matkallaan vuonna 1785. N\"{a}m\"{a} saaret, joissa niin harvoin k\"{a}ytiin, olivat j\"{a}\"{a}neet asumattomiksi, kunnes vuonna 1811 muuan amerikkalainen, Jonathan Lambert, ryhtyi tuomaan sinne siirtolaisia. H\"{a}n saapui sinne kahden kumppaninsa kanssa tammikuussa, ja he j\"{a}iv\"{a}t rohkeasti toteuttamaan siirtokuntasuunnitelmaansa. Hyv\"{a}ntoivonniemen englantilainen kuvern\"{o}\"{o}ri, joka oli saanut kuulla heid\"{a}n menestyksest\"{a}\"{a}n, tarjosi heille Englannin suojelusta. Jonathan otti sen vastaan ja nosti telttansa katolle Englannin lipun. Niinp\"{a} olisi luullut h\"{a}nen voivan turvallisesti hallita ``v\"{a}ke\"{a}\"{a}n'', johon kuului ainoastaan vanha italialainen ja er\"{a}s portugalilainen mulatti, mutta kerran ollessaan tutkimassa valtakuntansa rajoja h\"{a}n upposi tai upotettiin --- l\"{a}hemmin ei asiasta tiedet\"{a}. Tuli vuosi 1816. Napoleon vietiin vankina St. Helenalle, ja Englanti sijoitti h\"{a}nt\"{a} varmemmin vartioidakseen osaston varusv\"{a}ke\"{a} Ascensionin ja toisen Tristan da Cunhan saarelle. Tristanin varusv\"{a}ken\"{a} oli komppania Kapmaan tykist\"{o}st\"{a} ja osasto hottentotteja. N\"{a}m\"{a} oleilivat saarella vuoteen 1821, jolloin heid\"{a}t, St. Helenan vangin kuoltua, vietiin takaisin Kapmaahan. --- Mutta yksi ainoa eurooppalainen, Paganel lis\"{a}si --- muuan korpraali, skotlantilainen... --- Mit\"{a}? Skotlantilainenko? kysyi majuri, joka aina erikoisesti piti silm\"{a}ll\"{a} omia maanmiehi\"{a}\"{a}n. --- H\"{a}nen nimens\"{a} oli William Glass, Paganel vastasi, --- ja h\"{a}n j\"{a}i saarelle vaimonsa ja kahden hottentotin kanssa. Pian sen j\"{a}lkeen skotlantilaiseen yhtyi kaksi englantilaista, toinen matruusi ja toinen Thames-virran kalastaja, joka oli ennen ollut rakuunana Argentiinan ratsuv\"{a}ess\"{a}, ja sitten, viel\"{a} samana vuonna 1821, pelastui er\"{a}s \textit{Blendon Hallin} haaksirikkoisista nuoren vaimonsa kanssa Tristanin saarelle. Niinp\"{a} siis t\"{a}ll\"{a} saarella oli vuonna 1821 kaikkiaan kuusi miest\"{a} ja kaksi naista. Vuonna 1829 tiedet\"{a}\"{a}n t\"{a}\"{a}ll\"{a} olleen seitsem\"{a}n miest\"{a}, kuusi naista ja nelj\"{a}toista lasta. Vuonna 1835 oli ihmisten lukum\"{a}\"{a}r\"{a} noussut nelj\"{a}\"{a}nkymmeneen, ja nyt se on runsaasti kolminkertainen. --- N\"{a}in alkavat kansakunnat, Glenarvan lausui. --- Min\"{a} lis\"{a}isin, Paganel jatkoi, --- t\"{a}ydent\"{a}\"{a}kseni Tristan da Cunhan historiaa, ett\"{a} minusta t\"{a}m\"{a} saari tuntuu yht\"{a} hyvin kuin Juan Fernandez ansaitsevan Robinsonin saaren maineen. N\"{a}hk\"{a}\"{a}s, joskin Juan Fernandezille j\"{a}tettiin per\"{a}tysten kaksi matruusia, niin sama kohtalo oli sattua kahdelle tiedemiehelle Tristan da Cunhalla. Vuonna 1793 joutui muuan maanmiehi\"{a}ni, luonnontutkija Aubert Dupetit-Thouars, eksyksiin ker\"{a}tess\"{a}\"{a}n innoissaan kasveja, ja l\"{o}ysi laivan vasta, kun kapteeni jo oli k\"{a}skenyt nostaa ankkurin. Vuonna 1824 taas er\"{a}s teid\"{a}n maanmiehenne, rakas Glenarvan, mainio piirt\"{a}j\"{a}, Auguste Earle, j\"{a}i tosiaankin t\"{a}lle saarelle kahdeksaksi kuukaudeksi. H\"{a}nen kapteeninsa ei muistanut, ett\"{a} h\"{a}n viel\"{a} oli maissa, ja purjehti Kapkaupunkiin. --- Sit\"{a}p\"{a} sopii sanoa hajamieliseksi kapteeniksi, majuri huomautti. --- Eik\"{o}h\"{a}n se liene ollut teid\"{a}n sukulaisenne, Paganel? --- Ellei ollut, majuri, niin olisi ainakin ansainnut olla! Tiedemiehen vastaus p\"{a}\"{a}tti t\"{a}m\"{a}n keskustelun. Y\"{o}n aikana oli \textit{Duncanin} miehist\"{o} saanut runsaan saaliin, ja noin viitisenkymment\"{a} suurta hyljett\"{a} oli saanut heitt\"{a}\"{a} henkens\"{a}. Kun lordi Glenarvan kerran oli sallinut pyydystyksen. h\"{a}n ei tietenk\"{a}\"{a}n voinut kielt\"{a}\"{a} saaliin k\"{a}ytt\"{o}\"{a}. Niinp\"{a} seuraava p\"{a}iv\"{a} kului \"{o}ljyn kokoamiseen, samalla kun n\"{a}iden hy\"{o}dyllisten el\"{a}inten vuotia muokattiin. Matkustajat k\"{a}yttiv\"{a}t tietenkin t\"{a}t\"{a} toisen p\"{a}iv\"{a}n viiv\"{a}hdyst\"{a} k\"{a}yd\"{a}kseen uudelleen saarella. Glenarvan ja majuri ottivat mukaan pyssyns\"{a} ampuakseen da Cunhan riistaa. T\"{a}ll\"{a} kertaa samottiin vuoren juurelle saakka, alueelle, joka oli t\"{a}ynn\"{a} kuonaa, huokoista ja mustaa laavaa ja kaikkinaisia tulivuorenpurkausten j\"{a}tteit\"{a}. Vuori kohosi sirpalekallioiden keskelt\"{a}. Olisi ollut vaikeata erehty\"{a} t\"{a}m\"{a}n huikean vuoren luonteesta, ja englantilainen kapteeni Carmichael oli kyll\"{a} ollut oikeassa arvellessaan sit\"{a} sammuneeksi tulivuoreksi. Mets\"{a}miehet saivat n\"{a}kyviins\"{a} muutamia villisikoja. Majuri ampui niist\"{a} yhden. Glevarvan tyytyi pudottamaan muutamia mustia pyit\"{a}. N\"{a}ist\"{a}h\"{a}n laivan kokki saattoi laittaa mainiota muhennosta. Korkeammilla paikoilla n\"{a}htiin suuri joukko vuorikauriita. Mit\"{a} taas tuli villikissoihin, jotka olivat \"{a}k\"{a}isi\"{a}, suuria ja voimakkaita, jopa koirillekin pelottavia, ne n\"{a}yttiv\"{a}t viihtyv\"{a}n hyvin ja aikaa my\"{o}ten varttuvan vaarallisiksi pedoiksi. Kello kahdeksan illalla olivat kaikki j\"{a}lleen laivalla, ja seuraavana y\"{o}n\"{a} j\"{a}tti \textit{Duncan} ainiaaksi Tristan da Cunhan saaret. \gutchapter{AMSTERDAMIN SAARI.} John Manglesin tarkoituksena oli k\"{a}yd\"{a} ottamassa hiili\"{a} Hyv\"{a}ntoivonniemelt\"{a}. H\"{a}nen oli siis hiukan poikettava 37. asteelta ja noustava kaksi astetta pohjoista kohti. \textit{Duncan} oli pasaatituulten alapuolella ja kohtasi nopeita, matkalleen eritt\"{a}in suotuisia l\"{a}nsituulia, ns. vastapasaatituulia, joiden rajana n\"{a}ytt\"{a}\"{a} olevan kolmaskymmenes leveysaste. Niinp\"{a} se p\"{a}\"{a}si vajaassa kuudessa p\"{a}iv\"{a}ss\"{a} ne noin kaksi ja puoli tuhatta kilometri\"{a}, jotka erottavat Tristan da Cunhan Afrikan etel\"{a}k\"{a}rjest\"{a}. Kello kolmen aikaan iltapuolella, 24. p\"{a}iv\"{a}n\"{a} marraskuuta, tuli n\"{a}kyviin Table-vuori, ja v\"{a}h\"{a}ist\"{a} my\"{o}hemmin totesi John ns. Signaali-vuoren, jonka ohitse tullaan poukamaan. Sinne saavuttiin noin kahdeksan paikkeilla ja ankkuri laskettiin Kapkaupungin satamaan. Maantieteellisen seuran j\"{a}senen\"{a} Paganel ei tietenk\"{a}\"{a}n voinut olla tiet\"{a}m\"{a}tt\"{a}, ett\"{a} Afrikan etel\"{a}k\"{a}rjen oli ensimm\"{a}isen kerran l\"{o}yt\"{a}nyt portugalilainen amiraali Bartolomeus Diaz vuonna 1486 mutta ett\"{a} sen ymp\"{a}ri oli kulkenut vasta kuuluisa Vasco di Gama vuonna 1497. Ja kuinkapa Paganel olisikaan voinut olla t\"{a}t\"{a} tiet\"{a}m\"{a}tt\"{a}, kun Camo\"{e}ns \textit{Lusiadeissaan} laulaa juuri t\"{a}m\"{a}n suuren l\"{o}yt\"{o}retkeilij\"{a}n kunniaa? Mutta h\"{a}n teki t\"{a}st\"{a} puhuessaan kuitenkin merkillisen huomautuksen: jos Diaz vuonna 1486, kuusi vuotta ennen Kristoffer Kolumbuksen ensimm\"{a}ist\"{a} matkaa, olisi kiert\"{a}nyt l\"{o}yt\"{a}m\"{a}ns\"{a} Hyv\"{a}ntoivonniemen, niin olisi Amerikan l\"{o}yt\"{a}minen voinut lykk\"{a}yty\"{a} ep\"{a}m\"{a}\"{a}r\"{a}iseksi ajaksi. Olihan n\"{a}et kulku t\"{a}m\"{a}n niemen ymp\"{a}ri lyhyin ja suorin tie It\"{a}-Intiaan. Ja mit\"{a} suuri genovalainen l\"{a}nteenp\"{a}in l\"{a}htiess\"{a}\"{a}n etsik\"{a}\"{a}n muuta kuin lyhyint\"{a} tiet\"{a} mausteiden maahan? Jos siis Hyv\"{a}ntoivonniemi olisi kierretty, h\"{a}nen retkens\"{a} olisi j\"{a}\"{a}nyt tarkoituksettomaksi ja siis arvattavasti tekem\"{a}tt\"{a}. Kapkaupungin, joka sijaitsee Kap-poukaman pohjukassa, perusti vuonna 1652 hollantilainen Van Riebeck. Siit\"{a} tuli p\"{a}\"{a}paikka t\"{a}rke\"{a}lle siirtokunnalle, joka vuonna 1815 tehdyiss\"{a} sopimuksissa lopullisesti joutui Englannille. \textit{Duncanin} matkustajat k\"{a}yttiv\"{a}t siell\"{a} poikkeamista hyv\"{a}kseen k\"{a}yd\"{a}kseen kaupunkia katsomassa. Heill\"{a} oli aikaa vain kaksitoista tuntia, sill\"{a} yksi p\"{a}iv\"{a} riitti kapteeni Johnille varastojen t\"{a}ydent\"{a}miseen, ja h\"{a}n halusi jatkaa matkaa 26. p\"{a}iv\"{a}n\"{a} marraskuuta, heti aamulla. Enemp\"{a}\"{a} ei muuten tarvittukaan s\"{a}\"{a}nn\"{o}llisten ruutujen l\"{a}pikulkuun t\"{a}ll\"{a} Kapkaupungin nimisell\"{a} shakkilaudalla, jolla sen kolmekymment\"{a}tuhatta asukasta, toiset valkoisia, toiset mustia, n\"{a}yttelev\"{a}t kuninkaan, kuningattaren, juoksijan tai talonpojan, jotkut ehk\"{a} hevosenkin osaa. N\"{a}in ainakin Paganel lausui. Ja tosiaan, kun on n\"{a}hnyt kaupungin kaakkoispuolella olevan linnan, hallintorakennuksen ja sen puutarhan, p\"{o}rssin, museon, Bartolomeus Diazin l\"{o}yt\"{o}ns\"{a} merkiksi pystytt\"{a}m\"{a}n kiviristin ja juonut lasin pontai-viini\"{a}, parasta mit\"{a} Constantin alueelta saadaan, niin voi huoleti l\"{a}hte\"{a}. Ja niin retkeilij\"{a}mme tekiv\"{a}tkin seuraavana p\"{a}iv\"{a}n\"{a} aamun valjetessa. \textit{Duncan} levitti viisto-, harus-, keula- ja latvapurjeet ja kaarsi muutamaa tuntia my\"{o}hemmin kuuluisan Myrskyniemen, jolle Portugalin hyv\"{a}ntoivoinen kuningas Juhana II t\"{a}ysin aiheettomasti antoi Hyv\"{a}ntoivonniemen nimen. Kapkaupungista Amsterdamin saarelle lasketaan olevan runsaasti viisituhatta kilometri\"{a}; suotuisissa oloissa saattoi \textit{Duncan} tehd\"{a} matkan noin kymmeness\"{a} p\"{a}iv\"{a}ss\"{a}. Ja retkeilij\"{a}t tuntuivat tosiaan olevan luonnonvoimien suosiossa, toisin kuin pampan poikki samotessaan. Tuuli ja vesi, jotka mantereella olivat liittoutuneet heit\"{a} vastaan, olivat nyt ryhtyneet viem\"{a}\"{a}n heit\"{a} eteenp\"{a}in. --- Ah, meri! meri! Paganel toisteli, --- se on ihmisvoimien etevin harjoituskentt\"{a}, ja laiva on kulttuurin varsinainen kulkuneuvo! Ajatelkaa, yst\"{a}v\"{a}ni! Jos maapallo olisi vain mannerta, ei siit\"{a} viel\"{a} yhdeks\"{a}nnell\"{a}toista vuosisadalla tunnettaisi tuhannetta osaa. Katsokaa vain, kuinka on suurten mannerten sis\"{a}osien laita. Siperian aroille, Keski-Aasian yl\"{a}ng\"{o}ille, Afrikan sademetsiin, Amerikan preerioille, Australian autiomaihin, napaseutujen j\"{a}isille lumikentille ihminen uskaitaa tuskin yritt\"{a}k\"{a}\"{a}n ja uskaliainkin ep\"{a}r\"{o}i. Ei p\"{a}\"{a}se kulkemaan. Kulkuneuvot ovat riitt\"{a}m\"{a}tt\"{o}m\"{a}t. Kuumuus, taudit, alkuasukkaiden julmuus ovat usein auttamattomina estein\"{a}. Parikymment\"{a} kilometri\"{a} er\"{a}maata erottaa ihmisi\"{a} enemm\"{a}n kuin viisisataa kilometri\"{a} vett\"{a}! Toisella rannalla ollaan toisen rannan naapureita, mutta muukalaisia, kun vain mets\"{a}kin on erottamassa! Englanti on Australian rajalla, kun taas Egypti esimerkiksi tuntuu olevan miljoonien kilometrien p\"{a}\"{a}ss\"{a} Senegalista ja Peking toisella puolella maapalloa kuin Pietari! Valtameren yli on nyky\"{a}\"{a}n helpompi kulkea kuin Saharan poikki kapeimmaltakaan kohdalta, ja merten ansio on, kuten muuan amerikkalainen oppinut sattuvasti on sanonut, ett\"{a} maailman eri osien v\"{a}lille on syntynyt yleinen sukulaisuus. Paganel oli puhunut innostuneesti, eik\"{a} majurillakaan ollut yht\"{a}\"{a}n sanaa tingitt\"{a}v\"{a}n\"{a} t\"{a}st\"{a} valtameren ylistyksest\"{a}. Jos Harry Grantin etsimiseksi olisi t\"{a}ytynyt seurata 37. leveysastetta yksinomaan maata pitkin, ei yritykseen olisi voitu lainkaan ryhty\"{a}; mutta nyt kantoi meri rohkeat etsij\"{a}t maasta toiseen ja 6. p\"{a}iv\"{a}n\"{a} joulukuuta, aamun sarastaessa, nousi uusi vuori n\"{a}kyviin aaltojen keskelt\"{a}. Se oli Amsterdamin saari, jonka asema on 37$^{\circ}$ 47' leveytt\"{a} ja 77$^{\circ}$ 34' pituutta ja jonka korkein huippu n\"{a}kyy kirkkaalla ilmalla yhdeks\"{a}nkymmenen kilometrin p\"{a}\"{a}h\"{a}n. Kello kahdeksan aikana sen viel\"{a} ep\"{a}m\"{a}\"{a}r\"{a}inen muoto muistutti hyvinkin Teneriffan huippua. --- Ja niinmuodoin, Glenarvan huomautti, --- se on my\"{o}s samanlainen kuin Tristan da Cunha. --- J\"{a}rkev\"{a}sti p\"{a}\"{a}telty, Paganel vastasi, --- sen maantieteellis-mittausopillisen selvi\"{o}n mukaan, ett\"{a} jos jotkut kaksi saarta ovat kolmannen n\"{a}k\"{o}isi\"{a}, ne ovat my\"{o}s kesken\"{a}\"{a}n yhdenn\"{a}k\"{o}isi\"{a}. Min\"{a} lis\"{a}isin, ett\"{a} samoin kuin Tristan da Cunha, my\"{o}s Amsterdamin saari on ja on ollut yht\"{a} rikas hylkeist\"{a} ja Robinsoneista. --- Onko siis Robinsoneja kaikkialla? lady Helena kysyi. --- Kautta kunniani, rouva, Paganel vastasi, --- min\"{a} tunnen v\"{a}h\"{a}n saaria, joilla ei olisi ollut sen luontoisia seikkailuja; jopa paljon ennen kuin teid\"{a}n kuolematon maamiehenne, Daniel Defoe, kirjoitti romaaninsa, oli sattuma sen jo toteuttanut. --- Herra Paganel, Mary Grant sanoi, --- sallitteko minun tehd\"{a} teille yhden kysymyksen? --- Kaksi, rakas neiti, ja min\"{a} lupaan vastata niihin. --- No, nuori neito jatkoi, --- olisiko teist\"{a} hyvin kamalaa joutua olemaan autiolla saarella? --- Minustako? Paganel huudahti. --- No no, yst\"{a}v\"{a}ni, majuri huomautti, --- \"{a}lk\"{a}\"{a} nyt sent\"{a}\"{a}n selitt\"{a}k\"{o}, ett\"{a} se on teid\"{a}n hartain halunne! --- Sit\"{a} en v\"{a}it\"{a}, maantieteilij\"{a} vastasi, --- mutta sellainen seikkailu ei olisi minusta kovin ik\"{a}v\"{a}k\"{a}\"{a}n. Min\"{a} aloittaisin uuden el\"{a}m\"{a}n. Mets\"{a}st\"{a}isin, kalastaisin, asuisin talvella luolassa, kes\"{a}ll\"{a} puussa, rakentaisin varastopaikkoja sadolle; sanalla sanoen, asuttaisin saareni. --- Ihan yksin\"{a}nnek\"{o}? --- Yksin tietenkin, jos tarvittaisiin. Muuten, onko ihminen milloinkaan yksin? Eik\"{o} h\"{a}n voi valita itselleen yst\"{a}vi\"{a} el\"{a}imist\"{a}, kesytt\"{a}\"{a} nuorta vuohenkaritsaa, puhuvaa papukaijaa, ovelaa apinaa? Ja jos kohtalo l\"{a}hett\"{a}\"{a} luoksenne jonkun kumppanin, kuten Robinsonille uskollisen Perjantain, mit\"{a} ihminen viel\"{a} tarvitsee ollakseen onnellinen? Kaksi yst\"{a}vyst\"{a} yhdell\"{a} kalliolla, sit\"{a}h\"{a}n on onni! Olettakaa esimerkiksi, ett\"{a} majuri ja min\"{a}... --- Kiitoksia, majuri vastasi, --- minulla ei ole halua ryhty\"{a} Robinsoniksi, ja min\"{a} sovin sellaiseen perin huonosti. --- Rakas herra Paganel, lady Helena puuttui puheeseen, --- teid\"{a}n mielikuvituksenne vie teid\"{a}t taas utukuvien maille. Mutta todellisuus on luullakseni hyvin erilainen kuin unelma. Te ajattelette vain sellaista kuviteltua Robinsonia, joka huolellisesti sijoitetaan hyvin valitulle saarelle ja jota luonto kohtelee hemmoitellen! Te n\"{a}ette asioista vain parhaan puolen! --- Mit\"{a}, rouva, ettek\"{o} usko, ett\"{a} ihminen voisi olla onnellinen autiolla saarella? --- En. Ihminen on luotu yhdysel\"{a}m\"{a}\"{a} eik\"{a} erist\"{a}ytymist\"{a} varten. Yksin\"{a}isyyden t\"{a}ytyy synnytt\"{a}\"{a} ep\"{a}toivoa. Se on vain ajan kysymys. Se ett\"{a} alussa aineellisen toimeentulon huolet, el\"{a}m\"{a}n tarpeet, vaatisivat aalloista juuri pelastuneen kaiken huomion, ett\"{a} nykyhetken v\"{a}ltt\"{a}m\"{a}tt\"{o}myys k\"{a}\"{a}nt\"{a}isi h\"{a}nen ajatuksensa pois tulevaisuuden toivottomuudesta, on kyll\"{a} mahdollista. Mutta sitten, kun h\"{a}n tuntee itsens\"{a} yksin\"{a}iseksi, olevansa kaukana vertaisistaan, ilman toivoa saada n\"{a}hd\"{a} j\"{a}lleen maansa ja omaisensa, mit\"{a} h\"{a}n ajatteleekaan, mit\"{a} k\"{a}rsiik\"{a}\"{a}n? H\"{a}nen saarensa on koko maailma. Koko ihmiskunta supistuu h\"{a}neen, ja kun kuolema tulee, kamala kuolema t\"{a}ss\"{a} yksin\"{a}isyydess\"{a}, h\"{a}n on kuin maailman viimeinen ihminen sen viimeisen\"{a} p\"{a}iv\"{a}n\"{a}. Uskokaa minua, Paganel, parempi on, ettei tarvitse olla se ihminen. Paganel alistui, vaikka haikein mielin, lady Helenan todisteluun, ja keskustelua jatkettiin n\"{a}in yksin\"{a}isyyden eduista ja haitoista, kunnes \textit{Duncan} laski ankkurin puolentoista kilometrin p\"{a}\"{a}h\"{a}n Amsterdamin saaren rannasta. T\"{a}h\"{a}n erilliseen ryhm\"{a}\"{a}n Intian valtameress\"{a} kuuluu kaksi saarta, jotka ovat noin viidenkymmenenviiden kilometrin p\"{a}\"{a}ss\"{a} toisistaan, samalla meridiaanilla kuin Intian niemimaan k\"{a}rki; pohjoisempana on Amsterdamin eli Pyh\"{a}n Pietarin saari, etel\"{a}mp\"{a}n\"{a} Pyh\"{a}n Paavalin saari, mutta on my\"{o}nnett\"{a}v\"{a}, ett\"{a} sek\"{a} maantieteilij\"{a}t ett\"{a} merenkulkijat ovat usein sekoittaneet ne. N\"{a}m\"{a} saaret l\"{o}ysi joulukuussa 1796 hollantilainen Vlaming, ja niit\"{a} tutki sittemmin d'Entrecasteaux, joka \textit{Esperance}- ja \textit{Recherche}-nimisill\"{a} laivoilla oli etsim\"{a}ss\"{a} Laperousea. T\"{a}st\"{a} matkasta johtuu saarten sekoittaminen toisiinsa. Merenkulkija Barrow, Beautemps-Beaupre d'Entrecasteauxin kartassa, Horsburg, Pinkerton ja muut maantieteilij\"{a}t ovat s\"{a}\"{a}nn\"{o}llisesti esitt\"{a}neet Pyh\"{a}n Pietarin saarta Pyh\"{a}n Paavalin saarena ja p\"{a}invastoin. Vuonna 1859 v\"{a}lttiv\"{a}t it\"{a}valtalaisen fregatin \textit{Novaran} upseerit tekem\"{a}st\"{a} t\"{a}t\"{a} erehdyst\"{a}, jonka Paganel erikoisesti tahtoi oikaista. Pyh\"{a}n Paavalin saari, joka on Amsterdamin saaren etel\"{a}puolella, on asumaton, kartiomaisesta vuoresta, arvatenkin entisest\"{a} tulivuoresta, muodostunut luoto. Amsterdamin saari taas, jonne vene kuljetti \textit{Duncanin} matkustajat, on noin kaksikymment\"{a} kilometri\"{a} ymp\"{a}rysmitaltaan. Siell\"{a} asuu muutamia vapaaehtoisia maanpakolaisia, jotka ovat valinneet itselleen t\"{a}m\"{a}n kaukaisen asuinpaikan. He valvovat kalastusta, joka koko saaren tavoin kuuluu er\"{a}\"{a}lle herra Otovanille, Reunion-saaren kauppiaalle. T\"{a}m\"{a} hallitsija, jota Euroopan suurvallat eiv\"{a}t viel\"{a} ole tunnustaneet, nostaa t\"{a}\"{a}lt\"{a} pankkitililleen seitsem\"{a}nkymment\"{a}viisi tai kahdeksankymment\"{a} tuhatta frangia kalastamalla, suolaamalla ja myym\"{a}ll\"{a} ``cheilodactylus'ta'', jota tavallisessa puheessa sanotaan turskaksi. Muuten t\"{a}m\"{a} Amsterdamin saari oli m\"{a}\"{a}r\"{a}tty tulemaan ja j\"{a}\"{a}m\"{a}\"{a}n ranskalaiseksi. Se kuului heti alusta alkaen, ensimm\"{a}isen valtaajan oikeudella herra Caminille, laivanvarustajalle Bourbonin Saint-Denisist\"{a}; sitten se luovutettiin, jonkinlaisen kansainv\"{a}lisen sopimuksen nojalla er\"{a}\"{a}lle puolalaiselle, joka piti malgachelaisia orjia sit\"{a} viljelem\"{a}ss\"{a}. Mik\"{a} on puolalaista, on ranskalaista, t\"{a}ss\"{a} tapauksessa viel\"{a}p\"{a} niin t\"{a}ydellisesti, ett\"{a} puolalainen saari muuttui j\"{a}lleen ranskalaiseksi herra Otovanin haltuun joutuessaan. \textit{Duncanin} saapuessa sinne 6. p\"{a}iv\"{a}n\"{a} joulukuuta 1864 oli sen v\"{a}est\"{o}n\"{a} kolme asukasta, yksi ranskalainen ja kaksi mulattia, kaikki kolme edell\"{a} mainitun kauppiaan ja omistajan palveluksessa. Jo hyvin i\"{a}k\"{a}s ranskalainen, kunnianarvoisa herra Viot, edusti varsin kohteliaasti saaren is\"{a}nt\"{a}\"{a}, etenkin saatuaan puristaa maanmiehens\"{a} Paganelin k\"{a}tt\"{a}. H\"{a}n lausui, ett\"{a} h\"{a}nelle oli onnen p\"{a}iv\"{a}, kun h\"{a}n sai vastaanottaa niin miellytt\"{a}vi\"{a} vieraita. Pyh\"{a}n Pietarin saarella k\"{a}vi vain hylkeenpyyt\"{a}ji\"{a} ja joku valaanpyyt\"{a}j\"{a}, karkeatapaista v\"{a}ke\"{a}, joka ei ole juurikaan sivistynyt seurusteltuaan ``meren koirien'' kanssa. Viot esitteli alamaisensa, molemmat mulatit; lukuunottamatta muutamia sis\"{a}maassa el\"{a}vi\"{a} villisikoja ja useita tuhansia tyhmi\"{a} pingviinej\"{a}, oli nyt koolla saaren koko el\"{a}v\"{a} asujamisto. Pieni h\"{o}kkeli, jossa n\"{a}m\"{a} kolme saarelaista asuivat, sijaitsi lounaassa luonnonsataman pohjukassa, joka oli syntynyt siten, ett\"{a} osa vuorta oli murtunut. Juuri v\"{a}h\"{a}\"{a} ennen Otovan I:n hallituskautta oli Pyh\"{a}n Pietarin saari ollut haaksirikkoisten turvapaikkana. Paganel her\"{a}tti kuulijoissaan suurta mielenkiintoa aloittamalla ensimm\"{a}isen kertomuksensa sanoilla: \textit{Kahden Amsterdamin saarelle j\"{a}tetyn skotlantilaisen tarina}. Se tapahtui vuonna 1827. Englantilainen laiva \textit{Palmira} huomasi saaren tullessa n\"{a}kyviin ilmaan nousevan savua. Kapteeni l\"{a}hestyi rantaa ja n\"{a}ki pian kaksi miest\"{a}, jotka antoivat h\"{a}t\"{a}merkkej\"{a}. H\"{a}n l\"{a}hetti maihin veneen, joka toi tullessaan Jacques Painen, kaksikymment\"{a}kaksivuotiaan miehen, ja Robert Proudfootin, joka oli noin nelj\"{a}nkymmenenkahdeksan ik\"{a}inen. N\"{a}m\"{a} kovaonniset olivat tuskin en\"{a}\"{a} ihmisen n\"{a}k\"{o}isi\"{a}. Kahdeksantoista kuukautta he olivat el\"{a}neet melkein ilman ruokaa ja raikasta vett\"{a}, el\"{a}telleet itse\"{a}\"{a}n simpukoilla, kalastelleet huonolla koukkupahaisella, saaneet silloin t\"{a}ll\"{o}in kiinni jonkun eksyneen villisianporsaan, mutta eiv\"{a}t nyt kolmeen p\"{a}iv\"{a}\"{a}n olleet sy\"{o}neet mit\"{a}\"{a}n, vaan valvoneet kuin vestaalit tulen \"{a}\"{a}ress\"{a}, jonka olivat sytytt\"{a}neet viimeisell\"{a} taulanpalasellaan, ja jota ei milloinkaan saanut laskea sammumaan, niin ett\"{a} he kuljettivat sit\"{a} mukana retkill\"{a}\"{a}n kalleimpana aarteenaan; he olivat siis viett\"{a}neet puutteen ja k\"{a}rsimysten t\"{a}ytt\"{a}m\"{a}\"{a} kurjaa el\"{a}m\"{a}\"{a}. Painen ja Proudfootin oli laskenut maihin er\"{a}s hylkeenpyynniss\"{a} ollut kuunari. Kalastajien piiriss\"{a} vallitsevan tavan mukaan heid\"{a}n piti kuukauden p\"{a}iv\"{a}t koota ihraa ja \"{o}ljy\"{a} odotellessaan kuunarin paluuta; mutta kuunari ei palannutkaan. Viisi kuukautta my\"{o}hemmin laski Van Diemenin maahan matkalla ollut \textit{Hope}, saaren rantaan, mutta jostakin k\"{a}sitt\"{a}m\"{a}tt\"{o}m\"{a}st\"{a}, julmasta oikusta sen kapteeni kielt\"{a}ytyi ottamasta skotlantilaisia mukaansa ja purjehti pois antamatta heille leiv\"{a}nmurua tai hiilenpalasta. Ep\"{a}ilem\"{a}tt\"{a} nuo molemmat onnettomat olisivat ennen pitk\"{a}\"{a} kuolleet, ellei \textit{Palmira} olisi sattunut kulkemaan Amsterdamin saaren l\"{a}helt\"{a} ja ottanut heit\"{a} mukaansa. Toinen seikkailu, jonka Amsterdamin saaren historia --- jos t\"{a}llaisella kalliolla voi olla historiaa --- mainitsee, on ranskalaisen kapteeni Peronin tarina. Se alkaa muuten samalla tavoin kuin molempain skotlantilaisten ja p\"{a}\"{a}ttyy my\"{o}s samoin: vapaaehtoinen maihinnousu saarelle, laiva, joka ei palaa, ja vieras laiva, jonka tuulten oikku tuo t\"{a}nne nelj\"{a}nkymmenen kuukauden kuluttua. Mutta kapteeni Peronin oleskelun aikana sattui verinen murhen\"{a}ytelm\"{a}, ja siin\"{a} on omituista yht\"{a}l\"{a}isyytt\"{a} niiden kuviteltujen tapahtumien kanssa, jotka odottivat Daniel Defoen sankaria h\"{a}nen palatessaan saarelleen. Kapteeni Peron oli noussut maihin yhdess\"{a} nelj\"{a}n matruusin kanssa: kahden englantilaisen ja kahden ranskalaisen; heid\"{a}n oli m\"{a}\"{a}r\"{a} viidentoista kuukauden ajan pyydyst\"{a}\"{a} merileijonia. Pyynti onnistui hyvin, mutta kun nuo viisitoista kuukautta olivat kuluneet, laiva ei palannutkaan, ja kun elintarvikkeet alkoivat loppua, syntyi ``kansainv\"{a}lisi\"{a} selkkauksia''. Molemmat englantilaiset nousivat kapinaan kapteeni Peronia vastaan, jonka he olisivat tappaneet, elleiv\"{a}t h\"{a}nen maanmiehens\"{a} olisi rient\"{a}neet h\"{a}nen avukseen. T\"{a}st\"{a} hetkest\"{a} aina l\"{a}ht\"{o}\"{o}n saakka molemmat puolet vaanivat toisiaan y\"{o}t\"{a} p\"{a}iv\"{a}\"{a}, aina aseissa, milloin voittajina, milloin vuorostaan voitettuina, ja viettiv\"{a}t hirvitt\"{a}v\"{a}\"{a} el\"{a}m\"{a}\"{a} kurjuudessa ja ahdistuksessa. Ja varmaan olisi toinen puolue lopulta tuhonnut toisen, ellei muuan englantilainen laiva olisi noutanut n\"{a}it\"{a} onnettomia, jotka kurja kansallisuuskysymys saattoi riitaan autioilla kallioilla Intian valtameress\"{a}. T\"{a}llaiset olivat n\"{a}m\"{a} seikkailut. Kaksi kertaa joutui Amsterdamin saari olemaan suojapaikkana sinne joutuneille merimiehille, jotka kaitselmus molemmilla kerroilla pelasti kurjuudesta ja kuolemasta. Mutta my\"{o}hemmin ei yksik\"{a}\"{a}n laiva ole haaksirikkoutunut n\"{a}ill\"{a} vesill\"{a}. Laivanhylyst\"{a} olisi ajautunut pirstaleita rannalle, ja haaksirikkoisia olisi saapunut Viotin kalastusasemalle; mutta ukko oli jo monta vuotta asunut saarella eik\"{a} h\"{a}nen koskaan ollut tarvinnut tarjota vieraanvaraisuuttaan meren uhreille. \textit{Britanniasta} ja kapteeni Grantista h\"{a}n ei tiennyt mit\"{a}\"{a}n. T\"{a}m\"{a}n haaksirikon n\"{a}ytt\"{a}m\"{o}n\"{a} ei ollut Amsterdamin saari eik\"{a} Pyh\"{a}n Paavalin saarikaan, miss\"{a} valaanpyyt\"{a}j\"{a}t ja kalastajat usein k\"{a}viv\"{a}t. Glenarvania ei t\"{a}m\"{a} vastaus kummastuttanut eik\"{a} h\"{a}n tullut alakuloiseksi. N\"{a}ill\"{a} eri satamiin poikkeamisillaan tiesiv\"{a}t h\"{a}nen kumppaninsa ja h\"{a}n itse kyselev\"{a}ns\"{a} kapteeni Grantia sielt\"{a}, miss\"{a} h\"{a}n ei ollut, eik\"{a} sielt\"{a}, miss\"{a} h\"{a}n oli. He tahtoivat vain todeta, ett\"{a} h\"{a}n ei ollut t\"{a}ll\"{a} kohtaa m\"{a}\"{a}r\"{a}tty\"{a} leveysastetta, siin\"{a} kaikki. \textit{Duncanin} l\"{a}ht\"{o} m\"{a}\"{a}r\"{a}ttiin siis seuraavaksi p\"{a}iv\"{a}ksi. Iltaan saakka viipyiv\"{a}t vieraat saarella, joka on hyvin vieh\"{a}tt\"{a}v\"{a}n n\"{a}k\"{o}inen. Mutta sen el\"{a}imist\"{o} j\"{a} kasvisto eiv\"{a}t olisi t\"{a}ytt\"{a}neet tarkimmankaan luonnontutkijan muistikirjaa. Nelijalkaisten, lintujen, kalojen ja valaiden luokat k\"{a}sittiv\"{a}t vain muutamia villisikoja, myrskylintuja, albatrosseja, ahvenia ja hylkeit\"{a}. L\"{a}mpimi\"{a} l\"{a}hteit\"{a} ja rautapitoista vett\"{a} pulppusi siell\"{a} t\"{a}\"{a}ll\"{a} mustahkosta laavasta, ja ne ty\"{o}nsiv\"{a}t paksua huurua tuliper\"{a}isen maan ylle. Muutamat n\"{a}ist\"{a} l\"{a}hteist\"{a} olivat hyvin kuumia. John Mangles tutki niist\"{a} er\"{a}st\"{a} l\"{a}mp\"{o}mittarilla, joka osoitti kahdeksankymment\"{a} astetta Celsiusta. Muutaman askelen p\"{a}\"{a}st\"{a} merest\"{a} saadut kalat saattoi viidess\"{a} minuutissa keitt\"{a}\"{a} t\"{a}ss\"{a} melkein kiehuvassa vedess\"{a}; Paganel p\"{a}\"{a}ttikin sen vuoksi olla uimatta siin\"{a}. Pitk\"{a}n k\"{a}velyretken j\"{a}lkeen Glenarvan lausui illansuussa j\"{a}\"{a}hyv\"{a}iset kunnianarvoisalle herra Viotille. Kaikki toivottivat h\"{a}nelle kaikkea mahdollista menestyst\"{a} autiolla saarellaan. Vanhus puolestaan toivotti mit\"{a} parasta onnea retkikunnan etsiskelylle, ja \textit{Duncanin} vene vei matkustajat laivaan. \gutchapter{JACQUES PAGANELIN JA MAJURI MACNABBSIN VEDONLY\"{O}NNIT.} Joulukuun 7. p\"{a}iv\"{a}n\"{a} kello kolme aamulla paloi jo tuli \textit{Duncanin} pannuissa; varppikela oli t\"{a}ydess\"{a} toimessa; ankkuri k\"{a}\"{a}ntyi pystyyn ja nousi pienen sataman hiekkapohjasta, potkuri pantiin py\"{o}rim\"{a}\"{a}n, ja laiva l\"{a}hti v\"{a}ljille vesille. Kun matkustajat kello kahdeksan aikaan nousivat kannelle, Amsterdamin saari h\"{a}ipyi jo n\"{a}k\"{o}piirin usviin. Se oli viimeinen pys\"{a}hdyspaikka matkalla pitkin 37. leveysastetta, noin kuuden tuhannen kilometrin p\"{a}\"{a}ss\"{a} Australian rannikosta. Jos l\"{a}nsituulta yh\"{a} kest\"{a}isi ja meri pysyisi suotuisana, \textit{Duncan} saapuisi perille kahdentoista p\"{a}iv\"{a}n kuluttua. Mary ja Robert Grant tunsivat liikutusta katsellessaan n\"{a}it\"{a} vesi\"{a}, joita \textit{Britannia} varmaan oli kynt\"{a}nyt muutamia p\"{a}ivi\"{a} ennen uppoamistaan. T\"{a}\"{a}ll\"{a}, ehk\"{a} oli jo aluksensa hallinnan ja miehi\"{a} menett\"{a}nyt kapteeni Grant, kamppaillut Intian valtameren hirvitt\"{a}vi\"{a} myrskyj\"{a} vastaan ja huomannut ajautuvansa rannikkoa kohti vastustamattomalla voimalla. John Mangles n\"{a}ytti nuorelle neidolle laivan kartoille merkityt merivirrat ja selitti h\"{a}nelle niiden muuttumattoman suunnan. Muiden muassa vie er\"{a}s Intian valtameren halki kulkeva virta Australian mantereelle, ja sen vaikutus tuntuu l\"{a}nnest\"{a} it\"{a}\"{a}n sek\"{a} Tyynell\"{a} valtamerell\"{a} ett\"{a} Atlantilla. Niinp\"{a} kun \textit{Britannian} mastot olivat poikki ja per\"{a}sin ep\"{a}kunnossa, niin ett\"{a} alus oli avuttomana tuulten ja aaltojen ajeltavana, sen oli t\"{a}ytynyt paiskautua maihin ja murskautua. T\"{a}ss\"{a} ilmeni kuitenkin muuan pulma. \textit{Mercantile and Shipping Gazetten} mukaan oli viimeiset tiedot kapteeni Grantista saatu Callaosta toukokuun 30. p\"{a}iv\"{a}n\"{a} 1862. Kuinka saattoi \textit{Britannia} 7. p\"{a}iv\"{a}n\"{a} kes\"{a}kuuta, kahdeksan p\"{a}iv\"{a}\"{a} sen j\"{a}lkeen, kun se oli l\"{a}htenyt Perun rannikolta, olla Intian merell\"{a}? Kun Paganelilta kysyttiin t\"{a}t\"{a} seikkaa, h\"{a}n antoi siihen niin todenn\"{a}k\"{o}isen vastauksen, ett\"{a} ep\"{a}ilevimm\"{a}tkin olisivat siihen tyytyneet. Oli ilta, 12. p\"{a}iv\"{a}n\"{a} joulukuuta, kuusi p\"{a}iv\"{a}\"{a} Amsterdamin saarelta l\"{a}hdetty\"{a}. Lordi ja lady Glenarvan, Robert ja Mary Grant, kapteeni John MacNabbs ja Paganel juttelivat salongissa. Tavan mukaan oli puheenaiheena \textit{Britannia}, sill\"{a} t\"{a}t\"{a} laivalla olevat alinomaa ajattelivat. Silloin tehtiin \"{a}kki\"{a} edell\"{a} mainittu huomautus, joka heti tyrm\"{a}si toiveikkaat ajatukset. Kun Glenarvan teki t\"{a}m\"{a}n odottamattoman huomautuksen, Paganel kohotti \"{a}kki\"{a} p\"{a}\"{a}t\"{a}\"{a}n. Mit\"{a}\"{a}n vastaamatta h\"{a}n meni sitten etsim\"{a}\"{a}n asiakirjaa. Palatessaan h\"{a}n vain kohautti olkap\"{a}it\"{a}\"{a}n kuten mies, jota h\"{a}vett\"{a}\"{a}, ett\"{a} h\"{a}n hetkeksik\"{a}\"{a}n oli antanut sellaisen mit\"{a}tt\"{o}myyden h\"{a}mment\"{a}\"{a} itse\"{a}\"{a}n. --- No, rakas yst\"{a}v\"{a}, Glenarvan sanoi, --- vastatkaa edes jotakin! --- En, Paganel sanoi, --- min\"{a} p\"{a}invastoin teen vain yhden kysymyksen ja k\"{a}\"{a}nnyn siin\"{a} kapteeni Johnin puoleen. --- Kysyk\"{a}\"{a}, herra Paganel, John Mangles lausui. --- Voiko hyv\"{a}kulkuinen laiva kulkea yhdess\"{a} kuukaudessa yli koko sen osan Tyynt\"{a} valtamerta, joka on Amerikan ja Australian v\"{a}lill\"{a}? --- Kyll\"{a}, jos se vuorokaudessa kulkee noin kolmesataa kilometri\"{a}. --- Onko se mik\"{a}\"{a}n tavaton nopeus? --- Ei ensink\"{a}\"{a}n. Moni purjelaiva kulkee usein parempaakin vauhtia. --- No niin, Paganel lausui silloin, --- sen sijaan, ett\"{a} asiakirjassa mainitaan `7. p\"{a}iv\"{a} kes\"{a}kuuta', olettakaamme, ett\"{a} meri on sy\"{o}nyt t\"{a}st\"{a} p\"{a}iv\"{a}m\"{a}\"{a}r\"{a}st\"{a} pois yhden numeron, ja lukekaamme siis joko 17. p\"{a}iv\"{a} kes\"{a}kuuta tai 27. p\"{a}iv\"{a}, ja asia on selv\"{a}. --- Tosiaan, lady Helena vastasi, --- toukokuun 30:nnen ja kes\"{a}kuun 27:nnen p\"{a}iv\"{a}n v\"{a}lill\"{a}... --- On kapteeni Grant voinut kulkea Tyynen valtameren poikki ja saapua Intian merelle! T\"{a}m\"{a} Paganelin p\"{a}\"{a}telm\"{a} her\"{a}tti vilkasta tyydytyst\"{a}. --- Siin\"{a} selvisi viel\"{a} yksi seikka, Glenarvan lausui, --- ja se on yst\"{a}v\"{a}mme ansiota! Meid\"{a}n on siis vain pyritt\"{a}v\"{a} Australiaan ja etsitt\"{a}v\"{a} \textit{Britannian} j\"{a}lki\"{a} sen l\"{a}nsirannikolta. --- Tai it\"{a}rannikolta, John Mangles huomautti. --- Siin\"{a} olette oikeassa, John. Asiakirjassa ei mik\"{a}\"{a}n osoita, ett\"{a} onnettomuus olisi tapahtunut l\"{a}nsi- eik\"{a} it\"{a}rannalla. Meid\"{a}n on siis etsiskelt\"{a}v\"{a} niilt\"{a} molemmilta kohdilta, miss\"{a} 37. leveysaste leikkaa Australiaa. --- Onko t\"{a}ss\"{a} suhteessa siis ep\"{a}selvyytt\"{a}, mylord? nuori neito kysyi. --- Ei suinkaan, neiti, John Mangles riensi vastaamaan haluten haihduttaa Mary Grantin huolestumisen. --- Mylord tahtoo varmaankin huomauttaa, ett\"{a} jos kapteeni Grant olisi joutunut maihin Australian it\"{a}rannikolla, h\"{a}n olisi melkein heti saanut apua. Koko t\"{a}m\"{a} rannikko on n\"{a}et englantilaista, siirtolaisten asuttamaa. \textit{Britannian} miehist\"{o}n ei olisi tarvinnut kulkea kahtakymment\"{a} kilometri\"{a} tavatakseen maanmiehi\"{a}. --- Oikein, kapteeni John, Paganel lausui. --- Min\"{a} olen samaa mielt\"{a}. It\"{a}rannikolla, Twofold-lahden rannalla, Edenin kaupungissa, ei kapteeni Grant olisi ainoastaan saanut suojaa englantilaisessa siirtolassa, vaan my\"{o}skin mahdollisuuden palata Eurooppaan. --- Haaksirikkoiset eiv\"{a}t siis ole voineet saada samaa apua siin\"{a} Australian osassa, jota kohti \textit{Duncan} nyt meit\"{a} vie? lady Helena kysyi. --- Eiv\"{a}t, rouva, Paganel vastasi, --- rannikko on autio. Sielt\"{a} ei vie yht\"{a}k\"{a}\"{a}n tiet\"{a} Melbourneen tai Adelaideen. Jos \textit{Britannia} on murskautunut sen rannikon kareihin, se on ollut yht\"{a} avuton kuin jos se olisi haaksirikkoutunut Afrikan kolkoilla er\"{a}maarannoilla. --- Mutta kuinka sitten is\"{a}ni on k\"{a}ynyt n\"{a}in\"{a} kahtena vuonna? Mary Grant kysyi. --- Rakas Mary, Paganel vastasi, --- pid\"{a}tteh\"{a}n varmana, eik\"{o} totta, ett\"{a} kapteeni Grant on haaksirikon j\"{a}lkeen p\"{a}\"{a}ssyt Australian mantereelle? --- Niin teen, herra Paganel, nuori neito vastasi. --- No, kuinka on kapteeni Grantin k\"{a}ynyt maihin p\"{a}\"{a}sty\"{a}\"{a}n? Sen olettaminen on helppoa. On vain kolme mahdollisuutta. Joko Harry Grant ja h\"{a}nen kumppaninsa ovat p\"{a}\"{a}sseet johonkin englantilaiseen siirtolaan tai joutuneet alkuasukasten k\"{a}siin, tai sitten he ovat menehtyneet Australian laajoissa autiomaissa. Paganel vaikeni ja etsi kuulijainsa katseista hyv\"{a}ksymist\"{a} p\"{a}\"{a}telmilleen. --- Jatkakaa, Paganel, lordi Glenarvan sanoi. --- Min\"{a} jatkan, Paganel vastasi; --- ja ensinn\"{a}kin hylk\"{a}\"{a}n ensimm\"{a}isen mahdollisuuden. Harry Grant ei ole voinut saapua englantilaiseen siirtolaan, sill\"{a} silloin h\"{a}nen pelastumisensa olisi ollut varma ja h\"{a}n olisi jo kauan sitten ollut lastensa luona Dundeen kelpo kaupungissa. --- Is\"{a}-parka! Mary Grant huokasi, --- kaksi vuotta erossa meist\"{a}! --- Anna herra Paganelin puhua, sisko, Robert sanoi, --- h\"{a}n ilmoittaa meille lopuksi... --- Ah, poikani, en! Kaikki, mit\"{a} voin vakuuttaa, on se, ett\"{a} kapteeni Grant on australialaisten vankina tai... --- Mutta n\"{a}m\"{a} alkuasukkaat, lady Glenarvan kysyi nopeasti, --- eiv\"{a}tk\"{o} ne ole... --- Rauhoittukaa, rouva, vastasi tiedemies, joka ymm\"{a}rsi lady Helenan ajatuksen, --- n\"{a}m\"{a} alkuasukkaat ovat tosin villej\"{a}, el\"{a}imellisi\"{a}, ihmis\"{a}lyn alhaisimmalla asteella, mutta hyv\"{a}ntapaisia eiv\"{a}tk\"{a} verenhimoisia, kuten heid\"{a}n naapurinsa Uudessa Seelannissa. Jos he ovat ottaneet \textit{Britannian} haaksirikkoiset vangiksi, niin he eiv\"{a}t koskaan uhanneet n\"{a}iden henke\"{a}, siin\"{a} saatte uskoa minua. Kaikki tutkijat ovat yksimielisi\"{a} siit\"{a}, ett\"{a} australialaiset kammoavat verenvuodatusta, ja monta kertaa he ovat saaneet n\"{a}ist\"{a} uskollisia liittolaisia torjuessaan heit\"{a} paljoa julmempien rikollisjoukkojen hy\"{o}kk\"{a}yksi\"{a}. --- Kuulkaa, mit\"{a} herra Paganel sanoo, lady Helena lausui k\"{a}\"{a}ntyen Mary Grantin puoleen. --- Jos is\"{a}nne on alkuasukkaiden k\"{a}siss\"{a}, kuten muuten asiakirjain mukaan on luultavaa, niin me l\"{o}yd\"{a}mme h\"{a}net. --- Mutta jos h\"{a}n on eksynyt \"{a}\"{a}rett\"{o}miin autiomaihin? neito huomautti katsahtaen kysyv\"{a}sti Paganeliin. --- Niin me l\"{o}yd\"{a}mme h\"{a}net sittenkin! maantieteilij\"{a} huudahti luottavaisella \"{a}\"{a}nell\"{a}. --- Eik\"{o} totta, yst\"{a}v\"{a}ni? --- Ep\"{a}ilem\"{a}tt\"{a}, vastasi Glenarvan, joka halusi antaa keskustelulle hilpe\"{a}mm\"{a}n suunnan. --- Mutta min\"{a} en oletakaan eksymist\"{a}... --- Enk\"{a} min\"{a}, Paganel vahvisti. --- Onko Australia suurikin? Robert kysyi. --- Australia, poikani, on pinta-alaltaan noin seitsem\"{a}nsataa seitsem\"{a}nkymment\"{a}viisi tuhatta miljoonaa hehtaaria eli toisin sanoen niin suuri kuin nelj\"{a} viidett\"{a}osaa Euroopasta. --- Niink\"{o} suuri? majuri kysyi. --- Niin, MacNabbs, melkein metrilleen. Ettek\"{o} my\"{o}nn\"{a}, ett\"{a} semmoista maata jo voi sanoa mantereeksi, kuten asiakirjassa sanotaan? --- Varmaan, Paganel. --- Mutta omituista, tiedemies lis\"{a}si, --- ett\"{a} vain harva tutkija on kuitenkaan kadonnut t\"{a}ss\"{a} laajassa maassa. Luulenpa melkein, ett\"{a} Leichardt on ainoa, jonka kohtalosta ei ole tietoa, ja olen Maantieteellisess\"{a} seurassa kuullut, ett\"{a} MacIntyre luuli l\"{o}yt\"{a}neens\"{a} j\"{a}lki\"{a} h\"{a}nest\"{a}. --- Eik\"{o} Australian kaikissa osissa ole viel\"{a} k\"{a}yty? lady Glenarvan kysyi. --- Ei, rouva, kaukana siit\"{a}! Paganel vastasi. --- T\"{a}t\"{a} mannerta ei tunneta sen paremmin kuin Sis\"{a}-Afrikkaa, eik\"{a} kuitenkaan rohkeista l\"{o}yt\"{o}retkeilij\"{o}ist\"{a} ole ollut puutetta. Vuodesta 1606 vuoteen 1862 ainakin viisikymment\"{a} tutkijaa on matkustellut sen sis\"{a}maassa ja rannikoilla maata tutkien. --- Oho, viisikymment\"{a}k\"{o}? majuri lausui ep\"{a}ilev\"{a}n n\"{a}k\"{o}isen\"{a}. --- Niin, MacNabbs, ainakin niin monta. Min\"{a} puhun nimitt\"{a}in merenkulkijoista, jotka ovat tutkineet Australian rannikkoa keskell\"{a} tuntemattomilla vesill\"{a} purjehtimisen vaaroja, ja niist\"{a} retkeilij\"{o}ist\"{a}, jotka ovat tunkeutuneet t\"{a}m\"{a}n laajan maan sis\"{a}osiin. --- Mutta viidess\"{a}kymmeness\"{a} on sent\"{a}\"{a}n kovin monta, majuri huomautti. --- On, mutta min\"{a} menen viel\"{a} pitemm\"{a}lle, MacNabbs, maantieteilij\"{a} kivahti, kuten aina vastav\"{a}itteist\"{a} kiihtyneen\"{a}. --- Tehk\"{a}\"{a} se, Paganel! --- Jos te \"{a}rsyt\"{a}tte minua, niin min\"{a} luettelen arvelematta n\"{a}m\"{a} viisikymment\"{a} nimelt\"{a}. --- No, no! majuri sanoi tyynesti. --- Nuo tiedemiehet eiv\"{a}t sitten ep\"{a}ile mit\"{a}\"{a}n! --- Majuri, Paganel sanoi, --- panetteko vetoon Purdey Moore \& Dickson-kiv\"{a}\"{a}rinne minun Secretan-kaukoputkeani vastaan? --- Miksen, Paganel, jos teit\"{a} huvittaa, MacNabbs vastasi. --- Hyv\"{a} on, majuri! tiedemies huudahti, --- silloin tied\"{a}n kiv\"{a}\"{a}rin, jolla te ette en\"{a}\"{a} ammu kauriita ettek\"{a} kettuja, ellen anna sit\"{a} teille lainaksi, kuten kuitenkin aina tulen kernaasti tekem\"{a}\"{a}n. --- Paganel, majuri vastasi vakavasti, --- kun tarvitsette minun kaukoputkeani, se on aina k\"{a}ytett\"{a}viss\"{a}nne. --- Alkakaamme siis, Paganel lausui. --- Hyv\"{a}t naiset ja herrat, te olette tuomareita. Sin\"{a}, Robert, pid\"{a}t kirjaa. Lordi ja lady Glenarvan, Mary ja Robert, majuri ja John Mangles, joita kiista huvitti, valmistautuivat kuuntelemaan maantieteilij\"{a}\"{a}. Koskihan se sit\"{a} paitsi Australiaa, jonne \textit{Duncan} heit\"{a} juuri vei, joten sen historiaa ei olisi voinut kertoa sopivammalla hetkell\"{a}. Paganelia kehotettiin siis aloittamaan muistitaidon n\"{a}yt\"{o}ksens\"{a}. --- Mnemosyne! h\"{a}n huudahti, --- muistin jumalatar, neitseellisten runotarten \"{a}iti, avusta uskollista ja palavaa palvelijaasi! Siit\"{a} on kaksisataa viisikymment\"{a}kahdeksan vuotta, yst\"{a}v\"{a}ni, kun Australia viel\"{a} oli tuntematon. Uumoiltiin tosin suuren etel\"{a}isen mantereen olevan olemassa; kaksi teid\"{a}n brittil\"{a}isen museonne kirjastossa s\"{a}ilytetty\"{a} karttaa, rakas Glenarvan, vuodelta 1550 mainitsevat Aasian etel\"{a}puolella suuren maan, jota ne nimitt\"{a}v\"{a}t Portugalin Suureksi Jaavaksi. Mutta n\"{a}iden karttojen alkuper\"{a} ei ole kiist\"{a}m\"{a}t\"{o}n. Siirryn siis seitsem\"{a}nnelletoista vuosisadalle, vuoteen 1606. Sin\"{a} vuonna er\"{a}s espanjalainen purjehtija, Quiros, l\"{o}ysi maan, jolle h\"{a}n antoi nimeksi Australia de Espiritu Santo --- Pyh\"{a}n Hengen etel\"{a}maa. Muutamat tutkijat ovat v\"{a}itt\"{a}neet, ett\"{a} h\"{a}n oli l\"{o}yt\"{a}nyt Uusien Hebridien saaret eik\"{a} Australiaa. Min\"{a} en k\"{a}y kiistelem\"{a}\"{a}n siit\"{a}. Merkitse muistiin t\"{a}m\"{a} Quiros, Robert, ja siirtyk\"{a}\"{a}mme seuraavaan. --- Yksi, Robert sanoi. --- Samana vuonna jatkoi Luiz Vaz de Torres, joka komensi Quiroksen toista laivuetta, uusien maiden tutkimista kauemmas etel\"{a}\"{a}n. Mutta varsinaisen suuren l\"{o}yd\"{o}n kunnia kuuluu hollantilaiselle Theodoric Hertogelle. H\"{a}n saapui Australian l\"{a}nsirannikolle 15:nnen leveysasteen kohdalla ja nimitti sen laivansa mukaan \textit{Eendrachtiksi}. H\"{a}nen j\"{a}lkeens\"{a} l\"{o}yt\"{o}retkeilij\"{o}iden lukum\"{a}\"{a}r\"{a} lis\"{a}\"{a}ntyy nopeasti. Vuonna 1618 Zeachen l\"{o}ysi Arnheimin ja Diemenin maiden pohjoisrannan. Vuonna 1619 kulki Jean Edels pitkin l\"{a}nsirannikkoa ja antoi sille oman nimens\"{a}. Vuonna 1622 eteni Leuwin saman nimiseen niemeen saakka. Vuonna 1627 Nuitz ja Witt, toinen l\"{a}nness\"{a}, toinen id\"{a}ss\"{a}, t\"{a}ydensiv\"{a}t edelt\"{a}jiens\"{a} l\"{o}yt\"{o}j\"{a}, ja heid\"{a}n j\"{a}lkeens\"{a} tuli kapteeni Carpenter, joka tunkeutui laivoillaan siihen laajaan poukamaan, jota viel\"{a}kin sanotaan Carpentaria-lahdeksi. Vihdoin, vuonna 1642, purjehti kuuluisa merenkulkija Tasman Van Diemenin saaren ymp\"{a}ri, jonka h\"{a}n luuli kuuluvan mannermaahan, ja antoi sille Batavian kenraalikuvern\"{o}\"{o}rin nimen, jonka j\"{a}lkimaailma oikeudenmukaisesti on muuttanut Tasmaniaksi. Nyt oli purjehdittu Australian ymp\"{a}ri; tiedettiin, ett\"{a} sit\"{a} ymp\"{a}r\"{o}iv\"{a}t Tyynen valtameren ja Intian meren vedet, ja vuonna 1665, juuri siihen aikaan, jolloin hollantilaisten purjehtijoiden loistoaika oli loppumassa, annettiin t\"{a}lle valtavalle Etel\"{a}n saarelle nimeksi Uusi Hollanti, jota se kuitenkaan ei saanut pit\"{a}\"{a}. Kuinka monta olen nyt maininnut? --- Kymmenen, Robert vastasi. --- Hyv\"{a}, Paganel jatkoi, --- pannaan siihen risti, ja min\"{a} siirryn englantilaisiin. Vuonna 1686 saapui merirosvop\"{a}\"{a}llikk\"{o} Williams Dampier, etel\"{a}n vesill\"{a} kuuluisan merirosvon la C\"{o}tren veli, monien my\"{o}t\"{a}- ja vastoink\"{a}ymisten j\"{a}lkeen \textit{Cygnet}-nimisell\"{a} laivalla Uuden Hollannin luoteisrannalle 16$^{\circ}$ 50' leveysasteen kohdalla; h\"{a}n asettui yhteyteen alkuasukkaiden kanssa ja laati heid\"{a}n tavoistaan, k\"{o}yhyydest\"{a}\"{a}n ja \"{a}lyllisest\"{a} tasostaan hyvin laajan kertomuksen. H\"{a}n palasi vuonna 1699 samaan lahteen, jossa Hertoge oli noussut maihin, ei en\"{a}\"{a} rosvona, vaan kuninkaalliseen laivastoon kuuluvan \textit{Roebuck}-nimisen aluksen p\"{a}\"{a}llikk\"{o}n\"{a}. Siihen saakka Uuden Hollannin l\"{o}yd\"{o}ll\"{a} ei kuitenkaan ollut muuta merkityst\"{a} kuin maantieteellisen\"{a} tosiasiana. Ei ajateltukaan siirtoloiden perustamista, eik\"{a} l\"{a}hes kolmen nelj\"{a}nnesvuosisadan aikana, vuodesta 1699 vuoteen 1770, yksik\"{a}\"{a}n purjehtija saapunut sinne. Mutta silloin saapui maailman kuuluisin merenkulkija, kapteeni Cook, ja pian avautui uusi maanosa Euroopan siirtolaisille. Kolmella mainiolla matkallaan James Cook k\"{a}vi Uuden Hollannin maissa, ensimm\"{a}isen kerran 31. p\"{a}iv\"{a}n\"{a} maaliskuuta 1770. Tehty\"{a}\"{a}n Otaheitissa tarkkoja huomioita Venuksen kulusta auringon ohi[1] Cook l\"{a}hti pienell\"{a} \textit{Endeavour}-nimisell\"{a} laivallaan l\"{a}nteen Tyynen valtameren yli. L\"{o}ydetty\"{a}\"{a}n Uuden Seelannin h\"{a}n saapui er\"{a}\"{a}seen Australian l\"{a}nsirannikon lahdelmaan, jonka h\"{a}n katsoi niin rikkaaksi uusista kasvilajeista, ett\"{a} antoi sille Botany-Bayn nimen, joka sill\"{a} viel\"{a}kin on. Mill\"{a} tavalla h\"{a}n oli tekemisiss\"{a} puoliksi el\"{a}imellisten alkuasukasten kanssa, siin\"{a} ei ole paljonkaan mielenkiintoista. H\"{a}n jatkoi matkaansa pohjoiseen, ja 16:nnen leveysasteen kohdalla, l\"{a}hell\"{a} Kap Tribulationia, tarttui \textit{Endeavour} koralliriutalle, kolmenkymmenen kilometrin p\"{a}\"{a}ss\"{a} rannasta. Uppoamisen vaara oli mit\"{a} suurin. Elintarvikkeet ja kanuunat heitettiin mereen, ja seuraavana y\"{o}n\"{a} nosti nousuvesi irti keventyneen aluksen, joka pysyi pinnalla sen sattuman avulla, ett\"{a} reik\"{a}\"{a}n j\"{a}\"{a}nyt korallikappale esti vuodon p\"{a}\"{a}sem\"{a}st\"{a} ylivoimaiseksi. Cook p\"{a}\"{a}si laivallaan pieneen lahteen, johon laskeva joki sai Endeavourin nimen. Laivan korjaus kesti kolme kuukautta, ja englantilaiset yrittiv\"{a}t t\"{a}ll\"{a} v\"{a}lin asettua hy\"{o}dylliseen yhteyteen alkuasukasten kanssa; mutta se ei sanottavasti onnistunut, ja he l\"{a}htiv\"{a}t purjehtimaan edelleen. \textit{Endeavour} jatkoi matkaansa pohjoiseen. Cook halusi tiet\"{a}\"{a}, onko Uuden Guinean ja Uuden Hollannin v\"{a}lill\"{a} salmea; uusien vaarojen j\"{a}lkeen, jolloin h\"{a}nen aluksensa oli sen seitsem\"{a}n kertaa uppoamaisillaan, h\"{a}n l\"{o}ysi kauas lounaaseen levenev\"{a}n meren. Salmi oli olemassa. Sen l\"{a}pi purjehdittiin. Cook nousi maihin er\"{a}\"{a}lle pienelle saarelle ja otti Englannin nimess\"{a} haltuunsa koko tutkimansa pitk\"{a}n rannikkoalueen ja antoi sille nimeksi Uusi Etel\"{a}-Wales. Kolme vuotta my\"{o}hemmin t\"{a}ll\"{a} rohkealla merenkulkijalla oli komennossaan kaksi laivaa \textit{Adventure} ja \textit{Resolution}; kapteeni Furneaux l\"{a}hti \textit{Adventurella} tutkimaan Van Diemenin maan rannikoita ja palasi siin\"{a} uskossa, ett\"{a} ne kuuluivat Uuteen Hollantiin. Vasta vuonna 1777, kolmannella matkallaan, Cook ankkuroi \textit{Resolution}- ja \textit{Discovery} laivoillaan Adventure-lahdessa Van Diemenin maan rannikolla, ja sielt\"{a} l\"{a}hdetty\"{a}\"{a}n h\"{a}n sitten, muutamia kuukausia my\"{o}hemmin, kohtasi kuolemansa Sandwich-saarilla. --- H\"{a}n oli suuri mies, Glenarvan sanoi. --- Kuuluisin merimies, mit\"{a} milloinkaan on ollut. H\"{a}nen mukanaan ollut Banks ehdotti sitten Englannin hallitukselle rangaistussiirtolan perustamista Botany-Bayhin. H\"{a}nen j\"{a}lkeens\"{a} t\"{a}nne riensi purjehtijoita kaikista maista. Viimeisess\"{a} Laperouselta saadussa kirjeess\"{a}, joka oli p\"{a}iv\"{a}tty Botany-Bayssa 7. p\"{a}iv\"{a}n\"{a} helmikuuta 1787, t\"{a}m\"{a} onneton merimies ilmoitti aikomuksenaan olevan tutkia Carpentaria-lahti ja koko Uuden Hollannin rannikko Van Diemenin maahan saakka. H\"{a}n l\"{a}hti, mutta j\"{a}i sille tielleen. Vuonna 1788 kapteeni Philipp perusti Port Jacksoniin ensimm\"{a}isen englantilaisen siirtokunnan. Vuonna 1791 Vancouver suoritti huomattavia tutkimuksia uuden maanosan etel\"{a}rannoilla. Vuonna 1792 Laperousea etsim\"{a}\"{a}n l\"{a}hetetty d'Entrecasteaux purjehti Uuden Hollannin l\"{a}nsi- ja etel\"{a}puolella l\"{o}yt\"{a}en tuntemattomia saaria matkallaan. Vuosina 1795 ja 1797 kaksi nuorta miest\"{a}, Flinders ja Bass jatkoivat rohkeasti etel\"{a}nrannikoiden tutkimista kahden ja puolen metrin veneell\"{a} ja vuonna 1797 Bass kulki Van Diemenin maan ja Uuden Hollannin v\"{a}lill\"{a} sen salmen l\"{a}pi, joka on saanut nimens\"{a} h\"{a}nen mukaansa. Samana vuonna teki Amsterdamin saaren l\"{o}yt\"{a}j\"{a} Vlaming tutkimuksia it\"{a}puolella Swan-River-nimist\"{a} jokea, jossa uiskenteli mit\"{a} kauneimpia mustia joutsenia. Flinders taas jatkoi vuonna 1801 omaper\"{a}isi\"{a} tutkimuksiaan ja kohtasi 138$^{\circ}$ 58' pituus- ja 35$^{\circ}$ 40' leveysasteella Encounter-Bayssa \textit{Geographen} ja \textit{Naturalisten}, kaksi ranskalaista laivaa, joita komensivat kapteenit Baudin ja Hamelin. --- Ah, kapteeni Baudinko? majuri kysyi. --- Niin! Miksi t\"{a}m\"{a} huudahdus? Paganel kysyi. --- Muuten vain. \"{A}lk\"{a}\"{a} siit\"{a} huoliko; jatkakaa, rakas Paganel! --- Min\"{a} jatkan siis lis\"{a}\"{a}m\"{a}ll\"{a} n\"{a}iden purjehtijain joukkoon kapteeni Kingin, joka vuodesta 1817 vuoteen 1822 t\"{a}ydensi Uuden Hollannin rannikoiden tuntemusta k\"{a}\"{a}nt\"{o}piirien v\"{a}lisell\"{a} alueella. --- Nyt on kaksikymment\"{a}nelj\"{a} nime\"{a}, Robert sanoi. --- Hyv\"{a}, Paganel vastasi, --- minulla on jo puolet majurin pyssyst\"{a}. Ja nyt lueteltuani merenkulkijat siirtyk\"{a}\"{a}mme mannermaan tutkijoihin. --- Mainiota, herra Paganel, lady Helena lausui. --- T\"{a}ytyy my\"{o}nt\"{a}\"{a}, ett\"{a} teill\"{a} on h\"{a}mm\"{a}stytt\"{a}v\"{a} muisti. --- Mik\"{a} on perin merkillist\"{a}, Glenarvan lis\"{a}si, --- miehell\"{a}, joka... --- On niin hajamielinen, Paganel riensi jatkamaan. --- Kas, min\"{a} muistan vain aikam\"{a}\"{a}ri\"{a} ja tapahtumia. Siin\"{a} kaikki. --- Kaksikymment\"{a}nelj\"{a}, Robert toisti. --- No, kaksikymment\"{a}viisi, luutnantti Daws. Se tapahtui vuonna 1789, vuotta Port Jacksonin siirtolan perustamisen j\"{a}lkeen. Uuden maanosan ymp\"{a}ri oli kuljettu; mutta mit\"{a} se sis\"{a}lsi, sit\"{a} ei kukaan osannut sanoa. Pitkin it\"{a}rannan suuntaa kulkeva pitk\"{a} vuorijono n\"{a}ytti kokonaan est\"{a}v\"{a}n p\"{a}\"{a}syn sis\"{a}maahan. Yhdeks\"{a}n p\"{a}iv\"{a}matkan j\"{a}lkeen oli luutnantti Dawsin pakko k\"{a}\"{a}nty\"{a} ja palata Port Jacksoniin. Samana vuonna kapteeni Tench yritti saman vuorijonon yli, mutta onnistumatta. N\"{a}m\"{a} molemmat ep\"{a}onnistuneet yritykset pid\"{a}ttiv\"{a}t l\"{o}yt\"{o}retkeilij\"{o}it\"{a} kolme vuotta ryhtym\"{a}st\"{a} uudelleen t\"{a}h\"{a}n vaikeaan yritykseen. Vuonna 1792 siin\"{a} ep\"{a}onnistui viel\"{a} eversti Paterson, rohkea afrikkalainen l\"{o}yt\"{o}retkeilij\"{a}. Seuraavana vuonna kulki tavallinen Englannin laivaston aliupseeri, uljas Hawkins, nelj\"{a}tt\"{a}kymment\"{a} kilometri\"{a} yli sen linjan, jota pitemm\"{a}lle h\"{a}nen edelt\"{a}j\"{a}ns\"{a} eiv\"{a}t olleet p\"{a}\"{a}sseet. Kahdeksantoista vuoden ajalta ei minulla sitten ole mainittavana kuin kaksi nime\"{a}, \"{a}sken mainittu kuuluisa purjehtija Bass ja herra Bareiller, er\"{a}s siirtokunnan insin\"{o}\"{o}ri, jotka eiv\"{a}t onnistuneet edelt\"{a}ji\"{a}\"{a}n paremmin, ja niin joudun vuoteen 1813, jolloin vihdoinkin l\"{o}ydettiin ylitysreitti Sydneyn l\"{a}nsipuolella. Kuvern\"{o}\"{o}ri Macquarie suoritti uskalletun matkan 1815, ja Bathurstin kaupunki perustettiin Sinivuorten toiselle puolelle. Siit\"{a} l\"{a}htien Throsby vuonna 1819, Oxley, joka samosi maata noin viisisataa kilometri\"{a}, Howel ja Hune, joiden l\"{a}ht\"{o}kohtana oli juuri Twofold-Bay, miss\"{a} 37. leveysaste kulkee, ja kapteeni Sturt, joka vuosina 1829 ja 1830 tutki Darlingin ja Murrayn virrat, rikastuttivat maantiedett\"{a} uusilla tiedoilla ja edistiv\"{a}t siirtokuntien kehittymist\"{a}. --- Kolmekymment\"{a}kuusi, Robert sanoi. --- Mainiota! Min\"{a} olen voiton puolella, Paganel vastasi. --- Minun on mainittava viel\"{a} Eyre ja Leichardt, jotka vuosina 1840 ja 1841 tutkivat osan maata; Sturt, vuonna 1845; Gregoryn veljekset ja Helpmann, vuonna 1846 Australian l\"{a}nsiosassa; Kennedy, vuonna 1847, Victoria-joella ja vuonna 1848 Pohjois-Australiassa; Gregory vuonna 1852; Austin, vuonna 1854; Gregoryn veljekset vuodesta 1855 vuoteen 1858 maan luoteisosassa; Babbage, Torrens-j\"{a}rvest\"{a} Eyre-j\"{a}rveen; ja niin tulen vihdoin Australian aikakirjoissa kuuluisaan matkailijaan, Stuartiin, joka teki kolme rohkeaa matkaa halki maanosan. H\"{a}nen ensimm\"{a}inen retkens\"{a} sis\"{a}maahan tapahtui vuonna 1860. Tuonnempana kerron, jos haluatte, kuinka Australian halki kuljettiin nelj\"{a} kertaa etel\"{a}st\"{a} pohjoiseen. Nyt rajoitun vain p\"{a}\"{a}tt\"{a}m\"{a}\"{a}n t\"{a}m\"{a}n pitk\"{a}n nimiluettelon ja vuosilta 1860-1862 lis\"{a}\"{a}n tieteen niin uljaiden tienraivaajien joukkoon viel\"{a} Dempsterin veljekset, Clarksonin ja Harperin, Burben ja Willsin, Neilsonin, Walkerin, Landsboroughin, Mackinleyn, Howitin... --- Viisikymment\"{a}kuusi! Robert huudahti. --- Hyv\"{a} majuri, Paganel jatkoi, --- min\"{a} annan teille kaupanp\"{a}\"{a}llisi\"{a}, sill\"{a} enh\"{a}n ole viel\"{a} maininnut Duperreyt\"{a}, en Bougainville\"{a}, en Fitz Royta, en Wickamia, en Stokesia... --- Riitt\"{a}\"{a}, majuri huusi, lukum\"{a}\"{a}r\"{a}n masentamana. --- En Perouta enk\"{a} Quoyta, Paganel jatkoi kuin pikajuna, --- enk\"{a} Bennetti\"{a}, enk\"{a} Cuninghamia, enk\"{a} Nutchelli\"{a}, en Tiersi\"{a}... --- Armoa! --- Enk\"{a} Dixonia, en Strelesky\"{a}, en Reidi\"{a}, en Wilkesi\"{a}, en Mitchelli\"{a}... --- Lopettakaa, Paganel, pyysi Glenarvan, joka nauroi katketakseen, --- \"{a}lk\"{a}\"{a} musertako MacNabbs-parkaa. Olkaa jalomielinen! H\"{a}n tunnustaa itsens\"{a} voitetuksi. --- Ent\"{a} h\"{a}nen pyssyns\"{a}? maantieteilij\"{a} kysyi voitonriemuisena. --- Se on teid\"{a}n, Paganel, majuri vastasi, --- ja min\"{a} muistelen sit\"{a} haikeana. Mutta onhan teill\"{a} muisti, jolla voi voittaa kokonaisen asevaraston. --- On varmaan mahdotonta tuntea Australiaa paremmin, lady Helena sanoi. --- Ei v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n nime\"{a}, ei v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n tapahtumaa... --- No, eik\"{o} v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n tapahtumaa? majuri sanoi p\"{a}\"{a}t\"{a}\"{a}n pudistaen. --- H\"{a}h? Mik\"{a} se on, MacNabbs, Paganel huudahti. --- Min\"{a} sanoin, ett\"{a} ehk\"{a} eiv\"{a}t sent\"{a}\"{a}n aivan kaikki Australian l\"{o}yt\"{o}\"{a} koskevat seikat ole teille tuttuja. --- Esimerkiksi? Paganel lausui ylev\"{a}n ylpe\"{a}n\"{a}. --- Ja jos mainitsisin teille yhden, jota ette tiet\"{a}isi, annatteko takaisin pyssyni? MacNabbs kysyi. --- Heti paikalla, majuri! --- Sovittu kauppa? --- Sovittu. --- Hyv\"{a}. Tied\"{a}ttek\"{o} te, Paganel, mink\"{a} vuoksi Australia ei kuulu Ranskalle? --- No niin, minusta tuntuu... --- Tai ainakin, mit\"{a} englantilaiset sanovat syyksi siihen? --- En, majuri, Paganel vastasi levottoman n\"{a}k\"{o}isen\"{a}. --- Yksinkertaisesti sen vuoksi, ett\"{a} kapteeni Baudin, joka ei kuitenkaan ollut arkalasta kotoisin, pel\"{a}styi vuonna 1802 australialaisten sammakoiden kurnutusta niin, ett\"{a} h\"{a}n mahdollisimman nopeasti nosti ankkurin ja l\"{a}hti tiehens\"{a} eik\"{a} sen koommin palannut. --- Mit\"{a}! tiedemies huudahti. --- Puhutaanko Englannissa sellaista? Mutta seh\"{a}n on huonoa pilaa! --- Perin huonoa, my\"{o}nn\"{a}n sen, majuri vastasi, --- mutta se on Englannissa historiaa. --- Se on roskaa! is\"{a}nmaallinen tiedemies huudahti. --- Oikeinko sellaista puhutaan vakavasti? --- Minun on pakko my\"{o}nt\"{a}\"{a}, rakas Paganel, vastasi lordi Glenarvan keskelt\"{a} yleist\"{a} naurua. --- Ettek\"{o} tosiaan tiennyt t\"{a}t\"{a}? --- En lainkaan. Mutta min\"{a} panen vastalauseeni. Englantilaisethan sanovat meit\"{a} sammakonsy\"{o}jiksi! Eik\"{a} tavallisesti sit\"{a} pel\"{a}t\"{a}, mit\"{a} sy\"{o}d\"{a}\"{a}n. --- Mutta niin kuitenkin sanotaan, Paganel, majuri vastasi vaatimattomasti hymyillen. Ja t\"{a}ll\"{a} tavoin j\"{a}i mainio Purdey Moore \& Dickson -kiv\"{a}\"{a}ri majuri MacNabbsin omaisuudeksi. \gutchapter{INTIAN VALTAMEREN MYRSKYT.} Kaksi p\"{a}iv\"{a}\"{a} t\"{a}m\"{a}n keskustelun j\"{a}lkeen ilmoitti John Mangles keskip\"{a}iv\"{a}merkint\"{a}ns\"{a} tehty\"{a}\"{a}n, ett\"{a} \textit{Duncan} oli 113$^{\circ}$ 37' pituuspiirill\"{a}. Matkustajat tutkivat karttaa ja huomasivat suureksi mielihyv\"{a}kseen, ett\"{a} en\"{a}\"{a} tuskin viisi astetta erotti heid\"{a}t Kap Bernouillista. T\"{a}m\"{a}n ja d'Entrecasteauxin niemen v\"{a}lill\"{a} on Australian rannikko kaaren muotoinen, jonka j\"{a}nteen\"{a} on 37. leveysaste. Jos \textit{Duncan} olisi kulkenut p\"{a}iv\"{a}ntasaajaa kohti, se olisi hyvin pian saanut n\"{a}kyviins\"{a} Kap Chathamin, joka oli siit\"{a} noin kahdensadan kilometrin p\"{a}\"{a}ss\"{a} pohjoiseen. Nyt se purjehti siin\"{a} Intian meren osassa, joka on Australian mantereen suojassa. Niinp\"{a} voitiin toivoa, ett\"{a} nelj\"{a}n p\"{a}iv\"{a}n kuluttua Kap Bernouilli alkaisi n\"{a}ky\"{a}. L\"{a}nsituuli oli siihen saakka suosinut laivan kulkua: mutta muutamia p\"{a}ivi\"{a} sitten se oli alkanut heiket\"{a} ja v\"{a}hitellen tyyntyi. Joulukuun 13. p\"{a}iv\"{a}n\"{a} se taukosi kokonaan, ja veltot purjeet riippuivat pitkin mastoja. Ilman voimakasta potkuriaan \textit{Duncan} olisi ollut valtameren tyynen ulapan vankina. T\"{a}t\"{a} s\"{a}\"{a}t\"{a} saattoi kest\"{a}\"{a} kuinka kauan tahansa. Illalla Glenarvan keskusteli t\"{a}st\"{a} asiasta John Manglesin kanssa. Nuori kapteeni, joka n\"{a}ki hiilis\"{a}ili\"{o}ittens\"{a} tyhjenev\"{a}n, n\"{a}ytti olevan hyvin huonolla tuulella t\"{a}st\"{a} tuulettomuudesta. H\"{a}n oli nostattanut yl\"{o}s kaikki mahdolliset purjeet, jopa sivu- ja haruspurjeetkin, k\"{a}ytt\"{a}\"{a}kseen hyv\"{a}kseen pienint\"{a}kin tuulahdusta; mutta, kuten matruusit sanoivat, tuulta ei ollut edes yht\"{a} lakint\"{a}ytt\"{a}. --- Mutta, Glenarvan sanoi, --- eih\"{a}n meill\"{a} kuitenkaan ole liikoja valittamista, parempihan on tyven kuin vastatuuli. --- Siin\"{a} kyll\"{a} olette oikeassa, Mylord, John Mangles vastasi, --- mutta juuri n\"{a}m\"{a} \"{a}killiset tyvenet ovat ilmanmuutoksen oireita. Ja siit\"{a} min\"{a} olen levoton; me purjehdimme monsuunien[2] rajalla, jotka raivoavat koillisesta p\"{a}in lokakuusta huhtikuuhun, ja jos joudumme hiukankin kokemaan niit\"{a}, hidastuu matkamme tuntuvasti. --- Ent\"{a} sitten, John? Jos sattuu vastoink\"{a}yminen, siihen t\"{a}ytyy alistua. Seh\"{a}n merkitsisi korkeintaan vain hiukan matkan hidastumista. --- Niin, ellei myrsky puutu asiaan. --- Pelk\"{a}\"{a}ttek\"{o} s\"{a}\"{a}n huonontuvan? Glenarvan kysyi tarkastellen taivasta, joka kuitenkin horisontista sen laelle saakka oli ihan pilvet\"{o}n. --- Pelk\"{a}\"{a}n, kapteeni vastasi, --- min\"{a} sanon sen teille, mylord, mutta en tahtoisi s\"{a}ikytt\"{a}\"{a} lady Glenarvania ja neiti Grantia. --- Siin\"{a} teette viisaasti. Kuinka asia on? --- On varmoja rajuilman oireita. \"{A}lk\"{a}\"{a} luottako taivaan selkeyteen, mylord. Ei mik\"{a}\"{a}n ole pett\"{a}v\"{a}mp\"{a}\"{a}. Jo kaksi p\"{a}iv\"{a}\"{a} on ilmapuntari laskenut huolestuttavasti; se osoittaa t\"{a}ll\"{a} hetkell\"{a} seitsem\"{a}nsataakolmekymment\"{a} ja yhdeks\"{a}n kymmenesosaa millimetri\"{a}.[3] Se on merkki, jota en voi olla ottamatta huomioon. Min\"{a} pelk\"{a}\"{a}n n\"{a}et erikoisesti etel\"{a}meren myrskyj\"{a}, sill\"{a} olen ennenkin kamppaillut niiden kanssa. Etel\"{a}navan suunnattomilla j\"{a}\"{a}tik\"{o}ill\"{a} tiivistyneet h\"{o}yryt aiheuttavat \"{a}\"{a}rimm\"{a}isen voimakasta ilmanpainetta. Siit\"{a} aiheutuu napa-ja p\"{a}iv\"{a}ntasaajatuulten taistelu, joka panee liikkeelle syklonit, tornaadot ja muut hirmumyrskyt, joita vastaan yksik\"{a}\"{a}n laiva ei kamppaile vaurioita saamatta. --- John, Glenarvan vastasi, --- \textit{Duncan} on tukeva alus ja sen kapteeni taitava merimies. Antaa myrskyn tulla, me pystymme puolustautumaan. Kertoessaan n\"{a}m\"{a} huolensa John Mangles noudatti merimiesvaistoaan. H\"{a}n oli etev\"{a} \textit{weather-wise}, kuten englantilaiset nimitt\"{a}v\"{a}t s\"{a}\"{a}profeettaa. Ilmapuntarin yht\"{a}mittainen laskeminen sai h\"{a}net ryhtym\"{a}\"{a}n kaikkiin varokeinoihin laivallaan. H\"{a}n odotti ankaraa myrsky\"{a}, vaikka taivas ei sit\"{a} viel\"{a} ennustanut; mutta h\"{a}nen erehtym\"{a}t\"{o}n ilmapuntarinsa ei voinut erehty\"{a}; ilmavirrat liikkuvat niiss\"{a} paikoissa, joissa ilmapuntari on korkealla, niit\"{a} kohti, miss\"{a} se laskee; mit\"{a} l\"{a}hemp\"{a}n\"{a} toisiaan n\"{a}m\"{a} kohdat ovat, sit\"{a} nopeammin palautuu tasapaino ilmakerroksissa ja sit\"{a} suurempi on tuulen nopeus. John j\"{a}i kannelle koko y\"{o}ksi. Noin kello yhdentoista aikaan taivas alkoi tummeta etel\"{a}ss\"{a}. John komensi kaikki miehens\"{a} mastoihin korjaamaan pikkupurjeita; h\"{a}n j\"{a}tti vain keulapurjeen, em\"{a}purjeen, latvapurjeen ja haruspurjeet. Puoleny\"{o}n tienoilla tuuli yltyi. Se k\"{a}vi pian melko navakaksi, niin ett\"{a} ilmahiukkaset kiitiv\"{a}t kymmenen metri\"{a} sekunnissa. Mastojen ryske, k\"{o}ysien kitin\"{a}, purjeiden natina, hytinseinien pauke kertoi matkustajille, mit\"{a} he eiv\"{a}t viel\"{a} tienneet. Paganel, Glenarvan, majuri ja Robert nousivat kannelle sek\"{a} uteliaisuudesta ett\"{a} ollakseen apuna. Taivaalla, joka \"{a}sken oli ollut sees ja t\"{a}htikirkas, vy\"{o}ryi paksuja pilvi\"{a}, ja niiden v\"{a}liss\"{a} oli leopardin turkin tapaan pilkullisia juovia. --- Myrsky? Glenarvan kysyi ykskantaan John Manglesilta. --- Ei viel\"{a}, mutta pian, kapteeni vastasi. Samalla h\"{a}n antoi k\"{a}skyn reivata latvapurjetta. Matruusit kiipesiv\"{a}t yl\"{o}s tuulen p\"{a}\"{a}lt\"{a} ja saivat suurella vaivalla purjeen pintaa pienennetyksi kiinnitt\"{a}m\"{a}ll\"{a} sen reivik\"{o}ysist\"{a} alaslaskettuun raakapuuhun. John Mangles halusi muuten pit\"{a}\"{a} mahdollisimman paljon purjeita tukeakseen alusta ja lievitt\"{a}\"{a}kseen sen keinahtelua. N\"{a}iden varotoimien j\"{a}lkeen h\"{a}n antoi Tom Austinille ja toiselle per\"{a}miehelle m\"{a}\"{a}r\"{a}yksi\"{a} myrskyn puhkeamisen varalta, joka ei en\"{a}\"{a} voinut viipy\"{a} kauan. Veneiden k\"{o}ysi\"{a} ja kaikkia surrausk\"{o}ysi\"{a} lujitettiin. Kanuunan tukipuita vahvistettiin. Vantit ja partuunit kiristettiin. Luukut tiivistettiin. Taistelua johtavana upseerina John ei poistunut kannelta, vaan yritti komentosillalta temmata myrskyiselt\"{a} taivaalta sen salaisuudet. Nyt oli ilmapuntari laskenut seitsem\"{a}\"{a}nsataanviiteen millimetriin, mik\"{a} on perin harvinaista, ja myrskylasi[4] osoitti myrsky\"{a}. Kello oli yksi y\"{o}ll\"{a}. Lady Helena ja neiti Grant, joita myrsky pahoin heitteli kajuutassaan, yrittiv\"{a}t tulla kannelle. Tuulen nopeus oli silloin kaksikymment\"{a}viisi metri\"{a} sekunnissa. Se vinkui k\"{o}ysist\"{o}ss\"{a} huimasti. N\"{a}m\"{a} viulunkielten kaltaiset metallij\"{a}nteet soivat kuin ne olisi kiristetty jollakin j\"{a}ttil\"{a}isjousella nopeasti v\"{a}risem\"{a}\"{a}n; hihnapy\"{o}r\"{a}t kalskahtelivat vastakkain; purjek\"{o}ydet kitisiv\"{a}t rosoisissa uurroksissaan kime\"{a}sti, purjeet paukahtelivat kuin kanuunanlaukaukset; aallot hy\"{o}kk\"{a}siv\"{a}t valtavan suurina p\"{a}in alusta, joka kellui niiden vaahtoharjoilla kuin kuningaskalastaja. Kun kapteeni John huomasi naismatkustajat, h\"{a}n kiiruhti heid\"{a}n luokseen ja pyysi heit\"{a} palaamaan kannen alle; laineita p\"{a}rskyi jo yli laidan ja vesi saattoi min\"{a} hetken\"{a} hyv\"{a}ns\"{a} sy\"{o}ks\"{a}ht\"{a}\"{a} yli koko kannen. Luonnonvoimien jymin\"{a} oli niin kova, ett\"{a} lady Helenan oli vaikea kuulla kapteenin puhetta. --- Eih\"{a}n ole mit\"{a}\"{a}n vaaraa? h\"{a}n sai kuitenkin er\"{a}\"{a}n\"{a} v\"{a}lihetken\"{a} kysytyksi. --- Ei, mylady, John Mangles vastasi, --- mutta te ette voi j\"{a}\"{a}d\"{a} kannelle ettek\"{a} te, neiti Mary. Lady Glenarvan ja neiti Grant eiv\"{a}t vastustaneet t\"{a}t\"{a} pyynn\"{o}n muodossa annettua k\"{a}sky\"{a}, vaan palasivat alas juuri kun er\"{a}s per\"{a}n yli sy\"{o}ksyv\"{a} aalto sai heid\"{a}n hyttiens\"{a} ikkunat t\"{a}risem\"{a}\"{a}n. Samalla k\"{a}vi myrsky kahta ankarammaksi; mastot taipuivat purjeiden painosta, ja alus tuntui nousevan irti aalloista. --- Nostakaa keulapurje! John Mangles huusi, --- alas latvapurje ja haruspurjeet! Matruusit riensiv\"{a}t paikoilleen; laskunuoria hellitettiin, nostonuoria kiristettiin, haruspurjeet vedettiin alas kohinalla, joka voitti myrskynkin mylvin\"{a}n, ja \textit{Duncan}, jonka piippu oksenteli sakean mustaa savua, pieksi ep\"{a}tasaisesti merta potkurinsa tuon tuostakin vedest\"{a} kohoavilla siivill\"{a}. Glenarvan, majuri, Paganel ja Robert katselivat kauhunsekaisella ihailulla t\"{a}t\"{a} \textit{Duncanin} taistelua merta vastaan; he piteliv\"{a}t lujasti kiinni varppeiden vaarnoista, voimatta vaihtaa sanaakaan kesken\"{a}\"{a}n, ja t\"{a}hystiv\"{a}t myrskylintujen pahaenteisi\"{a} parvia, joita lensi t\"{a}llaisessa hirmumyrskyss\"{a}. \"{A}kki\"{a} kuului huumaavaa sihin\"{a}\"{a} yli myrskyn metelin. H\"{o}yry sy\"{o}ksyi ulos, ei varaventtiilist\"{a}, vaan kattilan l\"{a}ppien kautta; h\"{a}t\"{a}pilli huusi kime\"{a}sti; alus kallistui pelottavasti, ja per\"{a}simess\"{a} seisovan Wilsonin paiskasi odottamaton aalto nurin. \textit{Duncan} k\"{a}\"{a}ntyi kyljitt\"{a}in aaltoihin eik\"{a} en\"{a}\"{a} totellut per\"{a}sint\"{a}. --- Mik\"{a} nyt on? John Mangles huusi ja riensi komentosillalle. --- Laiva kallistuu! Tom Austin vastasi. --- Onko per\"{a}sin rikki? --- Kone on hajonnut! kuului koneenk\"{a}ytt\"{a}j\"{a}n huuto. John kiiruhti konehuoneeseen heitt\"{a}ytyen portaita alas. Se oli h\"{o}yryst\"{a} sakeana; m\"{a}nn\"{a}t eiv\"{a}t liikkuneet sylintereiss\"{a} eiv\"{a}tk\"{a} siis py\"{o}ritt\"{a}neet akselia. N\"{a}hdess\"{a}\"{a}n kaikki ponnistukset turhiksi ja pel\"{a}ten pannujen r\"{a}j\"{a}ht\"{a}v\"{a}n koneenk\"{a}ytt\"{a}j\"{a} riensi sulkemaan h\"{o}yryn tuloputken ja p\"{a}\"{a}st\"{a}m\"{a}\"{a}n h\"{o}yry\"{a} ulos toista putkea my\"{o}ten. --- Mit\"{a} t\"{a}m\"{a} oikein merkitsee? kapteeni kysyi. --- Potkuri on rikki tai juuttunut kiinni, koneenk\"{a}ytt\"{a}j\"{a} vastasi, --- se ei toimi. --- Voiko sen saada taas liikkeelle? --- Mahdotonta. Nyt ei ollut aikaa yritt\"{a}\"{a} korjata t\"{a}t\"{a} vauriota; tilanne oli auttamaton; potkuri ei toiminut, ja h\"{o}yry, joka ei voinut liikuttaa m\"{a}nt\"{a}\"{a}, tunkeutui ulos l\"{a}ppien kautta. Johnin t\"{a}ytyi siis j\"{a}lleen turvautua purjeisiin ja etsi\"{a} apua samalta tuulelta, joka oli h\"{a}nen vaarallisin vihollisensa. H\"{a}n nousi kannelle ja selitti tilanteen parilla sanalla lordi Glenarvanille; sitten h\"{a}n vaati t\"{a}t\"{a} muiden matkustajien kanssa menem\"{a}\"{a}n kajuuttaan. Glenarvan tahtoi j\"{a}\"{a}d\"{a} kannelle. --- Ei, mylord, John Mangles vastasi p\"{a}\"{a}tt\"{a}v\"{a}sti, --- minun t\"{a}ytyy olla t\"{a}\"{a}ll\"{a} yksin miehist\"{o}ni kanssa. Menk\"{a}\"{a} hyttiinne! Laiva voi kallistua entist\"{a} pahemmin ja laineet pyyhk\"{a}ist\"{a} teid\"{a}t armottomasti mereen. --- Mutta me voimme auttaa... --- Menk\"{a}\"{a}, mylord, se on v\"{a}ltt\"{a}m\"{a}t\"{o}nt\"{a}! Er\"{a}iss\"{a} oloissa min\"{a} olen t\"{a}\"{a}ll\"{a} komentajana. Menk\"{a}\"{a}, min\"{a} vaadin! Kun John Mangles k\"{a}ytti t\"{a}llaisia sanoja, t\"{a}ytyi aseman olla \"{a}\"{a}rimm\"{a}isen vaarallinen. Glenarvan ymm\"{a}rsi, ett\"{a} h\"{a}nen oli annettava esimerkki kuuliaisuudesta. H\"{a}n poistui siis kannelta kolmen kumppaninsa seuraamana ja palasi naisten luo, jotka levottomina odottivat t\"{a}m\"{a}n luonnonvoimien kanssa k\"{a}yt\"{a}v\"{a}n kamppailun p\"{a}\"{a}ttymist\"{a}. --- Tarmokas mies tuo kunnon John! Glenarvan sanoi p\"{a}\"{a}sty\"{a}\"{a}n laivan ruokasaliin. --- On, Paganel vastasi, --- h\"{a}n tuo mieleeni suuren Shakespearenne puosun, joka n\"{a}ytelm\"{a}ss\"{a} \textit{Myrsky} huutaa kuninkaalle, kuljettaessaan h\"{a}nt\"{a} aluksessaan: --- Pois t\"{a}\"{a}lt\"{a}! Hiljaa! Hyttiinne! Ellette voi k\"{a}ske\"{a} luonnonvoimia vaikenemaan, niin olkaa itse vaiti! Pois tielt\"{a}, sanon min\"{a} teille! T\"{a}ll\"{a} v\"{a}lin ei John Mangles hukannut sekuntiakaan pelastaakseen laivan siit\"{a} vaarallisesta asemasta, johon se oli joutunut potkurinsa vioittumisen vuoksi. H\"{a}n p\"{a}\"{a}tti suunnata aluksensa tiukasti vastatuuleen, joutuakseen niin v\"{a}h\"{a}n kuin suinkin pois oikealta reitilt\"{a}. Purjeita oli siis pidett\"{a}v\"{a} levitettyin\"{a}, mutta viistoon ahdettuina, niin ett\"{a} laivan toinen kylki oli tuulta vasten. M\"{a}rssypurje nostettiin matalalle reivattuna, ja lis\"{a}ksi oli auki jonkinlainen em\"{a}haruspurje; per\"{a}simen kampi k\"{a}\"{a}nnettiin tuulen alle. Laiva, joka erinomaisesti sopi meripurjehdukseen, k\"{a}ytt\"{a}ytyi kuin virma hevonen tuntiessaan kannukset ja k\"{a}\"{a}nsi kylkens\"{a} ahdistavia aaltoja vastaan. Kest\"{a}isiv\"{a}tk\"{o} n\"{a}in pienennetyt purjeet? Ne olivat kyll\"{a} tukevimmasta Dundeenpalttinasta, mutta mik\"{a} kangas voisi kest\"{a}\"{a} sellaista tuulta? T\"{a}st\"{a} tiukasti p\"{a}in tuulta kulkemisesta oli se etu, ett\"{a} laineet l\"{o}iv\"{a}t laivan vahvimpiin osiin ja ett\"{a} voitiin pysytell\"{a} alkuper\"{a}isess\"{a} suunnassa. Mutta se ei ollut vaaratonta, sill\"{a} alus saattoi j\"{a}\"{a}d\"{a} aaltojen v\"{a}lisiin valtaviin laaksoihin kykenem\"{a}tt\"{a} j\"{a}lleen kohoamaan. John Manglesilla ei kuitenkaan ollut valinnanvaraa; niinp\"{a} h\"{a}n p\"{a}\"{a}tti pysy\"{a} t\"{a}ss\"{a} asennossa niin kauan kuin mastot ja purjeet kestiv\"{a}t. Miehist\"{o} pysytteli h\"{a}nen n\"{a}kyviss\"{a}\"{a}n valmiina menem\"{a}\"{a}n mihin milloinkin tarvittiin. John piteli kiinni touvista ja tarkasteli vimmastunutta merta. Loppuy\"{o} kului t\"{a}ss\"{a} j\"{a}nnityksess\"{a}. Toivottiin myrskyn hellitt\"{a}v\"{a}n p\"{a}iv\"{a}n koittaessa. Turha toivo. Kello kahdeksan aikaan aamulla se p\"{a}invastoin kiihtyi; tuuli, jonka vauhti oli kolmekymment\"{a}kaksi metri\"{a} sekunnissa, yltyi hirmumyrskyksi. John ei puhunut mit\"{a}\"{a}n, mutta h\"{a}n vapisi laivansa ja siin\"{a} olevien ihmisten puolesta. \textit{Duncan} kallisteli hirvitt\"{a}v\"{a}sti; se natisi liitoksissaan, ja joskus raakapuiden nokat pieksiv\"{a}t aaltojen harjaa. Kerran luultiin jo, ettei laiva en\"{a}\"{a} nousisi. Kirveet k\"{a}dess\"{a} aikoivat matruusit rient\"{a}\"{a} hakkaamaan poikki isonmaston vantteja, kun purjeet riuhtautuivat irti kiinnikkeist\"{a}\"{a}n ja lensiv\"{a}t tiehens\"{a} kuin j\"{a}ttil\"{a}isalbatrossit. \textit{Duncan} nousi taas; mutta ilman tukea laineilla, ilman per\"{a}npidon mahdollisuutta se heittelehti niin hirvitt\"{a}v\"{a}sti, ett\"{a} mastot uhkasivat katketa juurta my\"{o}ten. Se ei voisi kauan kest\"{a}\"{a} t\"{a}llaista heilahtelua, sen kyljet antaisivat periksi, ja pian sen irtoavat laidat ja h\"{o}ltyneet liitokset j\"{a}tt\"{a}isiv\"{a}t laineille vapaan tien. John Manglesilla oli j\"{a}ljell\"{a} vain yksi mahdollisuus: saada pystyyn myrskypurje ja paeta my\"{o}t\"{a}tuuleen. Se onnistui monen tunnin ty\"{o}n j\"{a}lkeen, johon ainakin parikymment\"{a} kertaa oli ryhdytt\"{a}v\"{a} uudelleen, ennen kuin se saatiin tehdyksi. Vasta kello kolme iltap\"{a}iv\"{a}ll\"{a} saatiin keulapurje vihdoin nostetuksi asianmukaiseen kuntoon. T\"{a}m\"{a}n kankaankappaleen varassa pakeni \textit{Duncan} nyt tuulta huimaa vauhtia. Se kulki myrskyn ty\"{o}nt\"{a}m\"{a}n\"{a} koillista kohti. P\"{a}\"{a}asia oli vain p\"{a}\"{a}st\"{a} eteenp\"{a}in mahdollisimman nopeaa vauhtia, sill\"{a} siit\"{a} riippui aluksen turvallisuus. Ter\"{a}v\"{a}ll\"{a} keulallaan rikkoen aaltoja, joita myrsky niin ik\"{a}\"{a}n kiid\"{a}tti eteenp\"{a}in, se toisinaan sukelsi niihin kuin suuri valas ja antoi veden hulahtaa ylitseen per\"{a}st\"{a} keulaan. Mutta v\"{a}lill\"{a} sen vauhti oli en\"{a}\"{a} sama kuin laineiden, per\"{a}sin menetti merkityksens\"{a}, ja laiva oli joka hetki vaarassa k\"{a}\"{a}nty\"{a} poikittain. Sattuipa niinkin, ett\"{a} myrsky lenn\"{a}tti laineita nopeammin kuin sit\"{a}; silloin sy\"{o}ksyi vesi per\"{a}n yli ja ry\"{o}ps\"{a}hti pitkin alusta per\"{a}st\"{a} keulaan vastustamattomalla voimalla. T\"{a}ss\"{a} tuskallisessa tilassa, toivon ja toivottomuuden vaiheilla, kului 15. p\"{a}iv\"{a} joulukuuta ja sit\"{a} seuraava y\"{o}. John Mangles ei poistunut paikaltaan hetkeksik\"{a}\"{a}n; h\"{a}n ei huolinut mist\"{a}\"{a}n ravinnosta; ainoakaan ilme h\"{a}nen v\"{a}r\"{a}ht\"{a}m\"{a}tt\"{o}miss\"{a} kasvoissaan ei ilmaissut kalvavaa pelkoa, jota h\"{a}n tunsi, ja h\"{a}nen katseensa koetti vain itsepintaisesti tunkeutua pohjoiseen ker\"{a}ytyneen usvan l\"{a}pi. H\"{a}nell\"{a} oli tosiaan syyt\"{a} pel\"{a}t\"{a} pahinta. Suuntansa menett\"{a}nyt \textit{Duncan} sy\"{o}ksyi Australian rannikkoa kohti huimaa vauhtia, jota ei mik\"{a}\"{a}n voinut hillit\"{a}. John Mangles tunsi, tosin vaistomaisesti, ett\"{a} ilmassa oli ukkosta ennustava s\"{a}hk\"{o}varaus. Joka hetki alus saattoi kolahtaa karille, joka murskaisi sen tuhansiksi sirpaleiksi. Rannikko ei h\"{a}nen laskelmansa mukaan voinut olla kahtakymment\"{a} kilometri\"{a} kauempana suoraan tuulen alla. N\"{a}iss\"{a} oloissa maa merkitsi samaa kuin haaksirikko, aluksen menetys. Sata kertaa parempi oli \"{a}\"{a}ret\"{o}n ulappa, jonka raivoa vastaan laiva sent\"{a}\"{a}n voi puolustautua, vaikkapa sitten t\"{a}ytyisikin antaa periksi. Mutta kun myrsky heitt\"{a}isi sen maihin, se oli mennytt\"{a} kalua. John Mangles meni tapaamaan lordi Glenarvania ja puhui h\"{a}nen kanssaan kahden kesken; selitti h\"{a}nelle aseman vaikeuden, avoimesti, niin kylm\"{a}verisesti kuin kaikkeen valmiin merimiehen on tapana, ja sanoi lopuksi, ett\"{a} h\"{a}nen kenties oli pakko antaa \textit{Duncanin} paiskautua maihin. --- Ihmisten pelastamiseksi, jos mahdollista, mylord. --- Tehk\"{a}\"{a} niin, John, Glenarvan vastasi. --- Ent\"{a} lady Helena ja neiti Grant? --- Min\"{a} en sano sit\"{a} heille ennen kuin viime hetkell\"{a}, kun ei en\"{a}\"{a} ole mit\"{a}\"{a}n toivoa pysytell\"{a} merell\"{a}. Sanottehan minulle hetken? --- Sanon, mylord. Glenarvan palasi naismatkustajien luo, jotka vaaran todellista suuruutta tiet\"{a}m\"{a}tt\"{a} kuitenkin tunsivat sen uhkaavan. He osoittivat suurta rohkeutta, ainakin yht\"{a} suurta kuin heid\"{a}n miehiset toverinsa. T\"{a}ll\"{a} per\"{a}ti sopimattomalla hetkell\"{a} Paganel selitti ilmavirtojen suunnan teoriaa; h\"{a}n esitti h\"{a}nt\"{a} kuuntelevalle Robertille mielenkiintoisia eroavaisuuksia tornadojen, syklonien ja suorasuuntaisten myrskyjen v\"{a}lill\"{a}. Majuri puolestaan n\"{a}ytti odottavan loppua kuin sallimukseen uskova muhamettilainen. Kello yhdentoista tienoilla tuntui hirmumyrsky hiukan hellitt\"{a}v\"{a}n, kostea usva h\"{a}lveni, ja kun hetken oli valoisampaa, John n\"{a}ki matalan juovan maata noin kymmenen kilometrin p\"{a}\"{a}ss\"{a} tuulen alla. Laiva kiiti sit\"{a} kohti t\"{a}ytt\"{a} vauhtia. Valtavat aallot nousivat sit\"{a} vastaan murtuessaan huikeaan korkeuteen, jopa kuuteentoista metriin ja siit\"{a}kin yli. Siit\"{a} John p\"{a}\"{a}tteli, ett\"{a} ne osuivat siell\"{a} kovaan kamaraan, joka heitti ne takaisin niin korkealle. --- Siell\"{a} on hietas\"{a}rkki\"{a}, h\"{a}n sanoi Austinille. --- Sit\"{a} mielt\"{a} min\"{a}kin olen, t\"{a}m\"{a} vastasi. --- Me olemme Jumalan k\"{a}dess\"{a}, John jatkoi. --- Ellei siell\"{a} ole \textit{Duncanille} salmea ja ellei H\"{a}n itse johda meit\"{a} sinne, niin me olemme hukassa. --- T\"{a}ll\"{a} hetkell\"{a} on vuoksen aika, kapteeni; ehk\"{a}p\"{a} p\"{a}\"{a}st\"{a}\"{a}n s\"{a}rkkien yli. --- Mutta katsokaa toki, Austin, noiden hyrskyjen raivoa. Mik\"{a} alus voi niit\"{a} kest\"{a}\"{a}? Rukoilkaamme Jumalan apua, yst\"{a}v\"{a}ni! Myrskypurje kiid\"{a}tti \textit{Duncania} yh\"{a} rantaa kohti hirvitt\"{a}v\"{a}\"{a} vauhtia. Pian se oli parin kilometrin p\"{a}\"{a}ss\"{a} s\"{a}rk\"{a}st\"{a}. Huurut estiv\"{a}t maata hetkeksik\"{a}\"{a}n n\"{a}kym\"{a}st\"{a}. Kuitenkin John luuli tuon vaahtovallin takana huomanneensa tyynemm\"{a}n pinnan. Siell\"{a} olisi \textit{Duncan} ollut joltisessakin turvassa. Mutta kuinka p\"{a}\"{a}st\"{a} sinne? John k\"{a}ski matkustajain nousta kannelle; h\"{a}n ei tahtonut, ett\"{a} he haaksirikon sattuessa olisivat kajuuttaan suljettuina. Glenarvan ja h\"{a}nen kumppaninsa katselivat pelottavaa merta. Mary Grant kalpeni. --- John, Glenarvan sanoi hiljaa kapteenille, --- min\"{a} koetan pelastaa vaimoni tai kuolen h\"{a}nen kanssaan. Pid\"{a} sin\"{a} huolta neiti Grantista. --- Kyll\"{a}, mylord, John Mangles vastasi, nostaen lordin k\"{a}den kosteille silmilleen. \textit{Duncan} oli en\"{a}\"{a} vain muutaman sadan metrin p\"{a}\"{a}ss\"{a} s\"{a}rk\"{a}st\"{a}. Kun oli nousuveden aika, olisi em\"{a}puun alla ep\"{a}ilem\"{a}tt\"{a} ollut riitt\"{a}v\"{a}sti vett\"{a}, jotta alus olisi p\"{a}\"{a}ssyt kulkemaan t\"{a}m\"{a}n vaarallisen matalikon yli. Mutta j\"{a}ttil\"{a}islaineet, jotka vuoron per\"{a}\"{a}n nostivat ja laskivat alusta, saisivat sen ehdottomasti tarttumaan pohjaan. Oliko siis mit\"{a}\"{a}n keinoa lauhduttaa laineiden liikett\"{a}, helpottaa nestehiukkasten liukumista, sanalla sanoen tyynnytt\"{a}\"{a} myllert\"{a}v\"{a}\"{a} merta? John Manglesin mieleen v\"{a}l\"{a}hti viimeinen keino. --- \"{O}ljy\"{a}! h\"{a}n huudahti. --- Pojat, laskekaa \"{o}ljy\"{a}, laskekaa \"{o}ljy\"{a}! N\"{a}m\"{a} sanat k\"{a}sitti heti koko miehist\"{o}. Oli yritett\"{a}v\"{a} keinoa, joka joskus onnistuu; aaltojen raivoa voi tyynnytt\"{a}\"{a} \"{o}ljypeitteell\"{a}, joka j\"{a}\"{a} pinnalle, lievent\"{a}\"{a} vesihiukkasten t\"{o}rm\"{a}yst\"{a} toisiaan vastaan ja tekee ne niljakkaiksi. Sen teho tuntuu heti, mutta menee \"{a}kki\"{a} ohi. Tuskin alus on kulkenut t\"{a}m\"{a}n keinotekoisen peitteen yli, kun meren raivo k\"{a}y kaksinkertaiseksi, ja onneton se, joka uskaltaa l\"{a}hte\"{a} \"{o}ljy\"{a} heitt\"{a}neen aluksen per\"{a}\"{a}n.[5] Hylkeen\"{o}ljy\"{a} sis\"{a}lt\"{a}v\"{a}t tynnyrit vipusi miehist\"{o}, jonka voiman vaara teki moninkertaiseksi, nopeasti laivan keulaan. Siell\"{a} iskettiin kannet kirveill\"{a} puhki, ja tynnyrit ripustettiin keulan kahden puolen. --- Pit\"{a}k\"{a}\"{a} varanne! John Mangles huusi otollista hetke\"{a} vaanien. Puolessa minuutissa oli alus hurjasti tyrskyv\"{a}n ylityspaikan \"{a}\"{a}rell\"{a}. Ratkaiseva hetki oli tullut. --- Jumalan nimeen, kaatakaa! kapteeni komensi. Tynnyrit heilautettiin nurin, ja niist\"{a} valahti alas valtava m\"{a}\"{a}r\"{a} \"{o}ljy\"{a}. Kohta kuoppaisen meren pinta tasoittui. \textit{Duncan} lensi tyyntyneen veden yli ja oli pian verrattain rauhallisessa suvannossa vaarallisten s\"{a}rkkien takana, samalla kun valtameri ikeens\"{a} heitt\"{a}en kohosi niiden takana sanomattomaan raivoon. \gutchapter{KAP BERNOUILLI.} John Manglesin ensimm\"{a}isen\"{a} huolena oli laivansa ankkuroiminen kahdella ankkurilla. Veden syvyys oli yhdeks\"{a}n metri\"{a}. Pohja oli hyv\"{a}, kovaa soraa, johon voi tarttua lujasti kiinni, niin ettei ollut pelkoa irtautumisesta tai ajautumisesta matalikolle. N\"{a}in monen vaarallisen tunnin j\"{a}lkeen oli \textit{Duncan} nyt jonkinlaisessa lahdelmassa, jota korkea, kaareva niemi suojasi ulapan tuulia vastaan. Lordi Glenarvan oli puristanut nuoren kapteenin k\"{a}tt\"{a}. --- Kiitos, John! Ja John tunsi saaneensa runsaan palkinnon n\"{a}ill\"{a} kahdella sanalla. Glenarvan piti pelkonsa omana tietonaan eik\"{a} lady Helena, enemp\"{a}\"{a} kuin Mary Grant tai Robertkaan aavistaneet sen vaaran suuruutta, josta he juuri olivat pelastuneet. Yksi t\"{a}rke\"{a} seikka oli saatava selville. Mille kohdalle rannikkoa t\"{a}m\"{a} kauhea myrsky oli \textit{Duncanin} heitt\"{a}nyt? Miss\"{a} se j\"{a}lleen kohtaisi m\"{a}\"{a}r\"{a}tyn leveysasteensa? Kuinka kaukana lounaassa oli Kap Bernouilli? N\"{a}m\"{a} olivat ensimm\"{a}iset John Manglesille tehdyt kysymykset. H\"{a}n ryhtyi heti havaintojen tekoon ja merkitsi ne merikortille. \textit{Duncan} ei ollut paljon poikennut suunnastaan; tuskin kahta astetta. Sen asema oli 136$^{\circ}$ 12' pituutta ja 35$^{\circ}$ 07' leveytt\"{a}, Kap Catastrophen kohdalla, joka on er\"{a}\"{a}n Etel\"{a}-Australian niemen k\"{a}rjess\"{a} noin viidensadan kilometrin p\"{a}\"{a}ss\"{a} Kap Bernouillista. Kap Castastrophe, pahaenteisen niminen Onnettomuuden niemi, on vastap\"{a}\"{a}t\"{a} Kap Bordaa, jonka muodostaa er\"{a}s Kengurusaaren ulkonema. N\"{a}iden kahden k\"{a}rjen v\"{a}lill\"{a} aukeaa Investigatorin salmi, joka johtaa kahteen jokseenkin syv\"{a}\"{a}n poukamaan, Spencerin lahteen pohjoisessa ja Saint Vincentin lahteen etel\"{a}ss\"{a}. J\"{a}lkimm\"{a}isen it\"{a}rannikolle on kaivettu Etel\"{a}-Australiaksi nimitetyn maakunnan p\"{a}\"{a}kaupungin Adelaiden satama. T\"{a}ss\"{a} kaupungissa, joka perustettiin 1836, on nelj\"{a}kymment\"{a}tuhatta asukasta, ja sill\"{a} on jokseenkin runsaat luonnonvarat. Mutta kaupunki harrastaa enemm\"{a}n hedelm\"{a}llisen maan viljelemist\"{a} ja rusinoiden, appelsiinien ja kaikenlaisten maantuotteiden vienti\"{a} kuin suuria teollisuusyrityksi\"{a}. Sen v\"{a}est\"{o}ss\"{a} on enemm\"{a}n maanviljelij\"{o}it\"{a} kuin insin\"{o}\"{o}rej\"{a}, eik\"{a} yleens\"{a} kauppaa tai teollisuutta sanottavasti ole. Saattoiko \textit{Duncanin} vaurioita korjata omin p\"{a}in? Siihen kysymykseen oli saatava vastaus. John Mangles tahtoi tiet\"{a}\"{a}, kuinka asian laita oli. H\"{a}n pani miehi\"{a} sukeltamaan laivan per\"{a}puolelle; he ilmoittivat, ett\"{a} yksi potkurin siivist\"{a} oli rikkoutunut ja k\"{a}\"{a}ntynyt per\"{a}vannasta kohti: sen vuoksi ei potkuri voinut py\"{o}ri\"{a}. Se oli vakava vaurio, jopa niin vakava, ett\"{a} sen korjaaminen vaati sellaisia apuneuvoja, joita ei Adelaidessa ollut saatavana. Pitk\"{a}\"{a}n harkittuaan Glenarvan ja kapteeni tekiv\"{a}t seuraavan p\"{a}\"{a}t\"{o}ksen: \textit{Duncan} kulkisi purjeiden avulla pitkin Australian rannikkoa etsien \textit{Britannian} j\"{a}lki\"{a}; pys\"{a}hdytt\"{a}isiin Kap Bernouillin luona, miss\"{a} teht\"{a}isiin viimeiset tiedustelut, ja laiva jatkaisi matkaansa etel\"{a}\"{a}n Melbourneen saakka, miss\"{a} sen vauriot voitaisiin helposti korjauttaa. Kun potkuri olisi saatu kuntoon, \textit{Duncan} l\"{a}htisi tarpeen vaatiessa risteilem\"{a}\"{a}n it\"{a}rannikolle p\"{a}\"{a}tt\"{a}\"{a}kseen etsiskelyjens\"{a} sarjan. T\"{a}m\"{a} suunnitelma hyv\"{a}ksyttiin. John Mangles p\"{a}\"{a}tti k\"{a}ytt\"{a}\"{a} hyv\"{a}kseen ensimm\"{a}ist\"{a} tuulta l\"{a}hte\"{a}kseen liikkeelle. H\"{a}nen ei tarvinnut odottaa kauan. Iltaan menness\"{a} oli hirmumyrsky kokonaan tauonnut. Sit\"{a} seurasi siedett\"{a}v\"{a} lounaistuuli. Ryhdyttiin panemaan purjeita kuntoon. Rikkoutuneiden tilalle kiinnitettiin uudet. Kello nelj\"{a} aamulla alkoivat matruusit v\"{a}\"{a}nt\"{a}\"{a} varppikelaa. Pian olivat ankkurit irti ja ylh\"{a}\"{a}ll\"{a}, ja keula-, latva-, prammi-, harus-, em\"{a}- ja kahvelipurje pystyss\"{a} l\"{a}hti \textit{Duncan} oikea kylki mahdollisimman paljon tuuleen suunnattuna pitkin Australian rannikkoa. Kaksi tuntia my\"{o}hemmin se oli kadottanut Kap Catastrophen n\"{a}kyvist\"{a}\"{a}n ja saapunut Investigatorin salmen kohdalle. Illalla kierrettiin Kap Borda ja kuljettiin pitkin Kengurusaaren rantaa muutaman sadan metrin p\"{a}\"{a}ss\"{a}. Se on suurin Australian pikkusaarista; sit\"{a} k\"{a}ytet\"{a}\"{a}n vankisiirtolasta karanneiden turvapaikkana. N\"{a}k\"{o}ala sinne oli ihana. Rannoille kasaantuneet kalliot olivat valtavien ruohokenttien peitossa. Samoin kuin saaren l\"{o}yt\"{o}vuotena 1802 n\"{a}htiin nytkin ep\"{a}lukuisia kenguruparvia vilahtelevan metsiss\"{a} ja aukeilla. Seuraavana p\"{a}iv\"{a}n\"{a} kulki \textit{Duncan} aivan l\"{a}helt\"{a} rantaa ja l\"{a}hetti venekuntia maihin tutkimaan rannikon s\"{a}rkki\"{a}. Oltiin n\"{a}et 36. leveysasteella; siit\"{a} 28. asteelle saakka ei Glenarvan tahtonut j\"{a}tt\"{a}\"{a} ainoatakaan kohtaa tutkimatta. Joulukuun 18. p\"{a}iv\"{a}n\"{a} laiva, joka kuin kilpa-alus kiiti hankatuulessa kaikki purjeet lev\"{a}ll\"{a}\"{a}n, sivuutti Encounterin poukaman rannikon. T\"{a}nne juuri saapui tutkimusretkeilij\"{a} Sturt vuonna 1828 l\"{o}ydetty\"{a}\"{a}n Murrayn, Etel\"{a}-Australian suurimman joen. T\"{a}\"{a}ll\"{a} ei en\"{a}\"{a} ollut Kenguru-saaren vihantia rantoja, vaan hedelm\"{a}tt\"{o}mi\"{a} louhikkoja, jotka tavan takaa katkaisivat matalan ja mutkittelevan rantaviivan yksitoikkoisuuden, siell\"{a} t\"{a}\"{a}ll\"{a} n\"{a}kyi joku harmaa rantakallio tai esiinpist\"{a}v\"{a} hietaniemi; sanalla sanoen kaikkialla vallitsi napamaan kalseus. T\"{a}ll\"{a} taipaleella olivat soutuveneet raskaassa ty\"{o}ss\"{a}. Mutta merimiehet eiv\"{a}t valittaneet. Melkein aina olivat Glenarvan, h\"{a}nen erottamaton kumppaninsa Paganel ja pikku Robert mukana. He tahtoivat omin silmin etsi\"{a} \textit{Britannian} j\"{a}lki\"{a}. Mutta tunnollisesta etsinn\"{a}st\"{a} huolimatta ei tavattu merkki\"{a}k\"{a}\"{a}n haaksirikosta. Australian rannat olivat t\"{a}ss\"{a} suhteessa yht\"{a} mykki\"{a} kuin Patagonian. Mutta eih\"{a}n toivoa saanut heitt\"{a}\"{a} ennen kuin oli k\"{a}yty asiakirjan tarkoin m\"{a}\"{a}rittelem\"{a}ll\"{a} paikalla. T\"{a}ss\"{a} noudatettiin vain ylenm\"{a}\"{a}r\"{a}ist\"{a} varovaisuutta, jotta ei mit\"{a}\"{a}n j\"{a}tett\"{a}isi sattuman varaan. Y\"{o}ksi \textit{Duncan} asetti purjeensa pakkiin pysytell\"{a}kseen mahdollisuuksien mukaan samalla paikalla, ja p\"{a}iv\"{a}ll\"{a} tutkittiin rannikkoa huolellisesti. N\"{a}in saavuttiin 20. p\"{a}iv\"{a}n\"{a} joulukuuta Kap Bernouillin edustalle, johon Lacepede-lahti p\"{a}\"{a}ttyy, v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n hylyn kappaletta l\"{o}yt\"{a}m\"{a}tt\"{a}. Mutta t\"{a}m\"{a} ep\"{a}onnistuminen ei todistanut mit\"{a}\"{a}n \textit{Britannian} kapteenin asiassa. Niin\"{a} kahtena vuonna, jotka olivat kuluneet haaksirikosta, oli meri saattanut hajottaa ja h\"{a}vitt\"{a}\"{a} fregatin pirstaleet tai peitt\"{a}\"{a} ne n\"{a}kyvist\"{a}. Tai alkuasukkaat, jotka haistavat haaksirikot kuten korpit raadot, olivat vieneet niiden pienimm\"{a}tkin rippeet. Ja Harry Grant molempien kumppaniensa kanssa oli aalloista maihin pelastuessaan joutunut vangiksi ja tietenkin viety rannikolta sis\"{a}maahan. Silloin Jacques Paganel lausui taas yhden nerokkaita huomioitaan. Niin kauan kuin oli puhe Argentiinasta, saattoi maantieteilij\"{a} hyv\"{a}ll\"{a} syyll\"{a} v\"{a}itt\"{a}\"{a} asiakirjan numeroiden tarkoittavan, ei haaksirikon, vaan vankinaolon paikkaa. Pampan suuret joet oli todella kuin luotu kuljettamaan mereen kallisarvoisen asiakirjan. T\"{a}\"{a}ll\"{a} sen sijaan, t\"{a}ss\"{a} osassa Australiaa, virtaa 37. leveysasteen poikki kovin v\"{a}h\"{a}n jokia; lis\"{a}ksi Colorado- ja Negro-virta laskevat mereen asumattomien ja asuttaviksi kelpaamattomien ranta-alueiden kohdalla, kun taas Australian p\"{a}\"{a}virrat Murray, Yarra, Torrens, Darling joko yhtyv\"{a}t toisiinsa tai laskevat mereen suistoissa, joihin usein poiketaan, onpa niihin muodostunut monien laivojen k\"{a}ytt\"{a}mi\"{a} satamia. Ei siis ollut juuri luultavaa, ett\"{a} hauras pullo olisi p\"{a}\"{a}ssyt kulkemaan n\"{a}it\"{a} vilkasliikkeisi\"{a} vesi\"{a} my\"{o}ten Intian mereen. T\"{a}m\"{a} huomautus oli v\"{a}h\"{a}nkin asiaa harkitessa my\"{o}nnett\"{a}v\"{a} oikeaksi. Paganelin Patagoniassa ja Argentiinan maakunnissa p\"{a}tev\"{a} olettamus olisi siis ollut j\"{a}rjenvastainen Australiassa. Paganel my\"{o}nsi sen keskustelussa, jonka majuri MacNabbs aloitti t\"{a}st\"{a} asiasta. Oli selv\"{a}\"{a}, ett\"{a} asiakirjassa mainittu aste koski vain haaksirikon paikkaa, ett\"{a} siis pullo oli heitetty mereen sill\"{a} kohtaa, miss\"{a} \textit{Britannia} oli Australian l\"{a}nsirannikolla murskautunut. Mutta, kuten Glenarvan sattuvasti huomautti, t\"{a}m\"{a} tulkinta ei kumonnut sit\"{a} olettamusta, ett\"{a} kapteeni Grant oli vankina. H\"{a}n p\"{a}invastoin viittasi siihen asiakirjassa n\"{a}ill\"{a} sanoilla, jotka tuli ottaa huomioon: \textit{miss\"{a} he joutuvat julmien alkuasukkaiden vangiksi}. Mutta niin ollen ei en\"{a}\"{a} ollut suurempaa syyt\"{a} etsi\"{a} vangiksi joutuneita 37. asteelta kuin milt\"{a} muulta tahansa. Pitk\"{a}n keskustelun j\"{a}lkeen ratkaistiin t\"{a}m\"{a} kysymys lopullisesti n\"{a}in, ja siit\"{a} oli seurauksena: ellei \textit{Britannian} j\"{a}lki\"{a} tavattaisi Kap Bernouillin luota, ei lordi Glenarvanilla ollut muuta teht\"{a}v\"{a}\"{a} kuin palata Eurooppaan. H\"{a}nen etsiskelyns\"{a} olivat olleet tuloksettomia, mutta h\"{a}n oli t\"{a}ytt\"{a}nyt velvollisuutensa uljaasti ja tunnollisesti. Se ei voinut olla suuresti masentamatta laivan matkustajien mielt\"{a} ja saamatta Mary ja Robert Grantia ep\"{a}toivoisiksi. Noustessaan maihin lordi ja lady Glenarvanin, John Manglesin, MacNabbsin ja Paganelin kanssa kapteenin molemmat lapset tunsivat, ett\"{a} heid\"{a}n is\"{a}ns\"{a} kohtalo nyt ratkaistaisiin lopullisesti. Lopullisesti, se t\"{a}ytyi sanoa, sill\"{a} er\"{a}\"{a}ss\"{a} edellisess\"{a} keskustelussa oli Paganel selv\"{a}sti osoittanut, ett\"{a} haaksirikkoiset olisivat jo aikoja sitten p\"{a}\"{a}sseet palaamaan is\"{a}nmaahansa, jos heid\"{a}n aluksensa olisi murskautunut it\"{a}rannikon kareihin. --- Toivoa! Toivoa! Ei milloinkaan saa luopua toivosta! lady Helena toisteli nuorelle neidolle istuessaan h\"{a}nen rinnallaan veneess\"{a}, joka vei heit\"{a} maihin. --- Ei Herra meit\"{a} hylk\"{a}\"{a}. --- Niin, neiti Mary, kapteeni John sanoi, --- kun ihmisilt\"{a} loppuvat keinot, tulee taivas avuksi ja raivaa jonkun odottamattoman sattuman kautta heille uusia teit\"{a}. --- Jumala kuulkoon sananne, herra John! Mary Grant vastasi. Ranta oli en\"{a}\"{a} vain kahdensadan metrin p\"{a}\"{a}ss\"{a}; noin kolmen kilometrin pituinen niemeke p\"{a}\"{a}ttyi loivaan k\"{a}rkeen. Vene laski maihin pieneen luonnonvalkamaan muodostumassa olevien koralliriuttojen v\"{a}liss\"{a}, joista aikaa my\"{o}ten tulisi karivy\"{o}hyke Australian etel\"{a}isen osan ymp\"{a}rille. Jo t\"{a}llaisinakin ne saattoivat hyvin tuhota laivan rungon, ja \textit{Britannia} oli kyll\"{a} voinut tuhoutua niihin miehineen p\"{a}ivineen. \textit{Duncanin} matkustajat nousivat hankaluuksitta maihin t\"{a}ysin autiolle rannalle. Erilaisista kerrostumista syntyneet rantakalliot olivat noin kahdenkymmenen, jopa kahdenkymmenenviiden metrin korkuisia. T\"{a}m\"{a}n luonnonvallin yli olisi ollut vaikea nousta ilman tikkaita ja koukkuja. Onneksi John Mangles keksi vajaata kilometri\"{a} etel\"{a}mp\"{a}n\"{a} varsin sopivan solan, joka oli syntynyt vuorensein\"{a}m\"{a}n luhistuessa. Ep\"{a}ilem\"{a}tt\"{a} meri oli ankarien p\"{a}iv\"{a}ntasaajamyrskyjen aikana piessyt t\"{a}t\"{a} murenevaa karstakivimuuria ja saanut siten raskaan yl\"{a}osan sortumaan. Glenarvan kumppaneineen tunkeutui solaan ja nousi jokseenkin jyrkk\"{a}\"{a} rinnett\"{a} pitkin kalliojonon harjalle. Notkean kissanpoikasen tavoin Robert kapusi yl\"{o}s melkein \"{a}kkijyrkk\"{a}\"{a} sein\"{a}m\"{a}\"{a} ja saapui ensimm\"{a}isen\"{a} harjun laelle Paganelin mielihaikeaksi, h\"{a}nt\"{a} kun n\"{o}yryytti se, ett\"{a} kaksitoistavuotiaan pienet s\"{a}\"{a}ret voittivat h\"{a}nen nelikymmenvuotiaat pitk\"{a}t koipensa. Sen sijaan h\"{a}n j\"{a}tti kauas taakseen maltillisen majurin, joka ei siit\"{a} muuten mit\"{a}\"{a}n piitannut. Pian kaikki olivat j\"{a}lleen yhdess\"{a} ja tarkastelivat silmiens\"{a} eteen levi\"{a}v\"{a}\"{a} lakeutta. Se oli laaja, viidakkoa ja pensaikkoa kasvava, viljelem\"{a}t\"{o}n maa, hedelm\"{a}t\"{o}n seutu, jota Glenarvan vertasi Skotlannin alangon kangasmaihin ja Paganel Bretagnen hedelm\"{a}tt\"{o}miin nummiin. Mutta vaikka t\"{a}m\"{a} seutu n\"{a}ytti olevan asumaton pitkin rannikkoa, osoittivat kuitenkin kauempana ihmisen l\"{a}sn\"{a}oloa --- ei villin, vaan pysyv\"{a}isen ahertajan --- muutamat kelvollisen n\"{a}k\"{o}iset rakennukset. --- Mylly! Robert huudahti. Noin viiden kilometrin p\"{a}\"{a}ss\"{a} py\"{o}riv\"{a}t tosiaankin tuulimyllyn siivet. --- Onhan se totisesti mylly, Paganel vahvisti k\"{a}\"{a}nnetty\"{a}\"{a}n kaukoputkensa kyseist\"{a} n\"{a}ky\"{a} kohti. --- Siin\"{a} on vaatimaton, mutta hy\"{o}dyllinen muistomerkki, jonka n\"{a}keminen ihastuttaa silm\"{a}\"{a}ni. --- Se on melkein kuin kellotapuli, lady Helena sanoi. --- Tosiaan, rouva, ja niill\"{a} on viel\"{a} sekin yht\"{a}l\"{a}isyys, ett\"{a} toinen jauhaa ruumiin, toinen sielun ravintoa. --- Menn\"{a}\"{a}np\"{a} tuonne myllylle! Glenarvan ratkaisi. L\"{a}hdettiin matkaan. Puoli tuntia k\"{a}velty\"{a}\"{a}n he n\"{a}kiv\"{a}t maaper\"{a}n olevan ihmisk\"{a}den muokkaamaa, toisen n\"{a}k\"{o}ist\"{a}. Oli \"{a}kki\"{a} siirrytty hedelm\"{a}tt\"{o}m\"{a}st\"{a} er\"{a}maasta viljeltyyn seutuun. Viidakoiden ja villien pensaiden asemesta ymp\"{a}r\"{o}i vihanta pensasaita vastakynnetty\"{a} peltomaata; muutamia h\"{a}rki\"{a} ja puoli tusinaa vuohia oli laitumella niityill\"{a}, joita ymp\"{a}r\"{o}iv\"{a}t suuret Kengurusaaren laajoista taimitarhoista tuodut akaasiat. V\"{a}hitellen n\"{a}kyi parin hehtaarin verran kylvettyj\"{a} viljapeltoja t\"{a}ynn\"{a} kullankeltaisia t\"{a}hk\"{a}p\"{a}it\"{a}, suurten mehil\"{a}ispesien muotoisia hein\"{a}rukoja, vasta-aidattuja hedelm\"{a}istutuksia, kaunis Horatiukselle arvollinen puutarha, jossa huvi ja hy\"{o}ty yhdistyiv\"{a}t, sitten k\"{a}yt\"{a}nn\"{o}llisesti j\"{a}rjestettyj\"{a} uiko- ja talousrakennuksia ja vihdoin yksinkertainen, mutta hauska asuinrakennus, jonka ylle suippohuippuinen mylly heitteli suurten siipiens\"{a} liikkuvaa varjoa. Nyt tuli p\"{a}\"{a}rakennuksesta ulos noin viisikymmenvuotias miellytt\"{a}v\"{a}n n\"{a}k\"{o}inen mies, samalla kun nelj\"{a} suurta koiraa haukkuen ilmoitti vieraiden tulosta. Viisi komeaa ja reipasta poikaa, kaikki h\"{a}nen omiaan, seurasi h\"{a}nt\"{a} ja lis\"{a}ksi heid\"{a}n \"{a}itins\"{a}, kookas ja roteva nainen. Siit\"{a} ei voinut erehty\"{a}: t\"{a}m\"{a} mies, uljaan perheens\"{a} ymp\"{a}r\"{o}im\"{a}n\"{a} viel\"{a} uusien rakennusten keskell\"{a}, t\"{a}ss\"{a} melkein koskemattomassa maassa, oli t\"{a}ysin tyypillinen irlantilainen siirtolainen, joka v\"{a}syneen\"{a} kotoisten olojen kurjuuteen oli l\"{a}htenyt etsim\"{a}\"{a}n onnea ja omaisuutta merten takaa. Glenarvan ja h\"{a}nen kumppaninsa eiv\"{a}t viel\"{a} olleet esitelleet itse\"{a}\"{a}n, he eiv\"{a}t olleet ehtineet viel\"{a} mainita nimi\"{a}\"{a}n tai arvojaan, kun heit\"{a} jo tervehdittiin seuraavin syd\"{a}mellisin sanoin: --- Vieraat, olkaa tervetulleet Paddy O'Mooren taloon. --- Oletteko irlantilainen? Glenarvan kysyi tarttuen siirtolaisen h\"{a}nelle ojentamaan k\"{a}teen. --- Niin olen ollut, Paddy O'Moore vastasi. --- Nyt olen australialainen. Astukaa sis\"{a}\"{a}n, keit\"{a} lienettekin, hyv\"{a}t herrasv\"{a}et, ja olkaa kuin kotonanne! N\"{a}in herttaista kutsua t\"{a}ytyi noudattaa kursailematta. Lady Helena ja Mary Grant astuivat sis\"{a}lle rouva O'Mooren saattamina, sill\"{a} v\"{a}lin kun uudisasukkaan pojat ottivat vastaan vieraiden aseet. Laaja, raikas ja valoisa pirtti, t\"{a}ytti vahvoista, p\"{a}\"{a}llekk\"{a}in ladotuista tammilankuista rakennetun talon alemman kerroksen. Kirkkaanv\"{a}risiksi maalattuihin seiniin kiinnitetyt puupenkit, kymmenkunta rahia, kaksi tammiarkkua, jotka sis\"{a}lsiv\"{a}t valkoisia porsliiniastioita ja kiilt\"{a}vi\"{a} tinakannuja, leve\"{a} ja pitk\"{a} p\"{o}yt\"{a}, jonka \"{a}\"{a}reen mahtui mukavasti kaksikymment\"{a} henke\"{a} olivat t\"{a}m\"{a}n tukevan talon ja sen rotevien asukkaiden arvoisena kalustona. P\"{a}iv\"{a}llisateria oli katettu. Liemikulho h\"{o}yrysi paahtopaistin ja lampaanreiden v\"{a}liss\"{a}, ymp\"{a}rill\"{a} suuria lautasia oliiveja, rusinoita ja appelsiineja; siin\"{a} oli kaikkea, mit\"{a} tarvittiin, viel\"{a}p\"{a} ylellisesti. Is\"{a}nt\"{a} ja em\"{a}nt\"{a} olivat niin vieraanvaraisen n\"{a}k\"{o}isi\"{a}, houkutteleva p\"{o}yt\"{a} oli niin laaja ja niin runsaaksi katettuna, ett\"{a} olisi ollut sopimatonta olla istumatta sen \"{a}\"{a}reen. Maatilan palvelijat, joita pidettiin is\"{a}nt\"{a}v\"{a}en vertaisina, olivat tulleet ottamaan osaa heid\"{a}n ateriaansa. Paddy O'Moore viittasi k\"{a}dell\"{a}\"{a}n vieraille varattuun paikkaan. --- Min\"{a} odotin teit\"{a}, h\"{a}n sanoi yksinkertaisesti lordi Glenarvanille. --- Tek\"{o}? t\"{a}m\"{a} vastasi kummastuneena. --- Min\"{a} odotan aina niit\"{a}, jotka tulevat, irlantilainen vastasi. Sitten h\"{a}n luki vakavalla \"{a}\"{a}nell\"{a} rukouksen perheens\"{a} ja palvelijoidensa kuunnellessa kunnioittavasti seisaallaan. Lady Helena tunsi liikuttuvansa t\"{a}llaisesta tapojen koruttomuudesta, ja h\"{a}nen puolisonsa katse osoitti h\"{a}nen samoin ihailevan sit\"{a}. Siit\"{a} tuli juhla-ateria. Kaikki ottivat osaa keskusteluun. Skotlantilaiset ja irlantilaiset ovat kuin samaa kansaa. Muutaman metrin levyinen Tweed-joki kaivaa Skotlannin ja Englannin v\"{a}lille syvemm\"{a}n kuilun kuin Irlannin kanaalin toista sataa kilometri\"{a}, jotka erottavat vanhan Kaledonian Vihre\"{a}st\"{a} Saaresta. Paddy O'Moore kertoi tarinansa. Se oli sama kuin kaikkien siirtolaisten, jotka kurjuus karkottaa kotimaastaan. Moni l\"{a}htee etsim\"{a}\"{a}n omaisuutta kaukaa, mutta ei l\"{o}yd\"{a} sielt\"{a} kuin vastoink\"{a}ymist\"{a} ja onnettomuutta. He syytt\"{a}v\"{a}t onnea, unohtaen syytt\"{a}\"{a} omaa tyhmyytt\"{a}\"{a}n, laiskuuttaan ja paheitaan. Jos on kohtuullinen ja rohkea, s\"{a}\"{a}st\"{a}v\"{a}inen ja kunnollinen, silloin kyll\"{a} menestyy. Sellainen oli ollut ja sellainen oli viel\"{a}kin Paddy 0'Moore. H\"{a}n j\"{a}tti Dundalkin, jossa h\"{a}n oli kuolla n\"{a}lk\"{a}\"{a}n, vei perheens\"{a} Australian rannikolle, nousi maihin Adelaidessa, halveksi kullankaivajan ty\"{o}t\"{a} antautuen maanviljelij\"{a}n v\"{a}hemm\"{a}n houkutteleviin vaivoihin, ja kahta kuukautta my\"{o}hemmin h\"{a}n aloitti menestyv\"{a}n viljelyksens\"{a}. Koko Etel\"{a}-Australian alue on jaettu noin kolmekymment\"{a} hehtaaria k\"{a}sitt\"{a}viin palstoihin. Hallitus antaa n\"{a}it\"{a} siirtolaisille, ja kustakin palstasta voi ahkera maanviljelij\"{a} saada elantonsa, viel\"{a}p\"{a} s\"{a}\"{a}st\"{a}\"{a} noin kahdeksankymment\"{a} puntaa vuodessa. Paddy 0'M\"{o}ore tiesi sen. H\"{a}nen maanviljelystaitonsa oli h\"{a}nelle hyv\"{a}n\"{a} apuna. H\"{a}n eli, s\"{a}\"{a}sti ja hankki uusia palstoja ensimm\"{a}isen voitolla. H\"{a}nen perheens\"{a} menestyi, h\"{a}nen taloutensa samoin. Irlantilaisesta m\"{o}kkil\"{a}isest\"{a} tuli tilanomistaja, ja vaikka h\"{a}nen viljelyksens\"{a} eiv\"{a}t viel\"{a} olleet kahta vuotta vanhat, h\"{a}n omisti jo yli kaksisataa hehtaaria ty\"{o}ns\"{a} hedelm\"{o}itt\"{a}m\"{a}\"{a} maata ja viisisataa p\"{a}\"{a}t\"{a} karjaa. H\"{a}n oli oma herransa oltuaan eurooppalaisten orja ja niin riippumaton kuin voidaan olla vain maailman vapaimmassa maassa. T\"{a}h\"{a}n irlantilaisen siirtolaisen kertomukseen vastasivat h\"{a}nen vieraansa vilpitt\"{o}m\"{a}sti ja l\"{a}mpim\"{a}sti onnittelemalla. Oman tarinansa p\"{a}\"{a}tetty\"{a}\"{a}n, Paddy O'Moore ep\"{a}ilem\"{a}tt\"{a} odotti luottamusta luottamuksesta, sit\"{a} kuitenkaan sanoin vaatimatta. H\"{a}n oli niit\"{a} hienotunteisia ihmisi\"{a}, jotka sanovat: t\"{a}llainen min\"{a} olen, mutta en kysy, keit\"{a} te olette. Glenarvanin mieli teki heti puhua \textit{Duncanista}, sen olosta Kap Bernouillin luona, ja niist\"{a} etsiskelyist\"{a}, joita h\"{a}n jatkoi v\"{a}sym\"{a}tt\"{o}m\"{a}n itsepintaisesti. Mutta miehen\"{a}, joka menee suoraan p\"{a}\"{a}asiaan, h\"{a}n ensin kyseli Paddy 0'Moorelta tietoja \textit{Britannian} haaksirikosta. Irlantilaisen vastaus ei ollut suotuisa. H\"{a}n ei koskaan ollut kuullut puhuttavan t\"{a}st\"{a} laivasta. Kahteen vuoteen t\"{a}ll\"{a} rannikolla ei ollut yksik\"{a}\"{a}n laiva haaksirikkoutunut, ei niemen kummallakaan puolella. Mutta tuo onnettomuus kuului sattuneen vain kaksi vuotta sitten. Niinp\"{a} h\"{a}n saattoi t\"{a}ysin varmasti vakuuttaa, ett\"{a} haaksirikkoutuneet eiv\"{a}t olleet joutuneet maihin t\"{a}ss\"{a} osassa l\"{a}nsirannikkoa. --- Nyt, mylord, h\"{a}n lis\"{a}si, --- sallinette minun kysy\"{a}, mink\"{a} vuoksi te kysytte t\"{a}t\"{a} minulta? Silloin Glenarvan kertoi siirtolaiselle asiakirjojen l\"{o}ytymisest\"{a}, \textit{Duncanin} matkasta ja heid\"{a}n yrityksist\"{a}\"{a}n l\"{o}yt\"{a}\"{a} kapteeni Grantin j\"{a}ljet; h\"{a}n ei salannut, ett\"{a} h\"{a}nen hartain toivonsa raukeni irlantilaisen varmoista vakuutuksista ja ettei h\"{a}n en\"{a}\"{a} uskonut milloinkaan l\"{o}yt\"{a}v\"{a}ns\"{a} \textit{Britannian} haaksirikkoisia. N\"{a}iden sanojen t\"{a}ytyi tehd\"{a} masentava vaikutus Glenarvanin kuulijoihin. Robert ja Mary olivat paikalla, ja heid\"{a}n silm\"{a}ns\"{a} kyyneltyiv\"{a}t. Paganel ei keksinyt ainoatakaan lohdutuksen ja toivon sanaa. John Mangles k\"{a}rsi surusta, jota h\"{a}n ei voinut lievent\"{a}\"{a}. Toivottomuus valtasi kaikkien n\"{a}iden jalomielisten ihmisten mielen, jotka \textit{Duncan} oli turhaan tuonut n\"{a}ille kaukaisille rannoille, kun huoneessa lausuttiin n\"{a}m\"{a} sanat: --- Mylord, kiitt\"{a}k\"{a}\"{a} ja ylist\"{a}k\"{a}\"{a} Jumalaa. Jos kapteeni Grant on elossa, niin h\"{a}n el\"{a}\"{a} Australiassa. \gutchapter{AYRTON.} H\"{a}mm\"{a}stys, jonka n\"{a}m\"{a} sanat synnyttiv\"{a}t, oli sanoin kuvaamaton. Glenarvan oli ponnahtanut pystyyn ja huudahti ty\"{o}nt\"{a}en istuimen taaksep\"{a}in: --- Kuka sanoo niin? --- Min\"{a}, vastasi er\"{a}s Paddy O'Mooren palvelijoista, joka istui p\"{o}yd\"{a}n p\"{a}\"{a}ss\"{a}. --- Sin\"{a}k\"{o}, Ayrton! siirtolainen lausui yht\"{a} h\"{a}mm\"{a}styneen\"{a} kuin Glenarvan. --- Min\"{a}, Ayrton vastasi liikuttuneella, mutta varmalla \"{a}\"{a}nell\"{a}, --- min\"{a}, skotlantilainen kuten tekin, mylord, min\"{a}, yksi \textit{Britannian} haaksirikkoisista! T\"{a}m\"{a} selitys teki mit\"{a} valtavimman vaikutuksen. Mary Grant, liikutuksesta py\"{o}rryksiss\"{a}, onnesta puolikuolleena, syleili lady Helenaa. John Mangles, Robert, Paganel nousivat paikoiltaan ja riensiv\"{a}t Paddy \"{O}'Mooren Ayrtoniksi nimitt\"{a}m\"{a}n miehen luo. T\"{a}m\"{a} oli nelj\"{a}nkymmenenviiden ik\"{a}inen karkeapiirteinen mies, h\"{a}nen kiiluva katseensa peittyi matalalla olevien kulmakarvojen kaaren alle. Muuten h\"{a}n n\"{a}ytti ruumiinsa laihuudesta huolimatta olevan tavattoman voimakas. H\"{a}n oli pelkki\"{a} luita ja j\"{a}nteit\"{a} eik\"{a}, k\"{a}ytt\"{a}\"{a}ksemme er\"{a}st\"{a} skotlantilaista sananpartta, tuhlannut aikaansa tehd\"{a}kseen lihansa ihraiseksi. H\"{a}n oli keskikokoinen, leve\"{a}harteinen, hyv\"{a}ryhtinen, kasvoilla \"{a}lyn ja tarmon ilme, joka piirteiden kovuudesta huolimatta teki edullisen vaikutuksen. My\"{o}t\"{a}tuntoa, jota h\"{a}n her\"{a}tti, lis\"{a}siv\"{a}t viel\"{a} \"{a}skett\"{a}in k\"{a}rsityn puutteen j\"{a}ljet, jotka olivat ly\"{o}neet leimansa h\"{a}nen kasvoihinsa. Selv\"{a}sti n\"{a}ki, ett\"{a} h\"{a}n oli paljon k\"{a}rsinyt, vaikka h\"{a}n n\"{a}yttikin pystyv\"{a}n kest\"{a}m\"{a}\"{a}n yht\"{a} ja toista, uhmaamaan k\"{a}rsimyksi\"{a} ja voittamaan ne. Glenarvan ja h\"{a}nen yst\"{a}v\"{a}ns\"{a} tajusivat sen ensi silm\"{a}ykselt\"{a}. Ayrtonin persoonallisuus tehosi heti alusta. Glenarvan tulkitsi kaikkien toiveita tekem\"{a}ll\"{a} h\"{a}nelle lukuisia kysymyksi\"{a}, joihin Ayrton vastasi. Glenarvanin ja Ayrtonin tapaaminen oli ilmeisesti her\"{a}tt\"{a}nyt kummassakin molemminpuolista liikutusta. Niinp\"{a} Glenarvanin ensimm\"{a}iset kysymykset tulivat hajanaisina melkein kuin vaistomaisesti. --- Oletteko te \textit{Britannian} haaksirikkoisia? h\"{a}n kysyi. --- Olen, mylord, kapteeni Grantin toinen per\"{a}mies, Ayrton vastasi. --- Pelastunutko h\"{a}nen kanssaan haaksirikon j\"{a}lkeen? --- En, mylord, en. Sin\"{a} hirve\"{a}n\"{a} hetken\"{a} jouduin erilleen muista, vesi pyyhk\"{a}isi minut laivan kannelta ja heitti minut lopulta rannikolle. --- Te ette ole siis toinen niist\"{a} kahdesta matruusista, jotka asiakirja mainitsee? --- En. Min\"{a} en tiennyt t\"{a}m\"{a}n asiakirjan olemassolosta. Kapteeni on heitt\"{a}nyt sen mereen, kun min\"{a} jo olin poissa laivasta. --- Mutta kapteeni? Kapteeni? --- Min\"{a} luulin h\"{a}nen hukkuneen, h\"{a}vinneen, hautautuneen \textit{Britannian} koko miehist\"{o}n mukana. Min\"{a} uskoin olevani ainoa eloonj\"{a}\"{a}nyt. --- Mutta teh\"{a}n sanoitte, ett\"{a} kapteeni Grant on elossa! --- En. Min\"{a} sanoin: jos kapteeni on elossa... --- Te lis\"{a}sitte: h\"{a}n el\"{a}\"{a} Australiassa!... --- Muualla h\"{a}n ei todellakaan voi olla. --- Ettek\"{o} siis tied\"{a}, miss\"{a} h\"{a}n on? --- En, mylord, min\"{a} toistan viel\"{a} kerran, ett\"{a} luulin h\"{a}nen hukkuneen aaltoihin tai murskautuneen kallioihin. Vasta teilt\"{a} kuulen, ett\"{a} h\"{a}n ehk\"{a} on viel\"{a} elossa. --- Mutta mit\"{a} te sitten tied\"{a}tte? Glenarvan kysyi. --- Vain t\"{a}m\"{a}n. Jos kapteeni Grant on elossa, h\"{a}n on Australiassa. --- Miss\"{a} sitten haaksirikko tapahtui? kysyi nyt majuri MacNabbs. Se oli ensimm\"{a}inen kysymys, joka olisi pit\"{a}nyt tehd\"{a}, mutta t\"{a}m\"{a}n tapaamisen h\"{a}mment\"{a}m\"{a}n\"{a} ei Glenarvan, joka ennen kaikkea tahtoi tiet\"{a}\"{a}, miss\"{a} kapteeni Grant oli, huomannut kysy\"{a} paikkaa, miss\"{a} \textit{Britannia} oli tuhoutunut. T\"{a}st\"{a} alkaen sai keskustelu, joka ensin oli ollut h\"{a}ilyv\"{a}\"{a}, sekavaa, hyppelev\"{a}\"{a} ja vain hipaisi asioita niihin syventym\"{a}tt\"{a} ja sekoitti tapahtumat, j\"{a}rkev\"{a}mm\"{a}n suunnan, ja pian t\"{a}m\"{a}n h\"{a}m\"{a}r\"{a}n tarinan yksityiskohdat olivat t\"{a}sm\"{a}llisin\"{a} ja tarkkoina kuulijoiden mieless\"{a}. MacNabbsin tekem\"{a}\"{a}n kysymykseen Ayrton vastasi n\"{a}in: --- Kun jouduin veteen, olin keulassa vet\"{a}m\"{a}ss\"{a} alas keulapurjetta, ja \textit{Britannia} kiiti Australian rannikkoa kohti. Se ei ollut siit\"{a} kolmensadan metrin p\"{a}\"{a}ss\"{a}. Haaksirikko tapahtui siis juuri sill\"{a} paikalla. --- 37. leveysasteella? John Mangles kysyi. --- 37. leveysasteella, Ayrton vastasi. --- L\"{a}nsirannikolla? --- Ei, vaan it\"{a}rannikolla, per\"{a}mies vastasi vilkkaasti. --- Milloin? --- Illalla 27. p\"{a}iv\"{a}n\"{a} kes\"{a}kuuta 1862. --- Niin, juuri niin! Glenarvan huudahti. --- Te n\"{a}ette siis, mylord, Ayrton lis\"{a}si, --- ett\"{a} minun sopi sanoa, ett\"{a} jos kapteeni Grant viel\"{a} el\"{a}\"{a}, niin h\"{a}nt\"{a} on etsitt\"{a}v\"{a} Australian mantereelta eik\"{a} muualta. --- Ja me etsimme h\"{a}nt\"{a}, ja me l\"{o}yd\"{a}mme h\"{a}net ja me pelastamme h\"{a}net, yst\"{a}v\"{a}ni! Paganel huudahti. --- Ah, kallisarvoinen asiakirja! h\"{a}n lis\"{a}si riemuissaan kuin lapsi, --- t\"{a}ytyy sanoa, ett\"{a} sin\"{a} olet joutunut ter\"{a}v\"{a}silm\"{a}isten miesten k\"{a}siin! Mutta kukaan ei varmaankaan kuullut Paganelin mairittelevia sanoja. Glenarvan ja lady Helena, Mary ja Robert Grant tunkeilivat Ayrtonin ymp\"{a}rill\"{a}. He puristivat h\"{a}nen k\"{a}si\"{a}\"{a}n. Tuntui kuin t\"{a}m\"{a}n miehen l\"{a}sn\"{a}olo olisi ollut varma tae Harry Grantin pelastumisesta. Kun matruusi oli pelastunut haaksirikon vaaroista, miksei kapteeni olisi voinut selvit\"{a} hengiss\"{a} t\"{a}st\"{a} tapaturmasta? Ayrton toisteli mielell\"{a}\"{a}n, ett\"{a} kapteeni Grant varmaankin oli hengiss\"{a} niin kuin h\"{a}nkin. Miss\"{a}, sit\"{a} h\"{a}n ei osannut sanoa, mutta varmaan t\"{a}ll\"{a} mantereella. H\"{a}n vastasi huomattavan \"{a}lykk\"{a}\"{a}sti ja t\"{a}sm\"{a}llisesti tuhansiin kysymyksiin, joilla h\"{a}nt\"{a} ahdistettiin. H\"{a}nen puhuessaan piti neiti Mary kiinni h\"{a}nen toisesta k\"{a}dest\"{a}\"{a}n. Seh\"{a}n oli h\"{a}nen is\"{a}ns\"{a} toveri, t\"{a}m\"{a} matruusi, yksi \textit{Britannian} merimiehi\"{a}! H\"{a}n oli el\"{a}nyt Harry Grantin parissa, kulkenut h\"{a}nen kanssaan halki merien, uhmannut samoja vaaroja! Mary ei voinut irrottaa katsettaan n\"{a}ist\"{a} karheista kasvoista ja itki onnesta. T\"{a}h\"{a}n saakka ei kenenk\"{a}\"{a}n mieleen ollut tullut ep\"{a}ill\"{a} per\"{a}miehen sanojen todenper\"{a}isyytt\"{a} ja sit\"{a}, ett\"{a} h\"{a}n todella oli ilmoittamansa henkil\"{o}. Ainoastaan majuri ja ehk\"{a} John Mangles, jotka eiv\"{a}t olleet niin herkk\"{a}uskoisia, ajattelivat voisiko Ayrtonin sanoihin ehdottomasti luottaa. H\"{a}nen odottamaton tapaamisensa saattoi her\"{a}tt\"{a}\"{a} ep\"{a}ilyksi\"{a}. Tosin Ayrton oli maininnut yhteensopivia asioita ja aikam\"{a}\"{a}ri\"{a} ja paikalleen osuvia yksityiskohtia. Mutta yksityiskohdat, olkoot kuinka t\"{a}sm\"{a}llisi\"{a} tahansa, eiv\"{a}t viel\"{a} anna varmuutta, ja yleens\"{a} on huomattu, ett\"{a} valhe perustuu yksityiskohtien tarkkuuteen. MacNabbs ei siis viel\"{a} m\"{a}\"{a}ritellyt mielipidett\"{a}\"{a}n eik\"{a} sanonut sit\"{a}. John Manglesin ep\"{a}ilykset taas eiv\"{a}t kauan kest\"{a}neet matruusin sanoja vastaan, ja kuultuaan h\"{a}nen puhuvan nuorelle neidolle t\"{a}m\"{a}n is\"{a}st\"{a}, h\"{a}n piti miest\"{a} tosiaan kapteeni Grantin per\"{a}miehen\"{a}. Ayrton tunsi hyvin Maryn ja Robertin. H\"{a}n oli n\"{a}hnyt heid\"{a}t Glasgowissa ennen \textit{Britannian} l\"{a}ht\"{o}\"{a}. H\"{a}n muisti heid\"{a}n olleen l\"{a}sn\"{a} kapteenin yst\"{a}ville laivalla annetuilla j\"{a}\"{a}hyv\"{a}isaamiaisilla. Pormestari MacIntyre oli my\"{o}s ollut siell\"{a}. Robert --- joka silloin oli tuskin kymmenvuotias --- oli uskottu vanhimman matruusin Dick Turnerin hoitoon, mutta oli livahtanut t\"{a}m\"{a}n k\"{a}sist\"{a} ja kiivennyt prammitangolle. --- Se on totta, se on totta! Robert Grant vahvisti. Ja Ayrton mainitsi n\"{a}in tuhat pikkuseikkaa n\"{a}ytt\"{a}m\"{a}tt\"{a} kiinnitt\"{a}v\"{a}n niihin sit\"{a} merkityst\"{a}, jonka niille antoi John Mangles. Ja kun h\"{a}n vaikeni, Mary pyysi h\"{a}nelt\"{a} suloisella \"{a}\"{a}nell\"{a}\"{a}n: --- Viel\"{a}, herra Ayrton, kertokaa viel\"{a} is\"{a}st\"{a}mme! Per\"{a}mies tyydytti parhaansa mukaan neidon toivomuksen. Glenarvan ei tahtonut keskeytt\"{a}\"{a} h\"{a}nt\"{a}, ja kuitenkin h\"{a}nen mielt\"{a}\"{a}n oli painamassa kymmeni\"{a} hy\"{o}dyllisempi\"{a} kysymyksi\"{a}; mutta lady Helena pyysi h\"{a}nt\"{a} malttamaan mielens\"{a}, viitaten Maryn riemuisaan liikutukseen. T\"{a}m\"{a}n keskustelun aikana Ayrton kertoi \textit{Britannian} tarinan ja sen matkat Tyynen valtameren vesill\"{a}. Mary Grant tunsi niist\"{a} suuren osan, sill\"{a} tietoja laivasta oli saapunut vuoden 1862 toukokuuhun saakka. T\"{a}n\"{a} vuoden kest\"{a}neen\"{a} ajanjaksona oli Harry Grant k\"{a}ynyt valtameren p\"{a}\"{a}saarilla. H\"{a}n k\"{a}vi Hebrideill\"{a}, Uudessa Guineassa, Uudessa Seelannissa, Uudessa Kaledoniassa, tavaten eri paikoissa valtauksia, jotka useinkin olivat varsin ep\"{a}oikeutettuja, ja saaden Englannin viranomaisten puolelta osakseen nyrpe\"{a}\"{a} kohtelua, sill\"{a} h\"{a}nen tulonsa oli ilmoitettu brittil\"{a}isiin siirtokuntiin. H\"{a}n oli kuitenkin l\"{o}yt\"{a}nyt t\"{a}rke\"{a}n paikan Papuan l\"{a}nsirannalla; skotlantilaisen siirtolan perustaminen sinne n\"{a}ytti h\"{a}nest\"{a} helpolta ja sen vaurastuminen varmalta. Kun siell\"{a} oli hyv\"{a} satama Molukkien ja Filippiinien v\"{a}lisell\"{a} reitill\"{a}, piti houkutella purjehtijoita, varsinkin sitten, kun Suezin kannaksen puhkaiseminen olisi tehnyt Hyv\"{a}ntoivonniemen kiert\"{a}misen harvinaisemmaksi. Harry Grant oli niit\"{a}, jotka Englannissa ylistiv\"{a}t herra de Lessepsin ty\"{o}t\"{a} eiv\"{a}tk\"{a} halunneet valtiollista kilpailua suuren kansainv\"{a}lisen yhteisty\"{o}n esteeksi. Papuan tutkimisen j\"{a}lkeen l\"{a}hti \textit{Britannia} Callaoon hakemaan muonaa ja j\"{a}tti t\"{a}m\"{a}n satamaan 30. p\"{a}iv\"{a}n\"{a} toukokuuta 1862 palatakseen Eurooppaan Intian valtameren ja Hyv\"{a}ntoivonniemen kautta. Kolme viikkoa l\"{a}hd\"{o}n j\"{a}lkeen runteli hirvitt\"{a}v\"{a} myrsky laivan avuttomaksi. Er\"{a}\"{a}n kallistumisen j\"{a}lkeen se ei en\"{a}\"{a} kyennyt nousemaan. T\"{a}ytyi hakata poikki mastot. Pohjaan oli syntynyt reik\"{a}, jota ei kyetty tukkimaan. Miehist\"{o} oli pian lopen n\"{a}\"{a}ntynyt. Ei jaksettu pumpata tarpeeksi. Kahdeksan p\"{a}iv\"{a}\"{a} oli \textit{Britannia} hirmumyrskyn leikkipallona. Sen ruumassa oli kaksi metri\"{a} vett\"{a}. Se alkoi v\"{a}hitellen vajota. Myrsky oli vienyt veneet. Edess\"{a} oli hukkuminen laivan mukana, niin uskottiin, kun illalla 27. p\"{a}iv\"{a}n\"{a} kes\"{a}kuuta, kuten Paganel osavasti oli arvioinut, saavuttiin Australian it\"{a}rannikolle. Pian sen j\"{a}lkeen laiva kolahti karille. Tuntui ankara t\"{a}r\"{a}hdys. T\"{a}ll\"{o}in pyyhk\"{a}isi muuan aalto Ayrtonin hyrskyihin, ja h\"{a}n menetti tajuntansa. Siit\"{a} tointuessaan h\"{a}n oli alkuasukkaiden vankina, ja n\"{a}m\"{a} veiv\"{a}t h\"{a}net maan sis\"{a}osiin. Sen koommin h\"{a}n ei ollut kuullut puhuttavan \textit{Britanniasta}, ja h\"{a}n oletti, eik\"{a} syytt\"{a}, sen tuhoutuneen t\"{a}ysin Twofold-lahden vaarallisiin kareihin. T\"{a}h\"{a}n p\"{a}\"{a}ttyi kapteeni Grantia koskeva kertomus. Monella kohtaa se aiheutti s\"{a}\"{a}livi\"{a} huudahduksia. Majuri ei olisi voinut, v\"{a}\"{a}ryytt\"{a} tekem\"{a}tt\"{a}, ep\"{a}ill\"{a} sen todenper\"{a}isyytt\"{a}. Mutta \textit{Britannian} tarinan j\"{a}lkeen Ayrtonin oma tarina tarjosi erikoista mielenkiintoa. Grant oli n\"{a}et, senh\"{a}n asiakirja varmisti, pelastunut haaksirikosta kahden matruusin kanssa, kuten Ayrton itsekin. Yhden kohtalosta saattoi ymm\"{a}rrett\"{a}v\"{a}sti tehd\"{a} p\"{a}\"{a}telmi\"{a}, kuinka toisten oli k\"{a}ynyt. Ayrtonia pyydettiin siis kertomaan omat seikkailunsa. H\"{a}n kertoikin hyvin yksinkertaisesti ja lyhyesti. Er\"{a}\"{a}n alkuasukasheimon vankina haaksirikkoutunut matruusi vietiin sis\"{a}maahan, Darling-joen kostuttamille tienoille, noin viisisataa kilometri\"{a} pohjoiseen 37. asteelta. Siell\"{a} h\"{a}n eleli suuressa puutteessa, sill\"{a} heimo itse oli k\"{o}yh\"{a} joskaan ei v\"{a}kivaltainen. Siit\"{a} tuli kaksi pitk\"{a}\"{a} tuskallisen orjuuden vuotta. Mutta vapautumisen toivo piti yll\"{a} h\"{a}nen rohkeuttaan. H\"{a}n vaani v\"{a}h\"{a}isint\"{a}kin pelastumisen tilaisuutta, vaikka pako saattaisikin h\"{a}net lukemattomiin vaaroihin. Er\"{a}\"{a}n\"{a} lokakuun y\"{o}n\"{a} 1864 h\"{a}n petti vartijoidensa valppauden ja katosi loputtomien metsien syvyyteen. Kuukauden ajan h\"{a}n harhaili n\"{a}iss\"{a} valtavissa er\"{a}maissa sy\"{o}den juuria, sy\"{o}t\"{a}vi\"{a} saniaisia ja mimoosanpihkaa, ottaen p\"{a}iv\"{a}ll\"{a} suunnan auringosta, y\"{o}ll\"{a} t\"{a}hdist\"{a}, ja usein ep\"{a}toivon masentamana. N\"{a}in h\"{a}n samosi halki r\"{a}meiden, poikki jokien, yli vuorien, l\"{a}pi koko sen asumattoman osan mannerta, jonka vain harvat l\"{o}yt\"{o}retkeilij\"{a}t ovat sitkeill\"{a} matkoillaan taivaltaneet. Vihdoin h\"{a}n saapui puolikuolleena, lopen n\"{a}\"{a}nnyksiss\"{a} Paddy 0'Mooren vierasvaraiseen asumukseen, miss\"{a} h\"{a}n ty\"{o}t\"{a}\"{a}n vastaan sai hyv\"{a}n toimeentulon. --- Ja jos Ayrton kiitt\"{a}\"{a} minua, irlantilainen siirtolainen sanoi, kun t\"{a}m\"{a} kertomus oli p\"{a}\"{a}ttynyt, --- niin minunkin t\"{a}ytyy kiitt\"{a}\"{a} h\"{a}nt\"{a}. H\"{a}n on \"{a}lyk\"{a}s, kunnon mies, hvv\"{a} ty\"{o}ntekij\"{a}, ja jos h\"{a}n vain itse haluaa, voi Paddy 0'Mooren talosta tulla h\"{a}nelle pitk\"{a}aikainen asuntopaikka. Ayrton kiitti irlantilaista k\"{a}denliikkeell\"{a} ja odotti vieraiden tekev\"{a}n h\"{a}nelle uusia kysymyksi\"{a}. Itsekseen h\"{a}n kuitenkin ajatteli, ett\"{a} kuulijoiden p\"{a}\"{a}asiallinen uteliaisuus varmaankin oli jo tyydytetty. Mihin h\"{a}n muuten en\"{a}\"{a} olisi voinut vastata, kun kaikki oli jo sata kertaa sanottu? Glenarvan aikoi juuri k\"{a}\"{a}nt\"{a}\"{a} keskustelun uuden suunnitelman laatimiseen k\"{a}ytt\"{a}en siin\"{a} hyv\"{a}ksi Ayrtonin tapaamista ja h\"{a}nelt\"{a} saatuja tietoja, kun majuri k\"{a}\"{a}ntyi matruusin puoleen ja kysyi: --- Olitteko te \textit{Britannian} toisena per\"{a}miehen\"{a}? --- Olin, Ayrton vastasi ep\"{a}r\"{o}im\"{a}tt\"{a}. Mutta ymm\"{a}rt\"{a}en, ett\"{a} jokin ep\"{a}luottamuksen tunne, jokin ep\"{a}ilys, vaikka v\"{a}h\"{a}inenkin, oli aiheuttanut t\"{a}m\"{a}n majurin kysymyksen, h\"{a}n lis\"{a}si: --- Minulla sattui muuten haaksirikossa olemaan pestauskirja taskussani. Ja h\"{a}n l\"{a}hti samalla pirtist\"{a} etsim\"{a}\"{a}n t\"{a}t\"{a} virallista paperia. H\"{a}n ei ollut poissa minuuttiakaan. Mutta Paddy 0'Moore ehti kuitenkin sanoa: --- Mylord, min\"{a} voin vakuuttaa, ett\"{a} Ayrton on rehellinen mies. Niin\"{a} kahtena kuukautena, jotka h\"{a}n on ollut palveluksessani, minulla ei ole ollut syyt\"{a} kertaakaan moittia h\"{a}nt\"{a}. Min\"{a} tunsin kertomuksen h\"{a}nen haaksirikostaan ja vankeudestaan. H\"{a}n on kunnon mies, joka ansaitsee t\"{a}ysin luottamuksenne. Glenarvan aikoi vastata, ettei h\"{a}n lainkaan ollut ep\"{a}illyt Ayrtonin rehellisyytt\"{a}, kun t\"{a}m\"{a} palasi ja n\"{a}ytti virallisen pestauskirjansa. Sen olivat allekirjoittaneet \textit{Britannian} varustajat ja kapteeni Grant, jonka k\"{a}sialan Mary hyvin tunsi. Se todisti, ett\"{a} ``Tom Ayrton, ensi luokan matruusi, oli otettu toiseksi per\"{a}mieheksi fregatti \textit{Britanniaan} Glasgowista''. Ei siis ollut en\"{a}\"{a} mahdollista ep\"{a}ill\"{a} sit\"{a}, ett\"{a} Ayrton oli se, mik\"{a} sanoi olevansa, sill\"{a} vaikeata olisi ollut v\"{a}itt\"{a}\"{a} t\"{a}m\"{a}n pestauskirjan joutuneen h\"{a}nelle, vaikka se ei kuuluisi h\"{a}nelle. --- Nyt, Glenarvan sanoi, --- vetoan kaikkien neuvokkuuteen ja pyyd\"{a}n heti keskustelemaan siit\"{a}, mit\"{a} on teht\"{a}v\"{a}. Varsinkin teid\"{a}n mielipiteenne, Ayrton, on meille arvokas, ja min\"{a} olisin teille hyvin kiitollinen, jos sanoisitte sen meille. Ayrton mietti pari silm\"{a}nr\"{a}p\"{a}yst\"{a} ja vastasi sitten: --- Min\"{a} kiit\"{a}n teit\"{a}, mylord, luottamuksestanne ja toivon voivani osoittaa ansaitsevani sen. Min\"{a} tunnen jonkin verran t\"{a}t\"{a} maata, sen asukkaiden tapoja, ja jos voin olla teille hy\"{o}dyksi... --- Aivan varmasti, Glenarvan huomautti. --- Olen samaa mielt\"{a} kuin tekin, Ayrton jatkoi, --- ett\"{a} kapteeni Grant on kahden matruusin kanssa pelastunut haaksirikosta; mutta koska he eiv\"{a}t ole p\"{a}\"{a}sseet englantilaisille asutuksille eiv\"{a}tk\"{a} ole j\"{a}lleen ilmestyneet ihmisten ilmoille, olen varma, ett\"{a} heid\"{a}n kohtalonsa on ollut sama kuin minunkin ja ett\"{a} he ovat jonkun alkuasukasheimon vankeina. --- Siin\"{a} te sanotte, Ayrton, aivan saman, mit\"{a} min\"{a}kin jo olen v\"{a}itt\"{a}nyt, Paganel lausui. --- Haaksirikkoiset ovat ilmeisesti joutuneet alkuasukkaiden vangeiksi, kuten pelk\"{a}siv\"{a}tkin. Mutta tuleeko meid\"{a}n olettaa, ett\"{a} heid\"{a}t on viety 37. asteen pohjoispuolelle, samoin kuin teid\"{a}t? --- Se on todenn\"{a}k\"{o}ist\"{a}, hyv\"{a} herra, Ayrton vastasi, --- vihollisheimot eiv\"{a}t juuri oleile englantilaisten hallinnassa olevien alueiden l\"{a}hettyvill\"{a}. --- Se vaikeuttaa etsiskely\"{a}mme, Glenarvan lausui masentuneena. --- On vaikea l\"{o}yt\"{a}\"{a} vankien j\"{a}lki\"{a} n\"{a}in suuren mantereen sis\"{a}osista. T\"{a}t\"{a} huomautusta seurasi pitk\"{a} hiljaisuus. Lady Helena loi kaikkiin kumppaneihinsa kysyv\"{a}n katseen saamatta mit\"{a}\"{a}n vastausta. Vastoin tapojansa oli itse Paganelkin vaiti. H\"{a}nen tavallinen nerokkuutensa j\"{a}tti h\"{a}net pulaan. John Mangles asteli huolestuneena pitkin askelin pirtin permannolla, ik\"{a}\"{a}n kuin se olisi ollut h\"{a}nen laivansa kansi. --- Ent\"{a} te, herra Ayrton, lady Helena sanoi silloin matruusille, --- mit\"{a} te tekisitte? --- Rouva, Ayrton vastasi vilkkaasti, --- min\"{a} nousisin j\"{a}lleen \textit{Duncaniin} ja menisin suoraa p\"{a}\"{a}t\"{a} haaksirikkopaikalle. Siell\"{a} toimisin olojen ja niiden viitteiden mukaan, joita sattumalta ehk\"{a} voitaisiin l\"{o}yt\"{a}\"{a}. --- Hyv\"{a}, Glenarvan sanoi; --- t\"{a}ytyy vain odottaa, ett\"{a} \textit{Duncan} saadaan korjatuksi. --- Ah! Onko laivanne rikkoutunut? Ayrton kysyi. --- On, John Mangles vastasi. --- Pahastikin? --- Ei, mutta vian korjaaminen vaatii ty\"{o}kalustoa, jota meill\"{a} ei ole laivalla. Yksi potkurin siivist\"{a} on v\"{a}\"{a}ntynyt eik\"{a} sit\"{a} voi korjata kuin Melbournessa. --- Ettek\"{o} voi kulkea purjein? per\"{a}mies kysyi. --- Kyll\"{a}, mutta jos sattuu vastatuulia, veisi pitk\"{a}\"{a}n ennen kuin \textit{Duncan} ehtisi Twofold-lahteen ja joka tapauksessa t\"{a}ytyy k\"{a}yd\"{a} Melbournessa. --- No, antaa \textit{Duncanin} purjehtia Melbourneen, Paganel huudahti, --- ja l\"{a}htek\"{a}\"{a}mme me ilman sit\"{a} Twofold-lahteen. --- Mutta kuinka? John Mangles kysyi. --- Kulkemalla Australian halki samoin kuin marssimme Amerikan halki pitkin 37. leveysastetta. --- Ent\"{a} \textit{Duncan?} Ayrton tiedusteli erikoisen j\"{a}nnittyneen\"{a}. --- \textit{Duncan} etsii meid\"{a}t tai me \textit{Duncanin}, kuinka sattuu. Jos matkallamme l\"{o}yd\"{a}mme kapteeni Grantin, palaamme yhdess\"{a} Melbourneen. Jos taas meid\"{a}n on jatkettava matkaamme rannikolle saakka, \textit{Duncan} tulee sinne meit\"{a} noutamaan. Kenell\"{a} on t\"{a}t\"{a} suunnitelmaa vastaan mit\"{a}\"{a}n muistuttamista? Majurilla ehk\"{a}? --- Ei, MacNabbs vastasi, --- jos Australian halki on mahdollista kulkea. --- Jopa niin mahdollista, Paganel vastasi, --- ett\"{a} min\"{a} ehdottaisin lady Helenalle ja neiti Grantille, ett\"{a} he tulisivat mukaan? --- Puhutteko tosissanne, Paganel? Glenarvan kysyi. --- Aivan tosissani, rakas lordi. Se on noin viidensadankuudenkymmenen kilometrin matka, ei enemp\"{a}\"{a}. Kulkemalla seitsem\"{a}ntoista kilometri\"{a} p\"{a}iv\"{a}ss\"{a} se kest\"{a}\"{a} vajaan kuukauden, juuri sen ajan, joka tarvitaan \textit{Duncanin} korjaukseen. Ah! Jos olisi puhe Australian mantereen halki marssimisesta l\"{a}hemp\"{a}n\"{a} p\"{a}iv\"{a}ntasaajaa, suurimman leveyden kohdalta, jos pit\"{a}isi samota \"{a}\"{a}rett\"{o}mien aavikoiden halki, jossa on hirvitt\"{a}v\"{a} kuumuus, siis tehd\"{a} mit\"{a} rohkeimmatkaan matkustajat eiv\"{a}t viel\"{a} ole yritt\"{a}neet, niin se olisi eri asia! Mutta t\"{a}m\"{a} 37. leveysaste leikkaa Victorian maakuntaa, miltei englantilaisten aluetta, miss\"{a} on teit\"{a}, rautateit\"{a} ja asutusta melkein kaikkialla pitkin matkaa. Sen matkan voi ajaa vaunuilla, jos haluaa, tai viel\"{a} paremmin rattailla. Se on kuin matka Lontoosta Edinburgiin. Ei muuta. --- Ent\"{a} petoel\"{a}imet? kysyi Glenarvan, joka halusi tehd\"{a} kaikki mahdolliset muistutukset. --- Australiassa ei ole petoel\"{a}imi\"{a}. --- No villit sitten? --- T\"{a}ll\"{a} leveysasteella ei ole villej\"{a}k\"{a}\"{a}n, eiv\"{a}tk\"{a} ne miss\"{a}\"{a}n tapauksessa ole julmia, niin kuin Uuden Seelannin asukkaat. --- Ent\"{a} rosvot? --- Australian etel\"{a}isiss\"{a} maakunnissa ei ole rosvoja; karkotetut on sijoitettu id\"{a}n maakuntiin. Victorian maakunta ei ainoastaan ole kielt\"{a}ytynyt vastaanottamasta niit\"{a}, vaan on laatinut lain, jonka mukaan toisten maakuntien vapautetutkaan rikolliset eiv\"{a}t saa tulla sen alueelle. Onpa Victorian hallitus t\"{a}n\"{a} vuonna uhannut peruuttaa Peninsular Companylle my\"{o}nt\"{a}m\"{a}ns\"{a} avustuksen, jos sen alukset k\"{a}yv\"{a}t ottamassa hiili\"{a} niiss\"{a} L\"{a}nsi-Australian satamissa, joissa karkotettujen on sallittu oleskella. Kuinka, ettek\"{o} te tied\"{a} sit\"{a}, vaikka olette englantilainen? --- Ensinn\"{a}k\"{a}\"{a}n min\"{a} en ole englantilainen, Glenarvan vastasi. --- Mit\"{a} herra Paganel sanoo, se on aivan totta, lausui nyt Paddy O'Moore. --- Ei ainoastaan Victorian maakunta, vaan Etel\"{a}-Australia, Queensland, jopa Tasmaniakin ovat yksimielisesti sulkeneet alueensa karkotetuilta. Sin\"{a} aikana kuin olen t\"{a}\"{a}ll\"{a} asunut, en ole kuullut puhuttavan ainoastakaan rosvosta. --- Enk\"{a} min\"{a}k\"{a}\"{a}n puolestani ole niit\"{a} milloinkaan tavannut, Ayrton lis\"{a}si. --- Ette siis, yst\"{a}v\"{a}ni, Jacques Paganel lausui, --- saa paljonkaan n\"{a}hd\"{a} villej\"{a}; ei ole petoel\"{a}imi\"{a} eik\"{a} rosvoja. Euroopassa ei liene sellaisia paikkoja, joista voi sanoa samaa! No, onko sovittu? --- Mit\"{a} te arvelette, Helena? Glenarvan kysyi. --- Samaa kuin me kaikki, rakas Edward, lady Helena vastasi k\"{a}\"{a}ntyen kumppaneidensa puoleen, --- matkaan, matkaan! \gutchapter{L\"{A}HT\"{O}.} Kun Glenarvan oli kerran tehnyt p\"{a}\"{a}t\"{o}ksen, h\"{a}n pani sen my\"{o}skin nopeasti toimeen. Kun siis Paganelin ehdotus oli hyv\"{a}ksytty, h\"{a}n antoi heti m\"{a}\"{a}r\"{a}yksen panna matkavalmistelut toimeen mahdollisimman ripe\"{a}sti. L\"{a}ht\"{o} m\"{a}\"{a}r\"{a}ttiin tapahtuvaksi ylihuomenna, 22. p\"{a}iv\"{a}n\"{a} joulukuuta. Mit\"{a} tuloksia saattoi t\"{a}st\"{a} Australian halki kulkemisesta odottaa? Kun kerran Harry Grantin katsottiin kiist\"{a}m\"{a}tt\"{o}m\"{a}n varmasti olevan Australiassa, saattoi t\"{a}st\"{a} retkest\"{a} olla suuria seurauksia. Se lis\"{a}si suotuisien mahdollisuuksien todenn\"{a}k\"{o}isyytt\"{a}. Ei kukaan odottanut, ett\"{a} kapteeni l\"{o}ytyisi juuri t\"{a}lt\"{a} 37. asteen linjalta, jota oli p\"{a}\"{a}tetty tarkoin seurata; mutta se saattoi ehk\"{a} leikata h\"{a}nen j\"{a}lki\"{a}\"{a}n, ja joka tapauksessa se veisi suoraan h\"{a}nen haaksirikkonsa paikalle. Se oli t\"{a}rkein kohta. Jos Ayrton lis\"{a}ksi suostuisi liittym\"{a}\"{a}n matkustajiin, opastamaan heit\"{a} Victorian maakunnan metsien l\"{a}pi, saattamaan heit\"{a} it\"{a}rannikolle saakka, se lis\"{a}isi viel\"{a} menestyksen toiveita. Glenarvan oivalsi sen hyvin; h\"{a}n halusi hartaasti varata itselleen Harry Grantin kumppanin arvokkaan avun ja kysyi h\"{a}nen is\"{a}nn\"{a}lt\"{a}\"{a}n, olisiko t\"{a}m\"{a} kovin pahoillaan, jos h\"{a}n pyyt\"{a}isi Ayrtonia tulemaan mukaan. Paddy O'Moore suostui siihen, vaikkakin pahoitteli menett\"{a}v\"{a}ns\"{a} niin erinomaisen rengin. --- No, Ayrton, suostutteko seuraamaan meit\"{a} l\"{a}htiess\"{a}mme etsim\"{a}\"{a}n \textit{Britannian} haaksirikkoisia? Ayrton ei vastannut heti t\"{a}h\"{a}n kysymykseen; n\"{a}yttip\"{a} h\"{a}n hetkisen ep\"{a}r\"{o}iv\"{a}nkin, mutta harkittuaan asiaa h\"{a}n lausui: --- Kyll\"{a}, mylord, min\"{a} seuraan teit\"{a}, ja ellen voikaan opastaa teit\"{a} kapteeni Grantin j\"{a}ljille, niin saatan teid\"{a}t ainakin h\"{a}nen laivansa haaksirikkopaikalle. --- Kiitos, Ayrton, Glenarvan vastasi. --- Yksi ainoa kysymys, mylord. --- Kysyk\"{a}\"{a}, yst\"{a}v\"{a}ni. --- Miss\"{a} te tapaatte \textit{Duncanin}? --- Melbournessa, ellei meid\"{a}n tarvitse marssia Australian halki toiselle rannikolle saakka. Jos taas etsiskelymme ulottuu sinne asti, niin tavataan it\"{a}rannikolla. --- Kuinka sen kapteeni...? --- Sen kapteeni odottaa m\"{a}\"{a}r\"{a}yst\"{a}ni Melbournen satamassa. --- Hyv\"{a}, mylord, luottakaa minuun. --- Niin luotankin, Ayrton, Glenarvan vastasi. \textit{Duncanin} matkustajat kiittiv\"{a}t l\"{a}mpim\"{a}sti \textit{Britannian} per\"{a}miest\"{a}. Etenkin kapteeni Grantin lapset kohtelivat h\"{a}nt\"{a} mit\"{a} herttaisimmin. Kaikki olivat hyvill\"{a}\"{a}n h\"{a}nen p\"{a}\"{a}t\"{o}ksest\"{a}\"{a}n, lukuunottamatta irlantilaista, joka menett\"{a}isi h\"{a}ness\"{a} \"{a}lykk\"{a}\"{a}n ja uskollisen apulaisen. Mutta Paddy ymm\"{a}rsi kuinka t\"{a}rke\"{a}n\"{a} Glenarvanin t\"{a}ytyi pit\"{a}\"{a} per\"{a}miehen mukaantuloa eik\"{a} v\"{a}itt\"{a}nyt vastaan. Glenarvan pyysi h\"{a}nt\"{a} varustamaan kulkuneuvot matkaa varten Australian halki, ja kun sopimus oli tehty ja Ayrtonille ilmoitettu, milloin taas tavattaisiin, palasivat matkustajat laivalle. Paluu tapahtui hilpe\"{a}n mielialan vallitessa. Kaikki oli muuttunut. Kaikki ep\"{a}r\"{o}inti h\"{a}lvennyt. Uljaiden etsij\"{o}iden ei tarvinnut en\"{a}\"{a} kulkea umpim\"{a}hk\"{a}\"{a}n pitkin t\"{a}t\"{a} 37. leveysasteen linjaa. Harry Grant, siit\"{a} ei voinut olla ep\"{a}ilyst\"{a}, oli pelastunut t\"{a}lle mantereelle ja jokainen tunsi syd\"{a}mess\"{a}\"{a}n sit\"{a} tyydytyst\"{a}, jonka ep\"{a}tiedon j\"{a}lkeen saatu varmuus antaa. Suotuisissa oloissa saattoi \textit{Duncan} kahden kuukauden kuluttua laskea Harry Grantin Skotlannin rannalle! Kun John Mangles kannatti ehdotusta, ett\"{a} matkustajat yritt\"{a}isiv\"{a}t kulkea Australian halki, h\"{a}n oletti t\"{a}ll\"{a} kertaa saavansa seurata retkikunnan mukana. H\"{a}n neuvottelikin siit\"{a} Glenarvanin kanssa. H\"{a}n esitti monia syit\"{a} t\"{a}m\"{a}n toivomuksensa tueksi, kiintymyst\"{a}ns\"{a} lady Helenaan ja lordiin itseens\"{a}, hy\"{o}dyllisyytt\"{a}\"{a}n matkueen j\"{a}rjest\"{a}j\"{a}n\"{a} ja tarpeettomuuttaan \textit{Duncanin} kapteenina, sanalla sanoen senkin seitsem\"{a}n p\"{a}tev\"{a}\"{a} perustetta, paitsi tietenkin sit\"{a} kaikkein p\"{a}tevint\"{a}, jonka Glenarvan tiesi muutenkin. --- Yksi ainoa kysymys, John, Glenarvan sanoi. --- Luotatteko ehdottomasti apulaiseenne? --- Tinkim\"{a}tt\"{a}, John Mangles vastasi. --- Tom Austin on hyv\"{a} merimies. H\"{a}n vie \textit{Duncanin} m\"{a}\"{a}r\"{a}paikkaansa, korjauttaa sen taitavasti ja tuo sen m\"{a}\"{a}r\"{a}p\"{a}iv\"{a}n\"{a} minne k\"{a}sket\"{a}\"{a}n. Torp on t\"{a}sm\"{a}llinen velvollisuuden ja kurin mies. H\"{a}n t\"{a}ytt\"{a}\"{a} aina saamansa k\"{a}skyn tarkasti ja vitkastelematta. Te voitte siis, mylord, luottaa h\"{a}neen niin kuin minuun itseeni. --- Asia on siis sovittu, John, Glenarvan vastasi, --- te tulette meid\"{a}n mukaamme; sill\"{a} onhan hyv\"{a}, h\"{a}n lis\"{a}si hymyillen, --- ett\"{a} te olette l\"{a}sn\"{a}, kun l\"{o}yd\"{a}mme Mary Grantin is\"{a}n. --- Voi, mylord! ... John Mangles mutisi. Enemp\"{a}\"{a} h\"{a}n ei saanut sanotuksi. H\"{a}n tunsi hetkeksi kalpenevansa ja tarttui lordi Glenarvanin h\"{a}nelle ojentamaan k\"{a}teen. Seuraavana p\"{a}iv\"{a}n\"{a} John Mangles palasi kirvesmiehen ja elintarvikkeita kuljettavien matruusien kanssa Paddy O'Mooren maatilalle. Oli j\"{a}rjestett\"{a}v\"{a} kulkuneuvot yksiss\"{a} tuumin irlantilaisen kanssa. Koko perhe odotti h\"{a}nt\"{a} valmiina ty\"{o}skentelem\"{a}\"{a}n h\"{a}nen m\"{a}\"{a}r\"{a}ystens\"{a} mukaan. Ayrton oli mukana eik\"{a} s\"{a}\"{a}st\"{a}nyt kokemukseensa perustuvia neuvoja. Paddy ja h\"{a}n olivat yht\"{a} mielt\"{a} siit\"{a}, ett\"{a} naismatkustajien piti matkata h\"{a}rk\"{a}vankkureissa ja miesten ratsain. Paddy otti toimittaakseen juhdat ja vankkurit. Vankkurit olivat kuusi ja puoli metri\"{a} pitk\"{a}t, \"{o}ljykangaskatoksella varustetut; py\"{o}r\"{a}t, joita oli nelj\"{a}, olivat umpinaiset puukiekot, ilman puolia ja vanteita. Vankkurien etup\"{a}\"{a}, joka oli hyvin kaukana takap\"{a}\"{a}st\"{a}, oli yhdistetty niihin alkeellisella laitteella, joka ei sallinut \"{a}kkik\"{a}\"{a}nn\"{o}ksi\"{a}. Etup\"{a}\"{a}h\"{a}n oli kiinnitetty kahdenkymmenenviiden metrin pituinen aisa; kahden puolen sijoitettaisiin kuusi h\"{a}rk\"{a}\"{a} parittain, kolme kummallekin puolelle. N\"{a}in valjastetut h\"{a}r\"{a}t vetiv\"{a}t vankkureita niska- ja hartiavoimalla, sill\"{a} ies oli kiinnitetty niskaan ja kaulahihna rautanalkilla ikeeseen. Kapean, pitk\"{a}n, heiluvan, tielt\"{a} helposti luisuvan kulkuneuvon ohjaamiseen ja valjakon ajamiseen kepin avulla vaadittiin suurta taitoa. Mutta Ayrton oli jo harjaantunut siihen irlantilaisen maatilalla, ja Paddy meni takuuseen h\"{a}nen taidostaan. H\"{a}n toimi siis ajurina. Glenarvan pyysi h\"{a}nt\"{a} varustamaan kulkuneuvot matkaa varten Australian halki, ja kun sopimus oli tehty j\"{a} Ayrtonille ilmoitettu, milloin taas tavattaisiin, palasivat matkustajat laivalle. Kun vankkureissa ei ollut jousia, ne olivat tietenkin ep\"{a}mukavat; mutta siihen t\"{a}ytyi tyyty\"{a}. Kun John Mangles ei voinut niiden k\"{o}mpel\"{o}lle rakenteelle mit\"{a}\"{a}n, h\"{a}n piti huolen siit\"{a}, ett\"{a} sis\"{a}puoli olisi mahdollisimman viihtyis\"{a}. Ensinn\"{a}kin se jaettiin lautasein\"{a}ll\"{a} kahteen osastoon. Taakse p\"{a}\"{a}tettiin sijoittaa ruokavarat, matkatavarat ja Olbinettin kantokeitti\"{o}. Etuosa kuuluisi kokonaan naismatkustajille. Kirvesmiehen k\"{a}siss\"{a} t\"{a}m\"{a} osasto muodostui mukavaksi, paksulla matolla verhotuksi kamariksi, jossa oli peilip\"{o}yt\"{a} ja kaksi vuodetta, toinen lady Helenalle, toinen Mary Grantille. Tarvittaessa saattoi etuosaston sulkea paksuilla nahkaverhoilla suojaksi \"{o}iden viileytt\"{a} vastaan. H\"{a}t\"{a}tilassa voivat miehetkin saada siell\"{a} turvaa rankkasateiden aikana; mutta lev\"{a}hdyspaikoille oli heit\"{a} varten varattu teltta. John Mangles koetti ahtaaseen tilaan saada mahtumaan kaikki molemmille naisille tarpeelliset kapineet ja onnistui siin\"{a}. Lady Helenan ja Mary Grantin ei tarvinnut t\"{a}ss\"{a} py\"{o}rill\"{a} liikkuvassa kammiossa ylenm\"{a}\"{a}rin ik\"{a}v\"{o}id\"{a} \textit{Duncanin} mukavia hyttej\"{a}. Miesmatkustajien varusteet olivat yksinkertaisempia: seitsem\"{a}n voimakasta hevosta varattiin lordi Glenarvanille, Paganelille, Robert Grantille, MacNabbsille, John Manglesille ja molemmille matruuseille, Wilsonille ja Mulradylle, jotka seurasivat is\"{a}nt\"{a}\"{a}ns\"{a} t\"{a}ll\"{a} uudella retkell\"{a}. Ayrtonilla oli oma paikkansa vankkurien ajopenkill\"{a}, ja Olbinett, jota ratsastaminen ei houkutellut, valmistautui kernaasti matkustamaan tavaraosastossa. Hevoset ja h\"{a}r\"{a}t olivat laitumella tilan niityill\"{a} ja sielt\"{a} helposti saatavissa koolle l\"{a}hd\"{o}n hetkell\"{a}. Kaikki varattuaan ja annettuaan viimeiset ohjeet kirvesmiehelle John Mangles palasi laivalle irlantilaisen perheen kanssa, joka halusi k\"{a}yd\"{a} tervehtim\"{a}ss\"{a} lordi Glenarvania. Ayrton oli katsonut sopivaksi tulla heid\"{a}n mukaansa, ja kello nelj\"{a}n aikaan John nousi seuralaisineen \textit{Duncanin} kannelle. Heid\"{a}t otettiin vastaan avosylin. Glenarvan tarjosi heille p\"{a}iv\"{a}llist\"{a} laivallaan. H\"{a}n ei tahtonut olla kohteliaisuudessa huonompi, ja h\"{a}nen vieraansa ottivat mielell\"{a}\"{a}n vastaan korvauksen australialaisesta vieraanvaraisuudestaan laivan salongissa. Paddy O'Moore oli ihmeiss\"{a}\"{a}n. Hyttien kalusto, verhoilu, koko vaahtera- ja palisanteripuinen sisustus her\"{a}tti h\"{a}nen ihailuaan. Ayrton sit\"{a} vastoin antoi n\"{a}ille kallisarvoisille ylellisyyksille vain niukan tunnustuksen. Mutta \textit{Britannian} toinen per\"{a}mies katsahti alusta sen sijaan enemm\"{a}n merikuntoisuuden kannalta; h\"{a}n tarkasti sen lastiruuman pohjaa my\"{o}ten; laskeutui konehuoneeseen; tutki konetta, kysyi sen voimaa ja hiilenkulutusta; k\"{a}vi sen hiiliruumissa, muonas\"{a}ili\"{o}iss\"{a}, ruutivarastossa ja osoitti erikoista harrastusta sen asevarastoon, keulapakkaan sijoitettuun kanuunaan ja t\"{a}m\"{a}n kantavuuteen. Glenarvan oli t\"{a}ss\"{a} tekemisiss\"{a} asiantuntijan kanssa; sen h\"{a}n saattoi hyvin huomata Ayrtonin erikoisista kysymyksist\"{a}. Vihdoin t\"{a}m\"{a} p\"{a}\"{a}tti kiertelyns\"{a} tarkastamalla mastot ja taklauksen. --- Teill\"{a} on t\"{a}ss\"{a} komea laiva, mylord, h\"{a}n sanoi. --- Ennen kaikkea hyv\"{a} laiva, Glenarvan vastasi. --- Kuinka suuri sen tonnim\"{a}\"{a}r\"{a} on? --- Kaksisataakymmenen tonnia. --- Erehtyisink\"{o} paljon, Ayrton lis\"{a}si, --- olettaessani, ett\"{a} \textit{Duncan} p\"{a}\"{a}see hyvinkin viisitoista solmua t\"{a}ydess\"{a} h\"{o}yryss\"{a}? --- Sanokaa seitsem\"{a}ntoista, John Mangles lausui, --- niin osutte oikeaan. --- Seitsem\"{a}ntoista! Ayrton huudahti, --- mutta sittenh\"{a}n eiv\"{a}t edes parhaat sotalaivat kykene saavuttamaan sit\"{a}! --- Ei ainoakaan! John Mangles vastasi. --- \textit{Duncan} on tosiaankin kilpa-alus, joka ei antaisi periksi miss\"{a}\"{a}n kilpailussa. --- Eik\"{o} siilonkaan, kun se k\"{a}ytt\"{a}\"{a} ainoastaan purjeita? Ayrton kysyi. --- Ei silloinkaan. --- No niin, mylord, ja te kapteeni, Ayrton lausui, --- sallikaa laivoja ymm\"{a}rt\"{a}v\"{a}n merimiehen onnitella teit\"{a}. --- Hyv\"{a} on, Ayrton, Glenarvan vastasi, --- j\"{a}\"{a}k\"{a}\"{a} siis laivallemme, ja vain teist\"{a} riippuu, saatteko t\"{a}m\"{a}n laivan haltuunne. --- Min\"{a}p\"{a} ajattelen asiaa, mylord, per\"{a}mies vastasi yksinkertaisesti. T\"{a}ll\"{a} hetkell\"{a} Olbinett tuli ilmoittamaan lordille, ett\"{a} p\"{a}iv\"{a}llinen oli katettu. Glenarvan ja h\"{a}nen vieraansa siirtyiv\"{a}t per\"{a}salonkiin. --- \"{A}lyk\"{a}s mies, tuo Ayrton, Paganel sanoi majurille. --- Liiankin \"{a}lyk\"{a}s! murahti MacNabbs, jota --- t\"{a}ysin syytt\"{a}, se t\"{a}ytyy sanoa --- toisen per\"{a}miehen kasvot ja eleet eiv\"{a}t miellytt\"{a}neet. Aterian aikana Ayrton kertoi mielenkiintoisia seikkoja Australian mantereesta, jonka h\"{a}n tunsi erinomaisesti. H\"{a}n tiedusti, kuinka monta matruusia lordi Glenarvan ottaisi mukaan retkelle. Kuultuaan, ett\"{a} vain kaksi heist\"{a}, Mulrady ja Wilson, tulisivat mukaan, h\"{a}n n\"{a}ytti h\"{a}mm\"{a}styneelt\"{a}. H\"{a}n kehotti Glenarvania valitsemaan joukkonsa \textit{Duncanin} parhaista merimiehist\"{a}. Olipa h\"{a}n t\"{a}ss\"{a} suhteessa niin itsep\"{a}inen, ett\"{a} sen olisi sivumennen sanoen pit\"{a}nyt haihduttaa kaikki ep\"{a}luulo majurin mielest\"{a}. --- Mutta, Glenarvan sanoi, --- onko matkamme Etel\"{a}-Australian poikki siis jossakin suhteessa vaarallinen? --- Ei laisinkaan, Ayrton kiiruhti vastaamaan. --- No, j\"{a}tt\"{a}k\"{a}\"{a}mme siis laivalle niin paljon v\"{a}ke\"{a} kuin mahdollista. \textit{Duncanin} purjeita hoitamaan ja sit\"{a} korjaamaan tarvitaan miehi\"{a}. Ennen kaikkea on t\"{a}rke\"{a}t\"{a}, ett\"{a} se on t\"{a}sm\"{a}llisesti m\"{a}\"{a}r\"{a}paikalla, joka sille tuonnempana ilmoitetaan. \"{A}lk\"{a}\"{a}mme siis v\"{a}hent\"{a}k\"{o} sen miehist\"{o}\"{a}. Ayrton n\"{a}ytti ymm\"{a}rt\"{a}v\"{a}n lordi Glenarvanin huomautuksen eik\"{a} intt\"{a}nyt enemp\"{a}\"{a}. Illan tullen erosivat skotlantilaiset ja irlantilaiset. Ayrton ja Paddy 0'Mooren perhe palasivat kartanoonsa. Hevosten ja vankkurien oli m\"{a}\"{a}r\"{a} olla valmiina huomiseksi. L\"{a}ht\"{o} m\"{a}\"{a}r\"{a}ttiin kello kahdeksaksi aamulla. Lady Helena ja Mary Grant suorittivat sitten viimeiset matkavarustelunsa. Ne olivat lyhyet ja varsinkin mutkattomammat kuin Jacques Paganelin. Tiedemies k\"{a}ytti osan y\"{o}t\"{a} kiert\"{a}\"{a}kseen auki, puhdistaakseen ja taas kiert\"{a}\"{a}kseen kiinni kaukoputkensa laseja. Niinp\"{a} h\"{a}n nukkui viel\"{a} seuraavana aamuna varhain, kun majuri kaikuvalla \"{a}\"{a}nell\"{a} her\"{a}tti h\"{a}net. Tavarat oli jo kuljetettu maatilalle John Manglesin toimesta. Vene odotti retkel\"{a}isi\"{a}, jotka astuivat siihen ripe\"{a}sti. Nuori kapteeni antoi viimeiset ohjeensa Tom Austinille, k\"{a}ski h\"{a}nen ehdottomasti odottaa lordi Glenarvanin m\"{a}\"{a}r\"{a}yksi\"{a} Melbournessa ja noudattaa niit\"{a} t\"{a}sm\"{a}llisen tarkasti, mit\"{a} ne sis\"{a}lt\"{a}isiv\"{a}tkin. Vanha merimies vastasi John Manglesille, ett\"{a} h\"{a}neen saattoi luottaa. Laivav\"{a}en puolesta h\"{a}n toivotti lordille menestyksek\"{a}st\"{a} retke\"{a}. Vene l\"{a}hti, ja miehist\"{o} kajahdutti ilmoille kaikuvan hurraa-huudon. Kymmenen minuutin kuluttua vene saapui rannalle. V\"{a}h\"{a}n my\"{o}hemmin matkustajat ehtiv\"{a}t irlantilaisen maatilalle. Kaikki oli valmiina. Lady Helena oli ihastunut vankkurikammioonsa. Valtavat ajoneuvot, niiden alkeelliset py\"{o}r\"{a}t ja tukevat palkit miellyttiv\"{a}t h\"{a}nt\"{a} erikoisesti. Parittain valjastetut kuusi h\"{a}rk\"{a}\"{a} olivat patriarkallisen n\"{a}k\"{o}isi\"{a}, mik\"{a} h\"{a}nt\"{a} suuresti vieh\"{a}tti. Ajokeppi k\"{a}dess\"{a} Ayrton odotti uuden is\"{a}nt\"{a}ns\"{a} k\"{a}skyj\"{a}. --- Peijakas, Paganel sanoi, --- onpas siin\"{a} kulkuneuvo, joka vastaa kaiken maailman postivaunuja! En tied\"{a} parempaa keinoa kulkea maailman ymp\"{a}ri silm\"{a}nk\"{a}\"{a}nt\"{a}jien tapaan. Talo, joka siirtyy, kulkee, pys\"{a}htyy minne hyv\"{a}ksi katsotte, voiko toivoa parempaa? Sen olivat muinaiset sarmaatit ymm\"{a}rt\"{a}neet ja matkasivat vain t\"{a}ll\"{a} tavoin. --- Herra Paganel, lady Helena vastasi, --- toivon saavani ilokseni vastaanottaa teid\"{a}t salongissani. --- Niink\"{o}, rouva, tiedemies vastasi, --- seh\"{a}n on minulle suuri kunnia. Oletteko m\"{a}\"{a}r\"{a}nnyt erikoisen vierailup\"{a}iv\"{a}n? --- Min\"{a} olen kotona joka p\"{a}iv\"{a} yst\"{a}vi\"{a}ni varten, lady Helena vastasi nauraen, --- ja te olette... --- Uskollisin kaikista, rouva, Paganel t\"{a}ydensi ritarillisesti. T\"{a}m\"{a}n kohteliaisuuksien vaihdon keskeytti seitsem\"{a}n t\"{a}ysin satuloidun hevosen saapuminen, joita yksi Paddyn pojista talutti. Lordi Glenarvan suoritti irlantilaiselle n\"{a}iden eri tilaustensa hinnan, lis\"{a}ten suuret kiitoksensa, joille kunnon siirtolainen antoi ainakin yht\"{a} paljon arvoa kuin guineoille. Annettiin l\"{a}ht\"{o}merkki. Lady Helena ja neiti Grant asettuivat osastoonsa, Ayrton istuimelleen, Olbinett vankkurien takaosaan; Glenarvan, majuri, Paganel, Robert, John Mangles ja molemmat matruusit, kaikki kiv\"{a}\"{a}reill\"{a} ja revolvereilla aseistettuina, nousivat ratsujen selk\"{a}\"{a}n. Paddy O'Moore lausui perheens\"{a} yhteen \"{a}\"{a}neen s\"{a}est\"{a}m\"{a}n\"{a}: --- Herran huomaan! Ayrton antoi kuulua omituisen \"{a}\"{a}nn\"{a}hdyksen ja pisti kepill\"{a} pitk\"{a}\"{a} valjakkoaan. Vankkurit heilahtivat, palkit natisivat, akselit kitisiv\"{a}t py\"{o}rien navoissa, ja pian oli tien k\"{a}\"{a}nteess\"{a} kunnon irlantilaisen vierasvarainen maatila kadonnut n\"{a}kyvist\"{a}. \gutchapter{VICTORIAN MAAKUNTA.} Oli 22. p\"{a}iv\"{a} joulukuuta 1864. T\"{a}t\"{a} kuukautta, joka pohjoisella pallonpuoliskolla on niin kylm\"{a}, kalsea ja kostea, olisi t\"{a}ll\"{a} mantereella pit\"{a}nyt nimitt\"{a}\"{a} kes\"{a}kuuksi. T\"{a}htitieteellisesti kes\"{a} olikin alkanut jo eilen, sill\"{a} 21. p\"{a}iv\"{a}n\"{a} joulukuuta oli aurinko saavuttanut Kauriin k\"{a}\"{a}nt\"{o}piirin ja se viipyi taivaanrannan yl\"{a}puolella jo muutaman minuutin v\"{a}hemm\"{a}n. Niinp\"{a} t\"{a}m\"{a} lordi Glenarvanin uusi matka oli suoritettava vuoden kuumimpana aikana ja melkein trooppisen auringon helteess\"{a}. Englantilaisia alueita t\"{a}ss\"{a} Tyynen valtameren osassa nimitet\"{a}\"{a}n yhteisesti Australasiaksi. Siihen kuuluu Uusi Hollanti, Tasmania, Uusi Seelanti ja muutamia l\"{a}hisaaria. Australian mannermaa taas on jaettu suuruudeltaan ja rikkaudeltaan hyvin erilaisiin, laajoihin maakuntiin. Kun luo silm\"{a}yksen Petermannin tai Preschoellin piirt\"{a}miin uusiin karttoihin, h\"{a}mm\"{a}styy aluksi n\"{a}iden jakojen suoraviivaisuutta. Englantilaiset ovat viivoittimella vet\"{a}neet sovinnaiset, n\"{a}it\"{a} suuria maakuntia erottavat rajat. Ne eiv\"{a}t ole v\"{a}litt\"{a}neet vuorijonoista, jokien uomista, ilmaston vaihtelusta tai rotujen eroavuuksista. N\"{a}m\"{a} siirtokunnat rajoittuvat suorakulmaisesti toinen toiseensa ja liittyv\"{a}t yhteen kuin shakkilaudan ruudut. T\"{a}ss\"{a} suorien viivojen ja suorien kulmien j\"{a}rjestelyss\"{a} n\"{a}kee maanmittarin, mutta ei maantieteilij\"{a}n k\"{a}sialan. Ainoastaan rannikkojen vaihtelevat mutkat, vuonot, lahdet, niemet ja poukamat panevat vieh\"{a}tt\"{a}v\"{a}ll\"{a} s\"{a}\"{a}nn\"{o}tt\"{o}myydell\"{a}\"{a}n luonnon nimess\"{a} vastalauseensa. T\"{a}m\"{a} shakkilaudan j\"{a}ljittely kiihdytti aina ja syyst\"{a} kyll\"{a} vilkasta Jacques Paganelia. Jos Australia olisi ollut Ranskan oma, niin ranskalaiset maantieteilij\"{a}t eiv\"{a}t varmastikaan olisi vieneet kulmamittarin ja viivoittimen intoa n\"{a}in pitk\"{a}lle. Valtameren suuren saaren maakuntia on nyky\"{a}\"{a}n luvultaan kuusi: Uusi Etel\"{a}-Wales, p\"{a}\"{a}kaupunkina Sydney; Queensland, p\"{a}\"{a}kaupunkina Brisbane; Victorian maakunta, p\"{a}\"{a}kaupunkina Melbourne; Etel\"{a}-Australia, p\"{a}\"{a}kaupunkina Adelaide; L\"{a}nsi-Australia, p\"{a}\"{a}kaupunkina Perth; ja vihdoin Pohjois-Australia, viel\"{a} ilman p\"{a}\"{a}kaupunkia. Uudisasukkaita asuu ainoastaan rannikoilla. Tuskin yht\"{a}\"{a}n t\"{a}rke\"{a}\"{a} kaupunkia on osattu perustaa kolmensadan kilometrin p\"{a}\"{a}h\"{a}n sis\"{a}maahan. Maan sis\"{a}osa, toisin sanoen se alue, joka on yht\"{a} suuri kuin kaksi kolmannesta Euroopasta, on melkein tuntematon. Onneksi 37. leveysaste ei kulje n\"{a}iden \"{a}\"{a}rett\"{o}mien er\"{a}maiden, luoksep\"{a}\"{a}sem\"{a}tt\"{o}mien seutujen kautta, jotka jo ovat maksaneet tieteelle useita uhreja. Glenarvan ei olisi voinut uhmata niit\"{a}. H\"{a}n oli tekemisiss\"{a} vain Australian etel\"{a}isen osan kanssa, johon kuului pieni kolkka Adelaiden maakuntaa, Victorian maakunta koko leveydelt\"{a}\"{a}n ja vihdoin nurink\"{a}\"{a}nnetyn kolmion muotoisen Uuden Etel\"{a}-Walesin etel\"{a}isin k\"{a}rki. Kap Bernouillista Victorian rajalle on matkaa tuskin sataa kilometri\"{a}. Se oli kahden p\"{a}iv\"{a}n taival, ei enemp\"{a}\"{a}, ja Ayrton arveli seuraavan p\"{a}iv\"{a}n iltana p\"{a}\"{a}st\"{a}v\"{a}n levolle Aspleyss\"{a}, Victorian maakunnan l\"{a}ntisimm\"{a}ss\"{a} kaupungissa. Alkumatkalla ovat ratsastajat ja hevoset aina innokkaita. Edellisten innosta ei ole mit\"{a}\"{a}n sanomista, mutta j\"{a}lkimm\"{a}isten vauhtia n\"{a}ytti olevan parasta hillit\"{a}. Jolla on pitk\"{a} matka edess\"{a}\"{a}n, sen on s\"{a}\"{a}stett\"{a}v\"{a} hevostaan. Niinp\"{a} p\"{a}\"{a}tettiin, ett\"{a} kunakin p\"{a}iv\"{a}n\"{a} kuljettaisiin keskim\"{a}\"{a}rin vain nelj\"{a}kymment\"{a}, korkeintaan viisikymment\"{a} kilometri\"{a}. H\"{a}r\"{a}t, jotka ovat suorastaan kuin koneita, jotka menett\"{a}v\"{a}t ajassa sen, mit\"{a} voittavat tehossa, astuvat tietysti hitaasti, ja hevosten oli sovellettava vauhtinsa niiden mukaan. Vankkurit matkustajineen ja varastoineen olivat karavaanin ytimen\"{a}, sen liikkuvana linnoituksena. Ratsastajat saattoivat kuljeksia sen sivuilla, mutta eiv\"{a}t milloinkaan et\"{a}\"{a}nty\"{a} siit\"{a} kauas. Niinp\"{a} kun ei mit\"{a}\"{a}n vakinaista marssij\"{a}rjestyst\"{a} ollut s\"{a}\"{a}detty, oli jokainen vapaa tietyiss\"{a} rajoissa noudattamaan omaa makuaan, mets\"{a}miehet samoilemaan seutua, seuramiehet keskustelemaan vankkurien asukkaiden kanssa, filosofit yhdess\"{a} filosofoimaan. Paganelin, jolla oli kaikki n\"{a}m\"{a} eri ominaisuudet, olisi pit\"{a}nyt olla yht\"{a} aikaa kaikkialla. Matka Adelaiden maakunnan kautta ei ollut mill\"{a}\"{a}n tavalla mielenkiintoinen. Matalia, mutta p\"{o}lyisi\"{a} kunnaita, suuria aloja ep\"{a}m\"{a}\"{a}r\"{a}ist\"{a} maaper\"{a}\"{a}, joilla siell\"{a} on yhteisnimen\"{a} ``bush'', luonnonniittyj\"{a}, joilla kasvavien suolapitoisten pensaiden kulmikkaita lehti\"{a} lampaat erityisesti himoitsevat, seurasi toinen toistaan peninkulmittain. Siell\"{a} t\"{a}\"{a}ll\"{a} n\"{a}kyi muutamia ``pig's-face'' nimisi\"{a}, Uudelle Hollannille ominaisia sikop\"{a}isi\"{a} lampaita, jotka liikuskelivat laitumella Adelaidesta rannikolle \"{a}skett\"{a}in rakennetun s\"{a}hk\"{o}lenn\"{a}tinlinjan pylv\"{a}iden v\"{a}liss\"{a}. T\"{a}h\"{a}n saakka n\"{a}m\"{a} tasangot muistuttivat suuresti Argentiinan pampan yksitoikkoisia lakeuksia. Sama ruohoinen ja tasainen maa. Sama taivasta vasten jyrk\"{a}sti rajoittuva n\"{a}k\"{o}piiri. MacNabbs v\"{a}itti, ettei ollut vaihdettu maata; mutta Paganel vakuutti, ett\"{a} seutu muuttuisi pian. H\"{a}n takasi, ett\"{a} saadaan n\"{a}hd\"{a} ihmeellisi\"{a} asioita. Kello kolmeen menness\"{a} vankkurit kulkivat laajan, puuttoman alueen yli, joka on tunnettu moskiittotasankona. Tiedemies sai maantieteelliseksi mielihyv\"{a}kseen todeta, ett\"{a} se ansaitsi nimens\"{a}. Mutta matkustajat ja el\"{a}imet k\"{a}rsiv\"{a}t kovasti n\"{a}iden kiusallisten hy\"{o}nteisten alituisista pistoista, joita oli mahdoton v\"{a}ltt\"{a}\"{a}; kirvely saatiin kuitenkin lievennetyksi mukana olleen l\"{a}\"{a}kevaraston ammoniakilla. Paganel ei voinut olla toivottamatta hornan kattilaan n\"{a}it\"{a} verenhimoisia s\"{a}\"{a}ski\"{a}, jotka raatelivat h\"{a}nen pitk\"{a}\"{a} vartaloaan kihelm\"{o}ivill\"{a} pistoillaan. Illemmalla p\"{a}\"{a}stiin seudulle, miss\"{a} muutamat vehmaat akasiapensaat vilkastuttivat tasankoa; tuolla t\"{a}\"{a}ll\"{a} oli rykelm\"{a} valkoisia kumipuita; kauempana tuoreita py\"{o}r\"{a}nj\"{a}lki\"{a}; sitten eurooppalaista alkuper\"{a}\"{a} olevia puita, oliivi- ja sitruunapuita ja vihantia tammia sek\"{a} vihdoin aitoja hyv\"{a}ss\"{a} kunnossa. Kello kahdeksan aikaan saapuivat juhdat, jouduttaen kulkuaan Ayrtonin kepin ajamina, Red Gumin asemalle. ``Asemalla'' tarkoitetaan sis\"{a}maan uudistaloja, joissa kasvatetaan karjaa, Australian p\"{a}\"{a}rikkautta. Karjankasvattajat, ``squatters'', maassa kyyh\"{o}tt\"{a}j\"{a}t, ovat saaneet nimens\"{a} englantilaisesta teonsanasta ``squat'', kyyh\"{o}tt\"{a}\"{a}; se onkin ensimm\"{a}inen asento, johon jokainen vaelluksiinsa n\"{a}ill\"{a} aavoilla alueilla v\"{a}synyt siirtolainen asettuu. Red Gumin asema oli pienehk\"{o} uudisasutus. Mutta Glenarvan sai siell\"{a} osakseen runsasta vieraanvaraisuutta. N\"{a}iden yksin\"{a}isten asumusten katon alla on p\"{o}yt\"{a} alituisesti katettuna matkamiest\"{a} varten, ja australialainen uudisasukas on aina kohtelias is\"{a}nt\"{a}. Seuraavana aamuna valjasti Ayrton juhtansa p\"{a}iv\"{a}n valjetessa. H\"{a}n tahtoi viel\"{a} samana iltana ehti\"{a} Victorian alueelle. Maaper\"{a} k\"{a}vi v\"{a}hitellen ep\"{a}tasaisemmaksi. Jono pieni\"{a}, helakanpunaisen hiekan peitt\"{a}mi\"{a} kunnaita aaltoili silm\"{a}nkantamattomiin. Se oli kuin suunnaton, tasangon ylle heitettv punainen vaippa, jonka poimuja tuuli paisutti, joukko valkot\"{a}pl\"{a}isi\"{a}, suora- ja sile\"{a}runkoisia ``malley"-kuusia levitteli oksiaan ja tummanvihreit\"{a} havujaan vehmaan ruohiston yll\"{a}, miss\"{a} vilisi hilpeit\"{a} hyppyrottia. Sen j\"{a}lkeen tuli pensaita ja nuoria kumipuita kasvavia laajoja kentti\"{a}; sitten alkoivat ryhm\"{a}t olla hajanaisempia, yksin\"{a}isten pensaiden sijasta n\"{a}kyi puita, ja nyt n\"{a}htiin ensimm\"{a}inen n\"{a}yte Australian metsist\"{a}. Victorian rajaa l\"{a}hestytt\"{a}ess\"{a} muuttui maan muoto yh\"{a} tuntuvasti. Matkustajat huomasivat olevansa uudenlaisella maaper\"{a}ll\"{a}. He kulkivat j\"{a}rk\"{a}ht\"{a}m\"{a}tt\"{a} suoraan eteenp\"{a}in, mink\"{a}\"{a}n esteen, j\"{a}rven tai vuoren pakottamatta heit\"{a} poikkeamaan syrj\"{a}\"{a}n tai tekem\"{a}\"{a}n kierroksia. He noudattivat k\"{a}yt\"{a}nn\"{o}ss\"{a} mittausopin ensimm\"{a}ist\"{a} s\"{a}\"{a}nt\"{o}\"{a} ja seurasivat poikkeuksetta lyhyint\"{a} tiet\"{a} kahden pisteen v\"{a}lill\"{a}. V\"{a}symyksest\"{a} ja hankaluuksista ei ollut puhettakaan. Vauhti sovellettiin h\"{a}rkien verkkaisen kulun mukaan, ja vaikka n\"{a}m\"{a} tyynet el\"{a}imet eiv\"{a}t marssineet nopeasti, ne eiv\"{a}t ainakaan pys\"{a}htyneet. Niinp\"{a} kuljettuaan kahtena p\"{a}iv\"{a}n\"{a} l\"{a}hes sata kilometri\"{a} karavaani saapui, joulukuun 23. p\"{a}iv\"{a}n illalla Aspleyhin, Victorian maakunnan ensimm\"{a}iseen kaupunkiin, joka sijaitsee 141. pituusasteen kohdalla Wimerran piiriss\"{a}. Ayrton ohjasi vankkurit majataloon, joka paremman puutteessa oli saanut nimekseen \textit{Kruunun hotelli}. Illallinen, joka oli valmistettu yksinomaan lampaanlihasta mit\"{a} moninaisimmalla tavalla, h\"{o}yrysi p\"{o}yd\"{a}ll\"{a}. Sy\"{o}tiin paljon, mutta puhuttiin viel\"{a} enemm\"{a}n. Kaikki halusivat oppia tuntemaan Australian mantereen erikoisuuksia ja kyseliv\"{a}t niit\"{a} uteliaasti maantieteilij\"{a}lt\"{a}. Paganel oli heti valmis ja kuvaili t\"{a}t\"{a} Victorian maakuntaa, jota sanotaan Onnelliseksi Australiaksi. --- V\"{a}\"{a}r\"{a} m\"{a}\"{a}ritelm\"{a}! h\"{a}n sanoi. --- Olisi parempi sanoa sit\"{a} Rikkaaksi Australiaksi, sill\"{a} maiden laita on kuin ihmistenkin: rikkaus ei tee onnea. Kultakaivostensa vuoksi Australia joutui julmien ja tuhoisien seikkailijoiden haltuun. Saatte sen n\"{a}hd\"{a}, kun tulemme kulta-alueille. --- Eik\"{o} Victorian siirtokunta ole jokseenkin \"{a}skett\"{a}in perustettu? lady Glenarvan kysyi. --- On, rouva, se ei ole viel\"{a} ollut olemassa t\"{a}ytt\"{a} kolmeakymment\"{a} vuotta. Kes\"{a}kuun 6 p\"{a}iv\"{a}n\"{a} 1835, er\"{a}\"{a}n\"{a} tiistaina... --- Kello nelj\"{a}nnest\"{a} yli seitsem\"{a}n illalla, lis\"{a}si majuri, jonka teki mieli nolata Paganel h\"{a}nen turhantarkkojen tietojensa vuoksi. --- Ei, vaan kymmenen minuuttia yli seitsem\"{a}n, maantieteilij\"{a} vastasi vakavasti, --- Batman ja Falckner perustivat uudisasutuksen sen lahden rannalle, miss\"{a} nyky\"{a}\"{a}n on suuri Melbournen kaupunki. Viidentoista vuoden aikana oli siirtokunta osana Uuden Etel\"{a}-Walesin maakuntaa ja sen p\"{a}\"{a}kaupungin Sydneyn alainen. Mutta vuonna 1851 se julistettiin itsen\"{a}iseksi ja otti Victorian nimen. --- No onko se sittemmin menestynyt? Glenarvan kysyi. --- P\"{a}\"{a}telk\"{a}\"{a} itse, jalo yst\"{a}v\"{a}ni, Paganel vastasi. --- Minulla on viimeisen tilaston numerot; ajatelkoon MacNabbs mit\"{a} hyv\"{a}ns\"{a}, mutta min\"{a} en tied\"{a} mit\"{a}\"{a}n kaunopuheisempaa kuin numerot. --- Antakaa kuulua, majuri sanoi. --- No kuulkaa sitten. Vuonna 1836 Port Philippen siirtokunnassa oli kaksisataa nelj\"{a}kymment\"{a}nelj\"{a} asukasta. Nyky\"{a}\"{a}n Victorian maakunnan asukasluku on viisisataaviisikymment\"{a} tuhatta. Seitsem\"{a}n miljoonaa viinik\"{o}ynn\"{o}st\"{a} tuottaa sille vuosittain satakaksikymment\"{a}yksi tuhatta gallonaa viini\"{a}. Satakolmetuhatta hevosta kiit\"{a}\"{a} sen tasangoilla ja kuusisataaseitsem\"{a}nkymment\"{a} viisi tuhatta kaksisataakahdeksankymment\"{a}kaksi sarvip\"{a}\"{a}t\"{a} saa elantonsa sen laajoilla laidunmailla. --- Eik\"{o} sent\"{a}\"{a}n ole jonkin verran sikojakin? MacNabbs kysyi. --- On, majuri, seitsem\"{a}nkymment\"{a}yhdeks\"{a}n tuhatta kuusisataakaksikymment\"{a}viisi, ellei teill\"{a} ole mit\"{a}\"{a}n sit\"{a} vastaan. --- Ent\"{a} paljonko lampaita, Paganel? --- Seitsem\"{a}n miljoonaa sataviisitoistatuhatta yhdeks\"{a}nsataa nelj\"{a}kymment\"{a}kolme, MacNabbs. --- Niihin luettuna sekin jota paraikaa sy\"{o}mme, Paganel? --- Ei, se v\"{a}hennettyn\"{a}, siit\"{a} kun on sy\"{o}ty jo kolme nelj\"{a}nnest\"{a}. --- Hyv\"{a}, herra Paganel! lady Helena huudahti nauraen syd\"{a}mens\"{a} pohjasta. --- T\"{a}ytyy my\"{o}nt\"{a}\"{a}, ett\"{a} te olette valmistautunut n\"{a}ihin maantieteellisiin kysymyksiin, ja tehk\"{o}\"{o}n serkku MacNabbs mit\"{a} tahansa, h\"{a}n ei saa teit\"{a} lankaan. --- Mutta minun ammattiinihan kuuluu, rouva, n\"{a}iden asioiden tiet\"{a}minen ja niiden ilmoittaminen teille tarvittaessa. Ja voitte uskoa minua, kun sanon, ett\"{a} t\"{a}m\"{a} omituinen maa n\"{a}ytt\"{a}\"{a} meille viel\"{a} ihmeit\"{a}. --- T\"{a}h\"{a}n saakka kuitenkaan ... huomautti MacNabbs, joka huvikseen \"{a}rsytti maantieteilij\"{a}\"{a} saadakseen h\"{a}net kiihtym\"{a}\"{a}n. --- Odottakaa toki, maltiton majuri! Paganel huudahti. --- Tuskin on viel\"{a} jalkanne rajalla, kun jo alatte nurkua! Mutta min\"{a} sanon teille, toistan viel\"{a} kerran, ett\"{a} t\"{a}m\"{a} seutu on merkillisin maan p\"{a}\"{a}ll\"{a}. Sen pinnanmuodot, sen luonto, sen tuotteet, sen ilmasto, jopa sen tuleva h\"{a}vi\"{a}minenkin ovat h\"{a}mm\"{a}stytt\"{a}neet ja h\"{a}mm\"{a}stytt\"{a}v\"{a}t nyt ja vastakin koko maailman tiedemiehi\"{a}. Kuvitelkaa, yst\"{a}v\"{a}ni, maata, jonka rannat, eik\"{a} keskus, ovat ensiksi nousseet laineista kuten j\"{a}ttil\"{a}isrengas; keskiosassa kenties on puoliksi kuivunut sis\"{a}meri; virrat kuivuvat p\"{a}iv\"{a} p\"{a}iv\"{a}lt\"{a}; ei ole kosteutta, ei ilmassa eik\"{a} maassa; puiden lehdet k\"{a}\"{a}nt\"{a}v\"{a}t reunansa eik\"{a} lapansa aurinkoa kohti eiv\"{a}tk\"{a} anna mit\"{a}\"{a}n varjoa; puu on usein palamatonta; sateella putoaa suuria kivi\"{a}; mets\"{a}t ovat matalia ja ruoho j\"{a}ttim\"{a}ist\"{a}; el\"{a}inkunta on kummallinen, nelijalkaisilla on nokka, kuten echidna- ja ornithorynchus-lajeilla, mik\"{a} on pakottanut luonnontieteilij\"{a}t luomaan niit\"{a} varten erikoisen uuden luokan, monotremit; kenguru hyppelee eripituisilla jaloillaan; lampailla on sianp\"{a}\"{a}; ketut loikkivat puusta puuhun; joutsenet ovat mustia; rotat tekev\"{a}t linnunpesi\"{a}; ``bowes-bird'' avaa salonkinsa oven siivekk\"{a}ille vierailleen; linnut h\"{a}mm\"{a}stytt\"{a}v\"{a}t meit\"{a} laulujensa ja kykyjens\"{a} vaihteluilla, yksi kun on kuin kello ja toinen viuhuu kuin postimiehen piiska, kolmas matkii tahkoamista, nelj\"{a}s ly\"{o} sekunteja kuin kellon heiluri, viides nauraa aamulla auringon noustessa ja kuudes itkee illalla sen laskiessa! Ah! Onhan t\"{a}m\"{a}, jos mik\"{a}\"{a}n, merkillist\"{a}, j\"{a}rjet\"{o}nt\"{a} seutua, arvoituksellista ja luonnotonta maata! Hyv\"{a}ll\"{a} syyll\"{a}h\"{a}n siit\"{a} on kuuluisa kasvitieteilij\"{a} Grimard voinut sanoa: --- T\"{a}llainen on Australia; jonkinlainen yleisten lakien irvikuva tai pikemminkin koko muun maailman kasvoja vasten heitetty uhma! Paganelin vuolas sanatulva ei n\"{a}ytt\"{a}nyt voivan loppua. Maantieteellisen seuran kaunopuheinen sihteeri oli haltioissaan. H\"{a}n puhui yh\"{a} edelleen liikutellen eloisasti k\"{a}si\"{a}\"{a}n ja heilutellen haarukkaa p\"{o}yt\"{a}naapureidensa suureksi vaaraksi. Mutta vihdoin h\"{a}nen \"{a}\"{a}nens\"{a} hukkui jyliseviin hyv\"{a}huutoihin, ja h\"{a}nen t\"{a}ytyi vaieta. T\"{a}llaisen Australian erikoisuuksien luettelon j\"{a}lkeen kukaan ei tietenk\"{a}\"{a}n ajatellut kysy\"{a} h\"{a}nelt\"{a} enemp\"{a}\"{a}. Mutta sittenk\"{a}\"{a}n majuri ei malttanut olla tyynell\"{a} \"{a}\"{a}nell\"{a}\"{a}n sanomatta: --- Onko siin\"{a} kaikki, Paganel? --- Kaikkiko? Ei toki! tiedemies vastasi uudelleen innokkaasti. --- Mit\"{a}? lady Helena kysyi eritt\"{a}in uteliaana. --- Onko Australiassa jotakin viel\"{a} h\"{a}mm\"{a}stytt\"{a}v\"{a}mp\"{a}\"{a}? --- On, rouva, sen ilmasto! Se vie omituisuudellaan kaikesta muusta voiton. --- Todellako? huudahdettiin. --- Min\"{a} en puhu happirikkaan ja typpik\"{o}yh\"{a}n Australian mantereen terveydellisist\"{a} ominaisuuksista; ei ole kosteita tuulia, kun pasaatituulet puhaltavat yhdensuuntaisina sen rannikoiden kanssa, ja useimmat taudit ovat t\"{a}\"{a}ll\"{a} tuntemattomia, lavantaudista tuhkarokkoon ja kroonisiin tauteihin saakka. --- Se ei olekaan mik\"{a}\"{a}n v\"{a}h\"{a}inen etu, Glenarvan huomautti. --- Ei olekaan, mutta min\"{a} en puhu siit\"{a}, Paganel vastasi. --- T\"{a}\"{a}ll\"{a} on ilmastolla er\"{a}s uskomaton ominaisuus. --- Mik\"{a}? John Mangles kysyi. --- Te ette kuitenkaan uskoisi minua. --- P\"{a}invastoin, kuulijat huudahtivat, ollen loukkaantuvinaan. --- No niin, se on... --- Mik\"{a} sitten? --- Siveytt\"{a} parantava. --- Siveytt\"{a} parantava? --- Niin, tiedemies vastasi vakuuttavasti. --- Siveytt\"{a} parantava. T\"{a}\"{a}ll\"{a} eiv\"{a}t metallit ruostu ilmassa eiv\"{a}tk\"{a} ihmiset. T\"{a}\"{a}ll\"{a} valkaisee puhdas ja kuiva ilma pian kaikki, pellavan ja sielut! Ja Englannissa oli varmaan huomattu t\"{a}m\"{a}n ilmaston edut, kun p\"{a}\"{a}tettiin t\"{a}h\"{a}n maahan l\"{a}hett\"{a}\"{a} siveellisen parannuksen tarpeessa olevat ihmiset. --- Mit\"{a}! Onko sellaista vaikutusta todella huomattavissa? lady Glenarvan kysyi. --- On, rouva, el\"{a}imiin ja ihmisiin. --- Ettek\"{o} laske leikki\"{a}, herra Paganel? --- En ensink\"{a}\"{a}n. Hevoset ja nautael\"{a}imet ovat t\"{a}\"{a}ll\"{a} huomattavan kuuliaisia. Saattehan n\"{a}hd\"{a}. --- Eih\"{a}n se ole mahdollista! --- Niin on asia. Ja t\"{a}h\"{a}n elvytt\"{a}v\"{a}\"{a}n ja terveelliseen ilmaan siirretyt pahantekij\"{a}t ovat kuin uudestisyntyneit\"{a} muutamassa vuodessa. Filantroopit tuntevat t\"{a}m\"{a}n vaikutuksen. Australiassa parantuvat kaikki luonteet. --- Mutta silloin, herra Paganel, lady Helena sanoi, --- mit\"{a} tuleekaan teist\"{a}, joka olette jo niin hyv\"{a}, t\"{a}ss\"{a} armoitetussa maassa? --- Erinomainen, rouva, Paganel vastasi, --- kerrassaan erinomainen! \gutchapter{WIMERRA-JOKI.} Seuraavana eli 24. p\"{a}iv\"{a}n\"{a} joulukuuta l\"{a}hdettiin liikkeelle auringon noustessa. L\"{a}mp\"{o} oli jo aikamoinen, mutta siedett\"{a}v\"{a}, tie melkein tasainen ja hevosille mukava. Matkue joutui harvanpuoleiseen viidakkoon. Hyv\"{a}n p\"{a}iv\"{a}matkan j\"{a}lkeen se illalla majoittui Valkean j\"{a}rven rannalle, jonka vesi oli suolapitoista ja juotavaksi kelpaamatonta. Siell\"{a} oli Jacques Paganelin pakko my\"{o}nt\"{a}\"{a}, ett\"{a} t\"{a}m\"{a} j\"{a}rvi ei ollut valkoinen enemp\"{a}\"{a} kuin Mustameri on musta, Punainen meri punainen, Keltainen joki keltainen tai Siniset vuoret sinisi\"{a}. Maantieteilij\"{a}n itserakkaus pakotti h\"{a}net kuitenkin kovasti v\"{a}ittelem\"{a}\"{a}n, mutta h\"{a}nen perustelujaan ei my\"{o}nnetty p\"{a}teviksi. Olbinett valmisti illallisaterian t\"{a}sm\"{a}llisesti kuten aina; sen j\"{a}lkeen matkustajat, toiset vankkureissa, toiset teltassa, riensiv\"{a}t nukkumaan huolimatta ``dingojen'', Australian sakaalien, valittavasta ulvonnasta. Ihana tasanko levisi Valkean j\"{a}rven toisella puolella kirjavanaan auringonkukkia. Her\"{a}tess\"{a}\"{a}n seuraavana p\"{a}iv\"{a}n\"{a} teki Glenarvanin ja h\"{a}nen kumppaniensa mieli kiljua ihastuksesta silmiens\"{a} eteen aukenevasta suurenmoisesta n\"{a}yst\"{a}. L\"{a}hdettiin matkaan. Ainoastaan muutamat kaukaiset kummut osoittivat maan kohoavan. Niin kauas kuin silm\"{a} kantoi oli kaikki vain ruoho- ja kukkakentt\"{a}\"{a} kev\"{a}isess\"{a} loistossaan. Hienolehtisen pellavan sinerv\"{a} vivahdus suli t\"{a}lle seudulle ominaisen \textit{acanthus}-lajin hele\"{a}\"{a}n punaan. T\"{a}t\"{a} vihannuutta el\"{a}v\"{o}ittiv\"{a}t viel\"{a} monet \textit{verbenaceae}-heimon lajit ja suolapitoinen maa peittyi vihert\"{a}vien tai punertavien, valtaiseen \textit{salsolaceae}-heimoon kuuluvien hanhenjalkojen, maksaruohojen ja juurikkaiden alle. Ne ovat teollisuudelle hy\"{o}dyllisi\"{a} kasveja, sill\"{a} niist\"{a} saa mainiota soodaa polttamalla ja tuhkaa liuottamalla. Paganel, josta kukkien keskell\"{a} tuli kasvitieteilij\"{a}, mainitsi kunkin eri lajin nimelt\"{a} eik\"{a} h\"{a}nelt\"{a}, kun h\"{a}n aina halusi esitt\"{a}\"{a} numeroita, j\"{a}\"{a}nyt huomauttamatta, ett\"{a} Australian kasvistossa oli t\"{a}h\"{a}n saakka tavattu nelj\"{a}tuhattakaksisataa lajia, jotka on jaettu sataankahteenkymmeneen heimoon. My\"{o}hemmin, kun oli nopeasti kuljettu parikymment\"{a} kilometri\"{a}, vieriv\"{a}t vankkurit korkeiden akaasia-, mimoosa- ja kukinnoltaan niin vaihtelevaisten, valkoisten kumipuumetsik\"{o}iden v\"{a}liss\"{a}. Kasvimaailma ei t\"{a}ll\"{a} ``spring-plainien'', l\"{a}hteiden kostuttamien tasankojen seudulla ollut kiitt\"{a}m\"{a}t\"{o}n p\"{a}iv\"{a}nkehr\"{a}lle, vaan antoi tuoksuina ja v\"{a}rein\"{a} takaisin, mit\"{a} aurinko antoi sille s\"{a}tein\"{a}. El\"{a}inmaailman tuotteet eiv\"{a}t olleet niin moninaisia. Muutamia kasuaareja hyppeli tasangolla, mutta niit\"{a} ei p\"{a}\"{a}sty l\"{a}hestym\"{a}\"{a}n. Majurin onnistui kuitenkin ampua kylkeen er\"{a}st\"{a} perin harvinaista el\"{a}int\"{a}, joka on sukupuuttoon kuolemassa. Se oli ``jabiru'', jota englantilaiset siirtolaiset sanovat j\"{a}ttil\"{a}iskurjeksi. T\"{a}m\"{a} lintu oli puolitoista metri\"{a} korkea, ja sen musta, leve\"{a}, kartiomainen ja ter\"{a}v\"{a}k\"{a}rkinen nokka oli nelj\"{a}kymment\"{a}viisi sentti\"{a} pitk\"{a}. Sen p\"{a}\"{a}n orvokinsiniset ja purppuranpunaiset vivahteet olivat kaulan kiilt\"{a}v\"{a}nvihre\"{a}n, kurkun h\"{a}ik\"{a}isev\"{a}nvalkoisen ja pitkien s\"{a}\"{a}rien helakanpunaisen v\"{a}rin r\"{a}ike\"{a}n\"{a} vastakohtana. Luonto n\"{a}ytti t\"{a}h\"{a}n lintuun tuhlanneen alkuper\"{a}isten v\"{a}riens\"{a} koko varaston. Lintua ihmeteltiin kovasti, ja majuri olisi ollut p\"{a}iv\"{a}n sankari, ellei pikku Robert olisi muutamaa kilometri\"{a} kauempana tavannut ja urhoollisesti tappanut er\"{a}st\"{a} oudon muotoista el\"{a}int\"{a}, joka oli puoleksi siili, puoleksi muurahaiskarhu, puolitekoinen olio kuten luomisen alkuaikojen el\"{a}imet. Sen hampaattomasta suusta roikkui venyv\"{a}, pitk\"{a} ja tahmea kieli, pyydyst\"{a}en muurahaisia, jotka ovat t\"{a}m\"{a}n el\"{a}imen p\"{a}\"{a}asiallisena ravintona. --- Se on muurahaispiikkisika! Paganel sanoi, antaen t\"{a}lle monotremille oikean nimen. --- Oletteko koskaan n\"{a}hnyt sellaista el\"{a}int\"{a}? --- Se on hirvitt\"{a}v\"{a}! Glenarvan lausui. --- Hirvitt\"{a}v\"{a}, mutta mielenkiintoinen, Paganel vastasi, --- muuten yksinomaan Australiassa el\"{a}v\"{a}, ja sit\"{a} saisi turhaan etsi\"{a} mist\"{a}\"{a}n muualta maailmassa. Tietenkin Paganel halusi ottaa inhottavan muurahaispiikkisian mukaan ja panna sen tavaraosastoon. Mutta Olbinett vastusti sit\"{a} niin ehdottomasti, ett\"{a} tiedemies luopui t\"{a}m\"{a}n monotremi-n\"{a}ytteen s\"{a}ilytt\"{a}misest\"{a}. T\"{a}n\"{a} p\"{a}iv\"{a}n\"{a} kulkivat matkustajat 141. pituusasteen yli noin puolen asteen verran. T\"{a}h\"{a}n saakka he olivat tavanneet v\"{a}h\"{a}n siirtolaisia, v\"{a}h\"{a}n squattereita. Maa n\"{a}ytti autiolta. Alkuasukkaista ei n\"{a}kynyt varjoakaan, sill\"{a} villit heimot harhailivat pohjoisempana pitkin suunnattomia, Darlingin ja Murrayn lis\"{a}jokien kostuttamia er\"{a}maita. Muuan omituinen n\"{a}ky kiinnitti kuitenkin Glenarvanin joukon huomiota. Se sai n\"{a}hd\"{a} er\"{a}\"{a}n niit\"{a} tavattoman suuria karjalaumoja, joita rohkeat yrittelij\"{a}t kuljettavat id\"{a}n vuorilta Victorian ja Etel\"{a}-Australian maakuntiin saakka. Kello nelj\"{a}n aikaan iltap\"{a}iv\"{a}ll\"{a} John Mangles huomasi viiden kilometrin p\"{a}\"{a}ss\"{a} edess\"{a}p\"{a}in horisontissa kohoavan suunnattoman p\"{o}lypilven. Mist\"{a} t\"{a}m\"{a} ilmi\"{o} johtui? Sit\"{a} oli vaikea sanoa. Paganel oli taipuvainen olettamaan jotakin meteoria, jolle h\"{a}nen vilkas mielikuvituksensa jo etsi luonnollista syyt\"{a}. Mutta Ayrton lopetti h\"{a}nen retkeilyns\"{a} arvailujen mailla ilmoittaen, ett\"{a} p\"{o}lyn nouseminen johtui liikkeell\"{a} olevasta karjalaumasta. Per\"{a}mies ei erehtynytk\"{a}\"{a}n. Paksu pilvi l\"{a}heni. Sen keskest\"{a} kuului loputonta m\"{a}\"{a}kin\"{a}\"{a}, hirnuntaa ja mylvin\"{a}\"{a}. T\"{a}h\"{a}n karjan m\"{o}lin\"{a}\"{a}n sekaantui ihmis\"{a}\"{a}ni\"{a}kin huutojen, vihellysten ja melun muodossa. Metel\"{o}iv\"{a}st\"{a} pilvest\"{a} tuli esiin muuan mies. H\"{a}n oli t\"{a}m\"{a}n nelijalkaisten armeijan ylijohtaja. Glenarvan meni h\"{a}nt\"{a} vastaan, ja tuttavuutta tehtiin kursailuitta. Johtaja tai, k\"{a}ytt\"{a}\"{a}ksemme h\"{a}nen oikeaa arvonime\"{a}\"{a}n ``stock-keeper'', omisti itse osan karjaa. H\"{a}n oli nimelt\"{a}\"{a}n Sam Machell ja tuli todellakin it\"{a}maakunnista ja oli matkalla Portlandin lahtea kohti. H\"{a}nen karjaansa kuului kaksitoistatuhatta seitsem\"{a}nkymment\"{a}viisi p\"{a}\"{a}t\"{a} eli tuhat nautaa, yksitoistatuhatta lammasta ja seitsem\"{a}nkymment\"{a}viisi hevosta. Kaikki n\"{a}m\"{a} el\"{a}imet oli ostettu laihoina Sinivuorten tasangoilla ja vietiin lihotettaviksi Etel\"{a}-Australian reheville laitumille, miss\"{a} ne taas myyt\"{a}isiin suurella voitolla. Niinp\"{a} Sam Machell saattoi hy\"{o}ty\"{a} seitsem\"{a}ntuhatta viisisataa puntaa voittaessaan kaksi puntaa naudalta ja puoli puntaa lampaalta. Se oli suuri yritys. Mutta millaista k\"{a}rsiv\"{a}llisyytt\"{a}, millaista tarmoa tarvittiinkaan t\"{a}m\"{a}n vastahakoisen lauman viemiseksi m\"{a}\"{a}r\"{a}paikkaan ja millaisia vaivoja pitik\"{a}\"{a}n kest\"{a}\"{a}! T\"{a}st\"{a} ankarasta ammatista saatu voitto oli raskaasti ansaittu! Sam Machell kertoi muutamalla sanalla tarinansa, karjan jatkaessa matkaansa mimoosametsik\"{o}iden v\"{a}liss\"{a}. Lady Helena, Mary Grant ja ratsastajat olivat laskeutuneet maahan ja kuuntelivat stock-keeperin kertomusta tuuhean kumipuun siimeksess\"{a} istuen. Karjakauppias oli l\"{a}htenyt matkalle seitsem\"{a}n kuukautta sitten. H\"{a}n p\"{a}\"{a}si noin viisitoista kilometri\"{a} p\"{a}iv\"{a}ss\"{a}, ja h\"{a}nen pitk\"{a} matkansa kest\"{a}isi viel\"{a} kolme kuukautta. H\"{a}nell\"{a} oli mukanaan apureina t\"{a}ss\"{a} ty\"{o}l\"{a}\"{a}ss\"{a} puuhassa kaksikymment\"{a} koiraa ja kolmekymment\"{a} miest\"{a}, joista viisi mustaa, erinomaisen taitavia l\"{o}yt\"{a}m\"{a}\"{a}n eksyneiden el\"{a}inten j\"{a}ljet. Kuudet vankkurit seurasivat armeijaa. Varustettuina ``stock-whipeill\"{a}'', ruoskilla, joiden varsi oli noin puolimetrinen ja siima kolme metri\"{a} pitk\"{a}, ajajat marssivat rivien v\"{a}liss\"{a} palauttaen usein h\"{a}iriytyv\"{a}n j\"{a}rjestyksen, koirien keve\"{a}n ratsuv\"{a}en kirmaillessa sivustoilla. Matkustajat ihmetteliv\"{a}t karjassa aikaansaatua kuria. Eri rodut kulkivat erill\"{a}\"{a}n, sill\"{a} naudat ja villit lampaat eiv\"{a}t tule hyvin toimeen kesken\"{a}\"{a}n; edelliset eiv\"{a}t suostu milloinkaan laitumeen, jonka poikki j\"{a}lkimm\"{a}iset ovat liikkuneet. Sen vuoksi oli pakko sijoittaa naudat etup\"{a}\"{a}h\"{a}n, miss\"{a} ne kulkivat kahteen pataljoonaan jaettuina. Niit\"{a} seurasi viisi rykmentti\"{a} lampaita kahdenkymmenen ajajan komennossa, ja hevoskomppania oli j\"{a}lkijoukkona. Sam Machell selitti kuulijoilleen, ett\"{a} armeijan oppaina eiv\"{a}t olleet koirat eik\"{a} miehet, vaan sonnit, \"{a}lykk\"{a}\"{a}t ``leaderit'', joiden etev\"{a}mmyyden niiden kumppanit tunnustivat. Ne marssivat eturiviss\"{a}, juhlallisen arvokkaina, noudattaen vaistomaisesti oikeaa suuntaa, syv\"{a}sti vakuuttuneina oikeudestaan kunnioittavaan kohteluun. Niit\"{a} kohdeltiin hell\"{a}varoen, sill\"{a} karja totteli n\"{a}it\"{a} johtajia empim\"{a}tt\"{a}. Jos niiden p\"{a}\"{a}h\"{a}n p\"{a}lk\"{a}hti pys\"{a}hty\"{a}, siihen oikkuun t\"{a}ytyi mukautua, ja turhaa olisi ollut yritt\"{a}\"{a} liikkeelle lev\"{a}hdyksen j\"{a}lkeen, elleiv\"{a}t ne itse antaneet l\"{a}ht\"{o}merkki\"{a}. Muutamat stock-keeperin lis\"{a}\"{a}m\"{a}t yksityiskohdat t\"{a}ydensiv\"{a}t kertomusta t\"{a}st\"{a} retkest\"{a}, joka olisi ansainnut olla itse Ksenofonin kuvaama, ellei suorastaan johtama. Niin kauan kuin armeija marssi tasangolla, oli kaikki hyvin. V\"{a}h\"{a}n hankaluutta, v\"{a}h\"{a}n vaivaa. El\"{a}imet s\"{o}iv\"{a}t kulkiessaan, sammuttivat janonsa laidunten monista puroista, nukkuivat y\"{o}n, marssivat p\"{a}iv\"{a}n ja kokoontuivat kuuliaisesti koirien haukunnasta. Mutta mantereen suurissa metsiss\"{a}, eukalyptus- ja mimoosametsik\"{o}iden kautta kuljettaessa vaikeudet lis\"{a}\"{a}ntyiv\"{a}t. Komppaniat, pataljoonat ja rykmentit sekaantuivat tai hajaantuivat, ja niiden uudelleenj\"{a}rjest\"{a}miseen meni pitk\"{a} aika. Jos onnettomuudeksi joku ``leader'' sattui eksym\"{a}\"{a}n, se t\"{a}ytyi l\"{o}yt\"{a}\"{a} kaikin mokomin yleisen hajaannuksen v\"{a}ltt\"{a}miseksi, ja mustilta meni usein monta p\"{a}iv\"{a}\"{a} n\"{a}ihin vaikeisiin etsiskelyihin. Jos sattui suuria sateita, laiskat el\"{a}imet heitt\"{a}ytyiv\"{a}t liikkumattomiksi, ja ankarat ukonilmat synnyttiv\"{a}t pelosta mielipuolten el\"{a}inten joukossa sekasortoista pakokauhua. Tarmokkaalla toimellaan stock-keeper oli kuitenkin suoriutunut n\"{a}ist\"{a} yh\"{a} uusiutuvista vaikeuksista. H\"{a}n marssi; kilometri kilometrilt\"{a} oli p\"{a}\"{a}sty eteenp\"{a}in; tasankoja, metsi\"{a}, vuoria oli j\"{a}\"{a}nyt sel\"{a}n taakse. Mutta jokien yli ment\"{a}ess\"{a} oli monen muun ominaisuuden lis\"{a}ksi tarpeen se suuri ominaisuus, jota sanotaan mielenmaltiksi ja joka kest\"{a}\"{a} kaikki koettelemukset, niin etteiv\"{a}t tunnit tai p\"{a}iv\"{a}t eiv\"{a}tk\"{a} edes viikot saa sit\"{a} masentaa. Kerrankin oli stock-keeperin pys\"{a}hdytt\"{a}v\"{a} er\"{a}\"{a}n virran eteen, jonka yli ei suinkaan ollut mahdoton kulkea, vaikka ei ollut kuljettu. Este johtui yksinomaan karjan itsep\"{a}isyydest\"{a}; el\"{a}imet tekiv\"{a}t ten\"{a}n. Sonnit haistelivat vett\"{a} ja k\"{a}\"{a}ntyiv\"{a}t takaisin. Lampaat pakenivat joka suuntaan, mutta eiv\"{a}t vain menneet veteen. Odotettiin y\"{o}t\"{a} lauman ajamiseksi jokeen; se ei onnistunut. Heitettiin v\"{a}kisin veteen karitsoita, mutta em\"{a}t eiv\"{a}t uskaltaneet menn\"{a} per\"{a}ss\"{a}. Koetettiin houkutella laumaa kiusaamalla sit\"{a} janolla useita p\"{a}ivi\"{a}; karja oli juomatta, mutta ei hievahtanut. Vietiin karitsat toiselle rannalle toivossa, ett\"{a} em\"{a}t tulisivat yli n\"{a}iden m\"{a}\"{a}kyn\"{a}st\"{a}; karitsat m\"{a}\"{a}kyiv\"{a}t, mutta em\"{a}t eiv\"{a}t l\"{a}hteneet toiselta rannalta. Sit\"{a} kesti kuukauden p\"{a}iv\"{a}t eik\"{a} stock-keeper en\"{a}\"{a} tiennyt, mit\"{a} tehd\"{a} m\"{a}\"{a}kyv\"{a}ll\"{a}, hirnuvalla ja mylviv\"{a}ll\"{a} laumallaan. Silloin er\"{a}\"{a}n\"{a} p\"{a}iv\"{a}n\"{a}, ilman syyt\"{a}, oikusta, ei tiedet\"{a} mink\"{a} vuoksi, meni er\"{a}s osasto joen yli, ja silloin syntyi uusi pulma est\"{a}\"{a} laumaa sy\"{o}ksym\"{a}st\"{a} siihen sikinsokin. Riveiss\"{a} syntyi ep\"{a}j\"{a}rjestyst\"{a} ja paljon el\"{a}imi\"{a} hukkui koskiseen virtaan. N\"{a}in kertoili Sam Machell. Sill\"{a} v\"{a}lin oli suuri osa laumasta marssinut ohi hyv\"{a}ss\"{a} j\"{a}rjestyksess\"{a}. H\"{a}nen oli aika palata armeijansa k\"{a}rkeen valitsemaan parhaita laidunmaita. H\"{a}n lausui siis j\"{a}\"{a}hyv\"{a}iset lordi Glenarvanille, nousi mainiolle maatiaisratsulleen, jota yksi h\"{a}nen miehist\"{a}\"{a}n piteli suitsista, ja k\"{a}tteli syd\"{a}mellisesti kaikkia. Hetken kuluttua h\"{a}n oli kadonnut p\"{o}lypilveen. Vankkurit jatkoivat p\"{a}invastaiseen suuntaan hetkeksi keskeytynytt\"{a} matkaansa ja pys\"{a}htyiv\"{a}t vasta illalla Talbot-vuoren juurelle. Paganel huomautti nyt sopivasti, ett\"{a} oli 25. p\"{a}iv\"{a} joulukuuta, siis joulup\"{a}iv\"{a}, jota englantilaisissa perheiss\"{a} on tapana viett\"{a}\"{a} niin juhlallisesti. Mutta muonamestari ei ollut sit\"{a} unohtanut, ja teltassa tarjottu runsas illallinen tuotti h\"{a}nelle aterioitsijoiden vilpitt\"{o}m\"{a}t kiitokset. T\"{a}ytyykin sanoa, ett\"{a} Olbinett oli todella tehnyt ihmeit\"{a}. H\"{a}n oli loihtinut varastostaan esille erin\"{a}isi\"{a} eurooppalaisia ruokalajeja, joita harvoin tavataan Australian er\"{a}maissa. Porons\"{a}\"{a}rt\"{a}, suolattua naudanlihaa, savustettua lohta, ohra- ja kaurakakkuja, teet\"{a} mielin m\"{a}\"{a}rin, viski\"{a} runsaasti ja muutamia pulloja portviini\"{a} kuului t\"{a}h\"{a}n h\"{a}mm\"{a}stytt\"{a}v\"{a}\"{a}n ateriaan. Olisi voinut luulla olevansa Malcolmin linnan suuressa ruokasalissa keskell\"{a} Skotlannin yl\"{a}maita. T\"{a}st\"{a} juhlasta ei tosiaankaan puuttunut mit\"{a}\"{a}n, inkiv\"{a}\"{a}riliemest\"{a} j\"{a}lkiruoan pikkutorttuihin saakka. Yht\"{a}kaikki katsoi Paganel velvollisuudekseen liitt\"{a}\"{a} ateriaan l\"{a}hist\"{o}kumpujen rinteill\"{a} kasvavien villien appelsiinipuiden hedelmi\"{a}. Alkuasukkaiden kesken niill\"{a} on nimen\"{a} ``moccady''; appelsiinit olivat jokseenkin mauttomia, mutta niiden siemenet purtuina kirpeit\"{a} kuin cayennen-pippuri. Rakkaudesta tieteeseen pureksi maantieteilij\"{a} niit\"{a} niin tunnollisesti, ett\"{a} h\"{a}nen kitalakeaan alkoi polttaa eik\"{a} h\"{a}n kyennyt vastaamaan majurin kysymyksiin australialaisten j\"{a}lkiruokien erikoisominaisuuksista. Seuraavana eli 26. p\"{a}iv\"{a}n\"{a} joulukuuta ei tapahtunut mit\"{a}\"{a}n mainitsemisen arvoista. Tavattiin Norton-puron ja v\"{a}h\"{a}\"{a} my\"{o}hemmin puoleksikuivuneen Mackenzie-joen l\"{a}hteet. S\"{a}\"{a} oli edelleen poutainen ja l\"{a}mp\"{o} varsin siedett\"{a}v\"{a}; tuuli puhalsi etel\"{a}st\"{a} ja vilvoitti ilmaa kuten pohjoistuuli olisi tehnyt pohjoisella pallonpuoliskolla, mist\"{a} Paganel huomautti yst\"{a}v\"{a}lleen Robert Grantille. --- Se on onnellinen seikka, h\"{a}n lis\"{a}si, --- sill\"{a} keskil\"{a}mp\"{o} on suurempi etel\"{a}isell\"{a} kuin pohjoisella pallonpuoliskolla. --- Mink\"{a} vuoksi? poika kysyi. --- Mink\"{a}k\"{o} vuoksi? Paganel vastasi. --- Etk\"{o} sin\"{a} ole koskaan kuullut puhuttavan, ett\"{a} maa on talvella l\"{a}hemp\"{a}n\"{a} aurinkoa? --- Olen, herra Paganel. --- Ja ett\"{a} talven kylmyys johtuu vain auringons\"{a}teiden vinoudesta? --- Sen tied\"{a}n. --- No, poikani, juuri t\"{a}st\"{a} syyst\"{a} on etel\"{a}isell\"{a} pallonpuoliskolla l\"{a}mpim\"{a}mp\"{a}\"{a}. --- Sit\"{a} min\"{a} en ymm\"{a}rr\"{a}, Robert vastasi silm\"{a}t suurina. --- Ajattelehan, Paganel selitti, --- kun meill\"{a} on talvi Euroopassa, mik\"{a} vuodenaika on silloin t\"{a}\"{a}ll\"{a} Australiassa, vastapuolella? --- Kes\"{a}, Robert vastasi. --- No, koska juuri t\"{a}n\"{a} vuodenaikana maa on l\"{a}hinn\"{a} aurinkoa ... ymm\"{a}rr\"{a}tk\"{o}? --- Ymm\"{a}rr\"{a}n... --- Niin on etel\"{a}isten seutujen kes\"{a} t\"{a}m\"{a}n l\"{a}heisyyden vuoksi kuumempi kuin pohjoisten seutujen kes\"{a}. --- Aivan oikein, herra Paganel. --- Niinp\"{a} kun sanotaan, ett\"{a} aurinko on l\"{a}hinn\"{a} maata `talvella', pit\"{a}\"{a} se paikkansa vain meill\"{a}, jotka asumme pohjoisella pallonpuoliskolla. --- Sit\"{a} min\"{a} en ollut tullut ajatelleeksi, Robert my\"{o}nsi. --- Mutta nyt, poikani, \"{a}l\"{a} en\"{a}\"{a} unohda sit\"{a}! Robert otti kernaasti vastaan t\"{a}m\"{a}n pienen opetuksen maailmanrakenteesta ja sai sitten tiet\"{a}\"{a}, ett\"{a} keskil\"{a}mp\"{o} Victorian maakunnassa on kaksikymment\"{a}kolme astetta Celsiusta. Illalla retkikunta majoittui kahdeksan kilometrin p\"{a}\"{a}h\"{a}n Lonsdale-j\"{a}rven rannalta, pohjoisessa kohoavan Drummont-vuoren ja Dryden-vuoren v\"{a}lill\"{a}, jonka matalahko huippu kohosi etel\"{a}isell\"{a} taivaanrannalla. Seuraavana p\"{a}iv\"{a}n\"{a} kello yhdentoista aikaan vankkurit saapuivat Wimerra-joen rannalle, 143. meridiaanin kohdalle. L\"{a}hes kilometrin levyinen joki virtasi kirkaspintaisena korkeiden kumi- ja akaasiapuu-reunusten v\"{a}liss\"{a}. Muutamat komeat myrttipuut, muiden muassa \textit{Metrosideros speciosa}, kohotti viiden metrin korkeuteen pitki\"{a} ja riippuvia punaisilla kukilla koristettuja oksiaan. Tuhansia lintuja, keltasirkkuja, peipposia, kultasiipisi\"{a} kyyhkysi\"{a}, puhumattakaan puheliaista papukaijoista, pyr\"{a}hteli vihre\"{a}ss\"{a} lehvist\"{o}ss\"{a}. Alhaalla vedenkalvossa uiskenteli joukko mustia joutsenia arkoina ja luoksep\"{a}\"{a}sem\"{a}tt\"{o}min\"{a}. T\"{a}m\"{a} Australian jokien \textit{rara avis}, harvinainen lintu, katosi pian Wimerran mutkiin, jotka oikullisina kostuttivat vieh\"{a}tt\"{a}v\"{a}\"{a} seutua. Vankkurit olivat pys\"{a}htyneet ruohikolle, jonka reunat riippuivat vilisev\"{a}n veden yll\"{a}. Ei ollut lauttaa, ei siltaa. T\"{a}ytyi kuitenkin p\"{a}\"{a}st\"{a} yli. Ayrton otti etsi\"{a}kseen sopivan kahlaamon. Puolta kilometri\"{a} ylemp\"{a}n\"{a} joki tuntui h\"{a}nest\"{a} matalammalta, ja silt\"{a} kohtaa h\"{a}n p\"{a}\"{a}tti menn\"{a} toiselle rannalle. Eri kohdilta tunnustellessa todettiin vain vajaa metri vett\"{a}. Vankkureilla saattoi siis ilman suurta vaaraa uskaltaa t\"{a}h\"{a}n syvyyteen. --- Eik\"{o} ole muuta keinoa p\"{a}\"{a}st\"{a} t\"{a}m\"{a}n joen poikki? Glenarvan kysyi per\"{a}miehelt\"{a}. --- Ei, mylord, Ayrton vastasi, --- mutta t\"{a}m\"{a} kahlaamo ei minusta n\"{a}yt\"{a} vaaralliselta. Me suoriudumme siit\"{a} kyll\"{a}. --- Onko lady Glenarvanin ja neiti Grantin noustava pois vankkureista? --- Ei mill\"{a}\"{a}n muotoa. Minun juhtani ovat tukevajalkaisia, ja min\"{a} otan pit\"{a}\"{a}kseni ne oikeassa suunnassa. --- Hyv\"{a} on, Ayrton, Glenarvan vastasi, --- min\"{a} luotan teihin. Ratsumiehet asettuivat raskaiden vaunujen ymp\"{a}rille, sitten ajettiin p\"{a}\"{a}tt\"{a}v\"{a}sti jokeen. Tavallisesti t\"{a}llaisten kahlaamoiden yli yritett\"{a}ess\"{a} ymp\"{a}r\"{o}id\"{a}\"{a}n vankkurit tyhjill\"{a} tynnyreill\"{a}, jotka kannattavat niit\"{a} veden pinnalla. Mutta t\"{a}\"{a}ll\"{a} ei ollut moista uimavy\"{o}t\"{a} saatavissa; t\"{a}ytyi siis luottaa taitavan Ayrtonin ohjaamien juhtien \"{a}lyyn. Kuskipenkill\"{a} istuen Ayrton ohjasi valjakkoa; majuri ja molemmat matruusit kahlasivat vuolaan virran yli muutamia metri\"{a} edell\"{a}. Glenarvan ja John Mangles pysytteliv\"{a}t kahden puolen vankkureita valmiina auttamaan naisia; Paganel ja Robert olivat j\"{a}lkijoukkona. Kaikki k\"{a}vi hyvin Wimerran keskikohdalle saakka. Mutta silloin vesi syveni ja nousi yli py\"{o}r\"{a}nkehien. Juhdat joutuivat pois suunnasta, ja kun jalka ei en\"{a}\"{a} tavoittaisi pohjaa, ne voisivat vet\"{a}\"{a} kieppuvat ajoneuvot mukanaan. Ayrton uhrautui rohkeasti; h\"{a}n heitt\"{a}ytyi veteen ja tarttuen juhtien sarviin sai el\"{a}imet j\"{a}lleen oikeaan suuntaan. T\"{a}ll\"{a} hetkell\"{a} sattui muuan uhkaava vaara, jota oli mahdoton aavistaa; kuului r\"{a}tin\"{a}\"{a}, ja vankkurit kallistuivat huolestuttavalla tavalla; vesi ulottui jo naisten jalkoihin, ja koko laitos alkoi liukua sivulle huolimatta Glenarvanin ja John Manglesin yrityksist\"{a} tukea sit\"{a}. Se oli tuskallinen hetki. Onneksi valjakon voimakas nyk\"{a}isy sai vankkurit vastaisen rannan t\"{o}rm\"{a}lle. Juhdat ja hevoset saivat kohoavasta rinteest\"{a} j\"{a}lleen tukevan jalansijan, ja pian olivat ihmiset ja el\"{a}imet turvassa toisella rannalla yht\"{a} tyytyv\"{a}isin\"{a} kuin likom\"{a}rkin\"{a}kin. Mutta onnettomuudessa oli vankkurien etuosa murtunut, ja Glenarvanin hevonen oli menett\"{a}nyt etujalkojensa keng\"{a}t. T\"{a}m\"{a} tapaturma vaati viipym\"{a}t\"{o}nt\"{a} korjausta. Matkailijat katselivat toisiaan neuvottomina, kunnes Ayrton tarjoutui l\"{a}htem\"{a}\"{a}n Black Pointin asemalle, nelj\"{a}\"{a}kymment\"{a} kilometri\"{a} pohjoiseen, noutamaan sepp\"{a}\"{a}. --- Menk\"{a}\"{a}, menk\"{a}\"{a}, kunnon Ayrton, lordi Glenarvan sanoi h\"{a}nelle. --- Paljonko aikaa tarvitsette p\"{a}\"{a}st\"{a}ksenne sinne ja tullaksenne takaisin? --- Ehk\"{a} noin viisitoista tuntia, Ayrton vastasi, --- mutta en enemp\"{a}\"{a}. --- L\"{a}htek\"{a}\"{a} siis, ja teid\"{a}n paluutanne odottaessa me majoitumme Wimerran rannalle. Wilsonin hevosella ratsastaen katosi per\"{a}mies tuuhean mimoosalehvist\"{o}n taakse. \gutchapter{BURKE JA STUART.} Loppuosa p\"{a}iv\"{a}\"{a} k\"{a}ytettiin keskusteluun ja k\"{a}velyihin. Jutellen ja ihmetellen k\"{a}veliv\"{a}t matkalaiset pitkin Wimerran rantoja. Tuhkanharmaita kurkia ja iibis-lintuja l\"{a}hti k\"{a}he\"{a}sti kirkuen lentoon heid\"{a}n l\"{a}hestyess\"{a}\"{a}n. Satiinilintu piiloutui villin viikunapuun latvalehvist\"{o}\"{o}n, kuhankeitt\"{a}j\"{a}t ja k\"{a}rp\"{a}ssiepot pyr\"{a}hteliv\"{a}t liljakasvien uhkeiden varsien v\"{a}liss\"{a}, j\"{a}\"{a}linnut j\"{a}ttiv\"{a}t tavallisen kalastelunsa, kun taas koko papukaijojen sivistyneempi heimo, seitsem\"{a}n v\"{a}rin koristama ``blue-mountain'', punap\"{a}inen, keltakurkkuinen pieni ``roschill'', ja puna- ja sinih\"{o}yheninen ``lori'' jatkoivat huumaavaa l\"{o}rp\"{o}ttely\"{a}\"{a}n kukkivien kumipuiden latvoissa. Milloin maaten nurmikolla solisevan veden rannalla, milloin umpim\"{a}hk\"{a}\"{a}n kuljeksien mimoosapensaiden v\"{a}liss\"{a} ihailivat k\"{a}velij\"{a}t t\"{a}t\"{a} kaunista luontoa p\"{a}iv\"{a}nlaskuun saakka. Lyhyen h\"{a}m\"{a}r\"{a}n j\"{a}lkeen heid\"{a}t yll\"{a}tti y\"{o} l\"{a}hes kilometrin p\"{a}\"{a}ss\"{a} majapaikasta. He palasivat sinne, mutta oppaana ei ollut Pohjant\"{a}hti, jota etel\"{a}isell\"{a} pallonpuoliskolla ei n\"{a}y, vaan Etel\"{a}n Risti, joka loisti taivaanlaen ja horisontin puoliv\"{a}liss\"{a}. Olbinett oli kattanut illallisen telttaan. Istuttiin p\"{o}yt\"{a}\"{a}n. Aterian huippukohtana oli Wilsonin ovelasti tappamien papukaijojen lihasta valmistettu er\"{a}\"{a}nlainen muhennos, jossa muonamestari oli osoittanut taitonsa. Illallisen j\"{a}lkeen nousi kysymys, kuka keksisi sopivan syyn, mink\"{a} vuoksi n\"{a}in kauniin illan ensi tunteina ei ment\"{a}isi levolle. Lady Helena lausui julki kaikkien toivomuksen pyyt\"{a}ess\"{a}\"{a}n Paganelia kertomaan suurten Australian tutkijoiden historian, mink\"{a} h\"{a}n jo kauan sitten oli luvannut tehd\"{a}. Paganel suostui siihen mielell\"{a}\"{a}n. H\"{a}nen kuulijansa asettuivat uhkean banksian juurelle; sikarien savu kohosi pian pime\"{a}\"{a}n peittyv\"{a}\"{a}n lehvist\"{o}\"{o}n saakka, ja maantieteilij\"{a} ryhtyi viipym\"{a}tt\"{a} kertomaan tyhjentym\"{a}tt\"{o}m\"{a}\"{a}n muistiinsa luottaen. --- Te muistatte, yst\"{a}v\"{a}ni, eik\"{a} ainakaan majuri liene sit\"{a} unohtanut, kerran \textit{Duncanilla} esitt\"{a}m\"{a}ni l\"{o}yt\"{o}retkeilij\"{o}iden luettelon. Kaikista niist\"{a}, jotka koettivat tunkeutua mantereen sis\"{a}osiin, onnistui vain nelj\"{a}n kulkea sen halki etel\"{a}st\"{a} pohjoiseen tai pohjoisesta etel\"{a}\"{a}n. Ne ovat: Burke vuonna 1860 ja 1861; MacKinlay vuonna 1861 ja 1862; Ladsborough vuonna 1862 ja Stuart niin ik\"{a}\"{a}n vuonna 1862. MacKinlaysta ja Landsboroughista minulla ei ole paljon sanomista. Edellinen samosi Adelaidesta Carpentaria-lahdelle, j\"{a}lkimm\"{a}inen Carpentaria-lahdelta Melbourneen, kumpikin australialaisten komiteoiden l\"{a}hett\"{a}m\"{a}n\"{a} etsim\"{a}\"{a}n Burkea, joka oli j\"{a}\"{a}nyt sille tielleen eik\"{a} koskaan palannutkaan. Burke ja Stuart ovat ne kaksi rohkeaa l\"{o}yt\"{o}retkeilij\"{a}\"{a}, joista aion teille puhua, ja nyt aloitankin ilman pitempi\"{a} esipuheita. Melbournen kuninkaallisen seuran l\"{a}hett\"{a}m\"{a}n\"{a} l\"{a}hti eronsaanut irlantilainen upseeri, Castlemainen entinen poliisip\"{a}\"{a}llikk\"{o}, nimelt\"{a} Robert O'Hara Burke, matkalle 20. p\"{a}iv\"{a}n\"{a} elokuuta 1860. H\"{a}nell\"{a} oli mukanaan yksitoista miest\"{a}, William John Wills, nuori, etev\"{a} t\"{a}htitieteilij\"{a}, tohtori Beckler, kasvitieteilij\"{a} Gray, King, nuori sotilas Intian armeijasta, Landells, Brahe ja useita sepoy-sotamiehi\"{a}. Kaksikymment\"{a}viisi hevosta ja kaksikymment\"{a}viisi kamelia kuljetti retkeilij\"{o}it\"{a}, heid\"{a}n tavaroitaan ja kahdeksaksitoista kuukaudeksi varattua muonaa. Retkikunnan oli m\"{a}\"{a}r\"{a} pyrki\"{a} Carpentaria-lahdelle, pohjoisrannikolle, seuraten aluksi Cooper-jokea. Vaivattomasti se p\"{a}\"{a}si Murrayn ja Darlingin yli ja saapui Menindien asemalle, siirtoloiden rajalle. Matkalla oli havaittu, ett\"{a} suuresta tavaram\"{a}\"{a}r\"{a}st\"{a} oli paljon haittaa. T\"{a}m\"{a} seikka sek\"{a} Burken jyrkk\"{a} luonne synnytti eripuraisuutta joukossa. Kamelien johtaja Landells erosi muutamien hindupalvelijoiden kanssa retkikunnasta ja palasi Darlingin rannoille. Burke jatkoi matkaansa eteenp\"{a}in. Milloin suurenmoisia, kosteita laidunmaita, milloin kivisi\"{a}, vedett\"{o}mi\"{a} teit\"{a} h\"{a}n taivalsi Cooper-jokea kohti. Marraskuun 20. p\"{a}iv\"{a}n\"{a}, kolme kuukautta l\"{a}ht\"{o}ns\"{a} j\"{a}lkeen, h\"{a}n sijoitti ensimm\"{a}isen muonavaraston joen rannalle. T\"{a}nne t\"{a}ytyi retkeilij\"{o}iden j\"{a}\"{a}d\"{a} joksikin aikaa, kun ei l\"{o}ytynyt pohjoiseen p\"{a}in sellaista kuljettavaa tiet\"{a}, jonka varrella vedensaanti olisi ollut taattu. Suurten vaikeuksien j\"{a}lkeen he saapuivat paikkaan, jolle annettiin nimeksi Fort Wills. Se oli puolitiess\"{a} Melbournesta Carpentaria-lahdelle, ja he pystyttiv\"{a}t siihen paaluaitauksen. Siell\"{a} Burke jakoi joukkonsa kahteen osaan. Toisen piti Brahen komentamana j\"{a}\"{a}d\"{a} Fort Willsiin kolmeksi kuukaudeksi tai pitemm\"{a}ksi aikaa, elleiv\"{a}t elintarvikkeet loppuisi, ja odottaa toisen paluuta. J\"{a}lkimm\"{a}iseen kuuluivat vain Burke, King, Gray ja Wills. He ottivat mukaansa kuusi kamelia ja ruokavaroja kolmeksi kuukaudeksi, nimitt\"{a}in 150 kiloa jauhoja, 20 kiloa riisi\"{a}, 20 kiloa kaurajauhoja, 50 kiloa kuivattua hevosenlihaa, 50 kiloa suolattua sianlihaa ja silavaa ja 15 kiloa korppuja, kaikki yhteens\"{a} mennen tullen noin kahdentuhannen kuudensadan kilometrin matkaa varten. N\"{a}m\"{a} nelj\"{a} miest\"{a} l\"{a}htiv\"{a}t siis matkalle. Vaivalloisen retken j\"{a}lkeen kivisen er\"{a}maan halki he saapuivat Eyre-joelle, kauimpana olevalle paikalle, mink\"{a} Sturt oli saavuttanut 1845, ja samosivat pohjoista kohti noudattaen sadattanelj\"{a}tt\"{a}kymment\"{a} meridiaania niin tarkoin kuin mahdollista. Tammikuun 7. p\"{a}iv\"{a}n\"{a} he marssivat etel\"{a}isen k\"{a}\"{a}nt\"{o}piirin poikki hehkuvassa auringonhelteess\"{a}, harhauttavien kangastusten eksytt\"{a}min\"{a} usein k\"{a}rsien veden puutetta, joskus ankarien rajuilmojen virkist\"{a}min\"{a}, tavaten siell\"{a} t\"{a}\"{a}ll\"{a} harhailevia alkuasukkaita, joista heill\"{a} ei ollut mit\"{a}\"{a}n valittamista; ylimalkaan oli verraten v\"{a}h\"{a}n haittaavia esteit\"{a} tiell\"{a}, jota eiv\"{a}t sulkeneet j\"{a}rvet, joet tai vuoret. Tammikuun 12. p\"{a}iv\"{a}n\"{a} n\"{a}kyi pohjoisessa muutamia kukkuloita, muiden mukana Forbes-vuori, ja jono graniittiharjuja, joilla on englanninkieless\"{a} nimen\"{a} ``range''. Siell\"{a} matka k\"{a}vi hankalaksi. P\"{a}\"{a}stiin t\"{o}in tuskin eteenp\"{a}in. El\"{a}imet eiv\"{a}t suostuneet marssimaan: --- Aina vain harjuja, kamelit hikoilevat pelosta, Burke kirjoitti p\"{a}iv\"{a}kirjaansa. Voimansa ponnistaen retkeilij\"{a}t p\"{a}\"{a}siv\"{a}t kuitenkin Turner-joen rannalle ja sitten latvapuolelle Flinders-jokea, jonka Stokes oli n\"{a}hnyt 1841 ja joka palmujen ja eukalyptusten reunustamana laskee Carpentaria-lahteen. Valtameren l\"{a}heisyytt\"{a} ilmaisi sarja suoper\"{a}isi\"{a} maita. Yksi kameleista hukkui niihin. Toiset kielt\"{a}ytyiv\"{a}t kulkemasta pitemm\"{a}lle. Kingin ja Grayn t\"{a}ytyi j\"{a}\"{a}d\"{a} niiden luokse. Burke ja Wills jatkoivat matkaa pohjoiseen ja suurten vaikeuksien j\"{a}lkeen, joista heid\"{a}n muistiinpanoissaan on hyvin h\"{a}m\"{a}r\"{a}sti mainittu, he saapuivat er\"{a}\"{a}lle kohdalle, miss\"{a} meren nousuvett\"{a} oli r\"{a}meill\"{a}, mutta eiv\"{a}t n\"{a}hneet itse merta. Se tapahtui 11. p\"{a}iv\"{a}n\"{a} helmikuuta 1861. --- Eiv\"{a}tk\"{o} n\"{a}m\"{a} uljaat miehet siis p\"{a}\"{a}sseet pitemm\"{a}lle? lady Glenarvan kysyi. --- Eiv\"{a}t hyv\"{a} rouva, Paganel vastasi. --- R\"{a}meet olivat kulkukelvottomia, ja heid\"{a}n t\"{a}ytyi k\"{a}\"{a}nty\"{a} paluumatkalle yhty\"{a}kseen tovereihinsa Fort Willsiss\"{a}. Surullinen paluu, sen saa sanoa! Heikkoina ja n\"{a}\"{a}nnyksiss\"{a} eteenp\"{a}in laahautuen Burke ja Wills p\"{a}\"{a}siv\"{a}t Greyn ja Kingin luo. Sitten he l\"{a}htiv\"{a}t nelisin, seuraten jo kulkemaansa tiet\"{a}, etel\"{a}\"{a}n Cooper-jokea kohti. T\"{a}m\"{a}n matkan vastuksia, vaaroja ja k\"{a}rsimyksi\"{a} emme tarkalleen tunne, sill\"{a} retkeilij\"{o}iden muistiinpanoissa ei niit\"{a} kuvata. Mutta niiden on t\"{a}ytynyt olla hirvitt\"{a}vi\"{a}. Saavuttuaan huhtikuussa Cooper-joen laaksoon, heit\"{a} ei en\"{a}\"{a} ollut kuin kolme. Gray oli kuollut uupumukseen. Nelj\"{a} kamelia oli menehtynyt. Jos Burken kuitenkin olisi onnistunut p\"{a}\"{a}st\"{a} Fort Willsiin, miss\"{a} Brahe h\"{a}nt\"{a} odotti muonavarastoineen, h\"{a}n olisi tovereineen pelastunut. He panivat peliin kaiken voimansa, laahustivat eteenp\"{a}in viel\"{a} muutamia p\"{a}ivi\"{a}, ja 21. p\"{a}iv\"{a}n\"{a} huhtikuuta he n\"{a}kiv\"{a}t varuspaikan aitauksen, p\"{a}\"{a}siv\"{a}t perille...! Mutta juuri sin\"{a} p\"{a}iv\"{a}n\"{a} oli, viisi kuukautta turhaan odotettuaan, Brahe l\"{a}htenyt. --- L\"{a}htenyt! pikku Robert huudahti. --- Niin, l\"{a}htenyt! Viel\"{a}p\"{a} onnettoman sattuman oikusta juuri samana p\"{a}iv\"{a}n\"{a}! Brahen j\"{a}tt\"{a}m\"{a} kirje ei ollut seitsem\"{a}\"{a} tuntia vanhempi. Mutta Burke ei voinut ajatellakaan h\"{a}nen tavoittamistaan. Oman onnensa nojaan j\"{a}\"{a}neet virkistiv\"{a}t itse\"{a}ns\"{a} hiukan varaston ruokavaroilla. Mutta heill\"{a} ei ollut mit\"{a}\"{a}n kulkuneuvoja, ja Darling oli viel\"{a} kuudensadankuudenkymmenen kilometrin p\"{a}\"{a}ss\"{a}. Silloin Burke p\"{a}\"{a}tti vastoin Willsin neuvoa pyrki\"{a} Hopeless-vuoren l\"{a}heisiin australialaisiin siirtoloihin, noin kahdensadankahdeksankymmenen kilometrin p\"{a}\"{a}h\"{a}n Fort Willsist\"{a}. L\"{a}hdettiin matkalle. Kahdesta j\"{a}ljell\"{a} olevasta kamelista toinen hukkui er\"{a}\"{a}seen Cooper-joen mutaiseen lis\"{a}jokeen, toinen ei jaksanut kulkea en\"{a}\"{a} askeltakaan; se t\"{a}ytyi tappaa ja sen lihat sy\"{o}d\"{a}. Pian olivat ruokavarat lopussa. Kolmen kovaonnisen miehen t\"{a}ytyi el\"{a}tt\"{a}\"{a} itse\"{a}\"{a}n ``nardulla'', vesikasvilla, jonka siitep\"{o}ly on sy\"{o}t\"{a}v\"{a}\"{a}. Kun heill\"{a} ei ollut vett\"{a} eik\"{a} keinoja kuljettaa sit\"{a} mukanaan, he eiv\"{a}t voineet j\"{a}tt\"{a}\"{a} Cooperin rantoja. Tulipalo poltti heid\"{a}n telttansa ja leiritavaransa. He olivat hukassa. Ei ollut edess\"{a} muuta kuin kuolema! Burke kutsui luokseen Kingin: --- Min\"{a} en el\"{a} en\"{a}\"{a} kuin muutaman tunnin, h\"{a}n sanoi t\"{a}lle; --- t\"{a}ss\"{a} on kelloni ja muistiinpanoni. Kun olen kuollut, pankaa oikeaan k\"{a}teeni pistooli ja j\"{a}tt\"{a}k\"{a}\"{a} minut paikalleni hautaamatta! T\"{a}m\"{a}n j\"{a}lkeen Burke ei en\"{a}\"{a} puhunut; h\"{a}n kuoli seuraavana aamuna kello kahdeksan. J\"{a}rkyttyneen\"{a} ja murheissaan King l\"{a}hti etsim\"{a}\"{a}n jotakin australialaista heimoa. Kun h\"{a}n palasi, oli Willskin kuollut. Kingin ottivat alkuasukkaat hoiviinsa, ja syyskuussa l\"{o}ysi h\"{a}net Howittin retkikunta, joka oli l\"{a}hetetty etsim\"{a}\"{a}n Burkea samaan aikaan kuin MacKinlay ja Landsborough. Niinp\"{a} nelj\"{a}st\"{a} retkeilij\"{a}st\"{a} t\"{a}lt\"{a} matkalta Australian mantereen poikki j\"{a}i yksi ainoa henkiin. Paganelin kertomus oli tehnyt h\"{a}nen kuulijoihinsa masentavan vaikutuksen. Kaikki ajattelivat kapteeni Grantia, joka kenties harhaili samoin kuin Burke tovereineen keskell\"{a} er\"{a}maata. Olivatko haaksirikkoiset pelastuneet niist\"{a} k\"{a}rsimyksist\"{a}, joihin n\"{a}m\"{a} uljaat retkeilij\"{a}t olivat menehtyneet? T\"{a}m\"{a} ajatus oli niin luonnollinen, ett\"{a} kyyneleet kihosivat Mary Grantin silmiin. --- Is\"{a}ni! Is\"{a}parkani! h\"{a}n huokasi. --- Neiti Mary, tyyntyk\"{a}\"{a}! John Mangles lohdutti. --- Joutuakseen t\"{a}llaisiin k\"{a}rsimyksiin t\"{a}ytyy kaiken uhalla l\"{a}hte\"{a} sis\"{a}maahan. Kapteeni Grant on alkuasukkaiden k\"{a}siss\"{a}, kuten King, ja pelastuu kuten King. H\"{a}n ei ole milloinkaan joutunut niin surkeaan asemaan. --- Ei olekaan, Paganel vahvisti, --- ja min\"{a} toistan teille, rakas neiti, ett\"{a} australialaiset ovat yst\"{a}v\"{a}llisi\"{a}. --- Jumala toteuttakoon sananne! neito vastasi. --- Ent\"{a} Stuart? kysyi Glenarvan, joka tahtoi k\"{a}\"{a}nt\"{a}\"{a} ajatukset pois surullisesta suunnasta. --- Stuartko? Paganel vastasi. --- Oh, Stuart oli onnekkaampi, ja h\"{a}nen nimens\"{a} on kuuluisa Australian aikakirjoissa. Vuodesta 1848 alkaen valmistautui John MacDougal Stuart, teid\"{a}n maanmiehi\"{a}mme, hyv\"{a}t yst\"{a}v\"{a}ni, retkilleen, seuraten Sturtia matkoilla Adelaiden pohjoispuolisissa er\"{a}maissa. Vuonna 1860 h\"{a}n yritti turhaan tunkeutua Australian sis\"{a}maahan vain kahden miehen seuraamana. Mutta h\"{a}n ei ollut niit\"{a} miehi\"{a}, jotka masentuvat. Vuonna 1861, tammikuun 1. p\"{a}iv\"{a}n\"{a}, h\"{a}n l\"{a}hti Chambers-joelta yhdentoista p\"{a}\"{a}tt\"{a}v\"{a}isen matkakumppanin etunen\"{a}ss\"{a} ja p\"{a}\"{a}si kahdensadankahdeksankymmenen kilometrin p\"{a}\"{a}h\"{a}n Carpentaria-lahdesta; mutta muonavarojen puutteen vuoksi h\"{a}nen t\"{a}ytyi palata Adelaideen p\"{a}\"{a}sem\"{a}tt\"{a} t\"{a}m\"{a}n hirvitt\"{a}v\"{a}n mantereen halki. Mutta h\"{a}n rohkeni koetella onnea viel\"{a}kin ja varustaa kolmannen retkikunnan, jonka tosiaan onnistui saavuttaa niin kiihke\"{a}sti tavoiteltu p\"{a}\"{a}m\"{a}\"{a}r\"{a}. Etel\"{a}-Australian eduskunta kannatti l\"{a}mpim\"{a}sti t\"{a}t\"{a} uutta l\"{o}yt\"{o}retke\"{a} ja my\"{o}nsi sit\"{a} varten kahdentuhannen punnan avustuksen. Stuart ryhtyi kaikkiin varokeinoihin, jotka kokemuksesta tiesi tarpeellisiksi. H\"{a}nen yst\"{a}v\"{a}ns\"{a}, luonnontutkija Waterhouse, vanhat kumppaninsa Thring ja Kekwick sek\"{a} lis\"{a}ksi Woodforde ja Auld, kaikkiaan kymmenen miest\"{a}, liittyiv\"{a}t h\"{a}neen. H\"{a}n otti mukaansa kaksikymment\"{a} amerikkalaista nahkas\"{a}kki\"{a}, joista kukin oli kolmenkymmenen litran vetoinen, ja 5. p\"{a}iv\"{a}n\"{a} huhtikuuta 1862 retkikunta oli saavuttanut Newcastle Waterin alueen, kahdeksannentoista leveysasteen takana, yht\"{a} kaukana pohjoisessa kuin kovaonninen Burke oli p\"{a}\"{a}ssyt. H\"{a}nen reittins\"{a} noudatti jokseenkin l\"{a}helt\"{a} 131. meridiaania ja poikkesi niin ollen seitsem\"{a}n astetta l\"{a}nteen Burken reitist\"{a}. Newcastle Waterin alueen piti olla uusien l\"{o}yt\"{o}retkien l\"{a}ht\"{o}kohtana. Stuart, jota kaikkialla ymp\"{a}r\"{o}i tihe\"{a} mets\"{a}, koetti turhaan tunkeutua pohjoiseen ja koilliseen. Yritys samota l\"{a}ntt\"{a} kohti Victoria-joelle ei my\"{o}sk\"{a}\"{a}n onnistunut; l\"{a}pip\"{a}\"{a}sem\"{a}tt\"{o}m\"{a}t viidakot sulkivat tien. Stuart p\"{a}\"{a}tti silloin muuttaa leiripaikkaa ja saikin sen siirretyksi v\"{a}h\"{a}n pohjoisemmaksi, Howerin r\"{a}meille. Sitten kulkiessaan it\"{a}\"{a} kohti h\"{a}n kohtasi keskell\"{a} ruohoisia tasankoja Daily-joen ja seurasi sit\"{a} noin viisikymment\"{a} kilometri\"{a}. Maaper\"{a} alkoi olla erinomaista; laitumet olisivat olleet squatterin ilona ja onnena; kumipuut kasvoivat sieil\"{a} tavattoman korkeiksi. Ihmeiss\"{a}\"{a}n jatkoi Stuart matkaamista eteenp\"{a}in; h\"{a}n saapui Strangeway-joen ja Leichardtin l\"{o}yt\"{a}m\"{a}n Roper-joen rannalle; niiden vedet virtasivat palmujen v\"{a}litse, jotka olivat t\"{a}m\"{a}n trooppisen seudun arvoisia; siell\"{a} eli alkuasukasheimoja, jotka ottivat l\"{o}yt\"{o}retkeilij\"{a}t yst\"{a}v\"{a}llisesti vastaan. Sielt\"{a} retkikunta k\"{a}\"{a}ntyi pohjoisluoteeseen pitkin hiekkaista ja rautapitoisten kallioiden peitt\"{a}m\"{a}\"{a} aluetta, etsien Van Diemenin lahteen laskevan Adelaide-joen l\"{a}hteit\"{a}. Se kulki t\"{a}ll\"{o}in Arnhemin maan l\"{a}pi, palmukaalien, bambujen ja pinjojen keskitse. Adelaide laajeni; sen rannat k\"{a}viv\"{a}t r\"{a}meisiksi; meri oli l\"{a}hell\"{a}. Tiistaina 22. p\"{a}iv\"{a}n\"{a} hein\"{a}kuuta Stuart leiriytyi Fresh Waterin r\"{a}meille jouduttuaan vaikeuksiin lukemattomien purojen vuoksi, jotka katkaisivat h\"{a}nen reittins\"{a}. H\"{a}n l\"{a}hetti kolme kumppaneistaan etsim\"{a}\"{a}n mahdollisia teit\"{a}; seuraavana p\"{a}iv\"{a}n\"{a} h\"{a}n saapui, milloin kierretty\"{a}\"{a}n ylip\"{a}\"{a}sem\"{a}tt\"{o}mi\"{a} virranpoukamia, milloin r\"{a}mmitty\"{a}\"{a}n upottavilla soilla, muutamille ruohoisille yl\"{a}tasangoille, miss\"{a} kasvoi kumipuurykelmi\"{a} ja kuitukuorisia puita; siell\"{a} lenteli parvittain hanhia, iibiksi\"{a} ja er\"{a}it\"{a} erikoisen kesytt\"{o}mi\"{a} vesilintuja. Alkuasukkaita oli v\"{a}h\"{a}n tai ei laisinkaan. Vain siell\"{a} t\"{a}\"{a}ll\"{a} savua kaukaisista leiripaikoista. Hein\"{a}kuun 24. p\"{a}iv\"{a}n\"{a}, yhdeks\"{a}n kuukautta Adelaidesta l\"{a}ht\"{o}ns\"{a} j\"{a}lkeen, Stuart l\"{a}hti kahtakymment\"{a} minuuttia yli kello kahdeksan aamulla liikkeelle pohjoista kohti; h\"{a}n tahtoi viel\"{a} samana p\"{a}iv\"{a}n\"{a} p\"{a}\"{a}st\"{a} meren rannalle. Rautamalmien ja vulkaanisten kallioiden peitt\"{a}m\"{a} maa kohosi hiljalleen; puut pieneniv\"{a}t ja alkoivat muistuttaa sellaisia, joita kasvaa merten rannoilla; eteen tuli laaja, mets\"{a}n reunustama vesij\"{a}tt\"{o}laakso. Stuart kuuli selv\"{a}sti murtuvien aaltojen kohinaa, mutta ei sanonut mit\"{a}\"{a}n kumppaneilleen. Vihdoin tultiin villien viinik\"{o}ynn\"{o}sten tukkimaan viidakkoon. Stuart astui muutaman askeleen. Silloin h\"{a}n oli Intian valtameren rannalla! --- Meri! Meri! huudahti Thring h\"{a}mm\"{a}styneen\"{a}. Toiset riensiv\"{a}t paikalle, ja kolme pitk\"{a}\"{a} hurraahuutoa tervehti Intian merta. Australian mantereen poikki oli p\"{a}\"{a}sty nelj\"{a}nnell\"{a} kerralla! Kuvern\"{o}\"{o}ri Richard Macdonnellille antamansa lupauksen mukaan Stuart pesi jalkansa, kasvonsa ja k\"{a}tens\"{a} merivedess\"{a}. Sitten h\"{a}n palasi laaksoon ja kaiversi er\"{a}\"{a}seen puuhun nimens\"{a} alkukirjaimet J.M.D.S. Leiri pantiin kuntoon pienen solisevan puron rannalle. Seuraavana p\"{a}iv\"{a}n\"{a} Thring l\"{a}hti tutkimaan, voisiko lounaaseen kulkemalla p\"{a}\"{a}st\"{a} Adelaide-joen suulle, mutta maaper\"{a} oli liian r\"{a}meist\"{a} hevosille, joten siit\"{a} t\"{a}ytyi luopua. Silloin Stuart valitsi korkean puun er\"{a}\"{a}ll\"{a} aukealla paikalla. H\"{a}n katkaisi sen alemmat oksat ja kiinnitti latvaan Australian lipun. Puun kaarnaan piirrettiin seuraavat sanat: \textit{Kaiva maata puolen metrin p\"{a}\"{a}ss\"{a} etel\"{a}\"{a}n}. Ja jos joku matkustaja kerran kaivaa maata silt\"{a} paikalta, h\"{a}n l\"{o}yt\"{a}\"{a} peltirasian ja siin\"{a} asiakirjan, jonka sanat ovat sy\"{o}pyneet muistiini: SUURI TUTKIMUSRETKI JA KULKU AUSTRALIAN HALKI ETEL\"{A}ST\"{A} POHJOISEEN. \begin{quotation} John MacDougal Stuartin johtamat tutkimusretkeilij\"{a}t saapuivat t\"{a}nne 25. p\"{a}iv\"{a}n\"{a} hein\"{a}kuuta 1862 kuljettuaan koko Australian halki Etel\"{a}merelt\"{a} Intian valtameren rannalle, samoten keskelt\"{a} mannerta. He olivat l\"{a}hteneet Adelaidesta 26. p\"{a}iv\"{a}n\"{a} lokakuuta 1861 ja j\"{a}ttiv\"{a}t 21. p\"{a}iv\"{a}n\"{a} tammikuuta 1862 taakseen viimeisen siirtolan pohjoisessa. T\"{a}m\"{a}n onnellisen tapahtuman muistoksi he pystyttiv\"{a}t t\"{a}h\"{a}n Australian lipun, merkiten siihen retkikunnan johtajan nimen. Kaikki on hyvin. Jumala varjelkoon kuningatarta.\end{quotation} Alle on kirjoitettu Stuartin ja h\"{a}nen seuralaistensa nimet. N\"{a}in todettiin t\"{a}m\"{a} suuri tapahtuma, joka her\"{a}tti tavatonta huomiota koko maailmassa. --- Ja p\"{a}\"{a}siv\"{a}tk\"{o} kaikki n\"{a}m\"{a} rohkeat retkeilij\"{a}t takaisin yst\"{a}viens\"{a} luo etel\"{a}\"{a}n? lady Helena kysyi. --- P\"{a}\"{a}siv\"{a}t, rouva, Paganel vastasi, --- kaikki, mutta eiv\"{a}t ilman kovia koettelemuksia. Stuart k\"{a}rsi kaikkein enimmin, h\"{a}n oli pahasti sairastunut keripukkiin l\"{a}htiess\"{a}\"{a}n paluumatkalle Adelaidea kohti. Syyskuun alussa h\"{a}nen tautinsa oli niin pahentunut, ettei h\"{a}n uskonut en\"{a}\"{a} n\"{a}kev\"{a}ns\"{a} asuttuja seutuja. H\"{a}n ei jaksanut en\"{a}\"{a} istua satulassa, vaan kulki kahden hevosen v\"{a}liin ripustetussa kantotuolissa maaten. Lokakuun lopulla h\"{a}n joutui verensy\"{o}ksyn takia viimeisilleen. Tapettiin hevonen, jotta h\"{a}nelle saatiin keitetyksi lihalient\"{a}; 28. p\"{a}iv\"{a}n\"{a} lokakuuta h\"{a}n luuli kuolevansa, mutta onnellinen taudink\"{a}\"{a}nne pelasti h\"{a}net, ja 10. p\"{a}iv\"{a}n\"{a} joulukuuta retkikunta saapui t\"{a}ysilukuisena ensimm\"{a}isille asutuksille. Adelaideen Stuart saapui 17. p\"{a}iv\"{a}n\"{a} joulukuuta asukkaiden riemuitessa. Mutta h\"{a}nen vointinsa oli yh\"{a} huono, ja pian, saatuaan Maantieteellisen seuran suuren kultamitalin, h\"{a}n astui \textit{Indus}-laivaan matkustaakseen rakkaaseen Skotlantiinsa, is\"{a}nmaahansa, miss\"{a} palatessamme viel\"{a} h\"{a}net tapaamme.[6] --- H\"{a}n oli mies, joka oli erinomaisen tarmokas, Glenarvan sanoi, --- ja se viel\"{a} enemm\"{a}n kuin ruumiillinen voima auttoi h\"{a}nt\"{a} suurtekoihin. Skotlanti on syyst\"{a} ylpe\"{a} saadessaan lukea h\"{a}net omiensa joukkoon. --- Eik\"{o} Stuartin j\"{a}lkeen kukaan ole yritt\"{a}nyt uusia l\"{o}yt\"{o}retki\"{a}? lady Helena kysyi. --- On kyll\"{a}, rouva, Paganel vastasi. --- Min\"{a} olen usein maininnut teille Leichardtin. T\"{a}m\"{a} retkeilij\"{a} oli jo vuonna 1844 tehnyt huomattavan tutkimusretken Pohjois-Australiaan. Vuonna 1848 h\"{a}n l\"{a}hti toiselle matkalle koilliseen. Seitsem\"{a}\"{a}ntoista vuoteen ei h\"{a}nest\"{a} sitten ole mit\"{a}\"{a}n kuulunut. Viime vuonna toimeenpani kuuluisa kasvitieteilij\"{a}, tohtori Muller Melbournesta rahanker\"{a}yksen retkikunnan kustantamista varten. Rahat saatiin helposti kokoon, ja joukko uljaita squattereita l\"{a}hti \"{a}lykk\"{a}\"{a}n ja rohkean MacIntyren johdolla 21. p\"{a}iv\"{a}n\"{a} kes\"{a}kuuta 1864 Paroo-joen laidunmailta. T\"{a}ll\"{a} hetkell\"{a}, jolloin teille puhun, se on Leichardtia etsiess\"{a}\"{a}n varmaankin tunkeutunut kauas mantereen sis\"{a}osiin. Onnistukoon sen ja onnistukoon meid\"{a}n kuten senkin l\"{o}yt\"{a}\"{a} etsityt rakkaat yst\"{a}v\"{a}t! T\"{a}h\"{a}n p\"{a}\"{a}ttyi maantieteilij\"{a}n kertomus. Oli jo my\"{o}h\"{a}inen ilta. Kiitettiin Paganelia, ja v\"{a}h\"{a}n ajan kuluttua nukkui itsekukin rauhallisesti, valkoisten kumipuiden lehdist\"{o}ss\"{a} piilev\"{a}n kellolinnun raksuttaessa s\"{a}\"{a}nn\"{o}llisesti t\"{a}m\"{a}n tyynen y\"{o}n sekunteja. \gutchapter{RAUTATIE MELBOURNESTA SANDHURSTIIN.} Majuri oli ollut hieman levoton n\"{a}hdess\"{a}\"{a}n Ayrtonin l\"{a}htev\"{a}n Wimerran leirilt\"{a} etsim\"{a}\"{a}n hevosenkengitt\"{a}j\"{a}\"{a} Black Pointin asemalta. Mutta h\"{a}n ei hiiskunut sanaakaan omista ep\"{a}ilyist\"{a}\"{a}n ja tyytyi vain pit\"{a}m\"{a}\"{a}n silm\"{a}ll\"{a} joen ymp\"{a}rist\"{o}\"{a}. N\"{a}iden rauhallisten seutujen tyyneytt\"{a} ei mill\"{a}\"{a}n tavoin h\"{a}iritty, ja y\"{o}n kestetty\"{a} muutamia tunteja aurinko nousi j\"{a}lleen taivaalle. Glenarvan puolestaan ei pel\"{a}nnyt muuta kuin ett\"{a} Ayrton tulisi takaisin yksin. Ellei saataisi sepp\"{a}\"{a}, vankkureilla ei p\"{a}\"{a}st\"{a}isi jatkamaan retke\"{a}. Matka keskeytyisi ehk\"{a} useiksi p\"{a}iviksi, ja Glenarvan, joka malttamattomana halusi pian p\"{a}\"{a}st\"{a} perille, ei suvainnut mit\"{a}\"{a}n viivytyst\"{a}. Onneksi Ayrton ei ollut hukannut aikaa eik\"{a} laiminly\"{o}nyt mit\"{a}\"{a}n. H\"{a}n palasi seuraavana p\"{a}iv\"{a}n\"{a} aamun valjetessa. H\"{a}nell\"{a} oli mukanaan mies, joka sanoi olevansa Black Pointin aseman sepp\"{a}. T\"{a}m\"{a} oli suuri ja reipas miehenroikale, tymp\"{a}isev\"{a}n ja el\"{a}imellisen n\"{a}k\"{o}inen. Mutta v\"{a}h\"{a}t sill\"{a}, jos h\"{a}n vain pystyisi teht\"{a}v\"{a}\"{a}ns\"{a}. H\"{a}n oli muuten perin v\"{a}h\"{a}puheinen eik\"{a} kuluttanut suutaan tarpeettomiin sanoihin. --- Onko h\"{a}n pystyv\"{a} ty\"{o}mies? John Mangles kysyi per\"{a}miehelt\"{a}. --- Min\"{a} en h\"{a}nt\"{a} tunne enemp\"{a}\"{a} kuin te, kapteeni, Ayrton vastasi. --- Saadaan n\"{a}hd\"{a}. Sepp\"{a} ryhtyi ty\"{o}h\"{o}ns\"{a}. H\"{a}n oli ammattimies, sen n\"{a}ki kyll\"{a} siit\"{a} tavasta, kuinka h\"{a}n korjasi vankkurien etuosan. H\"{a}n teki ty\"{o}t\"{a} taitavasti ja harvinaisen nopeasti. Majuri huomasi h\"{a}nen ranteidensa pahasti runnellussa ihossa mustahkot, melkein verest\"{a}v\"{a}t raidat. Ne olivat vereksien haavojen j\"{a}lki\"{a}, joita huonon pellavapaidan hihat vain osaksi peittiv\"{a}t. MacNabbs teki sep\"{a}lle n\"{a}it\"{a}, viel\"{a} varmaankin perin kipeit\"{a} vioittumia koskevan kysymyksen. Mutta mies ei vastannut, vaan jatkoi ty\"{o}t\"{a}\"{a}n. Kahden tunnin kuluttua oli vankkurit korjattu. Mit\"{a} Glenarvanin hevoseen tuli, se oli pian kunnossa. Sepp\"{a} oli ottanut mukaansa valmiita hevosenkenki\"{a}; niiss\"{a} oli muuan omituisuus, joka ei j\"{a}\"{a}nyt majurilta huomaamatta: etuosaan oli ly\"{o}ty selv\"{a} risti\"{a}ss\"{a}n kuva. Majuri huomautti sit\"{a} Ayrtonille. --- Se on Black Pointin merkki, per\"{a}mies vastasi. --- Sen avulla voi seurata asemalta kadonneiden hevosten j\"{a}lki\"{a} sekoittamatta niit\"{a} muihin. Keng\"{a}t oli pian sovitettu hevosen kavioihin. Sen j\"{a}lkeen sepp\"{a} pyysi palkkaansa ja l\"{a}hti tiehens\"{a} tuskin nelj\"{a} sanaa sanottuaan. Puoli tuntia my\"{o}hemmin olivat retkeilij\"{a}t matkalla. Mimoosamets\"{a}n takana levisi laajalti avoin tasanko, joka hyvin ansaitsi nimens\"{a} ``open plain''. Muutamia kvartsilohkareita ja rautapitoisia kivi\"{a} oli siell\"{a} t\"{a}\"{a}ll\"{a} pensaiden, korkean ruohikon ja aitausten v\"{a}liss\"{a}, miss\"{a} lukuisia karjalaumoja oli laitumella. Joitakin kilometrej\"{a} kauempana uursivat vankkurien py\"{o}r\"{a}t syv\"{a}lle vesiper\"{a}iseen maahan, jossa solisi s\"{a}\"{a}nn\"{o}tt\"{o}mi\"{a}, j\"{a}ttil\"{a}iskaislikon puoleksi peitt\"{a}mi\"{a} puroja. Sitten kuljettiin pitkin laajojen, rehev\"{o}ityvien suolapitoisten lampien reunoja. Matka sujui vaivattomasti ja, se t\"{a}ytyy sanoa, rattoisasti. Lady Helena kutsui herroja k\"{a}ym\"{a}\"{a}n luonaan vuoron per\"{a}\"{a}n, sill\"{a} h\"{a}nen salonkinsa oli kovin ahdas. Mutta n\"{a}in sai kukin lev\"{a}ht\"{a}\"{a} rasittavasta ratsastuksesta ja virkist\"{a}\"{a} itse\"{a}ns\"{a} keskustelulla vieh\"{a}tt\"{a}vien naisten kanssa. Neiti Maryn avustamana h\"{a}n hoiti py\"{o}riv\"{a}n talonsa em\"{a}nnyytt\"{a} mit\"{a} miellytt\"{a}vimmin. John Manglesia ei n\"{a}iss\"{a} jokap\"{a}iv\"{a}isiss\"{a} kutsuissa unohdettu, eik\"{a} h\"{a}nen hiukan juhlallista keskustelutapaansa pidetty ik\"{a}v\"{a}n\"{a}. P\"{a}invastoin. N\"{a}in kuljettiin kohtisuoraan poikki Growlandista Horshamiin johtavan postitien, pahasti p\"{o}lyisen tien muuten, jota jalkamiehet eiv\"{a}t juuri k\"{a}ytt\"{a}neet. Talbotin kreivikunnan \"{a}\"{a}rimm\"{a}isess\"{a} sopukassa sivuttiin ohimennen matalahkojen kunnaiden kukkuloita, ja illalla seurue saapui viiden kilometrin p\"{a}\"{a}h\"{a}n Maryboroughin yl\"{a}puolelle. Satoi hienoa vihmaa, joka miss\"{a} muussa maassa tahansa olisi liottanut kamaran, mutta t\"{a}\"{a}ll\"{a} kosteus haihtui niin ihmeellisesti, ett\"{a} leiripaikalla ei ollut siit\"{a} mit\"{a}\"{a}n haittaa. Seuraavana, 29. p\"{a}iv\"{a}n\"{a} joulukuuta kulkua hidastutti jonkin verran jono vuorennyppyl\"{o}it\"{a}, jotka muistuttivat jonkinlaista pienoiskokoista Sveitsi\"{a}. Tavan takaa piti nousta m\"{a}elle ja taas laskeutua, ja samalla k\"{a}rsi\"{a} ep\"{a}mieluisaa keinahtelua. Matkustajat k\"{a}veliv\"{a}t osan matkaa jalkaisin eiv\"{a}tk\"{a} sit\"{a} pahoitelleet. Kello yhdentoista aikaan saavuttiin Carlsbrookiin, joka on jokseenkin t\"{a}rke\"{a} kaupunki. Ayrton oli sit\"{a} mielt\"{a}, ett\"{a} olisi kierrett\"{a}v\"{a} sen ymp\"{a}ri sinne poikkeamatta, ajan voittamiseksi, h\"{a}n selitti. Glenarvan oli samaa mielt\"{a}, mutta aina utelias Paganel tahtoi k\"{a}yd\"{a} Carlsbrookissa. H\"{a}nen ehdotukseensa suostuttiin, ja vankkurit jatkoivat verkalleen kulkuaan. Tapansa mukaan Paganel otti Robertin seurakseen. H\"{a}nen k\"{a}yntins\"{a} Carlsbrookissa oli hyvin lyhyt, mutta riitti antamaan h\"{a}nelle tarkan yleiskuvan kaupungista. Siell\"{a} oli pankki, raatihuone, kauppatori, koulu, kirkko ja satakunta t\"{a}ysin samanlaista tiilitaloa, kaikki j\"{a}rjestettyn\"{a} s\"{a}\"{a}nn\"{o}lliseksi, yhdensuuntaisten katujen leikkelem\"{a}ksi suunnikkaaksi englantilaiseen tapaan. Ei mik\"{a}\"{a}n ole yksinkertaisempaa --- eik\"{a} my\"{o}sk\"{a}\"{a}n yksitoikkoisempaa. Kun kaupunki suurenee, pidennet\"{a}\"{a}n sen katuja kuten kasvavan pojan housuja, alkuper\"{a}ist\"{a} sopusuhtaa mill\"{a}\"{a}n tavoin rikkomatta. Carlsbrook oli vilkas kaupunki, mik\"{a} on n\"{a}iden vastaperustettujen kaupunkien huomattava ominaisuus. Australiassa n\"{a}ytt\"{a}v\"{a}t kaupungit kasvavan kuin puut auringon l\"{a}mm\"{o}ss\"{a}. Kiireisi\"{a} ihmisi\"{a} kulki kaduilla, kullan v\"{a}litt\"{a}ji\"{a} tungeskeli tuontitoimistoissa, alkuasukkaisiin kuuluvan poliisimiehist\"{o}n saattamana tuotiin kallista metallia Bendigon ja Mount Alexanderin kaivoksista. Kaikki n\"{a}m\"{a} etujensa kannustamat ihmiset ajattelivat vain kauppojaan, eik\"{a} t\"{a}m\"{a}n ahertavan v\"{a}est\"{o}n joukossa muukalaisia huomattukaan. K\"{a}ytetty\"{a}\"{a}n tunnin ajan vaellukseen Carlsbrookissa molemmat palasivat toveriensa luo huolellisesti viljellyn peltomaan halki. Sitten tuli laajoja ruohikkoja, nimelt\"{a}\"{a}n ``low level plains'', ja niill\"{a} n\"{a}kyi lukemattomia lammaslaumoja ja paimenh\"{o}kkeleit\"{a}. Edemp\"{a}n\"{a} alkoi er\"{a}maa v\"{a}litt\"{o}m\"{a}sti, Australian luonnolle ominaisen \"{a}kkin\"{a}isesti. Simpsonin kukkulat ja Tarrangowerin vuori osoittivat Loddon piirin etel\"{a}ist\"{a} k\"{a}rke\"{a} 144. pituusasteen kohdalla. T\"{a}h\"{a}n saakka ei kuitenkaan ollut tavattu yht\"{a}\"{a}n alkuasukasheimoista, jotka el\"{a}v\"{a}t villiss\"{a} tilassa. Glenarvan tuumiskeli, puuttuiko Australiasta australialaisia, kuten Argentiinan pampalta oli puuttunut intiaaneja. Mutta Paganel selitti h\"{a}nelle, ett\"{a} t\"{a}ll\"{a} leveysasteella liikuskelivat villit enimm\"{a}kseen Murrayn tasangoilla puolentoistasataa kilometri\"{a} idemp\"{a}n\"{a}. --- Me l\"{a}hestymme kultaseutua, h\"{a}n sanoi. --- Kahden p\"{a}iv\"{a}n p\"{a}\"{a}st\"{a} kuljemme Mount Alexanderin rikkaan alueen l\"{a}pi. Sinne rynt\"{a}siv\"{a}t vuonna 1852 kullanetsij\"{o}iden laumat. Alkuasukkaiden t\"{a}ytyi paeta heid\"{a}n tielt\"{a}\"{a}n er\"{a}maihin. Me olemme sivistyneess\"{a} maassa, vaikkei silt\"{a} n\"{a}yt\"{a}, ja ennen t\"{a}m\"{a}n p\"{a}iv\"{a}n p\"{a}\"{a}ttymist\"{a} olemme kulkeneet rautatien yli, joka yhdist\"{a}\"{a} Murrayn ja meren. Tarvitseeko sanoakaan, yst\"{a}v\"{a}ni, rautatie Australiassa tuntuu minusta yll\"{a}tt\"{a}v\"{a}lt\"{a}. --- Mink\"{a} vuoksi, Paganel? Glenarvan kysyi. --- Mink\"{a}k\"{o} vuoksi? Sen vuoksi, ett\"{a} se on ristiriitaista! Oh, min\"{a} tied\"{a}n kyll\"{a}, ett\"{a} te, jotka olette tottuneet asuttamaan kaukaisia alueita, te, joilla on s\"{a}hk\"{o}lenn\"{a}ttimi\"{a} ja maailmann\"{a}yttelyit\"{a} Uudessa Seelannissa, pid\"{a}tte sit\"{a} ihan luonnollisena! Mutta se sekoittaa minun kaltaiseni ranskalaisen mielt\"{a} ja kaikkia h\"{a}nen mielikuviaan Australiasta. --- Kun te katsotte entisyytt\"{a} ettek\"{a} nykyisyytt\"{a}, John Mangles huomautti. --- Olkoon, Paganel vastasi, --- mutta kun er\"{a}maiden halki kiit\"{a}v\"{a}t veturit, mimoosien ja kumipuiden oksiin kiertyv\"{a}t h\"{o}yrypilvet, pikajunien edest\"{a} pakenevat muurahaispiikkisiat, nokkael\"{a}imet ja kasuaarit, ja villit nousevat kello puoli nelj\"{a}n junaan matkustaakseen Melbournesta Kynetoniin, Castlemaineen, Sandhurstiin tai Echucaan, h\"{a}mm\"{a}stytt\"{a}\"{a} tuo kaikki jokaista muuta kuin englantilaista tai amerikkalaista. Teid\"{a}n rautatienne h\"{a}vitt\"{a}v\"{a}t er\"{a}maiden runollisuuden. --- Mit\"{a}p\"{a} siit\"{a}, jos edistys tulee tilalle! majuri lausui. Kime\"{a} vihellys keskeytti puheen. Matkustajat olivat vain puolentoista kilometrin p\"{a}\"{a}ss\"{a} rautatiest\"{a}. Muuan etel\"{a}st\"{a} tuleva ja hiljaista vauhtia kulkeva veturi pys\"{a}htyi juuri rautatien ja vankkurien k\"{a}ytt\"{a}m\"{a}n maantien risteykseen. T\"{a}m\"{a} rautatie yhdisti, kuten Paganel oli sanonut, Victorian p\"{a}\"{a}kaupungin Australian suurimpaan virtaan Murrayyn. T\"{a}m\"{a} valtava vesiuoma, jonka Sturt l\"{o}ysi vuonna 1828, alkaa Australian Alpeilta, saa lis\"{a}vett\"{a} Lachlanista ja Darlingista, on Victorian maakunnan koko pohjoisrajana ja laskee Encounter-lahteen l\"{a}hell\"{a} Adelaidea. Se ulottuu rikkaiden, hedelm\"{a}llisten seutujen halki, ja squatter-asemat yh\"{a} lis\"{a}\"{a}ntyv\"{a}t sen varsilla, kun n\"{a}in on saatu mukava kulkuyhteys Melbourneen. T\"{a}t\"{a} rautatiet\"{a} oli siihen aikaan valmiina 168 kilometri\"{a} Melbournesta Sandhurstiin; samalla se v\"{a}litti liikennett\"{a} Kynetoniin ja Castlemaineen. Parhaillaan rakennettiin sadankahdentoista kilometrin pituista jatkorataa Echucaan, juuri t\"{a}n\"{a} vuonna Murrayn varsille perustetun Riverinen siirtokunnan p\"{a}\"{a}kaupunkiin saakka. 37. leveysaste leikkasi rautatiet\"{a} muutamia kilometrej\"{a} Castlemainen pohjoispuolella juuri sill\"{a} kohtaa, miss\"{a} on Camden Bridge, Lutton-nimisen Murrayn lis\"{a}joen yli rakennettu silta. Sit\"{a} kohti Ayrton suuntasi vankkurinsa, ratsumiesten l\"{a}htiess\"{a} edelt\"{a} nelist\"{a}m\"{a}\"{a}n Camden Bridgelle. Heit\"{a} kannusti siihen muuten kova uteliaisuus. Rautatien siltaa kohti riensi n\"{a}et suuri ihmisjoukko. L\"{a}heisten asemien asukkaat j\"{a}ttiv\"{a}t talonsa ja paimenet laumansa, tungeksien tiell\"{a}, niin ett\"{a} oli vaikea p\"{a}\"{a}st\"{a} eteenp\"{a}in. Joukosta kuului usein toistuvia huutoja: --- Rautatielle! Rautatielle! Ilmeisesti oli sattunut jokin vakava tapahtuma, joka aiheutti kaiken t\"{a}m\"{a}n h\"{a}lin\"{a}n. Ehk\"{a}p\"{a} jokin suuri tapaturma. Glenarvan lis\"{a}si hevosensa vauhtia kumppaneidensa seuratessa. Muutaman minuutin kuluttua h\"{a}n oli Camden Bridgen luona. Siell\"{a} h\"{a}n ymm\"{a}rsi syyn rynt\"{a}ykseen. Oli tapahtunut hirvitt\"{a}v\"{a} onnettomuus, ei junien yhteent\"{o}rm\"{a}ys, vaan junan suistuminen radalta ja sy\"{o}ksyminen virtaan, mik\"{a} muistutti Amerikan suurimpia samantapaisia onnettomuuksia. Rautatien alitse kulkeva joki oli t\"{a}ynn\"{a} vaunuja ja veturin pirstaleita. Joko oli silta murtunut junan painosta tai juna joutunut pois raiteilta: viisi vaunua kuudesta oli suistunut Luttonin uomaan veturin per\"{a}ss\"{a}. Ainoastaan viimeinen vaunu pelastui kuin ihmeen kautta, sen kytkyt kun oli katkennut, ja seisoi radalla metrin p\"{a}\"{a}ss\"{a} kuilun partaalta. Alhaalla oli vain hirvitt\"{a}v\"{a} kasa mustuneita ja katkenneita akseleita, murskautuneita vaunuja, v\"{a}\"{a}ntyneit\"{a} kiskoja, hiiltyneit\"{a} ratap\"{o}lkkyj\"{a}. T\"{a}r\"{a}hdyksest\"{a} r\"{a}j\"{a}ht\"{a}nyt h\"{o}yrypannu oli lenn\"{a}tt\"{a}nyt metallikuoren sirpaleita pitk\"{a}n matkan p\"{a}\"{a}h\"{a}n. T\"{a}st\"{a} muodottomien esineiden rykelm\"{a}st\"{a} nousi viel\"{a} muutamia liekkej\"{a} ja h\"{o}yry\"{a} mustan savun keskelt\"{a}. Hirve\"{a}n sy\"{o}ksyn j\"{a}lkeen viel\"{a} hirve\"{a}mpi tulipalo! Suuria veril\"{a}t\"{a}k\"{o}it\"{a}, irrallisia j\"{a}seni\"{a}, hiiltyneiden ruumiiden tynki\"{a} n\"{a}kyi siell\"{a} t\"{a}\"{a}ll\"{a} eik\"{a} kukaan uskaltanut ajatella n\"{a}iden pirstaleiden alle hautautuneiden uhrien lukum\"{a}\"{a}r\"{a}\"{a}. Glenarvan, Paganel, majuri ja Mangles kuuntelivat joukon keskell\"{a} miehest\"{a} mieheen kulkevia puheita. Pelastust\"{o}iss\"{a} puuhaillessaan kukin koetti selitt\"{a}\"{a} tapaturmaa. --- Silta on murtunut, joku sanoi. --- Murtunutko! toinen vastasi. --- Se on yht\"{a} hyv\"{a}ss\"{a} kunnossa kuin se on aina ollut, mutta on unohdettu k\"{a}\"{a}nt\"{a}\"{a} paikalleen junan tullessa. Siin\"{a} kaikki. Siin\"{a} olikin k\"{a}\"{a}nt\"{o}silta, joka avattiin laivaa varten. Oliko siis anteeksiantamattoman huolimaton vartija unohtanut sulkea sen, niin ett\"{a} t\"{a}ytt\"{a} vauhtia kulkeva juna tyhj\"{a}n p\"{a}\"{a}lle jouduttuaan, oli n\"{a}in sy\"{o}ksynyt Luttonin veteen? T\"{a}m\"{a} olettamus tuntui hyvin todenn\"{a}k\"{o}iselt\"{a}. Vaikka toinen puoli siltaa oli murskana vaunujen pirstaleiden alla, riippui toinen, vastap\"{a}iselle rannalle k\"{a}\"{a}nnetty puoli viel\"{a} ehj\"{a}n\"{a} kannattimillaan. Ei ollut ep\"{a}ilyst\"{a}k\"{a}\"{a}n! Vartijan huolimattomuus oli aiheuttanut tapaturman. Se oli sattunut y\"{o}ll\"{a} junalle n:o 37, joka oli l\"{a}htenyt Melbournesta nelj\"{a}nnest\"{a} vaille kaksitoista illalla. Kello oli varmaankin ollut nelj\"{a}nnest\"{a} yli kolme aamulla, kun juna kaksikymment\"{a}viisi minuuttia Castlemainen asemalta l\"{a}hd\"{o}n j\"{a}lkeen saapui Camden Bridgelle ja kohtasi siin\"{a} tuhonsa. Viimeisen vaunun matkustajat ja virkailijat ryhtyiv\"{a}t heti etsim\"{a}\"{a}n apua, mutta s\"{a}hk\"{o}lenn\"{a}tin, jonka pylv\"{a}\"{a}t olivat kaatuneet maahan, ei en\"{a}\"{a} toiminut. Kului kolme tuntia, kunnes Castlemainen viranomaiset ehtiv\"{a}t saapua onnettomuuspaikalle. Kello oli siis kuusi aamulla, kun pelastusty\"{o} saatiin j\"{a}rjestetyksi siirtokunnan ylivalvojan Mitchellin toimesta ja er\"{a}\"{a}n poliisiupseerin komentaman poliisiosaston avulla. Squatterit ja heid\"{a}n v\"{a}kens\"{a} olivat tulleet my\"{o}s auttamaan ja ryhtyiv\"{a}t ensin sammuttamaan tulipaloa, joka hurjan kiihke\"{a}n\"{a} riehui pirstaleiden keskell\"{a}. Muutamia ruumiita, joita oli mahdoton tunnistaa, oli nostettu ratavallille. Ei voinut ajatellakaan, ett\"{a} kukaan selviytyisi el\"{a}v\"{a}n\"{a} t\"{a}st\"{a} palavasta p\"{a}tsist\"{a}. Tuli oli nopeasti t\"{a}ydent\"{a}nyt h\"{a}vityksen. Junan matkustajista, joiden lukum\"{a}\"{a}r\"{a}\"{a} ei tiedetty, oli j\"{a}\"{a}nyt eloon ainoastaan kymmenen, viimeisess\"{a} vaunussa olleet. Rautatien hallinto oli l\"{a}hett\"{a}nyt apuveturin noutamaan heit\"{a} Castlemaineen. T\"{a}ll\"{a} v\"{a}lin lordi Glenarvan, joka oli esitellyt itsens\"{a}, keskusteli ylivalvojan ja poliisiupseerin kanssa. J\"{a}lkimm\"{a}inen oli kookas ja laiha mies, j\"{a}rk\"{a}ht\"{a}m\"{a}tt\"{o}m\"{a}n kylm\"{a}verinen, joka ei ainakaan antanut tunteidensa n\"{a}ky\"{a} v\"{a}r\"{a}ht\"{a}m\"{a}tt\"{o}mill\"{a} kasvoillaan. H\"{a}n katseli t\"{a}t\"{a} hirvitt\"{a}v\"{a}\"{a} tuhoa kuin matemaatikko laskuteht\"{a}v\"{a}\"{a}: h\"{a}n yritti ratkaista sit\"{a} ja saada selville tuntemattoman tekij\"{a}n. Niinp\"{a} kun Glenarvan lausui: --- T\"{a}m\"{a} on suuri onnettomuus, h\"{a}n vastasi tyynesti: --- Viel\"{a} pahempaa, mylord. --- Viel\"{a} pahempaa! Glenarvan huudahti tuosta lausunnosta loukkaantuneena. --- Mit\"{a} t\"{a}ss\"{a} on `pahempaa' kuin onnettomuus? --- Rikos! poliisiupseeri vastasi tyynesti. Takertumatta t\"{a}llaiseen sopimattomaan puheeseen Glenarvan k\"{a}\"{a}ntyi herra Mitchellin puoleen, luoden h\"{a}neen kysyv\"{a}n katseen. --- Niin, mylord, ylivalvoja vastasi, --- tutkimuksemme on saanut meid\"{a}t varmistumaan, ett\"{a} t\"{a}m\"{a} on rikoksen tulos. Viimeinen tavaravaunu on ry\"{o}stetty. Eloon j\"{a}\"{a}neiden matkustajien kimppuun oli hy\"{o}k\"{a}nnyt viisi tai kuusi miest\"{a} k\"{a}sitt\"{a}v\"{a} rosvojoukko. Silta on j\"{a}tetty auki tahallisesti eik\"{a} ep\"{a}huomiossa, ja jos t\"{a}m\"{a}n seikan yhteydess\"{a} otetaan huomioon vartijan katoaminen, niin t\"{a}ytyy p\"{a}\"{a}tell\"{a}, ett\"{a} se roisto on ollut rosvojen liittolaisena. Poliisiupseeri pudisti p\"{a}\"{a}t\"{a}\"{a}n t\"{a}lle ylivalvojan p\"{a}\"{a}telm\"{a}lle. --- Ettek\"{o} te ole samaa mielt\"{a}? herra Mitchell kysyi h\"{a}nelt\"{a}. --- En, mit\"{a} vartijan osallisuuteen tulee. --- Mutta vain olettamalla sellaista tapahtuneen, ylivalvoja huomautti, --- voimme katsoa rikoksen Murrayn varsilla liikkuvien villien tekem\"{a}ksi. Ilman vartijan apua villit eiv\"{a}t olisi voineet avata k\"{a}\"{a}nt\"{o}siltaa, jonka rakenne on heille tuntematon. --- Aivan niin, poliisiupseeri vastasi. --- No, herra Mitchell lis\"{a}si, --- se laivuri, jonka alus kulki Camden Bridgen l\"{a}pi kello kymmenen nelj\"{a}kymment\"{a} illalla, on todistanut, ett\"{a} silta h\"{a}nen p\"{a}\"{a}sty\"{a}\"{a}n l\"{a}pi suljettiin s\"{a}\"{a}detyll\"{a} tavalla. --- Niin oikein. --- Niinp\"{a} siis vartijan osallisuus rikokseen n\"{a}ytt\"{a}\"{a} minusta olevan ratkaisevasti todistettu. Poliisiupseeri pudisteli yh\"{a} p\"{a}\"{a}t\"{a}\"{a}n. --- Ettek\"{o} siis te, herra, Glenarvan kysyi h\"{a}nelt\"{a}, --- katso rikosta villien tekem\"{a}ksi? --- En ensink\"{a}\"{a}n. --- Kenen sitten? T\"{a}ll\"{a} hetkell\"{a} kuului joen yl\"{a}juoksun puolelta noin puolen kilometrin p\"{a}\"{a}st\"{a} jokseenkin suurta melua. Sinne oli ker\"{a}\"{a}ntynyt v\"{a}kijoukko, joka ripe\"{a}sti suureni ja sitten pian saapui asemalle. Joukon keskell\"{a} kantoi kaksi miest\"{a} ruumista. Se oli vartijan jo kylmennyt ruumis. H\"{a}nt\"{a} oli isketty tikarilla syd\"{a}meen. Kantamalla h\"{a}nen ruumiinsa kauas Camden Bridgen luota olivat murhaajat ilmeisesti halunneet johtaa poliisin ep\"{a}luulot harhaan ensimm\"{a}isten etsiskelyjen aikana. Niinp\"{a} t\"{a}m\"{a} l\"{o}yt\"{o} vahvisti t\"{a}ydellisesti upseerin arvelun. Villeili\"{a} ei ollut mit\"{a}\"{a}n osuutta t\"{a}ss\"{a} rikoksessa. --- Tuon iskun antajat, h\"{a}n sanoi, --- ovat t\"{a}m\"{a}n pikkukojeen k\"{a}ytt\"{o}\"{o}n tottuneita. Ja n\"{a}in sanoessaan h\"{a}n n\"{a}ytti er\"{a}\"{a}nlaisia lukolla varustettuja, kaksiosaisesta renkaasta tehtyj\"{a} k\"{a}sirautoja. --- Ennen pitk\"{a}\"{a}, h\"{a}n lis\"{a}si, --- saanen ilon antaa heille t\"{a}m\"{a}n rannerenkaan uudenvuodenlahjaksi. --- Ep\"{a}ilettek\"{o} siis...? --- Niit\"{a}, jotka 'ovat matkustaneet vapaalipulla h\"{a}nen majesteettinsa laivoilla'. --- Mit\"{a}! Karkotettuja vankejako! huudahti Paganel, joka tunsi t\"{a}m\"{a}n Australian siirtokunnissa k\"{a}ytetyn sanontatavan. --- Min\"{a} luulin, Glenarvan huomautti, --- ett\"{a} karkotusvangeilla ei ollut oleskeluoikeutta Victorian maakunnassa. --- Mit\"{a} viel\"{a}, poliisiupseeri vastasi, --- jos ei heill\"{a} sit\"{a} oikeutta ole, niin he ottavat sen itselleen. Joskus karkotusvankien onnistuu livahtaa pakoon, ja suuresti erehtyisin, elleiv\"{a}t n\"{a}m\"{a} tule suoraa p\"{a}\"{a}t\"{a} Perthist\"{a}. No, he palaavat sinne my\"{o}s, voitte uskoa minua. Herra Mitchell vahvisti poliisiupseerin sanat ny\"{o}kk\"{a}\"{a}m\"{a}ll\"{a}. T\"{a}ll\"{a} hetkell\"{a} saapuivat vankkurit rautatiesillan kohdalle. Glenarvan tahtoi est\"{a}\"{a} naisia n\"{a}kem\"{a}st\"{a} Camden Bridgen hirve\"{a}\"{a} n\"{a}ytelm\"{a}\"{a}. H\"{a}n sanoi hyv\"{a}stit ylivalvojalle ja antoi yst\"{a}villeen merkin tulla mukaan. --- T\"{a}m\"{a}n vuoksi ei ole syyt\"{a} keskeytt\"{a}\"{a} matkaamme, h\"{a}n sanoi. Tultuaan vankkurien luo Glenarvan kertoi lady Helenalle vain, ett\"{a} oli tapahtunut rautatieonnettomuus, mainitsematta, mit\"{a} osuutta rikoksella oli ollut t\"{a}h\"{a}n tapahtumaan; niin ik\"{a}\"{a}n h\"{a}n j\"{a}tti ilmaisematta, ett\"{a} seudulla liikkui karkotusvankeja, p\"{a}\"{a}tt\"{a}en puhua siit\"{a} Ayrtonille erikseen. Sitten seurue ylitti rautatien muutamien satojen metrien p\"{a}\"{a}st\"{a} sillasta ja jatkoi matkaansa it\"{a}\"{a}np\"{a}in, kuten ennenkin. \gutchapter{ENSIMM\"{A}INEN PALKINTO MAANTIETEESS\"{A}.} N\"{a}kyviin kohosi muutamia leve\"{a}hk\"{o}j\"{a} kukkuloita, joihin tasanko p\"{a}\"{a}ttyi noin kolmen kilometrin p\"{a}\"{a}ss\"{a} rautatiest\"{a}. Pian vankkurit vieriv\"{a}t ahtaissa ja oikullisesti mutkittelevissa solissa. Mutta n\"{a}m\"{a} veiv\"{a}t kauniille seudulle, jossa kasvoi kauniita puita, ei metsin\"{a}, vaan erillisiksi ryhmiksi j\"{a}rjestynein\"{a} ja kerrassaan trooppisen rehevin\"{a}. Kaikkein komeimpia olivat ``casuarinat'', jotka n\"{a}yttiv\"{a}t lainanneen tammelta runkonsa lujan rakenteen, akaasialta tuoksuvat siemenkotansa ja m\"{a}nnylt\"{a} sinivihre\"{a}\"{a}n vivahtavien lehtiens\"{a} karheuden. Niiden oksien v\"{a}list\"{a} n\"{a}kyi ``banksia latifolian'' omituisia latvoja, joiden suippous, on niin erinomaisen vieh\"{a}tt\"{a}v\"{a}. Suuret, riippaoksaiset puut n\"{a}yttiv\"{a}t metsik\"{o}iss\"{a} liian t\"{a}ysist\"{a} altaista valuvalta vihre\"{a}lt\"{a} vedelt\"{a}. Katse ep\"{a}r\"{o}i kaikkien n\"{a}iden luonnonihmeiden keskell\"{a} eik\"{a} tiennyt, mihin kohdistaa ihailunsa. Matkaseurue oli hetkeksi pys\"{a}htynyt. Ayrton oli lady Helenan k\"{a}skyst\"{a} seisauttanut valjakkonsa. Vankkurien suuret py\"{o}r\"{a}t lakkasivat narisemasta kvartsipitoisella hiekalla. Puuryhmien alla levisi pitki\"{a} vihreit\"{a} nurmikoita; muutamat s\"{a}\"{a}nn\"{o}llisen muotoiset maaper\"{a}n kohopaikat jakoivat ne viel\"{a} aivan selv\"{a}sti huomattaviin ruutuihin kuin suuren sakkilaudan. Paganel ei erehtynyt n\"{a}hdess\"{a}\"{a}n n\"{a}m\"{a} vihannoivat, ik\"{a}\"{a}n kuin ikuista lepoa varten runollisesti j\"{a}rjestetyt erilliset kohdat. H\"{a}n tunsi n\"{a}m\"{a} hautausneli\"{o}t, joiden viimeiset j\"{a}ljet ruoho nyt h\"{a}vitt\"{a}\"{a} ja joita matkamies niin harvoin tapaa Australiassa. --- Tuonen viidat, h\"{a}n sanoi. H\"{a}nen silmiens\"{a} edess\"{a} oli todellakin alkuasukkaiden hautausmaa, mutta niin raikas, niin siimek\"{a}s, lintujen hilpe\"{a}n lentelyn el\"{a}v\"{o}itt\"{a}m\"{a}, niin puoleensavet\"{a}v\"{a}, ett\"{a} se ei her\"{a}tt\"{a}nyt ainoatakaan surullista ajatusta. Sit\"{a} olisi hyvin voinut pit\"{a}\"{a} jonakin Eedenin puutarhana silt\"{a} ajalta, jolloin kuolemaa ei ollut maan p\"{a}\"{a}ll\"{a}. Se n\"{a}ytti olevan luotu el\"{a}vi\"{a} varten. Mutta n\"{a}m\"{a} haudat, joita villi hoitaa niin hartaan huolellisesti, h\"{a}visiv\"{a}t jo vihannuuden tulvan alle. Valtaus oli karkottanut australialaisen kauas seudulta, miss\"{a} h\"{a}nen esi-is\"{a}ns\"{a} lep\"{a}siv\"{a}t, ja siirtolaisuus riensi pian muuttamaan n\"{a}m\"{a} kuolonkent\"{a}t karjan laidunmaiksi. Niinp\"{a} ovat n\"{a}m\"{a} tuonen viidat k\"{a}yneet harvinaisiksi; kuinka monia, jotka peitt\"{a}v\"{a}t hiljattain haudatun miespolven, tallaakaan jo v\"{a}linpit\"{a}m\"{a}tt\"{o}m\"{a}n matkailijan jalka! Paganel ja Robert, jotka olivat kiirehtineet kumppaniensa edelle, kierteliv\"{a}t pienill\"{a} varjoisilla k\"{a}yt\"{a}vill\"{a} kumpujen v\"{a}liss\"{a}. He puhelivat ja opettivat toinen toistaan, sill\"{a} maantieteilij\"{a} v\"{a}itti oppivansa paljon nuoren Grantin mielipiteist\"{a}. Mutta he eiv\"{a}t olleet ratsastaneet puolta kilometri\"{a}, kun lordi Glenarvan n\"{a}ki heid\"{a}n pys\"{a}htyv\"{a}n, laskeutuvan ratsailta ja sitten kumartuvan maata kohti. He n\"{a}yttiv\"{a}t tutkivan hyvin mielenkiintoista esinett\"{a} heid\"{a}n ilmeikk\"{a}ist\"{a} eleist\"{a}\"{a}n p\"{a}\"{a}tellen. Ayrton hoputti valjakkoaan, ja vankkurit olivat pian tavoittaneet molemmat yst\"{a}vykset. Syy heid\"{a}n pys\"{a}hdykseens\"{a} ja h\"{a}mm\"{a}stykseens\"{a} k\"{a}vi kohta ilmi. Muuan alkuasukaslapsi, pieni kahdeksanvuotias poika eurooppalaisissa pukimissa, nukkui rauhallista unta mahtavan banksian siimeksess\"{a}. H\"{a}nen rotupiirteist\"{a}\"{a}n ei olisi voinut erehty\"{a}: kiharat hiukset, melkein musta iho, litte\"{a} nen\"{a}, paksut huulet ja k\"{a}sivarsien tavaton pituus osoittivat heti h\"{a}nen kuuluvan sis\"{a}maan alkuasukkaisiin. Mutta h\"{a}nell\"{a} oli \"{a}lykk\"{a}\"{a}t kasvot, ja varmaan kasvatus oli jo kohottanut t\"{a}m\"{a}n pikku villin alhaiselta alkutasoltaan. Lady Helena astui maahan perin uteliaana katselemaan h\"{a}nt\"{a}, ja pian koko seurue ymp\"{a}r\"{o}i pienen alkuasukkaan, joka nukkui sike\"{a}sti. --- Lapsiparka, Mary Grant sanoi, --- onko h\"{a}n joutunut eksyksiin t\"{a}ss\"{a} er\"{a}maassa? --- Min\"{a} luulen, lady Helena vastasi, --- ett\"{a} h\"{a}n on tullut kaukaa k\"{a}yd\"{a}kseen n\"{a}iss\"{a} kuoleman lehdoissa! T\"{a}\"{a}ll\"{a} lep\"{a}\"{a} varmaankin h\"{a}nen rakkaimpiaan! --- Mutta h\"{a}nt\"{a} ei voi j\"{a}tt\"{a}\"{a} t\"{a}nne! Robert sanoi. --- H\"{a}n on yksin ja... Robertin lauseen keskeytti nuoren australialaisen liikahdus; poika k\"{a}\"{a}nn\"{a}hti kuitenkaan her\"{a}\"{a}m\"{a}tt\"{a}. Mutta silloin nousi kaikkien h\"{a}mm\"{a}stys huippuunsa. Pojan sel\"{a}ss\"{a} oli kirjoitus ja siin\"{a} luki: TOLINE, TO BE CONDUCTED TO ECHUCA, CARE OF JEFFRIES SMITH, RAILWAY PORTER, PREPAID[7] --- Aito englantilaista! Paganel huudahti. --- L\"{a}hett\"{a}v\"{a}t lapsen kuin tavaramytyn! Kirjoittavat osoitteen kuin pakettiin! Minulle oli kyll\"{a} siit\"{a} puhuttu, mutta en tahtonut uskoa sit\"{a}. --- Lapsiparka! lady Helena lausui. --- Oliko h\"{a}n Camden Bridgelt\"{a} suistuneessa junassa? Ehk\"{a} h\"{a}nen vanhempansa ovat saaneet surmansa, ja h\"{a}n on nyt yksin maailmassa! --- Sit\"{a} en usko, rouva, John Mangles vastasi. --- T\"{a}m\"{a} kirjoitus osoittaa p\"{a}invastoin, ett\"{a} h\"{a}n matkusti yksin. --- H\"{a}n her\"{a}\"{a}, Mary Grant sanoi. Lapsi todellakin her\"{a}si. H\"{a}nen silm\"{a}ns\"{a} avautuivat v\"{a}hitellen, mutta sulkeutuivat heti taas p\"{a}iv\"{a}n h\"{a}ik\"{a}isemin\"{a}. Mutta lady Helena tarttui h\"{a}nen k\"{a}teens\"{a}; poika nousi ja katseli kummastuneena matkailijajoukkoa. Pelon tunne v\"{a}r\"{a}hdytti aluksi h\"{a}nen piirteit\"{a}\"{a}n, mutta lady Glenarvanin l\"{a}sn\"{a}olo rauhoitti h\"{a}nt\"{a}. --- Ymm\"{a}rr\"{a}tk\"{o} englannin kielt\"{a}, yst\"{a}v\"{a}ni? t\"{a}m\"{a} kysyi h\"{a}nelt\"{a}. --- Ymm\"{a}rr\"{a}n ja puhunkin, lapsi vastasi matkustajien kielell\"{a}, mutta hyvin huomattavasti murtaen. H\"{a}nen \"{a}\"{a}nt\"{a}misens\"{a} muistutti ranskalaisten tapaa, kun n\"{a}m\"{a} puhuvat englannin kielt\"{a}. --- Mik\"{a} sinun nimesi on? lady Helena kysyi. --- Toline, pikku australialainen vastasi. --- Ah, Toline! Paganel huudahti. --- Ellen erehdy, se sana merkitsee australian kielell\"{a} kaarnaa? Toline ny\"{o}kk\"{a}si my\"{o}nt\"{a}v\"{a}sti ja katsoi j\"{a}lleen naisiin. --- Mist\"{a} sin\"{a} tulet, yst\"{a}v\"{a}ni? lady Helena kysyi. --- Melbournesta, Sandhurstin junalla. --- Olitko sin\"{a} siin\"{a} junassa, joka suistui radalta Camdenin sillalla? Glenarvan kysyi. --- Olin, herra, Toline vastasi, --- mutta Raamatun Jumala suojeli minua. --- Matkustitko yksin? --- Yksin. Pastori Paxton oli uskonut minut Jeffries Smithin huostaan. Onnettomuudeksi se miesparka sai surmansa! --- Etk\"{o} tuntenut ket\"{a}\"{a}n muuta junassa? --- En ket\"{a}\"{a}n, herra, mutta Jumala pit\"{a}\"{a} huolta lapsista eik\"{a} hylk\"{a}\"{a} heit\"{a} milloinkaan! Toline lausui n\"{a}m\"{a} sanat lempe\"{a}ll\"{a} \"{a}\"{a}nell\"{a}, joka koski syd\"{a}meen. Kun h\"{a}n puhui Jumalasta, h\"{a}nen \"{a}\"{a}nens\"{a} k\"{a}vi vakavammaksi, h\"{a}nen silm\"{a}ns\"{a} s\"{a}dehtiv\"{a}t, ja kuulija tunsi t\"{a}ss\"{a} nuoressa sielussa asuvan suuren hartauden. T\"{a}m\"{a} uskonnollinen innostus n\"{a}in nuoressa i\"{a}ss\"{a} on helposti selitett\"{a}viss\"{a}. Lapsi oli englantilaisten l\"{a}hetyssaarnaajien kastamia ja metodistiuskonnon ankariin menoihin totuttamia nuoria alkuasukkaita. H\"{a}nen tyynet vastauksensa, siisti k\"{a}yt\"{o}ksens\"{a} ja musta pukunsa muistuttivat jo pikku pappia. Mutta minne h\"{a}n oli menossa n\"{a}in autioiden seutujen halki ja miksi h\"{a}n oli l\"{a}htenyt Camden Bridgen luota? Lady Helena kysyi sit\"{a} h\"{a}nelt\"{a}. --- Min\"{a} palaan heimoni luo Lachlaniin, h\"{a}n vastasi. --- Min\"{a} haluan n\"{a}hd\"{a} j\"{a}lleen omaiseni. --- Ovatko he australialaisia? John Mangles kysyi. --- Ovat, Lachlanin australialaisia, Toline vastasi. --- Ja onko sinulla is\"{a} ja \"{a}iti? Robert Grant kysyi. --- On, veljeni, Toline vastasi tarjoten k\"{a}tens\"{a} pikku Robertille, jota t\"{a}m\"{a} veljen nimi liikutti syv\"{a}sti. H\"{a}n syleili pient\"{a} australialaispoikaa eik\"{a} enemp\"{a}\"{a} tarvittu tekem\"{a}\"{a}n heist\"{a} yst\"{a}vyksi\"{a}. T\"{a}ll\"{a} v\"{a}lin olivat matkustajat nuoren villin vastauksia tarkkaavaisesti seuraten v\"{a}hitellen istuutuneet h\"{a}nen ymp\"{a}rilleen ja kuuntelivat h\"{a}nen puhettaan. Aurinko laski jo suurten puiden taakse. Ja kun paikka n\"{a}ytti sopivalta pys\"{a}hdykseen eik\"{a} ollut suurta v\"{a}li\"{a}, kuljettiinko viel\"{a} muutama kilometri ennen y\"{o}n tuloa, antoi Glenarvan leiriytymisk\"{a}skyn. Ayrton riisui juhdat, pani ne Mulradyn ja Wilsonin avulla liekaan ja j\"{a}tti ne sy\"{o}m\"{a}\"{a}n mielin m\"{a}\"{a}rin. Teltta pystytettiin. Olbinett valmisti aterian. Toline suostui nauttimaan siit\"{a} osansa, ensin hiukan estelty\"{a}\"{a}n, vaikka h\"{a}nen oli n\"{a}lk\"{a}. Istuttiin siis p\"{o}yt\"{a}\"{a}n, molemmat lapset vierekk\"{a}in. Robert valitsi parhaat palat uudelle kumppanilleen, ja Toline otti ne vastaan arastelevan ja vieh\"{a}tt\"{a}v\"{a}n kiitollisena. Juttelu ei sill\"{a} v\"{a}lin keskeytynyt. Jokaista kiinnosti t\"{a}m\"{a} lapsi, ja kaikki tekiv\"{a}t h\"{a}nelle kysymyksi\"{a}. Haluttiin kuulla h\"{a}nen el\"{a}m\"{a}ntarinansa. Se oli hyvin yksinkertainen ja samanlainen kuin yleens\"{a} niiden k\"{o}yhien alkuasukaslasten, jotka jonkin siirtokunnan naapuriheimot jo pienin\"{a} uskovat hyv\"{a}ntekev\"{a}isyysyhdistysten huostaan. Australialaisilla on lempe\"{a}t tavat. He eiv\"{a}t osoita maahansa tunkeutuvia kohtaan sit\"{a} hurjaa vihaa, joka on ominainen Uuden Seelannin asukkaille ja kenties muutamille Pohjois-Australian heimoille. Heit\"{a} n\"{a}kee k\"{a}yv\"{a}n suurissa kaupungeissa, Adelaidessa, Sydneyss\"{a} ja Melbournessa, viel\"{a}p\"{a} k\"{a}velev\"{a}n siell\"{a} hyvin alkuper\"{a}isiss\"{a} pukimissa. He k\"{a}yv\"{a}t siell\"{a} kauppaa teollisuutensa pikku esineill\"{a}, mets\"{a}stys- tai kalastusvehkeill\"{a} ja aseilla, ja monet heimop\"{a}\"{a}llik\"{o}t antavat mielell\"{a}\"{a}n, ep\"{a}ilem\"{a}tt\"{a} taloudellisista syist\"{a}, lastensa hy\"{o}ty\"{a} englantilaisen kasvatuksen eduista. N\"{a}in tekiv\"{a}t my\"{o}s Tolinen vanhemmat, jotka olivat todellisia villej\"{a} Lachlanista, laajalta Murrayn takaiselta seudulta. Viiteen vuoteen, jotka lapsi oli viett\"{a}nyt Melbournessa, h\"{a}n ei ollut n\"{a}hnyt ket\"{a}\"{a}n omaisistaan. Ja kuitenkin h\"{a}nen syd\"{a}mess\"{a}\"{a}n yh\"{a} eli katoamaton sukuvaisto, ja h\"{a}n oli l\"{a}htenyt vaivalloiselle er\"{a}maamatkalle etsim\"{a}\"{a}n ehk\"{a} jo hajautunutta heimoaan ja ep\"{a}ilem\"{a}tt\"{a} harvennutta kotiperhett\"{a}\"{a}n. --- Ja kun olet tavannut vanhempasi, palaatko taas Melbourneen, lapseni? lady Glenarvan kysyi h\"{a}nelt\"{a}. --- Palaan, rouva, Toline vastasi luoden h\"{a}neen harrasta hellyytt\"{a} osoittavan katseen. --- Ja miksi sin\"{a} kerran aiot? --- Tahdon pelastaa veljeni k\"{o}yhyydest\"{a} ja tiet\"{a}m\"{a}tt\"{o}myydest\"{a}! Tahdon opettaa heit\"{a}, saattaa heid\"{a}t tuntemaan Jumalan ja rakastamaan H\"{a}nt\"{a}! Aion pyrki\"{a} l\"{a}hetyssaarnaajaksi! N\"{a}m\"{a} sanat, jotka kahdeksanvuotias lapsi lausui innostuneena, olisivat voineet naurattaa kevytmielisi\"{a} ja pilkallisia ihmisi\"{a}, mutta n\"{a}m\"{a} vakavat skotlantilaiset ymm\"{a}rsiv\"{a}t ne ja antoivat niille arvoa; he ihmetteliv\"{a}t t\"{a}m\"{a}n nuoren, jo taisteluun valmiin opetuslapsen uskonvoimaa. Paganel oli liikuttunut syd\"{a}njuuriaan my\"{o}ten ja tunsi vilpit\"{o}nt\"{a} my\"{o}t\"{a}tuntoa pient\"{a} australialaista kohtaan. Mutta totta puhuaksemme t\"{a}m\"{a} eurooppalaispukuinen villi ei aluksi ollut h\"{a}nt\"{a} juuri miellytt\"{a}nyt. H\"{a}n ei tullut Australiaan n\"{a}hd\"{a}kseen australialaisia herrasvaatteissa! H\"{a}n tahtoi n\"{a}hd\"{a} heit\"{a} vain tatuoituina. T\"{a}m\"{a} ``s\"{a}\"{a}dyllinen'' puku h\"{a}iritsi h\"{a}nen mielikuviaan. Mutta siit\"{a} hetkest\"{a}, kun Toline oli puhunut niin palavasti, h\"{a}n muutti mielens\"{a} ja selitti olevansa h\"{a}nen ihailijansa. Keskustelun loppuosa oli muuten omiaan tekem\"{a}\"{a}n kunnon maantieteilij\"{a}st\"{a} pikku australialaisen parhaan yst\"{a}v\"{a}n. Er\"{a}\"{a}seen lady Helenan kysymykseen Toline vastasi n\"{a}et k\"{a}yv\"{a}ns\"{a} pastori Paxtonin johtamaa ``normaalikoulua'' Melbournessa. --- Ja mit\"{a} siin\"{a} koulussa sinulle opetetaan? lady Glenarvan kysyi. --- Uskontoa, laskentoa, maantiedett\"{a}... --- Ah, maantiedett\"{a}! Paganel huudahti. Toline oli osunut h\"{a}nen herkimp\"{a}\"{a}n kohtaansa. --- Niin, herra, Toline vastasi. --- Olen saanut ensimm\"{a}isen palkinnon maantieteess\"{a} ennen tammikuun lomaa. --- Onko sinulla palkinto maantieteess\"{a}, poikani? --- T\"{a}ss\"{a} se on, herra, Toline sanoi ottaen taskustaan esiin er\"{a}\"{a}n kirjan. Se oli hyvin sidottu taskukokoinen Raamattu. Ensimm\"{a}isen lehden taakse oli kirjoitettu: \textit{Melbournen normaalikoulu, I palkinto maantieteess\"{a}, Toline Lachlanista}. Paganel oli haltioissaan! Australialainen, joka tunsi maantiedett\"{a}, ihastutti h\"{a}nt\"{a} ja h\"{a}n suuteli Tolinea molemmille poskille yht\"{a} hartaasti kuin jos olisi itse ollut pastori Paxton palkintojen jakop\"{a}iv\"{a}n\"{a}; Paganelin olisi kuitenkin pit\"{a}nyt tiet\"{a}\"{a}, ett\"{a} t\"{a}llainen tapaus ei ole harvinainen australialaisissa kouluissa. Nuoret villit k\"{a}sitt\"{a}v\"{a}t varsin helposti maantieteellisi\"{a} seikkoja, mutta ovat sit\"{a} vastoin kovin vastahakoisia laskennossa. Toline ei ollut ollenkaan ymm\"{a}rt\"{a}nyt tiedemiehen \"{a}killist\"{a} hyv\"{a}ily\"{a}. Lady Helenan t\"{a}ytyi selitt\"{a}\"{a} h\"{a}nelle, ett\"{a} Paganel oli kuuluisa maantieteilij\"{a} ja tarpeen tullessa etev\"{a} opettaja. --- Maantieteen opettaja! Toline vastasi. --- No, herra, kyselk\"{a}\"{a} minulta! --- Kyselisink\"{o} sinulta, poikaseni? Paganel sanoi. --- Enh\"{a}n parempaa pyyd\"{a}! Aioin tehd\"{a} niin ilman sinun lupaasikin. Tahdonkin mielell\"{a}ni n\"{a}hd\"{a}, kuinka maantiedett\"{a} opetetaan Melbournen normaalikoulussa! --- Ent\"{a}p\"{a} jos muna opettaisikin kanaa, Paganel! MacNabbs lausui. --- Mit\"{a} hittoa! maantieteilij\"{a} huudahti. --- Opettaa Ranskan Maantieteellisen seuran sihteeri\"{a}! Sitten asettaen silm\"{a}lasit nen\"{a}lleen, oikaisten pitk\"{a}n vartalonsa ja ottaen juhlallisen \"{a}\"{a}nen kuten opettajan tulee h\"{a}n aloitti kyselyns\"{a}. --- Oppilas Toline, h\"{a}n sanoi, --- nouskaa seisomaan. Toline, joka oli seisaallaan, ei voinut nousta lis\"{a}\"{a}. H\"{a}n odotti siis vaatimattomassa asennossa maantieteilij\"{a}n kysymyksi\"{a}. --- Oppilas Toline, Paganel jatkoi, --- mitk\"{a} ovat viisi maanosaa? --- Oseania, Aasia, Afrikka, Amerikka ja Eurooppa, Toline vastasi. --- Oikein. Puhukaamme ensiksi Oseaniasta, koska olemme t\"{a}ll\"{a} hetkell\"{a} siell\"{a}. Mitk\"{a} ovat sen p\"{a}\"{a}osat? --- Polynesia, Malaijien maa, Mikronesia ja Megalesia. Sen p\"{a}\"{a}saaret ovat Australia, joka kuuluu englantilaisille, Uusi Seelanti, joka kuuluu englantilaisille, Tasmania, joka kuuluu englantilaisille, Chatham, Auckland, Macquarie, Kermadec, Makin, Maraki ynn\"{a} muut saaret, jotka kuuluvat englantilaisille. --- Hyv\"{a}, Paganel sanoi, --- ent\"{a} Uusi Kaledonia, Sandwich-, Mendana- ja Pomotu-saaret? --- Ne ovat Ison Britannian suojeluksessa. --- Mit\"{a}! Ison Britannian suojeluksessa! Paganel huudahti. --- Mutta minun tiet\"{a}\"{a}kseni on p\"{a}invastoin Ranska... --- Ranska! pikku poika matki h\"{a}mm\"{a}styneen n\"{a}k\"{o}isen\"{a}. --- Kas, kas! Paganel sanoi. --- Niink\"{o} teille opetetaan Melbournen normaalikoulussa? --- Niin, herra opettaja, eik\"{o} se ole oikein? --- On, on! Aivan oikein, Paganel vastasi. --- Koko Oseania kuuluu englantilaisille. Se on sovittu asia! Jatkakaamme. Majurin riemuksi Paganel oli puoleksi suuttuneen, puoleksi \"{a}llistyneen n\"{a}k\"{o}inen. Kysely\"{a} jatkettiin. --- Menk\"{a}\"{a}mme Aasiaan, maantieteilij\"{a} sanoi. --- Aasia, Toline vastasi, --- on suunnattoman suuri alue. P\"{a}\"{a}kaupunki: Kalkutta. Suurimmat kaupungit: Bombay, Madras, Kalikut, Aden, Malakka, Singapore, Pegu, Colombo; saaria ovat Lakkadiivit, Malediivit, Chagos sek\"{a} monet muut; kuuluvat englantilaisille. --- Hyv\"{a}, hyv\"{a}, oppilas Toline! Ent\"{a} Afrikka? --- Afrikka k\"{a}sitt\"{a}\"{a} kaksi p\"{a}\"{a}siirtokuntaa: etel\"{a}ss\"{a} on Kapmaa, p\"{a}\"{a}kaupunkina Kapkaupunki, ja l\"{a}nness\"{a} englantilaiset alusmaat, t\"{a}rkein kaupunki Sierra Leone. --- Oikein vastattu! lausui Paganel, joka alkoi oivaltaa t\"{a}t\"{a} englantilaista maantiedett\"{a}. --- Hyvin opetettu. Mit\"{a} Algeriaan, Marokkoon ja Egyptiin tulee ... niin ne on pyyhitty pois brittil\"{a}isist\"{a} kartoista. Min\"{a} haluaisin nyt mielell\"{a}ni puhua hiukan Amerikasta! --- Se jaetaan, Toline jatkoi, --- Pohjois- ja Etel\"{a}-Amerikkaan. Edellinen kuuluu englantilaisille Kanadan, Uuden Braunschweigin, Uuden Skotlannin ja kuvern\"{o}\"{o}ri Johnsonin hallinnon alaisten Yhdysvaltain kautta. --- Kuvern\"{o}\"{o}ri Johnson! Paganel huudahti. --- Hullun orjuusintoilijan murhaaman, suuren ja hyv\"{a}n Lincolnin seuraaja! Oikein! Sen paremmin ei voi! Ja mit\"{a} Etel\"{a}-Amerikkaan tulee, niin Guyanan, Malvinas-saarten, Shetlandin saariston, Georgian, Jamaikan, Trinidadin ja muiden kautta kuuluu sekin englantilaisille! Min\"{a} en v\"{a}it\"{a} sit\"{a} vastaan. Mutta, Toline, tahtoisinpa kernaasti kuulla sinun tai paremmin sanoen sinun opettajiesi ajatuksen Euroopasta. --- Euroopastako? kysyi Toline, joka ei ymm\"{a}rt\"{a}nyt mit\"{a}\"{a}n maantieteilij\"{a}n kiintymyksest\"{a}. --- Niin, Euroopasta! Kenelle kuuluu Eurooppa? --- Tottahan Eurooppa kuuluu englantilaisille, lapsi vastasi vakaumusta kuvastavalla \"{a}\"{a}nell\"{a}. --- Sit\"{a} min\"{a} v\"{a}h\"{a}n ep\"{a}ilen, Paganel lausui. --- Mutta mill\"{a} tavalla? Sen min\"{a} tahtoisin tiet\"{a}\"{a}. --- Englannin, Skotlannin, Irlannin, Maltan, Jerseyn ja Guernseyn saarten kautta, ja sitten viel\"{a} Joonian saarten, Hebridien, Shetlandin, Orkneyn... --- Hyv\"{a}, hyv\"{a}, Toline! Mutta siell\"{a} on toisia valtakuntia, joita et muista mainita, poikani. --- Mit\"{a} sitten, herra? tiedusti lapsi, joka ei antanut h\"{a}mment\"{a}\"{a} itse\"{a}\"{a}n. --- Espanja, Ven\"{a}j\"{a}, It\"{a}valta, Preussi, Ranska! --- Ne ovat maakuntia eik\"{a} valtakuntia, Toline sanoi. --- Hemmetti, Paganel huudahti tempaisten lasit silmilt\"{a}\"{a}n. --- Ep\"{a}ilem\"{a}tt\"{a}. Espanja, p\"{a}\"{a}kaupunki Gibraltar. --- Mainiota! Verratonta! Suurenmoista! Ent\"{a} Ranska, sill\"{a} min\"{a} olen ranskalainen eik\"{a} olisi haitaksi saada tiet\"{a}\"{a}, kenelle kuulun! --- Ranska, Toline vastasi tyynesti, --- on Englannin maakunta, p\"{a}\"{a}kaupunki Calais. --- Calais! Paganel huudahti. --- Mit\"{a}! Luuletko sin\"{a}, ett\"{a} Calais kuuluu viel\"{a} Englannille? --- Ep\"{a}ilem\"{a}tt\"{a}. --- Ja ett\"{a} se on Ranskan p\"{a}\"{a}kaupunki? --- Niin, herra, ja siell\"{a} asuu kuvern\"{o}\"{o}ri, lordi Napoleon... N\"{a}ist\"{a} viimeisist\"{a} sanoista Paganel purskahti nauruun. Toline ei tiennyt mit\"{a} ajatella. H\"{a}nelt\"{a} oli kysytty, ja h\"{a}n oli vastannut parhaansa mukaan. Mutta h\"{a}nen vastaustensa omituisuutta ei voitu lukea h\"{a}nen syykseen; h\"{a}nell\"{a} ei ollut siit\"{a} edes aavistusta. Oli kuinka hyv\"{a}ns\"{a}, h\"{a}n ei n\"{a}ytt\"{a}nyt h\"{a}mmentyv\"{a}n, vaan odotti vakavana t\"{a}m\"{a}n k\"{a}sitt\"{a}m\"{a}tt\"{o}m\"{a}n hilpeydenpuuskan p\"{a}\"{a}ttymist\"{a}. --- Siin\"{a} nyt n\"{a}ette, majuri sanoi nauraen Paganelille. --- Enk\"{o} ollut oikeassa v\"{a}itt\"{a}ess\"{a}ni, ett\"{a} oppilas Toline antaisi teille uutta oppia? --- Olitte, yst\"{a}v\"{a}ni, maantieteilij\"{a} vastasi. --- Vai niink\"{o} maantiedett\"{a} opetetaan Melbournessa! Normaalikoulun opettajat hoitavat asiansa hyvin! Eurooppa, Aasia, Afrikka, Amerikka, Oseania, koko maailma, kaikki on englantilaisten! Totisesti, t\"{a}m\"{a} nerokas kasvatus tekee ymm\"{a}rrett\"{a}v\"{a}ksi, ett\"{a} alkuasukkaat alistuvat. No, Toline poikaseni, ent\"{a}s kuu, onko sekin englantilaisten! --- Tulee olemaan, nuori villi vastasi vakavasti. Silloin Paganel ei voinut en\"{a}\"{a} pysy\"{a} paikallaan. H\"{a}nen t\"{a}ytyi nauraa kyllikseen eik\"{a} h\"{a}n saanut naurunpuuskaansa hillityksi ennen kuin viidenkymmenen metrin p\"{a}\"{a}ss\"{a} leirist\"{a}. T\"{a}ll\"{a} v\"{a}lin oli Glenarvan k\"{a}ynyt etsim\"{a}ss\"{a} pienen kirjan matkakirjastosta. Se oli Samuel Richardsonin Englannissa yleisesti k\"{a}ytett\"{a}v\"{a} \textit{Maantiedon oppikirja}, joka pysyi paremmin totuutta vastaavalla kannalla kuin opettajat Melbournessa. --- Kuulepas, lapseni, h\"{a}n sanoi Tolinelle, --- ota t\"{a}m\"{a} kirja ja pid\"{a} se. Sinulla on maantieteess\"{a} erin\"{a}isi\"{a} v\"{a}\"{a}ri\"{a} mielikuvia, jotka on hyv\"{a} oikaista. Min\"{a} annan sen sinulle muistoksi t\"{a}st\"{a} kohtaamisestamme. Toline otti kirjan mit\"{a}\"{a}n vastaamatta; h\"{a}n katseli sit\"{a} tarkkaavasti pudistellen p\"{a}\"{a}t\"{a}\"{a}n ep\"{a}ilev\"{a}n n\"{a}k\"{o}isen\"{a} eik\"{a} osannut p\"{a}\"{a}tt\"{a}\"{a}, pannako sen taskuunsa. T\"{a}ll\"{o}in oli jo tullut pime\"{a}. Kello oli kymmenen illalla. T\"{a}ytyi ajatella nukkumaanmenoa, jotta p\"{a}iv\"{a}nkoitteessa voitaisiin nousta liikkeelle. Robert tarjosi yst\"{a}v\"{a}lleen Tolinelle puolet makuupaikastaan. Pikku australialainen suostui siihen. Lady Helena ja Mary Grant nousivat vankkureihin, matkamiehet meniv\"{a}t telttaan Paganelin naurunpurskahdusten sekoittuessa villien harakkain hiljaiseen r\"{a}k\"{a}tykseen. Mutta kun aurinko seuraavana aamuna kello kuuden aikaan her\"{a}tti nukkujat, he etsiv\"{a}t turhaan australialaista lasta. Toline oli kadonnut. Tahtoiko h\"{a}n viivyttelyitt\"{a} ehti\"{a} Lachlanin seuduille, vai oliko Paganelin nauru h\"{a}nt\"{a} loukannut? Sit\"{a} ei tiedetty. Mutta kun lady Helena her\"{a}si, h\"{a}n huomasi povellaan viuhkan koruttomia mimoosankukkia ja Paganel taas taskussaan Samuel Richardsonin \textit{Maantiedon}. \gutchapter{MOUNT ALEXANDERIN KAIVOKSET.} Vuonna 1844 sir Roderick Impey Murchison, Lontoon Kuninkaallisen maantieteellisen seuran nykyinen esimies, havaitsi vertailuja maan muodostumisesta tehdess\"{a}\"{a}n huomattavaa yht\"{a}l\"{a}isyytt\"{a} Ural-vuorten ja sen vuoriharjanteen v\"{a}lill\"{a}, joka l\"{a}helt\"{a} Etel\"{a}-Australian rannikkoa kulkee pohjoisesta etel\"{a}\"{a}n. Kun Ural-vuoret ovat kultapitoisia, oppinut geologi arveli, ett\"{a} t\"{a}t\"{a} kallisarvoista metallia pit\"{a}isi l\"{o}yty\"{a} my\"{o}s australialaisessa vuorijonossa. Eik\"{a} h\"{a}n siin\"{a} erehtynytk\"{a}\"{a}n. Kaksi vuotta my\"{o}hemmin l\"{a}hetettiin h\"{a}nelle todella muutamia kultan\"{a}ytteit\"{a} Uudesta Etel\"{a}-Walesista, ja h\"{a}n p\"{a}\"{a}tti toimittaa suuren joukon ty\"{o}miehi\"{a} Cornwallista siirtolaisiksi Uuden Hollannin kultamaille. Ensimm\"{a}iset kultan\"{a}ytteet oli Etel\"{a}-Australiasta l\"{o}yt\"{a}nyt herra Francis Dutton. Sitten l\"{o}ysiv\"{a}t herrat Forbes ja Smith Uuden Walesin ensimm\"{a}iset kultakent\"{a}t. Heti tiedon t\"{a}st\"{a} levitty\"{a} kullankaivajia saapui maapallon kaikilta kulmilta, englantilaisia, amerikkalaisia, italialaisia, ranskalaisia, saksalaisia, kiinalaisia. Mutta vasta 3. p\"{a}iv\"{a}n\"{a} huhtikuuta 1851 l\"{o}ysi herra Hargraves erityisen rikkaita kultakerroksia ja tarjoutui ilmoittamaan niiden paikan Sydneyn siirtokunnan kuvern\"{o}\"{o}rille, sir Ch. Fitz-Roylle, vaatimattomasta viidensadan punnan hinnasta. H\"{a}nen tarjoustaan ei hyv\"{a}ksytty, mutta huhu h\"{a}nen l\"{o}yd\"{o}st\"{a}\"{a}n oli levinnyt. Kullanetsij\"{o}it\"{a} l\"{a}hti samoamaan Summerhilli\"{a} ja Leni's Pondia kohti. Perustettiin Ophirin kaupunki, joka kultasaaliinsa runsauden vuoksi osoitti pian ansaitsevansa raamatullisen nimens\"{a}. Siihen saakka ei ollut puhettakaan Victorian maakunnasta, joka kuitenkin sitten vei muista voiton kultaesiintymien runsaudessa. Muutamia kuukausia my\"{o}hemmin, elokuussa 1851, kaivettiin n\"{a}et t\"{a}ss\"{a} maakunnassa esille ensimm\"{a}iset kultajyv\"{a}set, ja pian oli nelj\"{a}ll\"{a} alueella k\"{a}ynniss\"{a} laajat etsinn\"{o}t. N\"{a}m\"{a} nelj\"{a} olivat Ballarat, Owens, Bendigo ja Mount Alexander, kaikki hyvin rikkaita; mutta Owens-joella vedenpaljous vaikeutti ty\"{o}t\"{a}; Ballaratissa tuotti kultaesiintymien ep\"{a}tasaisuus kaivajille usein pettymyksi\"{a}; Bendigossa ei maaper\"{a} vastannut kaivajien vaatimuksia. Mount Alexanderin s\"{a}\"{a}nn\"{o}llisess\"{a} maaper\"{a}ss\"{a} olivat mukana kaikki menestyksen edellytykset, ja t\"{a}m\"{a} kallisarvoinen metalli, jonka arvo oli jopa 1441 frangia naulalta, saavutti korkeimman kurssin maailman kaikilla markkinoilla. Juuri t\"{a}lle tuhoisia pettymyksi\"{a} ja odottamattomia onnensattumia niin usein aiheuttaneelle paikalle johdatti 37. leveysasteen reitti kapteeni Harry Grantin etsij\"{a}t. Kuljettuaan koko 31. p\"{a}iv\"{a}n joulukuuta hyvin ep\"{a}tasaista maastoa, joka v\"{a}sytti hevosia ja juhtia, he n\"{a}kiv\"{a}t Mount Alexanderin py\"{o}ristyneet kukkulat. Leiriydyttiin er\"{a}\"{a}seen t\"{a}m\"{a}n lyhyen vuorijonon kapeaan solaan, ja el\"{a}inten annettiin lieka jalassa etsi\"{a} ruokaansa maassa lojuvien kvartsilohkareiden v\"{a}list\"{a}. T\"{a}m\"{a} ei ollut viel\"{a} kaivosaluetta. Seuraavana p\"{a}iv\"{a}n\"{a}, vuoden 1865 ensimm\"{a}isen\"{a}, uursivat vankkurien py\"{o}r\"{a}t j\"{a}lkens\"{a} t\"{a}m\"{a}n mineraalirikkaan seudun teihin. Jacques Paganel ja h\"{a}nen toverinsa olivat ihastuneita n\"{a}hdess\"{a}\"{a}n ohimennenkin t\"{a}m\"{a}n kuuluisan vuoren, jota australiaksi sanotaan Gebooriksi. Sinne teki rynn\"{a}k\"{o}n koko seikkailijoiden lauma, varkaita ja kunniallista v\"{a}ke\"{a}, hirtt\"{a}ji\"{a} ja hirtett\"{a}vi\"{a}. Ensimm\"{a}isen huhun levitess\"{a} t\"{a}st\"{a} suuresta l\"{o}yd\"{o}st\"{a} kultavuonna 1851 asukkaat, squatterit ja merimiehet j\"{a}ttiv\"{a}t kaupunkinsa, peltonsa ja laivansa. Kultakuume muuttui kulkutaudiksi, tarttuvaksi kuin rutto, ja monet kuolivat siihen luullessaan jo l\"{o}yt\"{a}neens\"{a} onnen. Luonto oli tuhlaavaisesti kylv\"{a}nyt miljoonia, sanottiin, 25. asteen alueelle t\"{a}ss\"{a} ihmeellisess\"{a} Australiassa. Nyt oli elonkorjuunaika ja n\"{a}m\"{a} uudet niittomiehet riensiv\"{a}t saamaan osansa. ``Diggerin'' kullankaivajan, ammatti oli arvokkaampi kuin kaikki muut, ja vaikka monet menehtyiv\"{a}t, oli kuitenkin muutamia, jotka tulivat rikkaiksi yhdell\"{a} ainoalla kuokaniskulla. Perikadosta ei puhuttu, rikastumisesta levenneltiin. N\"{a}iden onnenpotkujen kaiku kuului viidess\"{a} maanosassa. Pian tulvi kaikens\"{a}\"{a}tyisi\"{a} onnenonkijoita Australiaan, ja vuoden 1852 nelj\"{a}n\"{a} viimeisen\"{a} kuukautena saapui yksin Melbourneen viidenkymmenennelj\"{a}n tuhannen suuruinen siirtolaisarmeija, mutta ilman p\"{a}\"{a}llikk\"{o}\"{a} ja kuria, viel\"{a} saavuttamattoman voiton j\"{a}lkeisen p\"{a}iv\"{a}n armeija, sanalla sanoen nelj\"{a}kymment\"{a}nelj\"{a} tuhatta pahimmanlaatuista rosvoilevaa pahantekij\"{a}\"{a}. T\"{a}m\"{a}n hullun kiihkon ensimm\"{a}isin\"{a} vuosina vallitsi sanoinkuvaamaton sekasorto. Tavallisella tarmollaan p\"{a}\"{a}siv\"{a}t englantilaiset kuitenkin tilanteen herroiksi. Poliisit ja kotimaiset santarmit luopuivat varkaiden puolelta ja muuttuivat kunnon ihmisiksi. Tapahtui t\"{a}ydellinen muutos. Niinp\"{a} Glenarvan ei saanutkaan n\"{a}hd\"{a} mit\"{a}\"{a}n vuoden 1852 v\"{a}kivaltaisista n\"{a}ytelmist\"{a}. Kolmetoista vuotta oli kulunut siit\"{a} ajasta, ja nyt kultaa etsittiin n\"{a}ill\"{a} seuduilla j\"{a}rjestelm\"{a}llisesti, ankarien s\"{a}\"{a}nt\"{o}jen mukaan. Muuten alkoivat kaivokset jo ehty\"{a}. Oli kaivettu jo pohjaan saakka. Kuinkapa ei olisikaan tyhjennetty n\"{a}it\"{a} luonnon aarteita, kun kullankaivajat olivat Victorian maakunnasta vuosina 1852-1858 kaivaneet 63.107.478 puntaa? Siirtolaisten lukum\"{a}\"{a}r\"{a} onkin tuntuvasti v\"{a}hentynyt, ja he ovat siirtyneet viel\"{a} koskemattomille seuduille. Niinp\"{a} Uuden Seelannin Otagossa ja Marlboroughissa \"{a}skett\"{a}in l\"{o}ydetyt kultakent\"{a}t, ovat nyky\"{a}\"{a}n tuhansien kaksijalkaisten siivett\"{o}mien muurahaisten kaivettavina.[8] Kello yhdentoista tienoilla saavuttiin kaivosalueen keskustaan. Siell\"{a} kohosi todellinen kaupunki tehtaineen, pankkeineen, kirkkoineen, kasarmeineen, vuokrataloineen ja sanomalehden toimituksineen. Hotelleja, maataloja, huviloita ei my\"{o}sk\"{a}\"{a}n puuttunut. Olipa teatterikin, yleis\"{o}n suosima, vaikka paikka maksoi kymmenen sillingi\"{a}. Esitettiin suurella menestyksell\"{a} paikallista kappaletta \textit{Francis Obadiah eli onnellinen kullankaivaja}. Kun n\"{a}ytelm\"{a}n sankari ep\"{a}ioivon vallassa iskee kuokkansa maahan viimeist\"{a} kertaa, se lohkaisee irti uskomattoman suuren kultalohkareen. Glenarvan oli utelias n\"{a}kem\"{a}\"{a}n Mount Alexanderin laajat kultakaivokset ja antoi vankkurien l\"{a}hte\"{a} edell\"{a} Ayrtonin ja Mulradyn johtamina. H\"{a}n yhtyisi seuraan muutamaa tuntia my\"{o}hemmin. Paganel oli ihastunut t\"{a}st\"{a} p\"{a}\"{a}t\"{o}ksest\"{a} ja asettui tapansa mukaan pikku ryhm\"{a}n oppaaksi. H\"{a}nen neuvonsa mukaan mentiin ensin pankkiin. Kadut olivat leve\"{a}t, kivetyt ja huolellisesti astellut. Sen tapaiset toimistot kuin \textit{Golden Company Ltd, Digger's General Office, Nugget's Union} vetiv\"{a}t j\"{a}ttil\"{a}isilmoituksilla katseet puoleensa. Ty\"{o}voiman ja p\"{a}\"{a}oman yhtym\"{a} oli asettunut yksin\"{a}isen kullankaivajan tilalle. Kaikkialta kuului hiekkaa huuhtovien tai kallisarvoisten kvartsia murentavien koneiden meteli\"{a}. Asuntojen takana alkoivat kultakent\"{a}t, laajat kaivausalueet. Siell\"{a} kuokkivat yhti\"{o}iden runsaasti palkkaamat kullankaivajat. Silmin ei olisi voinut laskea maahan puhkaistujen reikien lukua. Rautalapiot v\"{a}lk\"{a}hteliv\"{a}t auringonpaisteessa yhten\"{a} s\"{a}ihkyn\"{a}n\"{a}. Kaivajien joukossa oli kaikkia kansallisuuksia. He eiv\"{a}t kinastelleet, vaan tekiv\"{a}t ty\"{o}t\"{a}\"{a}n \"{a}\"{a}nett\"{o}m\"{a}sti, kuten ainakin palkatut miehet. --- Ei sovi sent\"{a}\"{a}n luulla, Paganel sanoi, --- ettei Australiassa en\"{a}\"{a} olisi lainkaan niit\"{a} kuumeisia etsij\"{o}it\"{a}, jotka koettavat onneaan kullankaivamisen arpapeliss\"{a}. Tied\"{a}n kyll\"{a}, ett\"{a} useimmat myyv\"{a}t ty\"{o}voimansa yhti\"{o}ille pakostakin, kun kaikki kultapitoiset alueet ovat hallituksen myymi\"{a} tai vuokraamia. Mutta sill\"{a}, jolla ei ole mit\"{a}\"{a}n, joka ei voi vuokrata eik\"{a} ostaa, on j\"{a}ljell\"{a} viel\"{a} yksi keino rikastua. --- Mik\"{a}? lady Helena kysyi. --- `Jumpingin' mahdollisuus, Paganel vastasi. --- Sen avulla me, joilla ei ole mit\"{a}\"{a}n oikeutta n\"{a}ihin kaivoksiin, voimme kuitenkin --- jos k\"{a}y oikein hyv\"{a} onni, tietenkin --- ansaita omaisuuden. --- Mutta kuinka? majuri kysyi. --- Jumpingin avulla, kuten minulla oli kunnia teille sanoa. --- Mit\"{a} se jumping on? majuri kysyi j\"{a}lleen. --- Se on kullankaivajien v\"{a}linen sopimus, joka usein aiheuttaa tappelua ja ep\"{a}j\"{a}rjestyst\"{a}, mutta jota viranomaiset eiv\"{a}t ole voineet poistaa. --- Selitt\"{a}k\"{a}\"{a} tarkemmin, Paganel, sanoi taas majuri, --- teh\"{a}n saatte veden herahtamaan kielellemme. --- No niin, on sovittu, ett\"{a} kaikki se kaivosalueen keskell\"{a} oleva maa, joka on vuorokaudeksi, suuria juhlia lukuunottamatta, j\"{a}tetty silleen, niin ettei sit\"{a} kaiveta, joutuu yhteisomaisuudeksi. Kuka tahansa saa sen vallata, kaivaa sit\"{a} ja rikastua, jos onni on h\"{a}nelle suotuisa. Niinp\"{a}, Robert, poikaseni, koeta keksi\"{a} jokin hyl\"{a}tty kuoppa, ja se on sinun! --- Herra Paganel, Mary Grant sanoi, --- \"{a}lk\"{a}\"{a} panko veljeni p\"{a}\"{a}h\"{a}n sellaista! --- Min\"{a} lasken leikki\"{a}, neiti kulta, Paganel vastasi, --- ja Robert tiet\"{a}\"{a} sen hyvin. H\"{a}nk\"{o} kullankaivajaksi? Ei ikin\"{a}! Kaivaa maata, k\"{a}\"{a}nt\"{a}\"{a} sit\"{a} taas, muokata ja sitten kylv\"{a}\"{a} siihen ja vaatia silt\"{a} satoa vaivoistaan, se kyll\"{a} sopii! Mutta sen tonkiminen sokean myyr\"{a}n tavalla, jotta kouraan ehk\"{a} sattuisi siru kultaa, se on surkea ammatti, johon antautuakseen t\"{a}ytyy olla Jumalan ja ihmisten hylk\"{a}\"{a}m\"{a}! K\"{a}yty\"{a}\"{a}n p\"{a}\"{a}kaivoksen luona ja asteltuaan pitkin tannerta, joka oli suureksi osaksi kallioiden s\"{a}rkemisest\"{a} syntyneit\"{a} kvartsinsiruja, liuskeita ja soraa, saapuivat retkeilij\"{a}t pankkiin. Se oli laaja rakennus, katolla kansallislippu. Lordi Glenarvanin vastaanotti ylitarkastaja, joka esitteli h\"{a}nelle johtamaansa laitosta. Sinne sijoittavat yhti\"{o}t kuittia vastaan maasta kaivamansa kullan. Siit\"{a} oli jo kauan aikaa, kun siirtokunnan kauppiaat olivat nylkeneet alkuaikojen kullankaivajaa. He maksoivat h\"{a}nelle kaivospaikalla viisikymment\"{a}kolme sillingi\"{a} unssilta ja sitten Melbournessa myiv\"{a}t kuudestakymmenest\"{a}viidest\"{a}! Tosin kauppiaalla oli kuljetuksen riski; kun valtatiell\"{a} vilisi kulkureita, ei kulta aina saapunut perille. Vieraille n\"{a}ytettiin mielenkiintoisia kultan\"{a}ytteit\"{a}, ja ylitarkastaja teki selkoa, eri menettelytavoista t\"{a}m\"{a}n metallin kaivamiseksi. Sit\"{a} esiintyy yleens\"{a} kahdessa muodossa, vy\"{o}rykultana ja rapautuneena, joko malmina lietteen seassa tai kvartsisuonessa. Sen irrottamiseksi k\"{a}ytet\"{a}\"{a}nkin maan laadun mukaan pinta- tai syvyyskaivamista. Vy\"{o}rykulta piilee jokien, laaksojen ja vesiuurrosten pohjalla suuruutensa mukaan sijoittuneena, ensin rakeet, sitten levyt ja vihdoin hileet. Jos se sit\"{a} vastoin on rapautumakultaa, jonka suonen ilman vaikutus on hajoittanut, se on keskittynyt yhteen paikkaan, kasoiksi, joita kullankaivajat sanovat ``taskuiksi''. Jotkut n\"{a}ist\"{a} taskuista sis\"{a}lt\"{a}v\"{a}t suuren omaisuuden. Mount Alexanderin alueella tavataan kultaa varsinkin savimaakerroksissa ja liuskemaisten kallioiden lomissa. Siell\"{a} ovat kultarakeiden pes\"{a}t, siell\"{a} on onnekkaan kaivajan k\"{a}teen usein sattunut kulta-arpajaisten p\"{a}\"{a}voitto. Kun vierailijat olivat tarkastelleet eri kultan\"{a}ytteit\"{a}, he k\"{a}viv\"{a}t pankin mineralogisessa museossa. Siell\"{a} he n\"{a}kiv\"{a}t kaikkia niit\"{a} tuotteita, joista Australian maaper\"{a} on muodostunut, luokiteltuina ja nimilipuilla varustettuina. Kulta ei ole sen ainoa rikkaus; sit\"{a} voi syyst\"{a}kin pit\"{a}\"{a} suunnattomana arkkuna, jossa luonto s\"{a}ilytt\"{a}\"{a} kalleuksiaan. Lasilevyjen alla kiilsi valkoinen topaasi, joka kilpailee Brasilian topaasien kanssa, tummanvihre\"{a} granaatti, epidootti, er\"{a}\"{a}nlainen kauniin vihre\"{a} silikaatti, vaaleanpunainen rubiini, jota edustivat helakanpunaiset spinellat ja er\"{a}s tavattoman kaunis ruusunpunainen muunnos, vaalean- ja tummansinisi\"{a} safiireja, kuten esimerkiksi korundi, ja yht\"{a} haluttuja kuin Malabarin ja Tiibetin safiirit, punahohtoisia timantteja ja vihdoin Turonin rannoilta l\"{o}ydetty pieni timanttikristalli. Mit\"{a}\"{a}n ei puuttunut t\"{a}st\"{a} jalokivien loistavasta kokoelmasta eik\"{a} tarvinnut menn\"{a} kauas etsim\"{a}\"{a}n tarpeellista kultaa, johon ne voisi upottaa. Ellei tahtonut n\"{a}hd\"{a} niit\"{a} koruiksi valmistettuina, ei saattanut pyyt\"{a}\"{a} enemp\"{a}\"{a}. Glenarvan lausui j\"{a}\"{a}hyv\"{a}iset pankin tarkastajalle kiitt\"{a}en h\"{a}nt\"{a} kohteliaisuudesta, jota vierailijat olivat k\"{a}ytt\"{a}neet runsaasti hyv\"{a}kseen. Sitten palattiin kultakentille. Niin v\"{a}h\"{a}n kuin Paganel v\"{a}littikin t\"{a}m\"{a}n maailman mammonasta, h\"{a}n ei astunut askeltakaan tarkastamatta katseellaan t\"{a}t\"{a} maaper\"{a}\"{a}. Halu siihen oli ylivoimainen, eik\"{a} h\"{a}nen kumppaniensa leikinlasku voinut sille mit\"{a}\"{a}n. Yht\"{a} mittaa h\"{a}n kumartui, poimi maasta jonkin kivensirun, malminkappaleen tai kvartsihileen, tarkasteli niit\"{a} yksityiskohtaisesti ja heitti ne pian taas halveksien menem\"{a}\"{a}n. T\"{a}t\"{a} kesti koko matkan. --- Kuulkaas, Paganel, majuri lausui, --- oletteko hukannut jotakin? --- Aivan varmasti, Paganel vastasi, --- t\"{a}ss\"{a} kullan ja kalliiden kivien maassa on hukannut sen mit\"{a} ei ole l\"{o}yt\"{a}nyt. En tied\"{a}, miksi mieleni tekisi saada mukaani muutaman unssin painoinen rae tai vaikkapa isompikin. --- Ja mit\"{a} te sill\"{a} tekisitte, kelpo yst\"{a}v\"{a}ni? Glenarvan kysyi. --- Oh, se on kyll\"{a} selvill\"{a}, Paganel vastasi. --- Lahjoittaisin sen maalleni. Sijoittaisin sen Ranskan pankkiin... --- Joka ottaisi sen vastaan? --- Ep\"{a}ilem\"{a}tt\"{a}, rautatieosakkeiden muodossa. Paganelia onniteltiin tavasta, kuinka h\"{a}n aikoi tarjota kullan ``maallensa'', ja lady Helena toivoi h\"{a}nen l\"{o}yt\"{a}v\"{a}n maailman suurimman kimpaleen. Leikki\"{a} laskien retkeilij\"{a}t tarkastelivat n\"{a}in suurinta osaa kaivosaluetta. Kaikkialla tehtiin ty\"{o}t\"{a} s\"{a}\"{a}nn\"{o}llisesti, koneellisesti, mutta ilman innostusta. Kahden tunnin k\"{a}velyn j\"{a}lkeen Paganel huomasi hyvin siistin ravintolan, jossa h\"{a}n ehdotti istuttavaksi, kunnes olisi aika palata vankkurien luokse. Lady Helena suostui siihen, ja kun ravintolasta ei ole mihink\"{a}\"{a}n ilman virvokkeita, Paganel k\"{a}ski ravintoloitsijaa tarjoamaan jotakin paikkakunnan juomaa. Itsekullekin tuotiin niin sanottu ``nobler''. Tuollainen nobler on yksinkertaisesti grogi, mutta nurinp\"{a}inen grogi. Sen sijaan, ett\"{a} pantaisiin pieni lasillinen viinaa isoon lasiin vett\"{a}, pannaan pieni lasillinen vett\"{a} isoon lasiin viinaa, sokeroidaan ja juodaan. Se oli hieman liiaksi australialaista, ja ravintoloitsijan suureksi kummaksi muutettiin nobler ison vesikarahvin avulla brittil\"{a}iseksi grogiksi. Sitten puhuttiin kultakaivoksista ja kaivajista. T\"{a}ss\"{a}h\"{a}n oli sen paikka, jos miss\"{a}\"{a}n. Paganel oli hyvin tyytyv\"{a}inen n\"{a}kem\"{a}\"{a}ns\"{a}, mutta my\"{o}nsi kuitenkin, ett\"{a} olojen oli t\"{a}ytynyt ennen, Mount Alexanderin kaivauksen ensimm\"{a}isin\"{a} vuosina, olla viel\"{a} mielenkiintoisempia. --- Maa, h\"{a}n sanoi, --- oli silloin t\"{a}ynn\"{a} reiki\"{a} ja tulvillaan ty\"{o}myyri\"{a}, mutta mink\"{a}laisia myyri\"{a}! Kaikilla siirtolaisilla oli myyr\"{a}n into, mutta ei sen ymm\"{a}rryst\"{a}! Kultaa tuhlattiin mielett\"{o}m\"{a}sti. Se juotiin ja pelattiin, ja t\"{a}m\"{a} ravintola, jossa olemme, oli helvetti, kuten silloin sanottiin. Rahapelej\"{a} seurasivat puukoniskut. Poliisi ei mahtanut mit\"{a}\"{a}n, ja monta kertaa oli siirtokunnan kuvern\"{o}\"{o}rin pakko marssittaa sotav\"{a}ke\"{a} rauhoittamaan metel\"{o}ivi\"{a} kullankaivajia. Mutta lopulta h\"{a}n sai heid\"{a}t j\"{a}rkiins\"{a}, m\"{a}\"{a}r\"{a}si kaivamisoikeudesta veron, sai sen kannetuksi, vaikkakaan ei vaivattomasti, ja ylimalkaan olivat rikkomukset t\"{a}\"{a}ll\"{a} v\"{a}h\"{a}isempi\"{a} kuin Kaliforniassa. --- Saako siis, lady Helena kysyi, --- kuka tahansa harjoittaa kullankaivajan ammattia? --- Saa, rouva. Sit\"{a} varten ei tarvitse suorittaa tutkintoa. Hyv\"{a}t k\"{a}sivarret riitt\"{a}v\"{a}t. Kurjuuden ajamina seikkailijat saapuivat kulta-alueille enimm\"{a}kseen rahattomina, rikkailla kuokka, k\"{o}yhill\"{a} vain puukko, mutta kaikilla t\"{a}h\"{a}n ty\"{o}h\"{o}n into, jota he eiv\"{a}t olisi osoittaneet miss\"{a}\"{a}n oikeassa ammatissa. Oli omituista n\"{a}hd\"{a} n\"{a}it\"{a} kultamaita. Maa oli t\"{a}ynn\"{a} telttoja, \"{o}ljvkankaita ja mullasta, laudoista tai oksista kyh\"{a}ttyj\"{a} h\"{o}kkeleit\"{a} ja vajoja. Niiden keskell\"{a} kohosi Englannin lipulla varustettu hallituksen katos, sen asiamiesten sinisest\"{a} patjakankaasta tehtyj\"{a} telttoja, rahanvaihtajien, kultakauppiaiden ja muiden, t\"{a}ss\"{a} rikkauden ja k\"{o}yhyyden heilurissa kalastelevien liikemiesten kojuja. N\"{a}m\"{a} rikastuivat varmasti. Ja n\"{a}kemisen arvoisia olivat vedess\"{a} ja liejussa el\"{a}v\"{a}t pitk\"{a}partaiset ja punapaitaiset diggerit. Ilma oli t\"{a}ynn\"{a} kuokkien yht\"{a}mittaista kalahtelua ja maassa m\"{a}d\"{a}ntyvien el\"{a}inraatojen l\"{o}yhk\"{a}\"{a}. Tukahduttava p\"{o}ly peitti nuo onnettomat, jotka kohottivat kuolleisuuden tavattoman suureksi, ja ep\"{a}ilem\"{a}tt\"{a} ep\"{a}terveellisemm\"{a}ss\"{a} maassa olisi lavantauti tuhonnut melkein koko v\"{a}est\"{o}n. Ja jospa sitten kaikki n\"{a}m\"{a} seikkailijat olisivat onnistuneet! Mutta paljon k\"{a}rsimyst\"{a} j\"{a}i korvauksetta, ja l\"{a}hemmin tarkastaessa saataisiin n\"{a}hd\"{a}, ett\"{a} yht\"{a} rikastunutta kullankaivajaa kohti sata, kaksisataa, ehk\"{a}p\"{a} tuhat on kuollut k\"{o}yh\"{a}n\"{a} ja ep\"{a}toivoisena. --- Voisitteko selitt\"{a}\"{a} meille, Paganel, Glenarvan kysyi, --- miten kulta kaivettiin yl\"{o}s? --- Ei mik\"{a}\"{a}n ollut yksinkertaisempaa, Paganel vastasi. --- Ensimm\"{a}iset kullanetsij\"{a}t huuhtoivat sit\"{a}, kuten muutamilla Sevennien seuduilla Ranskassa viel\"{a}kin tehd\"{a}\"{a}n. Nyky\"{a}\"{a}n yhti\"{o}t menettelev\"{a}t toisin; he kaivautuvat siihen l\"{a}hteeseen asti, josta hileet, levyt ja rakeet tulevat. Mutta huuhtojat tyytyiv\"{a}t vain pesem\"{a}\"{a}n kultapitoisen hiekan, siin\"{a} kaikki. He kaivoivat maata, paljastivat ne kerrostumat, jotka heist\"{a} n\"{a}yttiv\"{a}t kultapitoisilta, ja valelivat niit\"{a} vedell\"{a} erottaakseen siit\"{a} kallisarvoisen malmin. T\"{a}m\"{a} huuhtelu tapahtui amerikkalaista alkuper\"{a}\"{a} olevan kehdoksi nimitetyn laitteen avulla. Se oli viiden tai kuuden jalan mittainen laatikko, er\"{a}\"{a}nlaatuinen avoin, kahteen osastoon jaettu ruuhi. Ensimm\"{a}isess\"{a} osassa oli harva seula ja sen alapuolella toisia tiuhempia seuloja; toinen osa oli alap\"{a}\"{a}st\"{a}\"{a}n suippeneva. Hiekka kasattiin toisessa p\"{a}\"{a}ss\"{a} olevaan seulaan, kaadettiin vett\"{a} p\"{a}\"{a}lle, ja laitetta liikuteltiin tai oikeammin keinuteltiin k\"{a}sin. Kivet j\"{a}iv\"{a}t ensimm\"{a}iseen seulaan, malmi ja hieno hiekka toisiin aina karheutensa mukaan, ja lionnut muta valui veden mukana pois toisesta p\"{a}\"{a}st\"{a}. Se oli tavallisimmin k\"{a}ytetty laite. --- Mutta sellainen piti sent\"{a}\"{a}n olla, John Mangles huomautti. --- Se ostettiin rikastuneilta tai rappiolle joutuneilta kaivajilta, kuinka sattui, Paganel vastasi, --- tai tultiin toimeen ilman sit\"{a}. --- Kuinka se k\"{a}vi laatuun? Mary Grant kysyi. --- Oli vain levy, rakas Mary, tavallinen peltilevy; heitettiin ilmaan maata niin kuin viljaa; viljajyvien sijasta saatiin joskus kultajyvi\"{a}. Ensimm\"{a}isen\"{a} vuonna ansaitsi moni kullankaivaja omaisuuden ilman muita apuv\"{a}lineit\"{a}. N\"{a}hk\"{a}\"{a}s, yst\"{a}v\"{a}ni, se oli hyv\"{a}\"{a} aikaa, vaikka saappaat maksoivat sataviisikymment\"{a} frangia pari ja lasillisesta limonadia piti maksaa kaksitoista frangia! Ensiksi tulleilla on aina paras onni. Kultaa oli kaikkialla runsaasti maan pinnalla; purot virtasivat metallipohjalla; sit\"{a} tavattiin Melbournen kaduiltakin; katuja kovetettiin kultasoralla. Niinp\"{a} sen kullan arvo, joka tammikuun seitsem\"{a}ss\"{a} viikossa alkupuolella vuotta 1852 hallituksen suojeluksen alaisena tuotiin Mount Alexanderista Melbourneen, olikin kahdeksan miljoonaa kaksisataa kolmekymment\"{a}kahdeksan tuhatta seitsem\"{a}nsataaviisikymment\"{a} frangia. Se tekee keskim\"{a}\"{a}rin satakuusikymment\"{a}nelj\"{a} tuhatta frangia p\"{a}iv\"{a}\"{a} kohti. --- Melkein yht\"{a} paljon kuin Ven\"{a}j\"{a}n keisarin pankkitilill\"{a}, Glenarvan sanoi. --- Mies-parka! majuri lausui. --- Tunnetaanko erikoisia onnenpotkuja? lady Helena kysyi. --- Muutamia kyll\"{a}, rouva. --- Tied\"{a}ttek\"{o} nekin? Glenarvan kysyi. --- Tottakai! Paganel vastasi. --- Vuonna 1852 l\"{o}ydettiin Ballaratista kimpale, joka painoi viisisataaseitsem\"{a}nkymment\"{a}kolme unssia, Gippslandissa toinen, jonka paino oli seitsem\"{a}nsataakahdeksankymment\"{a}kaksi unssia, ja vuonna 1861 kahdeksansadankolmenkymmenennelj\"{a}n unssin painoinen harkko. Vihdoin, taas Ballaratista, er\"{a}s kaivaja l\"{o}ysi tavattoman kimpaleen, joka painoi kuusikymment\"{a}viisi kiloa, mik\"{a} kolmentuhannen nelj\"{a}nsadan frangin mukaan kilolta tekee kaksisataaviisikymment\"{a}viisi tuhatta frangia. Kuokanisku, joka tuottaa kymmenentuhannen frangin korot, on jo aikamoinen! --- Miss\"{a} m\"{a}\"{a}rin kullantuotanto lis\"{a}\"{a}ntyi n\"{a}iden kaivosten l\"{o}yt\"{a}misen j\"{a}lkeen? John Mangles kysyi. --- Suunnattomasti, rakas John. Kullantuotanto ei t\"{a}m\"{a}n vuosisadan alussa ollut kuin nelj\"{a}kymment\"{a}seitsem\"{a}n miljoonaa vuodessa, mutta nyt, Euroopan, Aasian ja Amerikan kaivosten tuotanto mukaan luettuna, se tekee yhdeks\"{a}nsataa miljoonaa, toisin sanoen l\"{a}hes miljardin. --- Niinp\"{a}, herra Paganel, on ehk\"{a} paljonkin kultaa sill\"{a} paikalla, miss\"{a} nyt olemme, meid\"{a}n jalkojemme alla? pikku Robert kysyi. --- On, poikani, miljoonia. Me tallaamme sit\"{a}. Mutta me tallaamme sit\"{a} sen vuoksi, ett\"{a} halveksimme sit\"{a}! --- Eik\"{o} Australia kuitenkin ole hyvin onnellinen maa? --- Ei, Robert, maantieteilij\"{a} vastasi. --- Kultapitoiset maat eiv\"{a}t ole onnellisia. Ne synnytt\"{a}v\"{a}t vain heikkoa v\"{a}est\"{o}\"{a}, mutta eiv\"{a}t milloinkaan voimakasta ja ty\"{o}teli\"{a}st\"{a}. Katso Brasiliaa, Meksikoa, Kaliforniaa, Australiaa! Mit\"{a} ne ovat yhdeks\"{a}nnell\"{a}toista vuosisadalla? Oikein onnellinen maa, poikani, ei ole kulta-, vaan rautapitoinen maa! \gutchapter{AUSTRALIAN JA UUDEN SEELANNIN UUTISET.} Tammikuun 2. p\"{a}iv\"{a}n\"{a} auringon noustessa matkustajat ylittiv\"{a}t kulta-alueen ja Talbotin piirikunnan rajan. Heid\"{a}n hevosensa kaviot polkivat silloin Dalhousien piirikunnan p\"{o}lyisi\"{a} teit\"{a}. Muutamia tunteja my\"{o}hemmin he kahlasivat Colban- ja Campaspe-jokien yli 144$^{\circ}$ 35' ja 144$^{\circ}$ 45' pituusasteen v\"{a}lill\"{a}. Puolet matkasta oli tehty. Viel\"{a} viisitoista p\"{a}iv\"{a}\"{a} yht\"{a} onnellista kulkua, ja matkue saapuisi Twofold-lahden rannoille. Muuten olivat kaikki hyviss\"{a} voimissa. Paganelin v\"{a}ite t\"{a}m\"{a}n ilmaston terveellisyydest\"{a} piti paikkansa. Kosteutta v\"{a}h\"{a}n tai ei ollenkaan, ja varsin siedett\"{a}v\"{a} l\"{a}mp\"{o}tila. Se ei rasittanut hevosia eik\"{a} juhtia. Ei liioin ihmisi\"{a}k\"{a}\"{a}n. Yksi ainoa muutos marssij\"{a}rjestykseen oli tehty Camden Bridgelt\"{a} l\"{a}hdetty\"{a}. Kun Ayrton sai tiet\"{a}\"{a} rautatieonnettomuuden johtuneen rikoksesta, h\"{a}n neuvoi noudattamaan erin\"{a}isi\"{a} siihen saakka tarpeettomina pidettyj\"{a} varotoimia. Ratsastajat eiv\"{a}t saaneet j\"{a}tt\"{a}\"{a} vankkureita n\"{a}kyvist\"{a}\"{a}n. Lepohetkin\"{a} j\"{a}i aina yksi heist\"{a} vahtiin. Aamuin ja illoin pantiin uudet nallit pyssyihin. Oli varmaa, ett\"{a} rikollisjoukkue liikkui maassa, ja vaikkei mit\"{a}\"{a}n suoranaista pelkoa her\"{a}tt\"{a}v\"{a}\"{a} sattunut, piti olla valmiina kaiken varalta. Tarpeetonta on lis\"{a}t\"{a}, ett\"{a} n\"{a}ihin varotoimiin ryhdyttiin lady Helenan ja Mary Grantin tiet\"{a}m\"{a}tt\"{a}, joita Glenarvan ei tahtonut s\"{a}ik\"{a}ytt\"{a}\"{a}. Oikeastaan olikin syyt\"{a} menetell\"{a} n\"{a}in. Varomattomuus tai vain laiminly\"{o}ntikin saattoi k\"{a}yd\"{a} kalliiksi. Glenarvan ei muuten ollut ainoa, joka huolehti asioista t\"{a}ll\"{a} tavoin. Yksin\"{a}isill\"{a} tiloilla ja asemilla varustautuivat asukkaat ja squatterit mahdollista hy\"{o}kk\"{a}yst\"{a} tai yll\"{a}tyst\"{a} vastaan. Talot suljettiin pime\"{a}n tullen. Koirat laskettiin irti aitauksiin ja alkoivat haukkua v\"{a}h\"{a}nkin l\"{a}hestytt\"{a}ess\"{a}. Ei yksik\"{a}\"{a}n paimen, joka illalla ratsain kokosi suurta laumaansa kotiinpaluuta varten, liikkunut ilman satulannuppiin kiinnitetty\"{a} pyssy\"{a}. Uutinen Camdenin sillalla tapahtuneesta rikoksesta oli syyn\"{a} t\"{a}h\"{a}n poikkeukselliseen varovaisuuteen, ja moni siirtolainen, joka t\"{a}h\"{a}n saakka oli nukkunut ikkunat ja ovet avoinna, sulki ne nyt huolellisesti. Maakunnan hallituskin osoitti suurta intoa ja varovaisuutta. Kotimaisia santarmiosastoja l\"{a}hetettiin pitkin maata. Postinkuljetusta suojattiin erityisin toimenpitein. T\"{a}t\"{a} ennen oli posti kulkenut valtateill\"{a} ilman vartiostoa. Niinp\"{a} t\"{a}n\"{a}\"{a}n, juuri kun Glenarvanin matkue oli menossa Kilmoresta Heathcoteen ulottuvan tien poikki, kiiti posti ohitse niin kiivasta vauhtia kuin hevoset suinkin p\"{a}\"{a}siv\"{a}t, j\"{a}tt\"{a}en suuren p\"{o}lypilven j\"{a}lkeens\"{a}. Mutta niin nopeasti kuin se ohittikin, Glenarvan oli kuitenkin n\"{a}hnyt sen rinnalla ratsastavien poliisien pyssyjen v\"{a}lk\"{a}ht\"{a}v\"{a}n. Olisi luullut elett\"{a}v\"{a}n j\"{a}lleen sit\"{a} hirvitt\"{a}v\"{a}\"{a} aikaa, jolloin ensimm\"{a}isten kultakenttien l\"{o}ytyminen ajoi Australian mantereelle Euroopan kansakuntien kuonan. Pari kilometri\"{a} Kilmoren maantien yli ehditty\"{a}\"{a}n saapuivat vankkurit j\"{a}ttil\"{a}ispuiden sekaan, ja ensimm\"{a}ist\"{a} kertaa Kap Bernouillista l\"{a}hdetty\"{a}\"{a}n matkustajat joutuivat laajaan, useiden asteiden yli ulottuvaan mets\"{a}\"{a}n. Ihmetyksen huudahdus p\"{a}\"{a}si matkustajilta, kun he n\"{a}kiv\"{a}t yli puolen sadan metrin korkuisia kumipuita, joiden sienim\"{a}inen kaarna oli jopa yli kymmenen sentin paksuinen. Kuusi ja puoli metri\"{a} ymp\"{a}rysmitaltaan olevat rungot, joiden kuoressa oli hyv\"{a}nhajuista pihkaa sis\"{a}lt\"{a}vi\"{a} uurteita, kohosivat viidenkymmenen metrin korkeuteen ainoankaan haaran tai oksan tai edes satunnaisen silmun ja pahkuran h\"{a}iritsem\"{a}tt\"{a} niiden pintaa. Sile\"{a}mpi\"{a} ne eiv\"{a}t olisi voineet olla sorvarin k\"{a}dest\"{a} l\"{a}htiess\"{a}\"{a}n. Siin\"{a} oli sadoittain toistensa kaltaisia pylv\"{a}it\"{a}. Ne levittiv\"{a}t tavattoman korkealla k\"{a}yri\"{a} oksiaan, joiden p\"{a}iss\"{a} oli sikerm\"{a} lehti\"{a}; lehtihangoissa riippui yksin\"{a}isi\"{a} kukkia, joiden ter\"{a}t olivat kuin yl\"{o}salaisin k\"{a}\"{a}nnetty uurna. T\"{a}m\"{a}n ikivihre\"{a}n katoksen alla kierteli ilma vapaasti; alituinen ilmanvaihto vei kosteuden maasta; hevoset, h\"{a}rk\"{a}valjakko ja vankkurit saattoivat mukavasti liikkua n\"{a}iden harvassa seisovien puiden v\"{a}liss\"{a}, jotka olivat j\"{a}rjestyneet kuin hakkuun merkkipaalut. Siell\"{a} ei ollut pensasrykelmiin sulloutuneita puuryhmi\"{a}, ei kaatuneiden runkojen ja l\"{a}pip\"{a}\"{a}sem\"{a}tt\"{o}mien liaanien aarniomets\"{a}\"{a}, miss\"{a} vain rauta ja tuli voivat raivata tiet\"{a} uudisviljelij\"{o}ille. Vihre\"{a} nurmi puiden juurella, vihre\"{a} varjostin niiden latvoissa, pitk\"{a}t valtavien pylv\"{a}iden rivit, v\"{a}h\"{a}n varjoa, ylimalkaan v\"{a}h\"{a}n raikkautta, omituinen valaistus, joka muistutti ohuen kankaan l\"{a}pi tunkevaa valoa, s\"{a}\"{a}nn\"{o}lliset heijastukset, tarkkapiirteiset kuviot maassa, kaikki t\"{a}m\"{a} tarjosi eriskummaisen ja uusista vaikutelmista runsaan n\"{a}ytelm\"{a}n. Oseaanian mantereen mets\"{a} ei muistuta ensink\"{a}\"{a}n uuden maailman metsi\"{a}, ja kumipuu, alkuasukkaiden ``tara'', joka kuuluu miltei lukemattomia lajeja k\"{a}sitt\"{a}v\"{a}\"{a}n myrttien heimoon, on Australian kasviston huomattavin edustaja. Ettei n\"{a}iden vihreiden holvien alla ole varjoisampaa ja pime\"{a}mp\"{a}\"{a}, se riippuu siit\"{a}, ett\"{a} puiden lehtien asento on erikoinen. Lehtien lapa ei ole n\"{a}et k\"{a}\"{a}ntynyt aurinkoa kohti, vaan niiden ter\"{a}v\"{a} reuna. Silm\"{a} ei t\"{a}st\"{a} omituisesta lehvist\"{o}st\"{a} n\"{a}e muuta kuin syrj\"{a}t. Niinp\"{a} auringon s\"{a}teetkin p\"{a}\"{a}sev\"{a}t maahan asti ik\"{a}\"{a}n kuin s\"{a}lekaihtimen rakosista. Jokainen huomasi t\"{a}m\"{a}n ja n\"{a}ytti h\"{a}mm\"{a}styneen. Mist\"{a} t\"{a}m\"{a} omituinen j\"{a}rjestely? Se kysymys tehtiin tietenkin Paganelille. H\"{a}n vastasi kuten ainakin mies, joka ei joudu mist\"{a}\"{a}n h\"{a}milleen. --- Luonnon eriskuinmaisuus, h\"{a}n sanoi, --- ei h\"{a}mm\"{a}styt\"{a} minua t\"{a}\"{a}ll\"{a}. Se tiet\"{a}\"{a} kyll\"{a} mit\"{a} tekee, mutta kasvitieteilij\"{a}t eiv\"{a}t aina tied\"{a}, mit\"{a} sanovat. Luonto ei ole erehtynyt antaessaan n\"{a}ille puille t\"{a}m\"{a}n erikoisen lehvist\"{o}n, mutta ihmiset ovat hairahtuneet, kun niille on annettu nimi \textit{eukalyptus}. --- Mit\"{a} se sana merkitsee? Mary Grant kysyi. --- Se tulee kreikan kielen sanoista \textit{eu kalypto} ja merkitsee \textit{hyvin peit\"{a}n}. Varovasti kyll\"{a} erehdys on tehty kreikaksi, jottei sit\"{a} huomattaisi, mutta selv\"{a}\"{a}h\"{a}n on, ett\"{a} tuo puu peitt\"{a}\"{a} huonosti. --- My\"{o}nnet\"{a}\"{a}n, rakas Paganel, Glenarvan vastasi, --- mutta selitt\"{a}k\"{a}\"{a} meille nyt, mink\"{a} vuoksi lehdet ovat tuossa asennossa. --- Pelk\"{a}st\"{a} ulkonaisesta ja helposti ymm\"{a}rrett\"{a}v\"{a}st\"{a} syyst\"{a}, yst\"{a}v\"{a}ni, Paganel vastasi. --- T\"{a}ll\"{a} seudulla, miss\"{a} ilma on kuiva, miss\"{a} sateet ovat harvinaisia, miss\"{a} maaper\"{a} on kuivunut, eiv\"{a}t puut tarvitse tuulta eik\"{a} aurinkoa. Kun ei ole kosteutta, ei ole my\"{o}sk\"{a}\"{a}n m\"{a}ih\"{a}\"{a}. Siksi kumipuulla on kapeat lehdet, jotka koettavat suojautua aurinkoa ja liian suurta haihtumista vastaan. Siin\"{a} syy, miksi ne k\"{a}\"{a}nt\"{a}v\"{a}t reunansa eiv\"{a}tk\"{a} lapaansa auringons\"{a}teille. Ei ole mit\"{a}\"{a}n \"{a}lykk\"{a}\"{a}mp\"{a}\"{a} kuin lehti. --- Eik\"{a} mit\"{a}\"{a}n itsekk\"{a}\"{a}mp\"{a}\"{a}! majuri lis\"{a}si. --- Nuokin ovat ajatelleet vain itse\"{a}\"{a}n eiv\"{a}tk\"{a} ensink\"{a}\"{a}n matkustajia. Jokainen oli hiukan samaa mielt\"{a} kuin MacNabbs, paitsi Paganel, joka otsaansa kuivaten onnitteli itse\"{a}\"{a}n, ett\"{a} sai kulkea varjottomien puiden alla. T\"{a}m\"{a} lehtij\"{a}rjestelm\"{a} oli sittenkin ik\"{a}v\"{a}, kun matka n\"{a}iden metsien l\"{a}pi on usein varsin pitk\"{a} ja niin ollen kiusallinen, sill\"{a} mik\"{a}\"{a}n ei suojaa matkustajaa p\"{a}iv\"{a}n hellett\"{a} vastaan. Koko p\"{a}iv\"{a}n vieriv\"{a}t vankkurit n\"{a}it\"{a} loppumattomia kumipuukujia pitkin. Ei tavattu nelijalkaisia el\"{a}imi\"{a} eik\"{a} alkuasukkaita. Er\"{a}\"{a}nlaisia papukaijoja asusti puiden latvoissa, mutta niin korkealta niit\"{a} tuskin erotti, ja niiden p\"{a}rp\"{a}tys kuului vain ep\"{a}selv\"{a}n\"{a} sorinana. Joskus lensi parvi pikku papukaijoja jonkun kaukaisen kujanteen poikki ja vilkastutti sit\"{a} \"{a}killisell\"{a}, moniv\"{a}risell\"{a} v\"{a}ikkeell\"{a}. Mutta yleens\"{a} vallitsi t\"{a}ss\"{a} laajassa vehre\"{a}ss\"{a} pylv\"{a}st\"{o}ss\"{a} syv\"{a} hiljaisuus, ja vain hevosten astunta, muutamat silloin t\"{a}ll\"{o}in vaihdetut sanat, vankkurien py\"{o}rien kitin\"{a} ja Ayrtonin huudahdus h\"{a}nen hoputtaessaan hidasta valjakkoaan h\"{a}iritsiv\"{a}t avaraa autiutta. Illan tullen leiriydyttiin kumipuiden juurelle, joissa n\"{a}kyi j\"{a}lki\"{a} jokseenkin hiljan palaneesta tulesta. Ne olivat kuin korkeita tehtaanpiippuja, sill\"{a} liekki oli kolonut ne sis\"{a}puolelta pitkin koko niiden pituutta. Ne seisoivat aika tukevasti vain tyhj\"{a}n kuorensa varassa. Moinen squatterien tai alkuasukkaiden paha tapa h\"{a}vitt\"{a}\"{a} kuitenkin lopulta n\"{a}m\"{a} suurenmoiset puut, ja ne kuolevat sukupuuttoon niin kuin Libanonin nelisatavuotiset seetrit, jotka on poltettu taitamattomilla nuotiotulilla. Paganelin neuvoa seuraten Olbinett sytytti illallistulen yhteen n\"{a}ist\"{a} runkoputkista; heti syntyi tuntuva veto, ja savu haihtui lehvist\"{o}n tummaan katokseen. Y\"{o}ksi ryhdyttiin m\"{a}\"{a}r\"{a}ttyihin varotoimiin, ja Ayrton, Mulrady, Wilson ja John Mangles pitiv\"{a}t vahtia vuorotellen p\"{a}iv\"{a}nnousuun saakka. Pitkin tammikuun 3. p\"{a}iv\"{a}\"{a} lis\"{a}\"{a}ntyiv\"{a}t vain loputtoman mets\"{a}n sopusuhtaiset kujanteet. Tuntui kuin kumipuista ei koskaan tulisi loppua. Mutta iltaan menness\"{a} harvenivat jonot, ja muutamien kilometrien p\"{a}\"{a}ss\"{a} n\"{a}kyi joukko s\"{a}\"{a}nn\"{o}llisi\"{a} taloja pienell\"{a} aukealla. --- Seymour! Paganel huudahti. --- Se on Victorian maakunnan viimeinen kaupunki. --- Onko se suurikin? lady Helena kysyi. --- Rouva, Paganel vastasi, --- se on tavallinen kyl\"{a}, joka on saamassa kaupunkioikeudet. --- Onkohan siell\"{a} sopivaa majataloa? Glenarvan kysyi. --- Toivottavasti, maantieteilij\"{a} vastasi. --- Niinp\"{a} menk\"{a}\"{a}mme kaupunkiin, sill\"{a} reippaat naiskumppanimme eiv\"{a}t luullakseni pane pahakseen, jos saavat lev\"{a}ht\"{a}\"{a} siell\"{a} yhden y\"{o}n. --- Rakas Edward, lady Helena vastasi, --- Mary ja min\"{a} suostumme siihen sill\"{a} ehdolla, ett\"{a} se ei aiheuta hankaluutta eik\"{a} viivytyst\"{a}. --- Ei v\"{a}himm\"{a}ss\"{a}k\"{a}\"{a}n m\"{a}\"{a}rin, lordi Glenarvan vastasi, --- valjakkomme on v\"{a}synyt, ja sit\"{a} paitsi me jatkamme matkaa huomenna p\"{a}iv\"{a}n koitteessa. Kello oli silloin yhdeks\"{a}n. Kuu l\"{a}heni jo taivaanrantaa ja heitti en\"{a}\"{a} vain vinoja, sumuun haihtuvia s\"{a}teit\"{a}. V\"{a}hitellen tuli pime\"{a}. Matkue kulki pitkin Seymourin leveit\"{a} katuja Paganelin johdolla, h\"{a}n kun aina n\"{a}kyi tuntevan t\"{a}ysin tuntemattomankin paikkakunnan. Mutta h\"{a}n kulki vaistonsa mukaan, ja h\"{a}n saapui suoraan Campbell's North British nimiseen hotelliin. Hevoset ja h\"{a}r\"{a}t vietiin talliin, vankkurit vajaan, ja matkustajat ohjattiin varsin mukaviin huoneisiin. Kello kymmenen aikaan istuttiin p\"{o}yt\"{a}\"{a}n, jonka ruokia Olbinett oli tarkastanut asiantuntijan silm\"{a}ll\"{a}. Paganel oli k\"{a}ynyt kaupungilla Robertin kanssa ja kertoi iltavaikutelmistaan perin lyhyesti. H\"{a}n ei ollut n\"{a}hnyt kerrassaan mit\"{a}\"{a}n. V\"{a}hemm\"{a}n hajamielinen mies olisi kuitenkin huomannut Seymourin kaduilla erikoista liikett\"{a}: siell\"{a} t\"{a}\"{a}ll\"{a} ker\"{a}\"{a}ntyi ihmisi\"{a} joukkoihin, jotka v\"{a}hitellen suurenivat; puheltiin talojen porteilla; ihmiset kyseliv\"{a}t toisiltaan jotakin ilmeisen levottomina; p\"{a}iv\"{a}n sanomalehti\"{a} luettiin \"{a}\"{a}neen, niiden uutisista puhuttiin ja keskusteltiin. N\"{a}m\"{a} oireet eiv\"{a}t olisi voineet j\"{a}\"{a}d\"{a} v\"{a}h\"{a}nk\"{a}\"{a}n valppaalta tarkkailijalta huomaamatta. Mutta Paganel ei ollut ep\"{a}illyt mit\"{a}\"{a}n. Majuri sit\"{a} vastoin, vaikkei k\"{a}ynyt niin kaukana, eip\"{a} edes poistunut hotellista, otti selv\"{a}n huolestumisesta ja pikku kaupungissa parhaillaan vallitsevasta levottomuudesta. Keskusteltuaan kymmenen minuuttia hotellin puheliaan is\"{a}nn\"{a}n, Dicksonin kanssa h\"{a}n tiesi, mist\"{a} oli kysymys. Mutta h\"{a}n ei hiiskunut siit\"{a} sanaakaan. Vasta illallisen j\"{a}lkeen, kun lady Glenarvan, Mary ja Robert Grant olivat menneet huoneisiinsa, majuri pyysi kumppaneitaan j\"{a}\"{a}m\"{a}\"{a}n ja sanoi heille: --- Sandhurstin rautatiell\"{a} tapahtuneen rikoksen tekij\"{a}t on tunnistettu. --- Onko heid\"{a}t vangittu? Ayrton kysyi vilkkaasti. --- Ei, MacNabbs vastasi n\"{a}ytt\"{a}m\"{a}tt\"{a} kiinnitt\"{a}v\"{a}n huomiota per\"{a}miehen intoon, joka n\"{a}iss\"{a} oloissa muuten oli varsin ymm\"{a}rrett\"{a}v\"{a}. --- Sen pahempi, Ayrton lis\"{a}si. --- No, Glenarvan kysyi, --- kenen syyksi sit\"{a} rikosta luullaan? --- Lukekaa, majuri vastasi antaen Glenarvanille numeron Australian ja Uuden Seelannin Uutisia, --- niin saatte n\"{a}hd\"{a}, ett\"{a} poliisip\"{a}\"{a}llikk\"{o} ei erehtynyt. Glenarvan luki \"{a}\"{a}neen seuraavan uutisen: \begin{quotation} Sydney, 2. p. tammikuuta 1865. --- Kuten muistetaan, tapahtui Camden Bridgell\"{a}, kahdeksan kilometrin p\"{a}\"{a}ss\"{a} Castlemainen asemalta, Melbournesta Sandhurstiin johtavalla rautatiell\"{a}, viime joulukuun 29. ja 30. p\"{a}iv\"{a}n v\"{a}lisen\"{a} y\"{o}n\"{a} rautatieonnettomuus. Klo 11.45 l\"{a}htev\"{a} y\"{o}juna sy\"{o}ksyi t\"{a}ydess\"{a} vauhdissa Lutton-jokeen.\end{quotation} Camdenin silta oli j\"{a}tetty auki junan kulkiessa. Useat onnettomuuden j\"{a}lkeen tapahtuneet varkaudet ja kilometrin p\"{a}\"{a}ss\"{a} Camden Bridgelt\"{a} l\"{o}ydetty sillanvartijan ruumis osoittivat, ett\"{a} t\"{a}m\"{a} onnettomuus oli johtunut rikoksesta. \begin{quotation} Viranomaisten tutkimuksista onkin k\"{a}ynyt selville, ett\"{a} rikoksen on tehnyt joukko karkotusvankeja, jotka kuusi kuukautta sitten olivat p\"{a}\"{a}sseet karkuun Perthin ty\"{o}vankilasta L\"{a}nsi-Australiassa juuri kun heid\"{a}t piti siirt\"{a}\"{a} Norfolkin saarelle.[9]\end{quotation} \begin{quotation} N\"{a}it\"{a} karkotusvankeja on kaksikymment\"{a}yhdeks\"{a}n; heit\"{a} johtaa er\"{a}s Ben Joyce, mit\"{a} vaarallisin rikollinen, joka muutamia kuukausia sitten on saapunut Australiaan tuntemattomalla laivalla ja jota oikeudenpalvelijoiden ei ole onnistunut tavoittaa.\end{quotation} Kaupunkien asukkaita, uudisviljelij\"{o}it\"{a} ja asemien squattereita kehotetaan olemaan varuillaan ja antamaan ylitarkastajalle tietoja, jotka ovat avuksi etsinn\"{o}iss\"{a}. J.P. MITCHELL, ylitarkastaja. Kun Glenarvan oli lopettanut t\"{a}m\"{a}n uutisen lukemisen, MacNabbs k\"{a}\"{a}ntyi maantieteilij\"{a}n puoleen ja sanoi h\"{a}nelle: --- N\"{a}ette nyt, Paganel, ett\"{a} Australiassa saattaa olla karkotusvankeja. --- Karkureita kyll\"{a}! Paganel vastasi. --- Mutta ei karkotettuja, joilla olisi siihen laillinen lupa. Noilla miehill\"{a} ei ole oikeutta oleskella t\"{a}\"{a}ll\"{a}. --- T\"{a}\"{a}ll\"{a} he nyt kuitenkin ovat, Glenarvan sanoi, --- mutta k\"{a}sitt\"{a}\"{a}kseni meid\"{a}n ei pit\"{a}isi heid\"{a}n t\"{a}htens\"{a} muuttaa suunnitelmiamme tai keskeytt\"{a}\"{a} matkaamme. Mit\"{a} sin\"{a} siit\"{a} ajattelet, John? John Mangles ei vastannut heti; yht\"{a}\"{a}lt\"{a} suru, jonka aloitetun etsinn\"{a}n lopettaminen tuottaisi molemmille lapsille, ja toisaalta se pelko, ett\"{a} retkikunta joutuisi vaaraan, sai h\"{a}net ep\"{a}r\"{o}im\"{a}\"{a}n. --- Jos lady Glenarvan ja miss Grant eiv\"{a}t olisi mukana, h\"{a}n sanoi sitten, --- niin v\"{a}litt\"{a}isin v\"{a}h\"{a}t tuosta roistojoukosta. Glenarvan ymm\"{a}rsi ja lis\"{a}si: --- Sanomattakin on selv\"{a}\"{a}, ett\"{a} yrityksest\"{a}mme luopuminen ei tule kysymykseenk\"{a}\"{a}n; mutta kenties olisi matkaseuramme vuoksi varovinta, tavoittaa \textit{Duncan} Melbournessa ja sitten id\"{a}st\"{a} k\"{a}sin palata Harry Grantin j\"{a}ljille. Mit\"{a} te, MacNabbs, siit\"{a} ajattelette? --- Ennen kuin sanon sen, majuri vastasi, --- haluaisin kuulla Ayrtonin mielipiteen. Per\"{a}mies, jonka mielt\"{a} nimenomaan kysyttiin, katsahti Glenarvaniin. --- Min\"{a} ajattelen, h\"{a}n sanoi, --- ett\"{a} me olemme yli kolmensadan kilometrin p\"{a}\"{a}ss\"{a} Melbournesta ja ett\"{a} vaara, jos sit\"{a} on, voi olla yht\"{a} suuri matkalla etel\"{a}\"{a}n kuin it\"{a}\"{a}nkin. Kummallakaan suunnalla ei paljon kuljeta, ne ovat samanlaisia molemmat. Muuten en luule, ett\"{a} kolmisenkymment\"{a} rikollista voisi pelottaa kahdeksaa hyvin aseistautunutta ja p\"{a}\"{a}tt\"{a}v\"{a}ist\"{a} miest\"{a}. Niinp\"{a} min\"{a} melkein katsoisin parhaaksi l\"{a}hte\"{a} eteenp\"{a}in. --- Hyvin puhuttu, Ayrton, Paganel lausui. --- Matkaa jatkamalla voimme p\"{a}\"{a}st\"{a} kapteeni Grantin j\"{a}ljille. Palaamalla etel\"{a}\"{a}n p\"{a}invastoin loittonemme niist\"{a}. Min\"{a} ajattelen siis samoin kuin tekin ja v\"{a}lit\"{a}n v\"{a}h\"{a}t noista Perthin karkureista, joita rohkean miehen ei tulisi ajatellakaan! T\"{a}m\"{a}n j\"{a}lkeen \"{a}\"{a}nestettiin ehdotuksesta, ettei matkasuunnitelmaa mill\"{a}\"{a}n tavoin muutettaisi, ja se hyv\"{a}ksyttiin yksimielisesti. --- Yksi huomautus kuitenkin, mylord, Ayrton sanoi juuri kun piti erota. --- Puhukaa, Ayrton. --- Eik\"{o} olisi hyv\"{a} l\"{a}hett\"{a}\"{a} \textit{Duncanille} k\"{a}sky j\"{a}lleen l\"{a}hesty\"{a} rannikkoa? --- Mit\"{a} varten? John Mangles vastasi. --- Kun olemme saapuneet Twofold-lahdelle, on aika sen k\"{a}skyn l\"{a}hett\"{a}miseen. Jos jokin odottamaton sattuma pakottaisi meid\"{a}t pyrkim\"{a}\"{a}n Melbourneen, voisimme katua, ettemme siell\"{a} tapaisikaan \textit{Duncania}. Muuten sen vauriota ei luultavasti viel\"{a} ole korjattu. N\"{a}ist\"{a} eri syist\"{a} olisi minun mielest\"{a}ni parasta odottaa. --- Hyv\"{a}, Ayrton vastasi olematta itsep\"{a}inen. Seuraavana p\"{a}iv\"{a}n\"{a} l\"{a}hti retkikunta Seymourista aseissa ja valmiina kaiken varalta. Puolta tuntia my\"{o}hemmin se oli j\"{a}lleen kumipuumets\"{a}ss\"{a}, jota taas jatkui it\"{a}\"{a}np\"{a}in. Glenarvan olisi mieluummin kulkenut avoimessa maastossa. Silloin on v\"{a}hemm\"{a}n vaaraa v\"{a}ijytyksist\"{a} ja salahy\"{o}kk\"{a}yksist\"{a} kuin tihe\"{a}ss\"{a} mets\"{a}ss\"{a}. Mutta ei ollut valinnanvaraa, ja vankkurit eteniv\"{a}t koko p\"{a}iv\"{a}n suurten yksitoikkoisten puiden v\"{a}liss\"{a}. Kuljettuaan pitkin Angleseyn piirikunnan pohjoisrajaa ne leikkasivat illalla 146. meridiaanin, ja sitten leiriydyttiin Murrayn piirin rajalla. \gutchapter{MAJURI V\"{A}ITT\"{A}\"{A} ALKUASUKKAITA APINOIKSI.} Seuraavana aamuna, 5. p\"{a}iv\"{a}n\"{a} tammikuuta, saapuivat matkalaiset Murrayn laajalle alueelle. T\"{a}m\"{a} ep\"{a}m\"{a}\"{a}r\"{a}inen ja autio piirikunta ulottuu Australian alppien korkeaan vuorijonoon saakka. Sit\"{a} ei sivistys viel\"{a} ole jakanut eri hallintopiireihin. Se on maakunnan v\"{a}h\"{a}n tunnettu osa, jossa harvoin k\"{a}yd\"{a}\"{a}n. Uudisasukkaiden kirves kaataa kerran sen mets\"{a}t, karjankasvattajien karja ottaa valtaansa sen laitumet; mutta viel\"{a} se on koskematonta maata jollaisena se nousi Intian valtamerest\"{a}; se on suorastaan er\"{a}maata. Englantilaisilla kartoilla on n\"{a}ille alueille annettu kuvaava yhteinen nimi: \textit{Reserve for the blacks}, s.o. mustille varattu alue. Sinne ovat siirtolaiset h\"{a}ik\"{a}ilem\"{a}tt\"{a} ty\"{o}nt\"{a}neet alkuasukkaat. Siell\"{a} kaukaisilla tasangoilla, aarniometsiss\"{a}, on n\"{a}ille j\"{a}tetty erin\"{a}isi\"{a} m\"{a}\"{a}r\"{a}ttyj\"{a} alueita, joilla alkuper\"{a}inen rotu v\"{a}hitellen h\"{a}vi\"{a}\"{a}. Kuka hyv\"{a}ns\"{a} valkoinen mies, uudisasukas, siirtolainen, squatter, bushmanni, saa menn\"{a} n\"{a}iden varattujen alueiden ulkopuolelle. Mutta mustaihoinen yksin ei milloinkaan p\"{a}\"{a}se sielt\"{a} pois. Eteenp\"{a}in ratsastettaessa Paganel otti puheeksi t\"{a}m\"{a}n vakavan alkuasukkaita koskevan kysymyksen. Eik\"{a} oltu kuin yht\"{a} mielt\"{a} siit\"{a}, ett\"{a} Britannian menetelm\"{a} tarkoitti voitettujen v\"{a}est\"{o}jen n\"{a}\"{a}nnytt\"{a}mist\"{a}, niiden juurittamista pois seuduilta, miss\"{a} heid\"{a}n esivanhempansa eliv\"{a}t. T\"{a}m\"{a} tuhoamistarkoitus tuli esille kaikkialla, mutta Australiassa selvemmin kuin muualla. Siirtolaisuuden ensi aikoina kohtelivat karkotusvangit, jopa uudisasukkaatkin mustia kuin villej\"{a} el\"{a}imi\"{a}. Mets\"{a}stiv\"{a}t ja kaatoivat heit\"{a} pyssyill\"{a}ns\"{a}. Vedottiin viel\"{a}, kun heit\"{a} teurastettiin, lainoppineihin sen todistamiseksi, ett\"{a} australialainen muka oli luonnonlakien ulkopuolinen olio, jonka tappaminen ei ollut mik\"{a}\"{a}n rikos. Esittiv\"{a}tp\"{a} Sydneyn sanomalehdet tehokasta keinoa Hunter-j\"{a}rven heimojen h\"{a}vitt\"{a}miseksi: niiden joukkomyrkytyst\"{a}. Englantilaiset ottivat, kuten n\"{a}kyy, asutuksensa ensi avustajaksi murhan. Heid\"{a}n julmuutensa oli hirvitt\"{a}v\"{a}. He menetteliv\"{a}t Australiassa samoin kuin Intiassa, miss\"{a} viisi miljoonaa intialaista on kadonnut; samoin kuin Kap-maassa, miss\"{a} miljoonan suuruinen hottentottiv\"{a}est\"{o} on v\"{a}hentynyt sataantuhanteen. Niinp\"{a} alkuper\"{a}inen v\"{a}est\"{o} onkin huonon kohtelun ja v\"{a}kijuomien n\"{a}\"{a}nnytt\"{a}m\"{a}n\"{a} katoamassa t\"{a}lt\"{a} mantereelta murhaavan sivistyksen tielt\"{a}. Tosin muutamat kuvern\"{o}\"{o}rit antoivat julistuksia uudisasukkaiden verenhimoa vastaan. Uhkasivat muutamilla ruoskaniskuilla rangaista valkoista, joka leikkasi nen\"{a}n tai korvat mustalta tai katkaisi h\"{a}nelt\"{a} pikkusormen ``k\"{a}ytt\"{a}\"{a}kseen sit\"{a} piipputupakan tiivist\"{a}j\"{a}n\"{a}''. Turhia uhkauksia. Murhia tehtiin laajassa mittakaavassa, ja kokonaisia heimoja h\"{a}visi. Mainitkaamme vain, ett\"{a} Van Diemenin saarella vuosisadan alussa oli viisituhatta alkuasukasta, mutta vuonna 1863 ainoastaan seitsem\"{a}n henke\"{a}! Ja \"{a}skett\"{a}in saattoi \textit{Mercure} ilmoittaa viimeisen tasmanialaisen saapuneen Hobart-Towniin. Ei Glenarvan, ei majuri eik\"{a} John Mangles v\"{a}itt\"{a}nyt Paganelia vastaan. Ja vaikka he olisivat olleet englantilaisia, he eiv\"{a}t olisi puolustaneet maanmiehi\"{a}\"{a}n. Tosiasiat puhuivat selv\"{a}\"{a}, kiistatonta kielt\"{a}. --- Viisikymment\"{a} vuotta sitten, Paganel jatkoi, --- olisimme jo matkallamme tavanneet monta alkuasukasheimoa, mutta nyt emme ole n\"{a}hneet ensimm\"{a}ist\"{a}k\"{a}\"{a}n. Sadan vuoden p\"{a}\"{a}st\"{a} on musta rotu t\"{a}lt\"{a} mantereelta tyyten loppunut. Mustille varattu alue tuntui todellakin olevan t\"{a}ysin asumaton. Ei j\"{a}lke\"{a}k\"{a}\"{a}n majapaikoista tai h\"{o}kkeleist\"{a}. Aukeiden j\"{a}lkeen tuli taas suuria metsi\"{a}, ja v\"{a}hitellen muuttui seutu yh\"{a} selvemmin er\"{a}maaksi. N\"{a}yttip\"{a} silt\"{a} ettei n\"{a}ill\"{a} syrj\"{a}seuduilla ollut ainoatakaan el\"{a}v\"{a}\"{a} olentoa, ei ihmist\"{a} enemp\"{a}\"{a} kuin el\"{a}int\"{a}, kun Robert pys\"{a}htyi er\"{a}\"{a}n kumipuurykelm\"{a}n eteen ja huudahti: --- Apina! T\"{a}\"{a}ll\"{a} on apina! Ja h\"{a}n viittasi suureen mustaan olentoon, joka hypellen oksalta oksalle h\"{a}mm\"{a}stytt\"{a}v\"{a}n vikkel\"{a}sti siirtyi puun latvasta toiseen, ik\"{a}\"{a}n kuin n\"{a}kym\"{a}t\"{o}n k\"{o}ysi olisi pit\"{a}nyt sit\"{a} ilmassa. Lensiv\"{a}tk\"{o} siis apinat t\"{a}ss\"{a} kummallisessa maassa kuten er\"{a}\"{a}t ketut, joille luonto on antanut y\"{o}lepakon siivet. Vankkurit olivat pys\"{a}htyneet ja kukin tarkkaili el\"{a}int\"{a}, joka v\"{a}hitellen katosi kumipuiden latvuksiin. Pian sen n\"{a}htiin nopeana kuin salama laskeutuvan, juoksevan maata pitkin tehden senkin seitsem\"{a}n mutkaa ja sitten tarttuvan pitkin k\"{a}sivarsin suuren kumipuun sile\"{a}\"{a}n runkoon. Kummasteltiin, kuinka se p\"{a}\"{a}sisi yl\"{o}s t\"{a}t\"{a} suoraa ja liukasta puuta my\"{o}ten, jonka ymp\"{a}ri se ei ylettynyt. Mutta apina iski kirveentapaisella puunkuorta, saaden aikaan s\"{a}\"{a}nn\"{o}llisten v\"{a}limatkain p\"{a}\"{a}h\"{a}n pieni\"{a} pyk\"{a}li\"{a}, joiden avulla se kiipesi kumipuun haarukkaan. Muutamassa sekunnissa se katosi lehvist\"{o}n peittoon. --- Mik\"{a} ihmeen apina tuo on? majuri kysyi. --- Tuoko apina? Paganel vastasi. --- Se on puhdasverinen australialainen. Maantieteilij\"{a}n kumppanit eiv\"{a}t ehtineet edes kohauttaa olkap\"{a}it\"{a}\"{a}n, kun ihan l\"{a}hell\"{a} kuului huutoja: --- ku-ii! ku-ii! Ayrton hoputti juhtiaan, ja sadan askelen p\"{a}\"{a}ss\"{a} kohtasivat matkustajat odottamatta alkuasukasleirin. Mik\"{a} surkea n\"{a}ky! Kymmenkunta telttaa paljaalla maalla. N\"{a}m\"{a} tiilien tapaan p\"{a}\"{a}llekk\"{a}in ladotuista kaarnan kappaleista tehdyt ``gunyot'' eiv\"{a}t suojanneet kurjia asukkaitaan kuin yhdelt\"{a} puolen. Ja asukkaat itse oli puute painanut tymp\"{a}iseviksi. Heit\"{a} oli siell\"{a} kolmisenkymment\"{a}, miehi\"{a}, naisia ja lapsia, pukunaan kengurunnahkoja, jotka oli leikelty kaistaleiksi. Vankkurien l\"{a}hetess\"{a} he ensin aikoivat paeta. Mutta jotkut Ayrtonin sanat, jotka h\"{a}n lausui k\"{a}sitt\"{a}m\"{a}tt\"{o}m\"{a}ll\"{a} murteella, n\"{a}yttiv\"{a}t rauhoittavan heit\"{a}. Niinp\"{a} he palasivat puoliksi luottavaisina, puoliksi pelokkaina, kuten el\"{a}imet, joille tarjotaan herkkupalaa. N\"{a}ill\"{a} alkuasukkailla, joiden pituus vaihteli 160 sentist\"{a} 170 senttiin, oli nokimainen iho, ei suorastaan musta, vaan vanhan noen v\"{a}rinen, villava tukka, pitk\"{a}t k\"{a}sivarret, ulkoneva vatsa, karvapeitteinen ruumis t\"{a}ynn\"{a} tatuointien ja hautajaistilaisuuksissa leikattujen haavojen arpia. Oli hirvitt\"{a}v\"{a}\"{a} katsella heid\"{a}n muodottomia kasvojaan, suunnatonta suutaan, litte\"{a}t\"{a} ja poskille painunutta nen\"{a}\"{a}ns\"{a}, ulkonevaa alaleukaansa, josta valkoiset eteenp\"{a}in ty\"{o}ntyv\"{a}t hampaat pistiv\"{a}t esiin. Milloinkaan ei ollut n\"{a}hty n\"{a}in el\"{a}inten n\"{a}k\"{o}isi\"{a} ihmisolentoja. --- Robert ei erehtynyt, majuri sanoi, --- ne ovat apinoita, --- puhdasverisi\"{a}, olkoon niin, --- mutta apinoita kuitenkin. --- MacNabbs, lady Helena huomautti, --- my\"{o}nt\"{a}isittek\"{o} siis niiden olevan oikeassa, jotka mets\"{a}st\"{a}v\"{a}t n\"{a}it\"{a} kuin petoel\"{a}imi\"{a}? N\"{a}m\"{a} raukathan ovat ihmisi\"{a}. --- Ihmisi\"{a}k\"{o}! MacNabbs huudahti. --- Korkeintaan ihmisen ja orangutangin v\"{a}limuotoja! Ja jos viel\"{a} mittaisin heid\"{a}n kasvokulmansa, se olisi yht\"{a} ter\"{a}v\"{a} kuin apinan! MacNabbs oli t\"{a}ss\"{a} suhteessa oikeassa; australialaisen alkuasukkaan kasvojen kulma on hyvin ter\"{a}v\"{a} ja jokseenkin samanlainen kuin orangutangin eli noin kuusikymment\"{a} tai kuusikymment\"{a}kaksi astetta. Niinp\"{a} ei herra de Rienzi esitt\"{a}nytk\"{a}\"{a}n aivan syytt\"{a} n\"{a}it\"{a} olentoja luokiteltaviksi eri rotuun, jota h\"{a}n nimitti ``pithecomorpheiksi'', siis apinanmuotoisiksi ihmisiksi. Mutta lady Helena oli viel\"{a} oikeammassa kuin MacNabbs katsoessaan n\"{a}it\"{a} ihmisasteikon alimmalla portaalla olevia alkuasukkaita kuitenkin sielulla varustetuiksi olennoiksi. El\"{a}imen ja australialaisen v\"{a}lill\"{a} on se ylip\"{a}\"{a}sem\"{a}t\"{o}n kuilu, joka erottaa lajit. Pascal on sanonut aivan oikein, ett\"{a} ihminen ei miss\"{a}\"{a}n ole el\"{a}in. Tosin h\"{a}n yht\"{a} viisaasti lis\"{a}\"{a}: --- eik\"{a} enkelik\"{a}\"{a}n. T\"{a}ll\"{a} kertaa kuitenkin lady Helena ja Mary Grant kumosivat j\"{a}lkimm\"{a}isen puolen suuren ajattelijan v\"{a}itt\"{a}m\"{a}st\"{a}. Molemmat laupiaat naiset olivat astuneet maahan vankkureista; he ojensivat hyv\"{a}\"{a}tarkoittavaa k\"{a}tt\"{a} n\"{a}ille kurjille olennoille; tarjosivat heille ruokaa, jota villit ahmivat inhottavan ahnaasti. Alkuasukkaat taisivat sit\"{a}kin enemm\"{a}n luulla lady Helenaa joksikin jumalaksi, kun heid\"{a}n uskontonsa mukaan valkoiset ovat entisi\"{a} mustia, kuolemansa j\"{a}lkeen valkoisiksi muuttuneita. Naiset varsinkin her\"{a}ttiv\"{a}t lady Helenan ja Mary Grantin s\"{a}\"{a}li\"{a}. Mik\"{a}\"{a}n ei ole verrattavissa australialaisnaisen oloon; tyly luonto ei ole antanut h\"{a}nelle v\"{a}h\"{a}isint\"{a}k\"{a}\"{a}n viehkeyden vivahdusta; h\"{a}n on v\"{a}kisin viety orjatar, joka ei ole saanut muuta h\"{a}\"{a}lahjaa kuin ``waddien'', is\"{a}nt\"{a}ns\"{a} k\"{a}dess\"{a} aina pysyv\"{a}n kepin iskuja. Siit\"{a} hetkest\"{a} alkaen, ennenaikaisesti ja \"{a}kki\"{a} vanhentuneena, h\"{a}nen taakkanaan on kaikki kulkuriel\"{a}m\"{a}n raskaat vaivat: h\"{a}nen on kannettava kaislak\"{a}\"{a}r\"{o}\"{o}n kiedottujen lapsiensa ohella kalastus- ja mets\"{a}stysv\"{a}lineit\"{a} ynn\"{a} ``phormium tenax"-varastoja, josta h\"{a}n valmistaa verkkoja. H\"{a}nen t\"{a}ytyy hankkia elintarvikkeet perheelleen; h\"{a}n mets\"{a}st\"{a}\"{a} sisiliskoja, pussirottia ja k\"{a}\"{a}rmeit\"{a} puiden latvoihin saakka; h\"{a}n pienii polttopuut; h\"{a}n kiskoo tuohta telttaan; h\"{a}n on sanalla sanoen ty\"{o}juhta, joka ei tunne lepoa, ja sy\"{o} vasta is\"{a}nt\"{a}ns\"{a} j\"{a}lkeen niit\"{a} huonoja j\"{a}tteit\"{a}, joita t\"{a}m\"{a} ei en\"{a}\"{a} huoli. Muutamat n\"{a}ist\"{a} raukoista, jotka kenties eiv\"{a}t pitk\"{a}\"{a}n aikaan olleet saaneet ravintoa, koettivat juuri houkutella luokseen lintuja tarjoamalla niille jyvi\"{a}. He makasivat polttavassa maassa pitk\"{a}ll\"{a}\"{a}n liikkumattomina, kuin kuolleina, tuntikausia odotellen, ett\"{a} joku ymm\"{a}rt\"{a}m\"{a}t\"{o}n lintu tulisi heid\"{a}n k\"{a}tens\"{a} ulottuville! Pitemm\"{a}lle heid\"{a}n kekseli\"{a}isyytens\"{a} ei ansapyynnin alalla ulottunut, ja t\"{a}ytyy olla australialainen lintu joutuakseen mokomaan ansaan. Matkustajien anteliaisuuden kesytt\"{a}min\"{a} villit ker\"{a}\"{a}ntyiv\"{a}t v\"{a}hitellen heid\"{a}n ymp\"{a}rilleen, ja silloin t\"{a}ytyi pit\"{a}\"{a} varansa heid\"{a}n ilmeist\"{a} varasteluhaluaan vastaan. He puhuivat viheltelev\"{a}\"{a}, kielt\"{a} maiskuttelevaa murretta. Se muistutti el\"{a}inten \"{a}\"{a}ntely\"{a}. Kuitenkin heid\"{a}n \"{a}\"{a}ness\"{a}\"{a}n oli usein my\"{o}s hell\"{a}sti hyv\"{a}ilevi\"{a} \"{a}\"{a}nteit\"{a}; sana ``noki, noki'' toistui tuon tuostakin, ja eleet tekiv\"{a}t sen helposti ymm\"{a}rrett\"{a}v\"{a}ksi. Se merkitsi ``antakaa'' ja kohdistui matkustajien pienimpiinkin esineihin. Olbinettilla oli t\"{a}ysi ty\"{o} puolustaessaan tavaravarastoa ja varsinkin retkikunnan ruokavaroja. N\"{a}lkiintyneet raukat loivat vankkureihin huolestuttavia katseita ja n\"{a}yttiv\"{a}t ter\"{a}vi\"{a} hampaitaan, jotka kukaties olivat pureksineet ihmislihaa. Useimmat australialaiset heimot eiv\"{a}t tosin ole ihmissy\"{o}ji\"{a} rauhan aikana, mutta vain muutamat villit kielt\"{a}ytyv\"{a}t ahmimasta voitetun vihollisen lihaa. Helenan pyynn\"{o}st\"{a} Glenarvan k\"{a}ski kuitenkin jaella jonkin verran ruokavaroja. Villit ymm\"{a}rsiv\"{a}t h\"{a}nen aikomuksensa ja riemastuivat tavalla, joka olisi liikuttanut tunteettomintakin syd\"{a}nt\"{a}. He kiljahtelivat niin kuin villipedot, kun vartija tuo niille jokap\"{a}iv\"{a}ist\"{a} annosta. My\"{o}nt\"{a}m\"{a}tt\"{a} majurin olevan oikeassa ei kuitenkaan voinut kielt\"{a}\"{a}, ett\"{a} t\"{a}m\"{a} rotu oli l\"{a}hell\"{a} el\"{a}int\"{a}. Olbinett oli kohteliaana miehen\"{a} luullut olevan oikein ensin antaa naisille. Mutta n\"{a}m\"{a} olentoraukat eiv\"{a}t uskaltaneet sy\"{o}d\"{a} ennen pelottavia is\"{a}nti\"{a}\"{a}n, jotka sy\"{o}ksyiv\"{a}t korppujen ja kuivatun lihan kimppuun kuin saaliin ik\"{a}\"{a}n. Ajatellessaan is\"{a}ns\"{a} olevan yht\"{a} raakojen villien vankina Mary Grant tunsi kyynelten kihoavan silmiins\"{a}. H\"{a}n kuvitteli, kuinka suuresti Harry Grantin kaltaisen miehen t\"{a}ytyi k\"{a}rsi\"{a} n\"{a}iden vaeltavien heimojen orjana, puutteen, n\"{a}l\"{a}n ja huonon kohtelun uhrina. John Mangles, joka levottomana tarkkaili h\"{a}nt\"{a}, arvasi, mit\"{a} ajatuksia h\"{a}nen syd\"{a}mens\"{a} oli t\"{a}ynn\"{a}, ja eh\"{a}tti ennen pyynt\"{o}\"{a} puhuttelemaan \textit{Britannian} per\"{a}miest\"{a}. --- Ayrton, h\"{a}n sanoi, --- t\"{a}llaistenko villien kynsist\"{a} te p\"{a}\"{a}sitte pakenemaan? --- Niin, kapteeni, Ayrton vastasi. --- Kaikki sis\"{a}maan heimot ovat samanlaisia. Mutta t\"{a}\"{a}ll\"{a} te n\"{a}ette vain kourallisen heit\"{a}, kun sit\"{a} vastoin Darlingin rannoilla on v\"{a}kirikkaita heimoja, joiden p\"{a}\"{a}llik\"{o}ill\"{a} on pelottava valta. --- Mutta, John Mangles kysyi, --- mit\"{a} eurooppalainen voi tehd\"{a} n\"{a}iden villien keskuudessa? --- Mit\"{a} min\"{a}kin tein, Ayrton vastasi, --- h\"{a}n mets\"{a}st\"{a}\"{a}, kalastaa heid\"{a}n kanssaan, ottaa osaa heid\"{a}n taisteluihinsa; kuten jo olen teille sanonut, h\"{a}nt\"{a} kohdellaan sen mukaan mit\"{a} h\"{a}n tekee, ja jos h\"{a}n on \"{a}lyk\"{a}s ja uskalias mies, h\"{a}n saa heimossa huomattavan aseman. --- Mutta joutuuko h\"{a}n olemaan vankina? Mary Grant kysyi. --- Joutuu, ja vartioituna, Ayrton vahvisti, --- viel\"{a}p\"{a} sill\"{a} tavoin, ettei h\"{a}n voi astua askeltakaan y\"{o}ll\"{a} eik\"{a} p\"{a}iv\"{a}ll\"{a}. --- Mutta teid\"{a}n kumminkin onnistui karata, Ayrton, lausui majuri, joka tuli mukaan keskusteluun. --- Niin onnistui, herra MacNabbs, kun sattui taistelu minun heimoni ja er\"{a}\"{a}n naapuriheimon v\"{a}lill\"{a}. Min\"{a} onnistuin. Hyv\"{a} juttu, enk\"{a} sit\"{a} pahoittele. Mutta jos se t\"{a}ytyisi tehd\"{a} uudelleen, niin luulenpa, ett\"{a} valitsisin ikuisen orjuuden ennen kuin ne k\"{a}rsimykset, joita minun t\"{a}ytyi kest\"{a}\"{a} samotessani sis\"{a}maan er\"{a}maiden halki. Jumala varjelkoon kapteeni Grantia yritt\"{a}m\"{a}st\"{a} sellaista pelastusta! --- Niin tosiaan, John Mangles vastasi, --- toivokaamme, miss Mary, ett\"{a} is\"{a}nne on pysynyt alkuasukasheimon luona. Silloin l\"{o}yd\"{a}mme h\"{a}nen j\"{a}lkens\"{a} helpommin kuin jos h\"{a}n harhailisi mantereen metsiss\"{a}. --- Toivotteko te siis yh\"{a}? neito kysyi. --- Toivon toki, neiti Mary, n\"{a}kev\"{a}ni teid\"{a}t kerran onnellisena Jumalan avulla. Mary Grant saattoi kiitt\"{a}\"{a} nuorta kapteenia vain kyyneleisell\"{a} katseellaan. T\"{a}m\"{a}n keskustelun aikana oli villien kesken syntynyt tavatonta liikett\"{a}; he kiljahtelivat hirvitt\"{a}v\"{a}sti, juoksivat eri suuntiin, huitoivat k\"{a}si\"{a}ns\"{a} ja n\"{a}yttiv\"{a}t olevan hurjan raivon vallassa. Glenarvan ei tiennyt, mit\"{a} he tarkoittivat, kun majuri kysyi Ayrtonilta: --- Kun te olette kauan aikaa el\"{a}nyt australialaisten parissa, niin ymm\"{a}rr\"{a}tte varmaan n\"{a}idenkin kielt\"{a}? --- Enp\"{a} juuri, per\"{a}mies vastasi, --- sill\"{a} murteita on yht\"{a} monta kuin heimojakin. Mutta arvelisin, ett\"{a} n\"{a}m\"{a} villit haluavat kiitollisuuden osoitukseksi esitt\"{a}\"{a} taistelun\"{a}yt\"{o}ksen h\"{a}nen jalosukuisuudelleen. Se oli todellakin t\"{a}m\"{a}n metelin syyn\"{a}. Ilman enempi\"{a} valmisteluja villit hy\"{o}kk\"{a}siv\"{a}t toistensa kimppuun n\"{a}k\"{o}j\"{a}\"{a}n niin raivokkaasti, ett\"{a} ellei asiaa ennakolta olisi tiedetty, olisi kamppailua voinut luulla todelliseksi. Mutta australialaiset ovatkin tutkimusmatkailijoiden kertoman mukaan mainioita n\"{a}yttelij\"{o}it\"{a}, ja ainakin t\"{a}ss\"{a} tilaisuudessa he osoittivat erinomaista taitoa. Heid\"{a}n hy\"{o}kk\"{a}ys- ja puolustusaseinaan oli er\"{a}\"{a}nlainen puinen sotanuija, jolla voi puhkaista paksummankin kallon, omalaatuinen tomahawk, hyvin kova ter\"{a}v\"{a}ksi hiottu kivi, sitke\"{a}ll\"{a} kumilla kahden kepin v\"{a}liin kiinnitetty. T\"{a}ss\"{a} kirveess\"{a} on kolmimetrinen varsi; kamala sota-ase samalla kuin hy\"{o}dyllinen ty\"{o}kalu, jolla voi ly\"{o}d\"{a} poikki oksia tai p\"{a}it\"{a}, iske\"{a} miest\"{a} tai puuta, aina tarpeen mukaan. N\"{a}it\"{a} aseita heristeltiin hurjasti k\"{a}siss\"{a}, kauheasti kiljuen taistelijat sy\"{o}ksyiv\"{a}t toistensa niskaan; toisia kaatui kuolleina maahan, toisten hihkuessa voitonhuutoja. Kuin pahanhengen riivaamina kannustivat naiset, varsinkin vanhemmat, miehi\"{a} taisteluun, sy\"{o}ksyiv\"{a}t muka kuolleina makaavien kimppuun ja olivat raatelevinaan niit\"{a} niin hurjasti, ettei se olisi ollut raakamaisempaa todellisuudessakaan. Joka hetki lady Helena pelk\"{a}si leikin muuttuvan todelliseksi taisteluksi. Lapset, jotka olivat ottaneet osaa taisteluun, jatkoivatkin sit\"{a} t\"{a}ydell\"{a} todella. Pikku pojat ja tyt\"{o}t, joista varsinkin j\"{a}lkimm\"{a}iset olivat raivokkaita, mukiloivat toisiaan aika lailla. Taistelun\"{a}yt\"{o}st\"{a} oli kest\"{a}nyt jo kymmenen minuuttia, kun taistelijat \"{a}kki\"{a} pys\"{a}htyiv\"{a}t. Aseet putosivat heid\"{a}n k\"{a}sist\"{a}\"{a}n. Syv\"{a} hiljaisuus seurasi rajua meteli\"{a}. Villit j\"{a}iv\"{a}t liikkumattomiksi viimeisiin asentoihinsa kuin kuvaelman\"{a}yt\"{o}ksen henkil\"{o}t. Olisi voinut luulla heid\"{a}n kivettyneen. Mik\"{a} oli t\"{a}m\"{a}n muutoksen syy, ja mist\"{a} \"{a}kki\"{a} johtui t\"{a}m\"{a} j\"{a}hmettyminen paikalleen? Se saatiin pian tiet\"{a}\"{a}. T\"{a}ll\"{a} hetkell\"{a} tuli n\"{a}kyviin parvi papukaijoja kumipuiden latvojen tasalla. Linnut t\"{a}yttiv\"{a}t ilman kirkunallaan ja n\"{a}yttiv\"{a}t monikirjavine h\"{o}yhenineen lent\"{a}v\"{a}lt\"{a} taivaankaarelta. T\"{a}m\"{a} kirkas lintupilvi oli keskeytt\"{a}nyt taistelun. Sit\"{a} seurasi sotaa hy\"{o}dyllisempi linnustus. Er\"{a}s villeist\"{a} otti punaiseksi maalatun, omituisen muotoisen aseen, j\"{a}tti yh\"{a} liikkumattomina pysyv\"{a}t toverinsa ja hiipi puiden ja pensaiden v\"{a}litse lintuparvea kohti. Ei kuulunut pienint\"{a}k\"{a}\"{a}n \"{a}\"{a}nt\"{a} h\"{a}nen ry\"{o}miess\"{a}\"{a}n, h\"{a}n ei kahauttanut lehte\"{a}, ei kolauttanut kive\"{a}. H\"{a}n liikkui kuin varjo. Kun villi oli saapunut sopivan v\"{a}limatkan p\"{a}\"{a}h\"{a}n, h\"{a}n heitti aseensa vaakasuoraan, vain puoli metri\"{a} maasta. Ase lensi reilut kymmenen metri\"{a}; sitten se \"{a}kki\"{a}, mihink\"{a}\"{a}n koskettamatta, kohosi suorassa kulmassa kolmenkymmenen metrin korkeuteen, tappoi kymmenkunta lintua, k\"{a}\"{a}nn\"{a}hti ja palasi heitt\"{a}j\"{a}ns\"{a} jalkoihin. Glenarvan ja h\"{a}nen kumppaninsa h\"{a}mm\"{a}styiv\"{a}t; he eiv\"{a}t olleet uskoa silmi\"{a}\"{a}n. --- Se on bumerangi! Ayrton sanoi. --- Bumerangi, Paganel huudahti, --- australialainen bumerangi! Ja niin kuin lapsi h\"{a}n juoksi sieppaamaan tuon kummallisen aseen, --- n\"{a}hd\"{a}kseen, mit\"{a} se sis\"{a}lsi. Olisi tosiaan voinut luulla, ett\"{a} jokin laite sen sis\"{a}ll\"{a}, \"{a}kki\"{a} lauennut jousi, muutti sen suuntaa. Mutta niin ei ollut laita! Bumerangi oli yksinkertaisesti 75-100 senttimetrin pituinen, k\"{a}yristetty, kova puunkappale. Se oli keskelt\"{a} noin 7,5 sentin paksuinen ja molemmista p\"{a}ist\"{a} ter\"{a}v\"{a}. Sen kovera puoli oli painettu noin sentin verran sis\"{a}\"{a}np\"{a}in, ja kuperalla puolella oli kaksi hyvin ter\"{a}v\"{a}\"{a} reunaa. Se oli yht\"{a} yksinkertaista kuin k\"{a}sitt\"{a}m\"{a}t\"{o}nt\"{a}. --- T\"{a}m\"{a} siis nyt on se kuuluisa bumerangi! Paganel sanoi tutkittuaan tarkasti omituista asetta. --- Puunkappale, ei muuta. Mink\"{a} vuoksi se vaakasuoraan kulkiessaan nousee tietyll\"{a} hetkell\"{a} ilmaan ja palaa sielt\"{a} heitt\"{a}j\"{a}ns\"{a} k\"{a}teen? Sit\"{a} ongelmaa eiv\"{a}t matkamiehet ja tietoviisaat ole kyenneet selitt\"{a}m\"{a}\"{a}n. --- Eik\"{o}h\"{a}n syy ole sama, mink\"{a} vuoksi vanne m\"{a}\"{a}r\"{a}tyll\"{a} tavalla heitettyn\"{a} tulee takaisin l\"{a}ht\"{o}kohtaansa? John Mangles arveli. --- Tai pikemminkin, Glenarvan lis\"{a}si, --- sellainen takaisinp\"{a}in suuntautuva ponnahdus kuin iskett\"{a}ess\"{a} biljardipalloa m\"{a}\"{a}r\"{a}ttyyn kohtaan? --- Ei laisinkaan, Paganel vastasi. --- Niiss\"{a} molemmissa tapauksissa on jokin kohta, joka muuttaa liikkeen suunnan; vanteelle maa, biljardipallolle valli. Mutta t\"{a}ss\"{a} ei sellaista ole, bumerangi ei koske maahan, mutta ponnahtaa kuitenkin aika korkealle! --- No, kuinka te sen selit\"{a}tte, herra Paganel? lady Helena kysyi. --- Selitt\"{a}\"{a} en osaa, rouva, min\"{a} vain totean sen viel\"{a} kerran; vaikutus johtuu ilmeisesti siit\"{a} tavasta, kuinka bumerangia heitet\"{a}\"{a}n, ja itse esineen erikoisesta muodosta. Mutta tuo heittotapa on viel\"{a} australilaisten salaisuus. --- Joka tapauksessa se on hyvin nerokasta ... apinoiden keksim\"{a}ksi, lady Helena lis\"{a}si katsahtaen majuriin, joka pudisti p\"{a}\"{a}t\"{a}\"{a}n ep\"{a}uskoisen n\"{a}k\"{o}isen\"{a}. Mutta aika kului, ja Glenarvan arveli, ettei sopinut en\"{a}\"{a} viivytt\"{a}\"{a} matkaa it\"{a}\"{a}np\"{a}in; h\"{a}n aikoi siis pyyt\"{a}\"{a} matkalaisia nousemaan j\"{a}lleen vankkureihin, kun er\"{a}s villi saapui juoksujalkaa ja sanoi muutamia sanoja kovin kiihtyneen\"{a}. --- Ah, Ayrton ilmoitti, --- he ovat n\"{a}hneet kasuaareja! --- Mit\"{a}, onko puhe niiden pyydyst\"{a}misest\"{a}? Glenarvan kysyi. --- Se pit\"{a}\"{a} n\"{a}hd\"{a}, Paganel huudahti. --- Se on varmaankin mielenkiintoista! Ehk\"{a}p\"{a} bumerangia j\"{a}lleen k\"{a}ytet\"{a}\"{a}n. --- Mit\"{a} te arvelette, Ayrton? --- Ei se kauan kest\"{a}, mylord, per\"{a}mies vastasi. Villit eiv\"{a}t olleet hukanneet sekuntiakaan. Tilaisuus mets\"{a}st\"{a}\"{a} kasuaareja on heille onnenpotku. Heimon ruokavarat olisi siten taattu moneksi p\"{a}iv\"{a}ksi. Niinp\"{a} pyydyst\"{a}j\"{a}t k\"{a}ytt\"{a}v\"{a}tkin kaiken taitonsa saadakseen sellaisen saaliikseen. Mutta kuinka he ilman pyssy\"{a} osuvat ja ilman koiria tavoittavat niin nopean el\"{a}imen? Se oli hyvin j\"{a}nnitt\"{a}v\"{a} seikka Paganelin haluamassa n\"{a}ytelm\"{a}ss\"{a}. Emu, eli kyp\"{a}r\"{a}t\"{o}n kasuaari, er\"{a}s strutsilaji, villien kielell\"{a} ``mur\"{o}k'', alkaa jo olla harvinainen el\"{a}in Australian tasangoilla. T\"{a}m\"{a}n kookkaan, metrin korkuisen linnun liha on valkoista, ja muistuttaa suuresti kalkkunan lihaa; sen p\"{a}\"{a}ss\"{a} on sarveismainen levy; silm\"{a}t ovat kirkkaan ruskeat, nokka musta ja ylh\"{a}\"{a}lt\"{a} alas kaareva; varpaissa sill\"{a} on valtavat kynnet; siivet tai oikeammin siiventyng\"{a}t eiv\"{a}t voi nostaa sit\"{a} lentoon; h\"{o}yhenet, jotka ovat melkein kuin turkispeite, ovat tummemmat kaulan ja rinnan kohdalla. Mutta vaikkei se lenn\"{a}, se osaa juosta ja voittaisi kilparadalla nopeimmankin hevosen. Sit\"{a} ei siis voi saavuttaa muutoin kuin viekkaudella, ja silloin saakin olla eritt\"{a}in viekas. Niinp\"{a} villien p\"{a}\"{a}llik\"{o}n k\"{a}skyst\"{a} kymmenkunta miest\"{a} asettui riviin kuin sotilasosasto. Pyyntialueena oli kaunis tasanko, jossa villin\"{a} kasvava indigo teki maan siniseksi kukkasillaan. Matkalaiset pys\"{a}htyiv\"{a}t katselemaan mimoosametsik\"{o}n reunaan. Villien l\"{a}hestyess\"{a} kasuaarit, joita oli kuusi, l\"{a}htiv\"{a}t pakoon ja pys\"{a}htyiv\"{a}t vasta noin kilometrin p\"{a}\"{a}ss\"{a} levolle. Kun heimon johtaja oli pannut merkille niiden aseman, h\"{a}n antoi tovereilleen merkin j\"{a}\"{a}d\"{a} paikalleen. N\"{a}m\"{a} heitt\"{a}ytyiv\"{a}t pitk\"{a}kseen maahan, mutta johtaja otti laukustaan kaksi taitavasti ommeltua kasuaarinnahkaa ja pukeutui niihin. H\"{a}n piti oikeaa k\"{a}tt\"{a} p\"{a}\"{a}ns\"{a} yl\"{a}puolella ja matki eleill\"{a}\"{a}n ravintoa etsiv\"{a}n kasuaarin liikkeit\"{a}. Pyydyst\"{a}j\"{a} hiipi lintuparvea kohti; joskus h\"{a}n pys\"{a}htyi ollen poimivinaan joitakin jyv\"{a}si\"{a}; joskus kaapi maata jaloillaan nostaen ymp\"{a}rilleen p\"{o}lypilven. Kaikki n\"{a}m\"{a} temput suoritettiin mainiosti. Ei mik\"{a}\"{a}n voinut olla t\"{a}ydellisemp\"{a}\"{a} kuin t\"{a}m\"{a} kasuaarin matkiminen. Mies p\"{a}\"{a}sti ilmoille karkeita \"{a}\"{a}nn\"{a}hdyksi\"{a}, jotka olisivat pett\"{a}neet itse lintuakin. Ja lopulta niin k\"{a}vikin. Villi oli pian huolettoman parven keskell\"{a}. \"{A}kki\"{a} h\"{a}nen k\"{a}sivartensa heilautteli nuijaa, ja viisi kasuaaria kuudesta kaatui h\"{a}nen ymp\"{a}rilleen. Mets\"{a}st\"{a}j\"{a} oli onnistunut; pyynti oli p\"{a}\"{a}ttynyt. Nyt Glenarvan, naiset ja muu matkaseura sanoivat j\"{a}\"{a}hyv\"{a}iset australialaisille. N\"{a}m\"{a} eiv\"{a}t n\"{a}ytt\"{a}neet t\"{a}t\"{a} eroa pahoittelevan. Ehk\"{a} oli kasuaarimets\"{a}styksen onnistuminen saanut heid\"{a}t unohtamaan n\"{a}lk\"{a}ns\"{a} tyydytt\"{a}misen. Heill\"{a} ei ollut edes vatsan kiitollisuutta, joka raakalaisissa ja el\"{a}imiss\"{a} on suurempi kuin syd\"{a}men. Oli miten tahansa, muutamissa suhteissa ei voinut olla ihmettelem\"{a}tt\"{a} heid\"{a}n \"{a}ly\"{a}\"{a}n ja taitavuuttaan. --- Nyt, rakas MacNabbs, lady Helena sanoi, --- te kai sent\"{a}\"{a}n my\"{o}nt\"{a}nette, ett\"{a} australialaiset eiv\"{a}t ole apinoita? --- Senk\"{o} vuoksi, ett\"{a} he taitavasti matkivat el\"{a}inten eleit\"{a}? majuri vastasi. --- Seh\"{a}n p\"{a}invastoin vahvistaisi minun olettamustani. --- Leikinlasku ei ole vastaus, lady Helena sanoi. --- Min\"{a} vaadin, majuri, teit\"{a} peruuttamaan v\"{a}itteenne. --- No niin, hyv\"{a} serkku, pit\"{a}nee my\"{o}nt\"{a}\"{a} tai oikeammin kielt\"{a}\"{a}. Australialaiset eiv\"{a}t ole apinoita, mutta apinat ovat australialaisia. --- Mit\"{a} ihmett\"{a}! --- Niin, muistakaa mit\"{a} neekerit v\"{a}itt\"{a}v\"{a}t mielenkiintoisesta orangutangien rodusta. --- Mit\"{a} he v\"{a}itt\"{a}v\"{a}t? lady Helena kysyi. --- He v\"{a}itt\"{a}v\"{a}t, majuri vastasi, --- ett\"{a} apinat ovat mustia kuten hekin, mutta ilke\"{a}mpi\"{a}: --- Se ei puhu, ettei tarvitsisi tehd\"{a} ty\"{o}t\"{a}, sanoi kateellinen neekeri kesyst\"{a} orangutangista, jota h\"{a}nen is\"{a}nt\"{a}ns\"{a} el\"{a}tti ilman aikojaan. \gutchapter{UPPORIKKAAT KARJANOMISTAJAT.} Vietetty\"{a}\"{a}n rauhallisen y\"{o}n 146$^{\circ}$ 15' pituusasteen kohdalla matkailijat jatkoivat 6. p\"{a}iv\"{a}n\"{a} tammikuuta kello seitsem\"{a}n aamulla retke\"{a}\"{a}n laajan pirikunnan poikki. He kulkivat yh\"{a} auringonnousua kohti, ja heid\"{a}n askeltensa j\"{a}ljet ulottuivat suorana viivana lakeudella. Kaksi kertaa he tapasivat pohjoiseen kulkeneiden karjankasvattajien j\"{a}lki\"{a}, ja silloin n\"{a}m\"{a} eri j\"{a}ljet olisivat sekaantuneet, ellei Glenarvanin hevonen olisi j\"{a}tt\"{a}nyt maahan kahdesta apilastaan tunnettua Black Pointin merkki\"{a}. Tasankoa uursivat siell\"{a} t\"{a}\"{a}ll\"{a} mutkittelevat, puksipensaiden reunustamat joet, joissa oli toisinaan vett\"{a} mutta ei aina. Ne alkoivat Buffalo Ranges-nimisen horisontin reunaan aaltomaisena piirtyv\"{a}n keskikorkean vuorijonon rinteilt\"{a}. Illalla p\"{a}\"{a}tettiin y\"{o}py\"{a} sinne. Ayrton hoputti valjakkoaan, ja juhdat olivat silloin hiukan v\"{a}syneit\"{a} noin viidenkymmenen kilometrin p\"{a}iv\"{a}matkan j\"{a}lkeen. Teltta pystytettiin suurten puiden alle; kun oli jo hyvin my\"{o}h\"{a}, illallinen sy\"{o}tiin nopeasti. Sellaisen p\"{a}iv\"{a}matkan j\"{a}lkeen ajateltiin enemm\"{a}n nukkumista kuin sy\"{o}mist\"{a}. Paganel, jolla oli ensimm\"{a}inen vahtivuoro, ei pannut maata, vaan paremmin valveilla pysy\"{a}kseen k\"{a}veli pyssy olalla edestakaisin pitkin leiri\"{a}. Vaikka ei ollut kuutamoa, y\"{o} oli melkein valoisa etel\"{a}n t\"{a}htisikermien tuikkeesta. Tiedemies luki mielihyvin t\"{a}t\"{a} taivaan aina avointa, suurta ja sen tuntevalle niin mielenkiintoista kirjaa. Uinuvan luonnon syv\"{a}\"{a} hiljaisuutta ei keskeytt\"{a}nyt muu kuin hevosten jalkoihin sidottujen liekojen rahina. Paganel antautui siis t\"{a}htitieteellisiin mietteisiins\"{a} ja oli enemm\"{a}n kiinnostunut taivaan kuin maan asioista, kun kaukainen \"{a}\"{a}ni her\"{a}tti h\"{a}net ajatuksistaan. H\"{a}n kuunteli tarkasti ja oli suureksi h\"{a}mm\"{a}styksekseen kuulevinaan pianonsoittoa. Muutamat korkeat ja matalat soinnut v\"{a}reiliv\"{a}t h\"{a}nen korvaansa saakka. H\"{a}n ei voinut erehty\"{a}. --- Piano er\"{a}maassa! Paganel mutisi. --- Sit\"{a} en ikin\"{a} my\"{o}nn\"{a} todeksi. Se oli todella kovin outoa ja Paganel uskoi mieluummin, ett\"{a} jokin omituinen Australian lintu j\"{a}ljitteli Pleyel- tai Erard-pianon sointuja kuten toiset j\"{a}ljittelev\"{a}t kellon raksutusta ja tahkon sihin\"{a}\"{a}. Mutta silloin kuului ilmassa puhdas \"{a}\"{a}ni. Pianonsoittajaan yhtyi laulaja. Paganel kuunteli tahtomatta uskoa korviaan. Mutta muutaman sekunnin kuluttua h\"{a}nen oli pakko my\"{o}nt\"{a}\"{a}, ett\"{a} h\"{a}nen korviinsa kuului ihana s\"{a}velm\"{a}. Se oli ``\textit{Il mio tesoro tanto}'', oopperasta \textit{Don Juan}. --- Hemmetti! ajatteli Paganel, --- niin merkillisi\"{a} kuin Australian linnut ovatkin ja vaikka ne olisivat maailman musikaalisimpia papukaijoja, eiv\"{a}t ne voi laulaa Mozartia! Sitten h\"{a}n kuunteli loppuun saakka mestarin suurenmoisen s\"{a}vellyksen. T\"{a}m\"{a}n sulavan, kuulakkaassa y\"{o}ss\"{a} kaikuvan s\"{a}velm\"{a}n vaikutus oli sanoin kuvaamaton. Paganel oli kauan aikaa sanomattoman hurmion vallassa; sitten \"{a}\"{a}ni vaikeni, ja kaikki oli j\"{a}lleen hiljaa. Kun Wilson tuli vapauttamaan Paganelia, h\"{a}n tapasi t\"{a}m\"{a}n syviin mietteisiin vaipuneena. Paganel ei sanonut mit\"{a}\"{a}n matruusille; h\"{a}n p\"{a}\"{a}tti ilmoittaa merkillisen havaintonsa vasta huomenna Glenarvanille ja meni telttaan nukkumaan. Seuraavana aamuna odottamaton koirien haukunta her\"{a}tti koko seurueen. Glenarvan nousi heti. Kaksi komeaa, korkeajalkaista pointteria, englantilaisen lintukoirarodun verratonta edustajaa, juoksenteli metsik\"{o}n reunassa. Matkalaisten l\"{a}hestyess\"{a} ne per\"{a}ytyiv\"{a}t puiden suojaan haukkuen kiivaammin. --- T\"{a}ss\"{a} er\"{a}maassa on siis jokin siirtola, Glenarvan sanoi, --- ja mets\"{a}st\"{a}ji\"{a}, sill\"{a} n\"{a}m\"{a}h\"{a}n ovat jahtikoiria. Paganel avasi jo suunsa kertoakseen viime\"{o}iset havaintonsa, kun paikalle ilmestyi kaksi nuorta miest\"{a} ratsastaen kahdella komealla rotuhevosella, todellisilla ``huntereilla''. Molemmat siroa mets\"{a}styspukua k\"{a}ytt\"{a}v\"{a}t herrat pys\"{a}htyiv\"{a}t n\"{a}hdess\"{a}\"{a}n pienen, mustalaistapaan leiriytyneen joukkion. He n\"{a}yttiv\"{a}t aprikoivan, mit\"{a} aseellisten miesten l\"{a}sn\"{a}olo t\"{a}ll\"{a} paikkakunnalla oikeastaan merkitsi, kun huomasivat vankkureista juuri nousevat naiset. Silloin he astuivat ratsailta alas ja tulivat n\"{a}it\"{a} kohti lakki kourassa. Lordi Glenarvan meni heit\"{a} vastaan ja ilmoitti vieraana nimens\"{a} ja arvonsa. Nuoret miehet kumarsivat, ja heist\"{a} vanhempi sanoi: --- Mylord, n\"{a}m\"{a} naiset, teid\"{a}n seuralaisenne ja te, tahdotteko suoda meille sen kunnian, ett\"{a} lev\"{a}ht\"{a}isitte meid\"{a}n asunnossamme? --- Hyv\"{a}t herrat...? Glenarvan sanoi. --- Michel ja Sandy Patterson, Hottam-aseman omistajat. Te olette jo talon tiluksilla eik\"{a} sinne ole edes puolen kilometrin matkaa. --- Hyv\"{a}t herrat, Glenarvan vastasi, --- en tahtoisi v\"{a}\"{a}rink\"{a}ytt\"{a}\"{a} niin kohteliaasti tarjoamaanne vieraanvaraisuutta... --- Mylord, Michel Patterson huomautti, --- suostumalla saatatte vain kiitollisuudenvelkaan erakkoparat, jotka olisivat perin onnellisia saadessaan tarjota teille, mit\"{a} er\"{a}maassa on mahdollista. Glenarvan kumarsi suostumuksen merkiksi. --- Hyv\"{a} herra, Paganel sanoi silloin k\"{a}\"{a}ntyen Michel Pattersonin puoleen, --- olenko liian utelias, jos kysyn, tek\"{o} eilen illalla lauloitte jumalaisen Mozartin aarian? --- Min\"{a}, hyv\"{a} herra, vastaus kuului, --- ja veljeni Sandy s\"{a}esti minua. --- Jaha, Paganel jatkoi, --- ottakaa siin\"{a} tapauksessa vastaan vilpit\"{o}n kiitos ranskalaiselta, t\"{a}m\"{a}n musiikin innokkaalta ihailijalta. Paganel ojensi k\"{a}tens\"{a} nuorelle herrasmiehelle, joka tarttui siihen eritt\"{a}in herttaisesti. Sitten Michel Patterson osoitti oikeanpuolista tiet\"{a}, jota my\"{o}ten oli ment\"{a}v\"{a}. Hevoset j\"{a}tettiin Ayrtonin ja matruusien hoitoon. Molempien nuorten miesten opastamina matkailijat l\"{a}htiv\"{a}t puhellen ja ihmetellen Hottam-aseman kartanoon. Se oli tosiaan suurenmoinen tila, englantilaisten puistojen ankaraan tyyliin j\"{a}rjestetty. Suunnattomia, aidattuja niittyj\"{a} aukeni silm\"{a}nkantamattomiin. Siell\"{a} oli laitumella tuhansia nautoja, miljoonia lampaita. Suuri joukko paimenia ja viel\"{a} enemm\"{a}n koiria oli t\"{a}t\"{a} meluavaa armeijaa vartioimassa. Mylvin\"{a}\"{a}n ja m\"{a}\"{a}kyn\"{a}\"{a}n sekaantui koirien haukunta ja ruoskien \"{a}\"{a}nek\"{a}st\"{a} m\"{a}iskett\"{a}. Id\"{a}ss\"{a} katse pys\"{a}htyi myrtti- ja kumipuu-rajaan, jota hallitsi Hottam-vuoren valtava huippu yli kahdentuhannen metrin korkuisena. Pitki\"{a}, ikivihreiden puiden reunustamia kujia ulottui s\"{a}teitt\"{a}in joka suuntaan. Siell\"{a} t\"{a}\"{a}ll\"{a} oli tiheit\"{a} ``grass-tree"-rykelmi\"{a}, kolmen metrin korkuisia k\"{a}\"{a}pi\"{o}palmuja muistuttavia pensaita, jotka peittyiv\"{a}t kapeiden ja pitkien lehtiens\"{a} verhoon. Ilma oli t\"{a}ynn\"{a} laakeriminttujen, joiden valkoiset kukkakimput juuri olivat parhaassa kukoistuksessaan, mit\"{a} hienointa tuoksua. N\"{a}iden kotimaisten puiden vieh\"{a}tt\"{a}viin ryhmiin liittyi eurooppalaisesta ilmastosta t\"{a}nne siirrettyj\"{a} kasveja. Persikka-, p\"{a}\"{a}ryn\"{a}-, omena-, viikuna- ja appelsiinipuita, jopa tammiakin, saivat matkalaiset t\"{a}\"{a}ll\"{a} mielikseen katsella; jos he eiv\"{a}t viel\"{a} kovin kummastelleet, ett\"{a} olivat joutuneet kotimaansa puiden siimekseen, he \"{a}llistyiv\"{a}t ainakin n\"{a}hdess\"{a}\"{a}n oksien lomissa lentelevi\"{a} lintuja, silkkih\"{o}yhenisi\"{a} atlaslintuja ja muita ik\"{a}\"{a}n kuin puoliksi kultaan, puoliksi mustaan samettiin puettuja siivekk\"{a}it\"{a}. Muiden muassa he nyt saivat ensimm\"{a}ist\"{a} kertaa ihailla ``menurea''. Se on lyyralintu, jonka pyrst\"{o} muistuttaa Orfeuksen kaunista soitinta. Se pakeni puumaisten sanajalkojen v\"{a}liin, ja kun sen pyrst\"{o} kosketti oksia, teki melkein mieli kummastella, ettei kuulunut niit\"{a} sulosointuja, joista Amfion innostui rakentamaan uudelleen Theban muurit. Paganel olisi tahtonut soitella sill\"{a}. Mutta lordi Glenarvan ei tyytynyt vain ihailemaan t\"{a}m\"{a}n Australian er\"{a}maahan loihditun keitaan lumoavia ihmeit\"{a}. H\"{a}n kuunteli nuorten herrojen kertomusta. Englannissa, sen sivistyneell\"{a} maaseudulla, olisi taloon astunut vieras heti aluksi ilmoittanut is\"{a}nn\"{a}lleen, mist\"{a} oli tulossa ja minne menossa. Mutta t\"{a}\"{a}ll\"{a} katsoivat Michel ja Sandy Patterson herk\"{a}n hienotunteisina velvollisuudekseen ilmoittaa matkalaisille, keiden vieraina he olivat. Niinp\"{a} he kertoivat tarinansa. Se oli sama kuin kaikkien niiden nuorten, \"{a}lykk\"{a}iden ja yritteli\"{a}iden englantilaisten, jotka eiv\"{a}t katso rikkauden vapauttavan ty\"{o}nteosta. Michel ja Sandy Patterson olivat lontoolaisen pankkiirin poikia. Kun he olivat tulleet parinkymmenen vuoden ik\"{a}\"{a}n, perheen p\"{a}\"{a}mies oli sanonut heille: --- T\"{a}ss\"{a} on miljoonia, nuoret miehet. Menk\"{a}\"{a} johonkin kaukaiseen siirtokuntaan; perustakaa siell\"{a} jokin hy\"{o}dyllinen yritys; oppikaa ty\"{o}ss\"{a} tuntemaan el\"{a}m\"{a}\"{a}. Jos onnistutte, sen parempi. Jos yrityksenne ei menesty, ei ole v\"{a}li\"{a}. Me emme sure miljoonia, jotka ovat tehneet teist\"{a} miehi\"{a}. Nuoret miehet tottelivat. He valitsivat australialaisen Victorian maakunnan kylv\"{a}\"{a}kseen sinne is\"{a}n antamat rahat, eik\"{a} heid\"{a}n tarvinnut sit\"{a} katua. Kolmen vuoden kuluttua oli maatila kukoistavassa kunnossa. Victorian, Uuden Etel\"{a}-Walesin ja Etel\"{a}-Australian maakunnissa lasketaan olevan yli kolmetuhatta asemaa; toisia n\"{a}ist\"{a} johtavat karjaa kasvattavat squatterit, toisia muut uudisviljelij\"{a}t, joiden p\"{a}\"{a}elinkeinona on maanviljelys. N\"{a}iden nuorten englantilaisten tuloon saakka oli suurin t\"{a}m\"{a}nlaatuisista tiloista er\"{a}\"{a}n Jamesonin. Sen pinta-ala oli sata neli\"{o}kilometri\"{a} kahdenkymmenenviiden kilometrin matkalla Darlingin lis\"{a}joen Paroon rannalla. Nyt oli Hottamin asema ylitt\"{a}nyt sen sek\"{a} laajuuden ett\"{a} tuotannon puolesta. Sen is\"{a}nn\"{a}t olivat samalla kertaa sek\"{a} karjanhoitajia ett\"{a} maanviljelij\"{o}it\"{a}. He hoitivat valtavaa tilaansa harvinaisen taitavasti ja, mik\"{a} viel\"{a} vaikeampaa, tavattoman tarmokkaasti. T\"{a}m\"{a} asema sijaitsi pitk\"{a}n matkan p\"{a}\"{a}ss\"{a} kaupungeista, Murrayn melkein asumattomien er\"{a}maiden keskell\"{a}. Se t\"{a}ytti 146$^{\circ}$ 48' ja 147$^{\circ}$ v\"{a}lisen alueen, toisin sanoen kahdenkymmenenkahden kilometrin pituisen ja levyisen alan Buffalo Rangesin ja Mount Hottamin v\"{a}lill\"{a}. T\"{a}m\"{a}n laajan neli\"{o}n pohjoiskulmissa kohosi vasemmalla Mount Aberdeen ja oikealla High-Barvenin kukkula. Kauniita ja kiemurtelevia puroja ei puuttunut: ne olivat Murrayhin pohjoisessa yhtyv\"{a}n Owenin joen lis\"{a}jokia ja poukamia. Niinp\"{a} t\"{a}\"{a}ll\"{a} menestyiv\"{a}t karjanhoito ja maanviljelys yht\"{a}lailla. Nelj\"{a}tuhatta hehtaaria j\"{a}rkiper\"{a}iseen vuoroviljelykseen palstoitettua maata antoi ulkomaisten tuotteiden ohella kotimaista satoa, ja miljoonittain el\"{a}imi\"{a} oli lihomassa vihannilla laitumilla. Hottam-aseman tuotteet olivatkin korkeassa kurssissa Castlemainen ja Melbournen markkinoilla. Kun Michel ja Sandy Patterson olivat saaneet kerrotuksi n\"{a}m\"{a} piirteet yritteli\"{a}\"{a}st\"{a} toiminnastaan, n\"{a}kyi asuinrakennus er\"{a}\"{a}n casuarina-kujan p\"{a}\"{a}ss\"{a}. Se oli vieh\"{a}tt\"{a}v\"{a}, puusta ja tiilist\"{a} rakennettu talo emerophilis-puistikon keskell\"{a}, siroa sveitsil\"{a}ist\"{a} huvilatyyli\"{a} ja kiinalaisin lyhdyin koristettu kuistikko ymp\"{a}r\"{o}i koko rakennusta kuin muinaisajan impluvium. Ikkunoiden edess\"{a} oli moniv\"{a}risi\"{a}, ik\"{a}\"{a}n kuin kukkivia kaihtimia. Ei mik\"{a}\"{a}n voisi olla viehke\"{a}mm\"{a}n ja houkuttelevamman n\"{a}k\"{o}ist\"{a}, mutta ei my\"{o}sk\"{a}\"{a}n mukavampaa. Nurmikoilla ja metsik\"{o}iss\"{a} l\"{a}hist\"{o}ll\"{a} n\"{a}htiin pronssisia kynttil\"{a}njalkoja, joissa oli sirot lyhdyt; illan tullessa valaistiin koko puisto valkoisella kaasuliekill\"{a} pienest\"{a} s\"{a}ili\"{o}st\"{a}, joka oli tuuheiden puumaisten saniaisten peitossa. Muuten ei n\"{a}kynyt ulkohuoneita, talleja tai vajoja, ei mit\"{a}\"{a}n maanviljelykseen viittaavaa. Kaikki n\"{a}m\"{a} lis\"{a}rakennukset --- kokonainen kyl\"{a}, jossa oli yli kaksikymment\"{a} vajaa ja taloa --- sijaitsivat puolen kilometrin p\"{a}\"{a}ss\"{a}, pienen laakson pohjalla. S\"{a}hk\"{o}langat pitiv\"{a}t yll\"{a} jatkuvaa yhteytt\"{a} t\"{a}m\"{a}n kyl\"{a}n ja is\"{a}ntien asunnon v\"{a}lill\"{a}. Kaukana kaikesta melusta j\"{a}lkimm\"{a}inen peittyi ulkomaisten puiden metsikk\"{o}\"{o}n. Pian oltiin casuarina-kujan p\"{a}\"{a}ss\"{a}. Pieni, solisevan puron yli rakennettu, siro rautasilta lis\"{a}si eristetyn puiston vaikutelmaa. Astuttiin toiselle puolelle. Juhlallisen n\"{a}k\"{o}inen vouti saapui tulijoita vastaan; talon ovet avattiin, ja Hottam-aseman vieraat astuivat tiili- ja kukkakuoren alaisiin komeisiin huoneisiin. Taiteellisen ja uhkean el\"{a}m\"{a}n koko loisto avautui heid\"{a}n silmiens\"{a} eteen. Eteisest\"{a}, jonka koristeiden aiheet oli otettu kilparata- ja mets\"{a}stysaloilta, tultiin suureen, viisi-ikkunaiseen saliin. Piano, jonka kansi oli t\"{a}ynn\"{a} klassisia ja uusia nuotteja, taulutelineet alulle pantuine maalauksineen, marmoriveistokset jalustoineen, flaamilaisten mestarien taulut seinill\"{a}, upeat matot, jalalle niin suloiset kuin paksu ruoho, hilpe\"{a}t gobeliinit viehkeist\"{a} mytologisista aiheista, antiikkinen lamppu katossa, kallisarvoiset fajanssiesineet, hienot ja aistikkaat korut, tuhannet arvokkaat pikkuesineet, joita oli h\"{a}mm\"{a}stytt\"{a}v\"{a} n\"{a}hd\"{a} australialaisessa asunnossa, olivat todistamassa taiteiden ja mukavuudenhalun onnistuneinta yhtym\"{a}\"{a}. Kaikkea, mik\"{a} saattoi lievent\"{a}\"{a} vapaaehtoisen maanpaon vaivoja, kaikkea, mik\"{a} oli omiaan palauttamaan mieleen eurooppalaisten olojen muiston, oli t\"{a}ss\"{a} tarumaisessa salissa. Olisi luullut olevansa jossakin Ranskan tai Englannin linnassa. Viiden ikkunan kaihtimet p\"{a}\"{a}stiv\"{a}t hienon kudoksen l\"{a}pi kuistikon puolih\"{a}m\"{a}r\"{a}n jo vaimentamaa valoa. Lady Helena ihastui astuessaan t\"{a}h\"{a}n huoneeseen. T\"{a}lt\"{a} puolelta rakennusta oli n\"{a}k\"{o}ala laajaan la\"{a}ksoon, joka ulottui id\"{a}ss\"{a} kohoavien vuorten juurelle saakka. Niittyjen ja metsik\"{o}iden vuorottelu, siell\"{a} t\"{a}\"{a}ll\"{a} laajoja lakeuksia, sirosti py\"{o}ristyneiden kukkuloiden kokonaisuus, maaper\"{a}n vaihteleva korkeus tarjosi sanoin kuvaamattoman kauniin n\"{a}kym\"{a}n. Mit\"{a}\"{a}n muuta seutua ei olisi voinut verrata siihen, ei edes kuuluisaa Paratiisilaaksoa Telemarkin Norjanpuoleisella rajalla. T\"{a}m\"{a} laaja, suuriin varjo- ja valol\"{a}ikkiin jaettu n\"{a}k\"{o}ala muutti joka hetki muotoaan auringon oikkujen mukaan. Mielikuvitus ei voinut keksi\"{a} mit\"{a}\"{a}n enemp\"{a}\"{a}, ja ihana n\"{a}ky tyydytti katseen kaikki mielihalut. T\"{a}ll\"{a} v\"{a}lin talon vouti oli Sandy Pattersonin k\"{a}skyst\"{a} valmistanut aamiaisen, ja ennen kuin nelj\"{a}nnestunti oli kulunut heid\"{a}n saapumisestaan, istuivat matkalaiset uhkeasti katetun p\"{o}yd\"{a}n ymp\"{a}rill\"{a}. Ruokien ja viinien laatu oli verraton; mutta eniten miellytti kaiken t\"{a}m\"{a}n ylenpalttisuuden keskell\"{a} nuorten karjankasvattajien ilo siit\"{a}, ett\"{a} saivat kattonsa alla tarjota t\"{a}t\"{a} loistavaa vieraanvaraisuutta. He saivat pian tiet\"{a}\"{a} retkikunnan tarkoituksen ja kuuntelivat hartaasti kertomusta Glenarvanin etsiskelyst\"{a}, antoivatpa viel\"{a} hyvi\"{a} toiveita kapteeni Grantin lapsille. --- Harry Grant, Michel sanoi, --- on ilmeisesti joutunut alkuasukkaiden k\"{a}siin, koska h\"{a}nt\"{a} ei ole n\"{a}kynyt rannikon asutuksilla. H\"{a}n tiesi tarkasti asemansa, kuten asiakirja todistaa, ja kun h\"{a}n ei ole saapunut mihink\"{a}\"{a}n englantilaiseen siirtolaan, h\"{a}nen on t\"{a}ytynyt heti maihin p\"{a}\"{a}stess\"{a}\"{a}n joutua villien vangiksi. --- Juuri niin tapahtui h\"{a}nen per\"{a}miehelleen Ayrtonille, John Mangles sanoi. --- Mutta te, herrat, lady Helena kysyi, --- ettek\"{o} te ole milloinkaan kuulleet puhuttavan \textit{Britannian} haaksirikosta? --- Emme milloinkaan, rouva, Michel vastasi. --- Mink\"{a}laisen kohtelun on kapteeni Grant teid\"{a}n luullaksenne saanut australialaisten vankina? --- Australialaiset eiv\"{a}t ole julmia, rouva, nuori karjankasvattaja vastasi, --- ja neiti Grant voi olla huoleton siin\"{a} suhteessa. Heid\"{a}n luonteensa lempeydest\"{a} on useita esimerkkej\"{a}, ja moni eurooppalainen on kauan aikaa asunut heid\"{a}n parissaan voimatta milloinkaan valittaa heid\"{a}n julmuuttaan. --- King muiden muassa, Paganel sanoi, --- ainoa Burken retkikunnasta eloonj\"{a}\"{a}nyt. --- Ei ainoastaan se rohkea retkeilij\"{a}, Sandy huomautti, --- vaan my\"{o}s er\"{a}s englantilainen sotamies, nimelt\"{a}\"{a}n Buckley, joka karattuaan vuonna 1803 Port Philipin rannikolle joutui alkuasukkaiden vangiksi ja eli kolmekymment\"{a}kolme vuotta heid\"{a}n parissaan. --- Ja sittemmin, Michel Patterson lis\"{a}si, --- er\"{a}s \textit{Ausiralasianin} viimeisi\"{a} numeroita kertoo, ett\"{a} muuan Morrill on \"{a}skett\"{a}in palannut maanmiestens\"{a} pariin kuusitoista vuotta kest\"{a}neen orjuuden j\"{a}lkeen. Kapteenin on luultavasti k\"{a}ynyt samoin kuin h\"{a}nen, sill\"{a} h\"{a}n joutui \textit{Peruviennen} haaksirikon johdosta 1846 alkuasukkaiden vangiksi, ja he veiv\"{a}t h\"{a}net sis\"{a}maahan. Niinp\"{a} luulen, ett\"{a} voitte olla hyv\"{a}ss\"{a} toivossa. N\"{a}m\"{a} sanat her\"{a}ttiv\"{a}t suurta iloa nuoren karjankasvattajan kuulijoissa. Ne sopivat yhteen Paganelin ja Ayrtonin jo ennen antamien tietojen kanssa. Kun naiset olivat nousseet p\"{o}yd\"{a}st\"{a}, puheltiin karanneista rikollisista. Squatterit tunsivat Camden-sillan tapahtuman, mutta karkulaisjoukko ei her\"{a}tt\"{a}nyt heiss\"{a} levottomuutta, sill\"{a} sellaiset pahantekij\"{a}t eiv\"{a}t uskaltaisi hy\"{o}k\"{a}t\"{a} aseman kimppuun, jonka henkil\"{o}kuntaan kuului toista sataa miest\"{a}. Sit\"{a} paitsi oli luultavaa, ett\"{a} he eiv\"{a}t painuisi Murrayn er\"{a}maihin, miss\"{a} heill\"{a} ei ollut mit\"{a}\"{a}n tekemist\"{a}, eik\"{a} Uuden Etel\"{a}-Walesin puolelle, jonka tiet ovat hyvin vartioituja. Se oli my\"{o}s Ayrtonin mielipide. Lordi Glenarvan ei voinut kielt\"{a}yty\"{a} viipym\"{a}st\"{a} koko t\"{a}t\"{a} p\"{a}iv\"{a}\"{a} rakastettavien is\"{a}ntiens\"{a} vieraana Hottam-asemalla. Se oli kahdentoista tunnin viivytys, josta aiheutui kahdentoista tunnin lepo; hevoset ja juhdat saivat omaksi edukseen virkisty\"{a} aseman mukavissa talleissa. Niinp\"{a} asia oli sovittu, ja molemmat nuoret miehet laativat vierailleen p\"{a}iv\"{a}n ohjelman, johon innostuneina suostuttiin. Puolenp\"{a}iv\"{a}n aikaan t\"{o}misteli seitsem\"{a}n voimakasta mets\"{a}styshevosta p\"{a}\"{a}rakennuksen portilla. Naisille varattu siro ``break'', jonka eteen oli valjastettu nelj\"{a} hevosta, antoi ajajalle tilaisuuden n\"{a}ytt\"{a}\"{a} taitoaan nelivaljakon ohjauksessa. Erinomaisilla mets\"{a}styspyssyill\"{a} varustettuina nousivat herrat satulaan, palvelijoiden ratsastaessa edell\"{a}, ja nelistiv\"{a}t vaunujen vierell\"{a}, pointterijoukon hilpe\"{a}sti haukahdellessa pitkin pensaikkoja. Nelj\"{a}n tunnin ajan samosi ratsuseurue pitkin k\"{a}yt\"{a}vi\"{a} ja teit\"{a} t\"{a}ss\"{a} puistossa, joka oli suuri kuin joku Saksan pikku ruhtinaskunta. Reuss-Schleitz tai Saksi-Koburg-Gotha olisivat mahtuneet sinne kokonaan. Vaikka ei tavattu juurikaan asukkaita, siell\"{a} vilisi sen sijaan lampaita. Mit\"{a} riistaan tuli, niin kokonainen ajomiesarmeija ei olisi voinut ajaa sit\"{a} enemp\"{a}\"{a} mets\"{a}st\"{a}jien pyssynkantaman p\"{a}\"{a}h\"{a}n. Pian kuuluikin sarja metsien ja laitumien rauhallisia vieraita pelottelevia paukauksia. Nuori Robert teki ihmeit\"{a} majuri MacNabbsin rinnalla. Rohkea poika oli aina etunen\"{a}ss\"{a} ja ensimm\"{a}isen\"{a} tulessa, sisarensa varoitteluista huolimatta. Mutta John Mangles otti h\"{a}net valvontaansa, ja Mary Grant rauhoittui j\"{a}lleen. T\"{a}m\"{a}n mets\"{a}styksen aikana kaadettiin useita t\"{a}lle maalle tyypillisi\"{a} el\"{a}imi\"{a}, joita Paganel siihen saakka tunsi vain nimelt\"{a}: muiden muassa ``wombat'' ja ``bandicoot''. Wombat on ruohonsy\"{o}j\"{a}, joka kaivaa k\"{a}yt\"{a}vi\"{a} niin kuin m\"{a}yr\"{a}; se on lampaan kokoinen, ja sen liha on erinomaista. Bandicoot on er\"{a}\"{a}nlainen pussiel\"{a}in, joka voisi kilpailla eurooppalaisen ketun kanssa ja antaa sille opetusta kanatarhojen ry\"{o}st\"{o}ss\"{a}. T\"{a}m\"{a}n ulkomuodoltaan jokseenkin ep\"{a}miellytt\"{a}v\"{a}n, puolimetrisen el\"{a}imen ampui Paganel, joka mets\"{a}st\"{a}j\"{a}n itserakkautta tuntien piti sit\"{a} vieh\"{a}tt\"{a}v\"{a}n\"{a}. --- Ihastuttava el\"{a}in, h\"{a}n sanoi. Muiden huomattavien el\"{a}inten joukossa oli Robertin taitavasti ampuma ``dasyure'', er\"{a}\"{a}nlainen pieni kettu, jonka valkopilkkuinen musta turkki on n\"{a}\"{a}d\"{a}nnahan veroinen, sek\"{a} pari pussirottaa, jotka piileksiv\"{a}t suurten puiden tihe\"{a}ss\"{a} lehvist\"{o}ss\"{a}. Mutta mielenkiintoisin kaikista n\"{a}ist\"{a} urot\"{o}ist\"{a} oli kielt\"{a}m\"{a}tt\"{a} kengurun mets\"{a}stys. Kello nelj\"{a}n tienoilla alkoivat koirat ahdistaa n\"{a}iden ihmeellisten pussiel\"{a}inten laumaa. Poikaset pakenivat kiireesti em\"{a}ns\"{a} pussiin, ja koko joukko l\"{a}hti jonossa pakoon. Kummallista oli n\"{a}hd\"{a} kengurujen tavattomia loikkauksia, jolloin etujalkoja kahta vertaa pitemm\"{a}t takajalat ponnahtelivat kuin jouset. Pakenevan lauman k\"{a}rjess\"{a} loikki puolentoista metrin korkuinen koiras, suurenmoinen ``macropus giganteus"-lajin edustaja, ``vanha mies'', kuten uudisasukkaat sanovat. Takaa-ajoa jatkettiin innokkaasti seitsem\"{a}n tai kahdeksan kilometri\"{a}. Kengurut eiv\"{a}t v\"{a}syneet, ja koirat, jotka syyst\"{a} pelk\"{a}siv\"{a}t niiden voimakasta, ter\"{a}v\"{a}kyntist\"{a} k\"{a}p\"{a}l\"{a}\"{a}, eiv\"{a}t uskaltaneet l\"{a}hesty\"{a} niit\"{a}. Vihdoin juoksu alkoi kuitenkin rasittaa, lauma pys\"{a}htyi, ja ``vanha mies'' nojautui puunrunkoa vasten valmiina puolustautumaan. Er\"{a}s liikaa innostunut koira sattui kompastumaan sen l\"{a}hell\"{a}. Seuraavassa silm\"{a}nr\"{a}p\"{a}yksess\"{a} lensi onneton pointteri ilmaan ja putosi maahan maha revittyn\"{a}. Koko koiraparvi ei olisi kyennyt pit\"{a}m\"{a}\"{a}n puoliaan n\"{a}it\"{a} voimakkaita pussiel\"{a}mi\"{a} vastaan. Tarvittiin siis lopuksi pyssynlaukauksia, ja vain luodit saattoivat kaataa t\"{a}m\"{a}n jyhke\"{a}n el\"{a}imen. T\"{a}ll\"{a} hetkell\"{a} Robert oli v\"{a}h\"{a}ll\"{a} joutua varomattomuutensa uhriksi. P\"{a}\"{a}st\"{a}kseen varmaan t\"{a}ht\"{a}yspaikkaan h\"{a}n l\"{a}hestyi kengurua niin l\"{a}helle, ett\"{a} se hypp\"{a}si vastaan. Robert kaatui; kajahti huuto. Ajoneuvoilla seisten Mary Grant ojensi k\"{a}si\"{a}\"{a}n velje\"{a}\"{a}n kohti kauhistuksesta mykistyneen\"{a} ja miltei sokaistuneena. Ei kukaan uskaltanut ampua el\"{a}int\"{a}, sill\"{a} luoti olisi voinut osua my\"{o}s lapseen. Mutta mets\"{a}styspuukko kourassa John Mangles sy\"{o}ksyi \"{a}kki\"{a} kengurua kohti omaa henke\"{a}\"{a}n ajattelematta ja iski el\"{a}int\"{a} syd\"{a}meen. Kenguru kaatui, ja Robert nousi maasta haavoittumattomana. Seuraavassa silm\"{a}nr\"{a}p\"{a}yksess\"{a} h\"{a}n oli sisarensa syliss\"{a}. --- Kiitos, herra John, kiitos! Mary Grant sanoi ja ojensi k\"{a}tens\"{a} nuorelle kapteenille. --- Min\"{a}h\"{a}n lupasin vastata h\"{a}nest\"{a}, John Mangles huomautti tarttuen neidon vapisevaan k\"{a}teen. T\"{a}m\"{a} tapaus p\"{a}\"{a}tti mets\"{a}styksen. Kengurulauma oli hajaantunut johtajansa kaaduttua, ja saalis vietiin kartanoon. Kello oli silloin kuusi illalla. Suurenmoinen p\"{a}iv\"{a}llinen odotti mets\"{a}st\"{a}ji\"{a}. Ruokalajien joukossa oli australialaiseen tapaan kengurunh\"{a}nnist\"{a} valmistettua lient\"{a}, josta tuli aterian huippukohta. J\"{a}lkiruoan, j\"{a}\"{a}tel\"{o}iden ja virvoitusjuomien j\"{a}lkeen siirryttiin saliin. Ilta omistettiin musiikille. Lady Helena oli hyv\"{a} pianonsoittaja ja antoi karjanomistajien nauttia t\"{a}st\"{a} taidosta. Michel ja Sandy Patterson lauloivat erinomaisen kauniisti kappaleita Gounodin, Victor Mass\'{e}n, F\'{e}licien Davidin, jopa Richard Wagnerinkin, monen mielest\"{a} suurenmoisen neron, uusimmista s\"{a}vellyksist\"{a}. Kello yksitoista tarjottiin teet\"{a}; se oli valmistettu niin verrattomasti kuin vain englantilaiset osaavat. Mutta kun Paganel oli pyyt\"{a}nyt saada maistaa australialaista teet\"{a}, h\"{a}nelle tuotiin pikimustaa nestett\"{a}, litra vett\"{a}, jossa puoli naulaa teet\"{a} oli kiehunut nelj\"{a} tuntia. Paganelin suu v\"{a}\"{a}ntyi, mutta h\"{a}n vakuutti juoman olevan erinomaista. Puoliy\"{o}n aikaan saatettiin vieraat ilmaviin ja mukaviin makuusuojiin, joissa he viel\"{a} n\"{a}kiv\"{a}t unta p\"{a}iv\"{a}n nautinnoista. Varhain seuraavana aamuna he lausuivat nuorille karjanomistajille j\"{a}\"{a}hyv\"{a}iset. Kiiteltiin ja luvattiin tavata j\"{a}lleen Euroopassa, Malcolmin linnassa. Sitten vankkurit l\"{a}htiv\"{a}t liikkeelle, k\"{a}\"{a}ntyiv\"{a}t Hottam-vuoren juuren ymp\"{a}ri, ja pian oli kartano kadonnut matkalaisten silmist\"{a} kuin hetkellinen ilmestys. Viel\"{a} viiden tunnin ajan polki heid\"{a}n hevosensa jalka aseman aluetta. Vasta kello yhdeks\"{a}n aikaan p\"{a}\"{a}stiin viimeisen aitauksen l\"{a}pi, ja seurue eteni Victorian maakunnan melkein tuntemattomia tienoita pitkin. \gutchapter{AUSTRALIAN ALPIT.} Kaakossa tien katkaisi valtava vuoriharjanne. Se oli Australian alppijono, joka kuin suunnattomana linnoituksena s\"{a}\"{a}nn\"{o}tt\"{o}mine vallituksineen on parin tuhannen kilometrin pituinen ja tavoittelee pilvi\"{a} yli tuhannen metrin korkeudella. Pilvinen ilma ei p\"{a}\"{a}st\"{a}nyt l\"{a}mp\"{o}\"{a} maahan kuin tihe\"{a}n sumuverhon l\"{a}pi. Kuumuus ei siis haitannut, mutta kulku oli hankalaa maaper\"{a}ll\"{a}, joka oli jo hyvin ep\"{a}tasaista. T\"{a}\"{a}ll\"{a} maa alkoi kohoilla yh\"{a} useammin. Siell\"{a} t\"{a}\"{a}ll\"{a} n\"{a}kyi vihantien kumipuiden peitt\"{a}mi\"{a} kukkuloita. Kauempana n\"{a}m\"{a} kuhmut nousivat yh\"{a} korkeammiksi, suurten alppien ensimm\"{a}isiksi portaiksi. Piti edet\"{a} yh\"{a} ylemm\"{a}s, ja se tuntui hyvinkin juhtien ponnistuksissa, ja ikeet natisivat raskaiden vankkurien painosta; el\"{a}imet l\"{a}\"{a}h\"{a}ttiv\"{a}t kovasti, ja niiden polvitaipeiden lihakset pingoittuivat melkein katketakseen. Ajoneuvojen palkit narskuivat odottamattomista kolauksista, joita Ayrton ei voinut v\"{a}ltt\"{a}\"{a}, niin taitava kuin olikin. Naiset alistuivat nauraen kohtaloonsa. John Mangles molempine matruuseineen ratsasti muutamia satoja askelia edell\"{a} valitsemassa sopivia teit\"{a} tai paremmin sanoen ``salmia'', sill\"{a} kaikki n\"{a}m\"{a} maaper\"{a}n kumpareet olivat kuin kareja, joiden v\"{a}list\"{a} vankkurit hakivat parasta kanavaa. Heid\"{a}n oli pakko suorastaan kuin luovia vaikeakulkuisilla vesill\"{a}. Teht\"{a}v\"{a} oli vaikea, usein vaarallinenkin, ja monta kertaa t\"{a}ytyi Wilsonin kirveen raivata tiet\"{a} tiheiden pensaikkojen l\"{a}pi. Savinen ja kostea maa livetti jalkaa. Tiet\"{a} pitensiv\"{a}t ne tuhannet mutkat, joita t\"{a}ytyi tehd\"{a} ylip\"{a}\"{a}sem\"{a}tt\"{o}mien esteiden, korkeiden graniittikallioiden, syvien kuilujen ja ep\"{a}ilytt\"{a}vien l\"{a}t\"{a}k\"{o}iden vuoksi. Iltaan menness\"{a} oli siksi p\"{a}\"{a}sty tuskin puolta astetta eteenp\"{a}in. Leiriydyttiin alppien juurella pienen Cobongra-joen rannalla, er\"{a}\"{a}n v\"{a}h\"{a}isen aukeaman laidalla; siell\"{a} kasvoi reilun metrin korkuisia pensaita, joiden kirkkaanpunaiset lehdet hiveliv\"{a}t silm\"{a}\"{a}. --- Meid\"{a}n on hankala p\"{a}\"{a}st\"{a} eteenp\"{a}in, Glenarvan sanoi silm\"{a}illen vuorijonoa, jonka piirteet jo h\"{a}ipyiv\"{a}t illan pimeyteen. --- Alpit! Siin\"{a} nimi, joka antaa ajattelemista. --- Siit\"{a} saa sent\"{a}\"{a}n tinki\"{a}, rakas Glenarvan, Paganel huomautti. --- \"{A}lk\"{a}\"{a} luulko, ett\"{a} teill\"{a} on aivan t\"{a}ydellinen Sveitsi edess\"{a}nne. Australiassa on kyll\"{a} Grampian-vuori, Pyreneit\"{a}, Alppeja, Sinivuoria kuten Euroopassa ja Amerikassa, mutta pienoiskoossa. Se todistaa vain, ett\"{a} maantieteilij\"{a}n mielikuvitus ei ole rajaton tai ett\"{a} nimist\"{a} on puutetta. --- Siis n\"{a}m\"{a} Australian alpit...? lady Helena kysyi. --- Ovat taskuun mahtuvia vuoria, Paganel vastasi. --- Me kuljemme niiden yli miltei huomaamatta. --- Puhukaa omasta puolestanne! majuri sanoi. --- Vain hajamielinen mies voi kulkea vuorten yli sit\"{a} huomaamatta. --- Hajamielinen! Paganel huudahti. --- Enh\"{a}n min\"{a} en\"{a}\"{a} ole hajamielinen! Min\"{a} vetoan naisiin. Enk\"{o} ole pit\"{a}nyt lupaustani siit\"{a} saakka, kun astuin maihin? Olenko ollut kertaakaan hajamielinen? Voiko minua moittia ainoastakaan hairahduksesta? --- Ei ainoastakaan, herra Paganel, Mary Grant vastasi. --- Te olette nyt niin moitteeton kuin mies voi olla. --- Liiankin mallikelpoinen, lady Helena lis\"{a}si nauraen. --- Teid\"{a}n hajamielisyytenne puuskat sopivat teille hyvin. --- Eik\"{o} totta, rouva? Paganel vastasi. --- Kun minussa ei en\"{a}\"{a} ole mit\"{a}\"{a}n virhett\"{a}, olen kuin kaikki muutkin ihmiset. Toivon siis ennen pitk\"{a}\"{a} tekev\"{a}ni jonkun tyhmyyden, jolle saatte herttaisesti nauraa. N\"{a}hk\"{a}\"{a}s, ellen hairahdu, niin en mielest\"{a}ni t\"{a}yt\"{a} kutsumustani. Huolimatta luottavaisen maantieteilij\"{a}n vakuutuksista p\"{a}\"{a}si joukko vain perin vaivalloisesti kulkemaan alppien solissa seuraavana eli 9. p\"{a}iv\"{a}n\"{a} tammikuuta. T\"{a}ytyi ajaa onnella, uskaltautua ahtaisiin ja syviin rotkoihin, jotka saattoivat p\"{a}\"{a}tty\"{a} umpikujaan. Ayrton olisi ep\"{a}ilem\"{a}tt\"{a} joutunut pahaan pulaan, ellei tunnin matkan j\"{a}lkeen odottamatta olisi er\"{a}\"{a}n vuoripolun varrella n\"{a}hty ravintolaa, kurjaa ``tapia''. --- Totisesti! Paganel huudahti, --- tuon kapakan is\"{a}nt\"{a} ei voine koota omaisuuksia t\"{a}llaisessa seudussa! Mihin tuotakin tarvittanee? --- Antamaan meille reitist\"{a}mme niit\"{a} tietoja, joita tarvitsemme, Glenarvan vastasi. --- Menk\"{a}\"{a}mme sis\"{a}\"{a}n. Ayrtonin saattamana Glenarvan astui ravintolan kynnyksen yli. \textit{Bush-Innin} --- se nimi oli ravintolan kyltiss\"{a} --- is\"{a}nt\"{a} oli karkeatekoinen, tymp\"{a}isev\"{a}n n\"{a}k\"{o}inen mies, joka n\"{a}ht\"{a}v\"{a}sti itse oli kapakkansa viinaksien ahkerin k\"{a}ytt\"{a}j\"{a}. Tuskinpa t\"{a}nne koskaan poikkesi muita kuin joku matkalla oleva karjankasvattaja tai karjankuljettaja. H\"{a}n vastaili nyre\"{a}n n\"{a}k\"{o}isen\"{a} kysymyksiin. Mutta se riitti kuitenkin antamaan Ayrtonille varmuuden siit\"{a}, minnep\"{a}in oli kuljettava. Glenarvan korvasi muutamalla kruunulla kapakanis\"{a}nn\"{a}n vaivat ja oli juuri l\"{a}hd\"{o}ss\"{a} ulos, kun er\"{a}s sein\"{a}\"{a}n kiinnitetty ilmoitus her\"{a}tti h\"{a}nen huomiotansa. Se oli siirtomaapoliisin tiedonanto, joka ilmoitti vankien karanneen Perthist\"{a} ja julisti palkinnon Ben Joycen p\"{a}\"{a}st\"{a}. Sata puntaa sille, joka toimittaisi h\"{a}net kiinni. --- Se lurjus siet\"{a}isi joutua hirteen, Glenarvan sanoi per\"{a}miehelle. --- Ja varsinkin vangiksi! Ayrton vastasi. --- Sata puntaa! Onpa se summa! H\"{a}n ei ole sen arvoinen. --- Ravintolanis\"{a}nt\"{a}, Glenarvan lis\"{a}si, --- ei minussa my\"{o}sk\"{a}\"{a}n her\"{a}t\"{a} luottamusta, kyltist\"{a} huolimatta. --- Eik\"{a} minussa, Ayrton vastasi. Glenarvan ja per\"{a}mies palasivat vankkurien luo, ja sitten l\"{a}hdettiin etenem\"{a}\"{a}n sinnep\"{a}in, miss\"{a} Lucknowin tie p\"{a}\"{a}ttyy. Siell\"{a} kiemurteli kapea sola, joka meni viistoon vuoren yli. Noustiin yh\"{a} yl\"{o}sp\"{a}in. Se oli hankala reitti, ja monta kertaa saivat naiset ja heid\"{a}n seuralaisensa astua maahan. T\"{a}ytyi auttaa raskaita vankkureita py\"{o}rist\"{a} ty\"{o}nt\"{a}m\"{a}ll\"{a}, usein pid\"{a}tell\"{a} niit\"{a} vaarallisissa ahteissa, riisua juhdat valjaista, kun k\"{a}\"{a}nteet olivat liian jyrkki\"{a}, ja panna kiiloja alle, milloin ajoneuvot uhkasivat liukua taaksep\"{a}in; monesti t\"{a}ytyi Ayrtonin my\"{o}s saada avukseen hevosia, vaikka n\"{a}m\"{a} jo olivat v\"{a}syneit\"{a} ponnisteltuaan yl\"{o}spain. Joko t\"{a}st\"{a} pitk\"{a}llisest\"{a} rasituksesta tai jostakin muusta syyst\"{a} menetettiin yksi hevosista t\"{a}m\"{a}n p\"{a}iv\"{a}n kuluessa. Se kaatui \"{a}kki\"{a} ilman mit\"{a}\"{a}n oireita. Se oli Mulradyn hevonen, ja kun sen is\"{a}nt\"{a} yritti sit\"{a} nostaa, se oli kuollut. Ayrton tuli tutkimaan maassa makaavaa el\"{a}int\"{a} eik\"{a} n\"{a}ytt\"{a}nyt ymm\"{a}rt\"{a}v\"{a}n syyt\"{a} sen \"{a}kkikuolemaan. --- Silt\"{a} on varmaankin jokin suoni revennyt, Glenarvan arveli. --- Ilmeisesti, Ayrton my\"{o}nsi. --- Ota minun hevoseni, Mulrady, Glenarvan lis\"{a}si, --- min\"{a} menen lady Helenan seuraan vankkureihin. Mulrady teki niin, ja joukko jatkoi vaivalloista nousuaan j\"{a}tetty\"{a}\"{a}n hevosenraadon korppien saaliiksi. Australian alppijono ei ole kovin leve\"{a}; juurelta noin nelj\"{a}toista kilometri\"{a}. Jos Ayrtonin valitsema reitti siis vei it\"{a}rinteelle, voitiin kahdessa vuorokaudessa p\"{a}\"{a}st\"{a} sen yli; siit\"{a} mereen saakka ei sitten en\"{a}\"{a} ollut ylip\"{a}\"{a}sem\"{a}tt\"{o}mi\"{a} esteit\"{a} eik\"{a} hankalaa tiet\"{a}. Tammikuun 10. p\"{a}iv\"{a}n\"{a} matkailijat saapuivat tiens\"{a} korkeimmalle kohdalle, noin kuudensadan metrin korkeuteen. He olivat t\"{a}ll\"{o}in aukealla yl\"{a}tasangolla, josta levisi laaja n\"{a}k\"{o}ala. Pohjoisessa kimalsi Omeo-j\"{a}rven tyyni pinta vesilintuineen, ja sen sivulla n\"{a}kyiv\"{a}t Murrayn laajat tasangot. Etel\"{a}ss\"{a} olivat Gippslandin vehre\"{a}t ruohikot, sen kultapitoiset kent\"{a}t, korkeat aarnioseutuja muistuttavat mets\"{a}t. Luonto oli siell\"{a} viel\"{a} tuotteidensa, vesiens\"{a} juoksun, hakkaamattomien metsiens\"{a} herrana, eiv\"{a}tk\"{a} silloin viel\"{a} harvalukuiset karjankasvattajat uskaltaneet k\"{a}yd\"{a} sen kimppuun. T\"{a}m\"{a} alppijono n\"{a}ytti erottavan kaksi aluetta, joista toinen oli s\"{a}ilytt\"{a}nyt villiytens\"{a}. Aurinko laski juuri ja punertavien pilvien l\"{a}pi tunkevat s\"{a}teet loivat eloisampaa v\"{a}ri\"{a} Murrayn piirikuntaan. Gippsland sit\"{a} vastoin h\"{a}ipyi ep\"{a}m\"{a}\"{a}r\"{a}iseen h\"{a}m\"{a}r\"{a}\"{a}n vuorenhuippujen takana, niin ett\"{a} olisi voinut sanoa varjon peitt\"{a}neen koko alppientakaisen seudun ennenaikaiseen y\"{o}h\"{o}n. T\"{a}m\"{a} vastakohta her\"{a}tti molempien n\"{a}in erotettujen seutujen v\"{a}lisiss\"{a} katsojissa syv\"{a}n tunnelman, kun he silm\"{a}iliv\"{a}t sit\"{a} melkein tuntematonta aluetta, jonka l\"{a}pi heid\"{a}n nyt oli matkattava Victorian maakunnan rajalle saakka. Y\"{o} vietettiin harjanteen aukeamalla, ja seuraavana aamuna aloitettiin laskeutuminen, joka sujui verrattain nopeasti. Tavattoman rankka raesade yll\"{a}tti retkel\"{a}iset ja pakotti heid\"{a}t etsim\"{a}\"{a}n suojaa kallioiden alta. Raskaat pilvet eiv\"{a}t syyt\"{a}neet vain rakeita, vaan k\"{a}mmenenlevyisi\"{a} j\"{a}\"{a}kappaleita. Lingollakaan ei niihin olisi voinut saada enemm\"{a}n voimaa, ja monet isot mustelmat opettivat Paganelille ja Robertille, ett\"{a} niiden iskuja oli paras v\"{a}ltt\"{a}\"{a}. Vankkurit vaurioituivat monesta kohtaa, ja harva katto olisi kest\"{a}nyt n\"{a}iden ter\"{a}vien j\"{a}\"{a}kappaleiden pommitusta; muutamat niist\"{a} iskeytyiv\"{a}t puiden runkojen sis\"{a}\"{a}n. T\"{a}ytyi siis odottaa t\"{a}m\"{a}n tavattoman ry\"{o}pyn p\"{a}\"{a}ttymist\"{a}, ellei tahtonut tulla kivitetyksi. Rajuilmaa kesti noin tunnin, mink\"{a} j\"{a}lkeen matkue taas jatkoi taivaltaan kallioiden rinteit\"{a} pitkin, jotka viel\"{a} olivat \"{a}skeisten rakeiden j\"{a}ljilt\"{a} liukkaat. Illan suussa pahoin kolhiutuneet ja eri kohdilta vaurioituneet vankkurit kulkivat yh\"{a} viel\"{a} tukevina puupy\"{o}rill\"{a}\"{a}n alppien viimeisi\"{a} rinteit\"{a} suurten yksin\"{a}isten kuusien v\"{a}liss\"{a}. Sola p\"{a}\"{a}ttyi Gippslandin tasangoille; alppien yli oli p\"{a}\"{a}sty onnellisesti, ja nyt ryhdyttiin tavallisiin leiriytymispuuhiin. Aamunkoitteessa 12. p\"{a}iv\"{a}n\"{a} tammikuuta jatkettiin matkaa yht\"{a} innokkaasti. Jokainen ik\"{a}v\"{o}i p\"{a}\"{a}sy\"{a} Tyynenmeren rannalle, juuri sille kohtaa, jossa \textit{Britannia} oli murskautunut. Ainoastaan siell\"{a} saattoi menestyst\"{a} toivoen j\"{a}lleen ryhty\"{a} etsim\"{a}\"{a}n haaksirikkoisten j\"{a}lki\"{a}, mutta ei Gippslandin er\"{a}maassa. Ayrton kehottikin lordi Glenarvania l\"{a}hett\"{a}m\"{a}\"{a}n k\"{a}skyn \textit{Duncanille} saapua rannikolle, jotta kaikki mahdolliset apuneuvot olisivat k\"{a}ytett\"{a}vin\"{a} tiedustelujen tekemiseksi. H\"{a}nen mielest\"{a}\"{a}n pit\"{a}isi kulkea Lucknowista Melbourneen johtavaa tiet\"{a}; my\"{o}hemmin se k\"{a}visi vaikeaksi, sill\"{a} suoraa yhteytt\"{a} p\"{a}\"{a}kaupunkiin ei ollut. N\"{a}m\"{a} Ayrtonin neuvot tuntuivat hyvilt\"{a}, ja Paganel pyysi kiinnitt\"{a}m\"{a}\"{a}n niihin huomiota. H\"{a}n arveli my\"{o}s, ett\"{a} \textit{Duncanista} olisi suurta hy\"{o}ty\"{a} n\"{a}iss\"{a} oloissa, ja lis\"{a}si, ett\"{a} kun kerran olisi menty Lucknowin tien poikki, ei en\"{a}\"{a} voitaisi p\"{a}\"{a}st\"{a} kosketuksiin Melbournen kanssa. Glenarvan oli kahden vaiheella ja olisi ehk\"{a} l\"{a}hett\"{a}nyt tuon k\"{a}skyn, jonka Ayrton erikoisesti tarjoutui viem\"{a}\"{a}n perille, ellei majuri olisi ankarasti vastustanut t\"{a}t\"{a} p\"{a}\"{a}t\"{o}st\"{a}. H\"{a}n huomautti, ett\"{a} Ayrtonin l\"{a}sn\"{a}olo oli retkikunnalle v\"{a}ltt\"{a}m\"{a}t\"{o}n, kun h\"{a}n tunsi tienoot l\"{a}hell\"{a} rannikkoa, ja jos sattumalta jouduttaisiin Harry Grantin j\"{a}ljille, h\"{a}n paremmin kuin kukaan muu pystyisi niit\"{a} seuraamaan, ja vihdoin, ett\"{a} h\"{a}n yksin saattoi n\"{a}ytt\"{a}\"{a} paikan, miss\"{a} \textit{Britannia} oli tuhoutunut. MacNabbs ehdotti siis matkaa jatkettavan suunnitelmia muuttumatta ja sai kannattajakseen John Manglesin, joka oli samaa mielt\"{a}. Huomauttipa nuori kapteeni, ett\"{a} lordin k\"{a}sky olisi helpompi vied\"{a} \textit{Duncanille} Twofold-lahdesta kuin sanansaattajan mukana, jonka oli samottava nelj\"{a}sataa kilometri\"{a} miltei asumattomia maita. T\"{a}m\"{a} mielipide voitti, ja niin p\"{a}\"{a}tettiin ryhty\"{a} toimiin Twofold-lahdelle saavuttua. Majuri tarkkaili Ayrtonia, joka tuntui h\"{a}nest\"{a} jokseenkin pettyneelt\"{a}; mutta h\"{a}n ei puhunut huomioistaan mit\"{a}\"{a}n, vaan piti tapansa mukaan ne omina tietoinaan. Australian alppien juurelta levi\"{a}v\"{a}t alangot olivat tasaisia ja loivasti it\"{a}\"{a}np\"{a}in viett\"{a}vi\"{a}. Suuria mimoosien ja eri kumipuiden rykelmi\"{a} oli siell\"{a} t\"{a}\"{a}ll\"{a} el\"{a}v\"{o}itt\"{a}m\"{a}ss\"{a} yht\"{a}mittaista yksitoikkoisuutta. ``Gastrolobium grandiflorum"-pensaat koristivat maata loistavilla kukillaan. Usein oli kuljettava pienten purojen poikki, jotka olivat t\"{a}ynn\"{a} lyhytt\"{a} kaislaa ja k\"{a}mmekk\"{a}lajeja. Niiden yli kahlattiin. Kaukaa pakeni trappi- ja kasuaariparvia retkel\"{a}isten l\"{a}hestyess\"{a}. Pensaiden yli hyppeli kenguruja kuin joustavia hyppynukkeja; mutta retkikunnan pyssymiehill\"{a} ei ollut mets\"{a}styshalua, eiv\"{a}tk\"{a} heid\"{a}n hevosensa olleet lis\"{a}jaloittelun tarpeessa. Seudulla vallitsi rasittava kuumuus; ilmassa oli runsaasti s\"{a}hk\"{o}\"{a}, ja sek\"{a} ihmiset ett\"{a} el\"{a}imet tunsivat sen vaikutuksen. Laahustettiin suoraan eteenp\"{a}in mist\"{a}\"{a}n muusta v\"{a}litt\"{a}m\"{a}tt\"{a}, ja hiljaisuuden keskeyttiv\"{a}t vain Ayrtonin huudot, kun h\"{a}n hoputti v\"{a}synytt\"{a} valjakkoaan. Keskip\"{a}iv\"{a}st\"{a} kello kahteen saakka kuljettiin kummallisen saniaismets\"{a}n l\"{a}pi, joka olisi her\"{a}tt\"{a}nyt v\"{a}hemm\"{a}n v\"{a}syneiden vaeltajien ihailua. N\"{a}m\"{a} t\"{a}ydess\"{a} kukassa olevat puumaiset kasvit olivat jopa kymmenen metrin korkuisia. Hevoset ja ratsastajat mahtuivat mukavasti niiden riippuvien oksien alitse, ja joskus kilahti kannus osuessaan puumaiseen runkoon. Niiden liikkumattoman katoksen alla vallitsi raikkaus, jota kenenk\"{a}\"{a}n mieleen ei juolahtanut moittia. Jacques Paganel p\"{a}\"{a}sti muutamia mielihyv\"{a}n huokauksia, jotka saivat suuren papukaijaparven pyr\"{a}ht\"{a}m\"{a}\"{a}n lentoon pel\"{a}stynein\"{a} ja r\"{a}h\"{a}ht\"{a}m\"{a}\"{a}n huumaavaan meteliin. Maantieteilij\"{a} jatkoi syd\"{a}mens\"{a} pohjasta tulevia riemunhuudahduksia, kun h\"{a}nen kumppaninsa \"{a}kki\"{a} n\"{a}kiv\"{a}t h\"{a}nen horjuvan hevosensa sel\"{a}ss\"{a} ja sitten kaatuvan hervottomana maahan. Oliko se huimausta vai viel\"{a} pahempaa, oliko h\"{a}n py\"{o}rtynyt kuuman s\"{a}\"{a}n takia? Riennettiin h\"{a}nen luokseen. --- Paganel, Paganel! Mik\"{a} teit\"{a} vaivaa? Glenarvan huusi. --- Se vain, yst\"{a}v\"{a}ni, ett\"{a} minulla ei en\"{a}\"{a} ole hevosta, Paganel vastasi irrottautuen jalustimesta. --- Mit\"{a}! Mik\"{a} hevoseenne tuli? --- Se on kuollut, \"{a}kki\"{a} kaatunut, niin kuin Mulradyn hevonen! Glenarvan, John Mangles, ja Wilson tutkivat el\"{a}int\"{a}. Paganel ei erehtynyt. H\"{a}nen hevosensa oli heitt\"{a}nyt henkens\"{a}. --- T\"{a}m\"{a}h\"{a}n on omituista, John Mangles sanoi. --- Perin omituista tosiaankin, majuri mutisi. Glenarvan ei voinut olla huolestumatta t\"{a}st\"{a} uudesta onnettomuudesta. Er\"{a}maassa sit\"{a} ei voinut korvata. Jos joku kulkutauti tappaisi retkikunnan kaikki hevoset, h\"{a}nell\"{a} olisi vaikeuksia jatkaa matkaa. Sana ``kulkutauti'' n\"{a}ytti saavan vahvistusta ennen p\"{a}iv\"{a}n p\"{a}\"{a}ttymist\"{a}. Kolmas hevonen, Wilsonin, kaatui kuoliaana maahan ja, mik\"{a} ehk\"{a} oli viel\"{a} arveluttavampaa, yksi juhdista kuoli \"{a}kki\"{a} samalla tavalla. Kulku- ja vetoneuvot olivat supistuneet kolmeen h\"{a}rk\"{a}\"{a}n ja nelj\"{a}\"{a}n hevoseen. Asema k\"{a}vi arveluttavaksi. Ratsunsa menett\"{a}neet miehet saattoivat kyll\"{a} marssia jalkaisin. Moni karjankasvattaja oli jo siten kulkenut n\"{a}iden autiomaiden halki. Mutta jos t\"{a}ytyisi j\"{a}tt\"{a}\"{a} vankkurit, kuinka k\"{a}visi naisten? Jaksaisivatko he jalkaisin kulkea ne kaksisataa kilometri\"{a}, jotka viel\"{a} erottivat heit\"{a} Twofold-lahdesta? John Mangles ja Glenarvan tutkivat perin levottomina j\"{a}ljell\"{a} olevia hevosia. Ehk\"{a}p\"{a} uudet onnettomuudet voisi ehk\"{a}ist\"{a}. Tutkimuksessa ei havaittu mink\"{a}\"{a}nlaisia oireita sairaudesta. Hevoset olivat t\"{a}ysin terveit\"{a} ja kestiv\"{a}t uljaasti matkan rasitukset. Niinp\"{a} Glenarvan toivoi, ett\"{a} t\"{a}m\"{a} omituinen kulkutauti ei vaatisi muita uhreja. Sama oli Ayrtoninkin ajatus; h\"{a}nkin my\"{o}nsi olevansa t\"{a}ysin ymm\"{a}ll\"{a} n\"{a}ist\"{a} \"{a}killisist\"{a} kuolemantapauksista. L\"{a}hdettiin j\"{a}lleen matkaan. Vankkurit olivat apuna my\"{o}s jalkamiehille, jotka lev\"{a}htiv\"{a}t niiss\"{a} vuoron per\"{a}\"{a}n. Illalla, kun oli p\"{a}\"{a}sty vain kuusitoista kilometri\"{a}, annettiin pys\"{a}hdysmerkki, leiri pantiin kuntoon, ja y\"{o} kului ilman ik\"{a}vyyksi\"{a} puumaisten saniaisten lehdossa, miss\"{a} lenteli suuria, syyst\"{a} kyll\"{a} lent\"{a}viksi ketuiksi nimitettyj\"{a} lepakoita. Seuraava eli 13. p\"{a}iv\"{a} tammikuuta oli suotuisa, eik\"{a} edellisen p\"{a}iv\"{a}n onnettomuudet uusiutuneet. Hevoset ja juhdat tekiv\"{a}t alttiisti teht\"{a}v\"{a}ns\"{a}. Lady Helenan salongissa oli hyvin vilkasta vierailijoiden suuren lukum\"{a}\"{a}r\"{a}n vuoksi. Olbinett tarjoili ahkerasti virvokkeita, jotka kolmenkymmenen asteen kuumuudessa olivatkin tarpeellisia. Puoli ankkuria skotlantilaista olutta tyhjennettiin kokonaan. Bacley \& C:o julistettiin Ison Britannian suurimmaksi mieheksi, viel\"{a}p\"{a} paremmaksi kuin Wellington, joka ei koskaan olisi valmistanut n\"{a}in hyv\"{a}\"{a} olutta. Siin\"{a} oli hyv\"{a} annos skotlantilaisten itserakkautta. Jacques Paganel joi paljon ja puheli viel\"{a} enemm\"{a}n \textit{de omni re scibili}, kaikista mahdollisista asioista. N\"{a}in hyvin alkanut p\"{a}iv\"{a} n\"{a}ytti my\"{o}skin p\"{a}\"{a}ttyv\"{a}n onnellisesti. Oli p\"{a}\"{a}sty runsaat kaksikymment\"{a}viisi kilometri\"{a} eteenp\"{a}in ja taitavasti suoriuduttu jokseenkin m\"{a}kisest\"{a}, punamultaisesta maasta. Kaikesta p\"{a}\"{a}tt\"{a}en saataisiin viel\"{a} samana iltana leiriyty\"{a} Snowyn melkoisen leve\"{a}lle joelle, joka t\"{a}\"{a}ll\"{a} Victorian etel\"{a}osassa laskee Tyyneen valtamereen. Pian piirsiv\"{a}t vankkurien py\"{o}r\"{a}t j\"{a}lkens\"{a} laajoille tasangoille mustahkoa vesij\"{a}tt\"{o}maata, rehevien ruohokasvien ja uusien gastrolobium-kenttien v\"{a}liin. Tuli ilta, ja n\"{a}k\"{o}piiriss\"{a} selv\"{a}sti erottautuva sumu osoitti Snowyn uomaa; viel\"{a} muutamia kilometri\"{a} kuljettiin reippaalla mielell\"{a}. Er\"{a}\"{a}ss\"{a} mutkassa pienen kunnaan takana oli metsikk\"{o} korkeita puita. Ayrton ohjasi v\"{a}syneen valjakkonsa oikop\"{a}\"{a}t\"{a} pimeyteen peittyneiden suurien runkojen v\"{a}liin ja oli juuri p\"{a}\"{a}sem\"{a}ss\"{a} mets\"{a}nreunaan kilometrin p\"{a}\"{a}ss\"{a} joesta, kun vankkurit \"{a}kki\"{a} vajosivat py\"{o}rien napaa my\"{o}ten. --- Huomio! h\"{a}n huusi per\"{a}ss\"{a}\"{a}n tuleville ratsastajille. --- Mik\"{a} nyt on? Glenarvan kysyi. --- Olemme tarttuneet liejuun, Ayrton vastasi. Huudoilla ja kepill\"{a}\"{a}n h\"{a}n hoputti juhtia, jotka olivat vajonneet liejuun polviin asti eiv\"{a}tk\"{a} p\"{a}\"{a}sseet hievahtamaan. --- J\"{a}\"{a}d\"{a}\"{a}n t\"{a}h\"{a}n, John Mangles sanoi. --- Se on kai parasta, Ayrton vastasi. --- Huomenna p\"{a}iv\"{a}nvalossa n\"{a}emme paremmin, kuinka t\"{a}st\"{a} p\"{a}\"{a}st\"{a}\"{a}n. --- Seis! Glenarvan huusi. Lyhyen h\"{a}m\"{a}r\"{a}n j\"{a}lkeen oli tullut pime\"{a}, mutta kuumuus ei v\"{a}hentynyt p\"{a}iv\"{a}nvalon mukana. Ilma oli t\"{a}ynn\"{a} tukahduttavia h\"{o}yryj\"{a}. Muutamia salamoita v\"{a}l\"{a}hteli taivaanrannalla merkkin\"{a} kaukaisesta ukonilmasta. Y\"{o}leiri j\"{a}rjestettiin. Kiinnitarttuneissa vankkureissa tehtiin makuutilat niin hyvin kuin taidettiin, ja suurten puiden tumma holvi suojasi miesten telttaa. Ellei sade sekaantuisi peliin, ei kell\"{a}\"{a}n ollut valittamista. Ayrtonin onnistui vaivoin saada kolme juhtaansa vapautetuksi vetel\"{a}st\"{a} maasta, johon ne olivat vajonneet jo kupeitaan my\"{o}ten. H\"{a}n pani ne liekaan yhdess\"{a} hevosten kanssa eik\"{a} luovuttanut kenellek\"{a}\"{a}n muulle huolenpitoa laidunpaikan valitsemisesta. H\"{a}n hoiti t\"{a}t\"{a} tointansa perin t\"{a}sm\"{a}llisesti, ja Glenarvan huomasi h\"{a}nen t\"{a}n\"{a} iltana olevan viel\"{a} entist\"{a} huolellisempi ja kiitti h\"{a}nt\"{a} siit\"{a}, sill\"{a} vetojuhtien s\"{a}ilyminen oli eritt\"{a}in t\"{a}rke\"{a}t\"{a}. T\"{a}ll\"{a} v\"{a}lin retkeilij\"{a}t s\"{o}iv\"{a}t jokseenkin pikaisen illallisen. V\"{a}symys ja kuumuus veiv\"{a}t n\"{a}l\"{a}n, ja he olivat enemm\"{a}n levon kuin ravinnon tarpeessa. Lady Helena ja neiti Grant toivottivat seuralaisilleen hyv\"{a}\"{a} y\"{o}t\"{a} ja meniv\"{a}t tavallisille makuupaikoilleen. Miehist\"{a} astuivat toiset telttaan; toiset, kukin halunsa mukaan, asettuivat levolle rehev\"{a}\"{a}n ruohikkoon jonkin puun juurelle, mist\"{a} t\"{a}ss\"{a} terveellisess\"{a} ilmastossa ei ole mit\"{a}\"{a}n haittaa. V\"{a}hitellen kaikki vaipuivat syv\"{a}\"{a}n uneen. Pimeytt\"{a} lis\"{a}siv\"{a}t viel\"{a} paksut, taivasta peitt\"{a}v\"{a}t pilvet. Ilmassa ei tuntunut tuulenhenk\"{a}yst\"{a}k\"{a}\"{a}n, ja y\"{o}n hiljaisuuden rikkoi ainoastaan p\"{o}ll\"{o}p\"{a}\"{a}sky, joka h\"{a}mm\"{a}stytt\"{a}v\"{a}n t\"{a}sm\"{a}llisesti hel\"{a}ytti molliterssin niin kuin Euroopan surullinen k\"{a}ki. Noin kello yksitoista majuri her\"{a}si huonosta, raskaasta ja v\"{a}sytt\"{a}v\"{a}st\"{a} unesta. H\"{a}nen viel\"{a} puoliksi sulkeutuneisiin silmiins\"{a} sattui ep\"{a}m\"{a}\"{a}r\"{a}ist\"{a} valoa, jota levisi suurten puiden alla. Sit\"{a} olisi voinut pit\"{a}\"{a} valkoisena vaippana, joka kimmelteli kuin vesi j\"{a}rvess\"{a}, ja MacNabbs luulikin ensin sen olevan maassa levi\"{a}v\"{a}\"{a} kuloa. H\"{a}n nousi pystyyn, astui mets\"{a}\"{a}n p\"{a}in ja h\"{a}mm\"{a}styi suuresti havaitessaan sen olevan aivan luonnollinen ilmi\"{o}. H\"{a}nen edess\"{a}\"{a}n levisi suunnaton kentt\"{a} sieni\"{a}, jotka heijastivat fosforimaista valoa. N\"{a}iden salasiitti\"{o}iden kiilt\"{a}v\"{a}t iti\"{o}t loistivat pime\"{a}ss\"{a} melko voimakkaasti.[10] Majuri, joka ei ollut itsek\"{a}s, aikoi her\"{a}tt\"{a}\"{a} Paganelin, jotta tiedemies saisi omin silmins\"{a} tarkastella t\"{a}t\"{a} ilmi\"{o}t\"{a}, kun er\"{a}s toinen seikka esti sen. Fosforimainen valo valaisi mets\"{a}\"{a} puolen kilometrin laajuudelta, ja MacNabbs oli n\"{a}kevin\"{a}\"{a}n varjojen liikkuvan nopeasti valaistulla alalla. Pettiv\"{a}tk\"{o} h\"{a}nen silm\"{a}ns\"{a}? Oliko se n\"{a}k\"{o}h\"{a}iri\"{o}? MacNabbs laskeutui pitk\"{a}lleen ja tarkasti t\"{a}hystelty\"{a}\"{a}n erotti selv\"{a}sti useita miehi\"{a}, jotka milloin kumartuivat maahan, milloin taas nousivat ja n\"{a}yttiv\"{a}t etsiv\"{a}n tuoreita j\"{a}lki\"{a}. Oli saatava selville, mit\"{a} n\"{a}m\"{a} miehet tahtoivat. Majuri ei ep\"{a}r\"{o}inyt. Her\"{a}tt\"{a}m\"{a}tt\"{a} tovereitaan h\"{a}n katosi korkeaan ruohistoon ry\"{o}mien maassa kuin ruohoaavikoiden intiaanit. \gutchapter{TEATTERITEMPPU.} Y\"{o} oli kauhea. Kello kaksi aamulla alkoi rankkasade, jota kesti aamuun saakka. Teltasta ei ollut riitt\"{a}v\"{a}\"{a} suojaa. Glenarvan ja h\"{a}nen toverinsa pakenivat vankkureihin. Nukkua ei voinut, vaan puheltiin kaikenlaista. Vain majuri, jonka lyhytt\"{a} poissaoloa ei kukaan ollut huomannut, tyytyi kuuntelemaan sanaakaan sanomatta. Hirvitt\"{a}v\"{a} sateenry\"{o}ppy ei hellitt\"{a}nyt ja nyt pel\"{a}ttiin sen saavan Snowyn tulvimaan, jolloin liejuun tarttuneet vankkurit joutuisivat vaaraan. Useita kertoja Mulrady, Ayrton ja John Mangles k\"{a}viv\"{a}tkin tutkimassa veden korkeutta joessa ja palasivat kiireest\"{a} kantap\"{a}\"{a}h\"{a}n m\"{a}rkin\"{a}. Vihdoin valkeni p\"{a}iv\"{a}. Sade lakkasi, mutta auringons\"{a}teet eiv\"{a}t tunkeutuneet paksun pilviverhon l\"{a}pi. Kaikkialle oli ilmestynyt suuria sameita l\"{a}t\"{a}k\"{o}it\"{a}. Lionneesta maasta nousi l\"{a}mmint\"{a} h\"{o}yry\"{a}, joka t\"{a}ytti ilman ep\"{a}terveellisell\"{a} kosteudella. Glenarvan k\"{a}\"{a}nsi huomionsa ensin vankkureihin. Ne olivat h\"{a}nen mielest\"{a}\"{a}n p\"{a}\"{a}asia. Tutkittiin raskasta ajoneuvoa, joka oli vajonnut sitke\"{a}\"{a}n saveen keskell\"{a} suurta syvennyst\"{a}. Etuosa oli melkein kokonaan kadonnut n\"{a}kyvist\"{a} ja takaosa py\"{o}rien akseliin saakka. Olisi vaikeata saada t\"{a}t\"{a} painavaa laitosta nostetuksi. Miesten, hevosten ja juhtien yhteisvoima tuskin riitt\"{a}isi. --- Joka tapauksessa t\"{a}ytyy ruveta heti t\"{o}ihin, John Mangles sanoi. --- Jos t\"{a}m\"{a} savi p\"{a}\"{a}see kuivahtamaan, k\"{a}y tilanne viel\"{a} vaikeammaksi. --- Aloitetaan, Ayrton vastasi. Glenarvan, molemmat matruusit, John Mangles ja Ayrton l\"{a}htiv\"{a}t mets\"{a}\"{a}n, miss\"{a} el\"{a}imet olivat olleet y\"{o}t\"{a}. Se oli synkk\"{a}, korkea kumipuumetsikk\"{o}; kaikkialla oli kuivuneita puita pitkien v\"{a}limatkojen p\"{a}\"{a}ss\"{a}, kolottuja jo vuosisatoja sitten tai pikemminkin nyljettyj\"{a}, kuten korkkipuut korjuun aikana. Yli viidenkymmenen metrin korkeudessa oli viel\"{a} ohut pienten riivittyjen oksien verkko. Ainoakaan lintu ei tehnyt pes\"{a}\"{a}ns\"{a} n\"{a}ihin ilmassa h\"{a}ilyviin luurankoihin, ainoatakaan lehte\"{a} ei lepattanut n\"{a}ill\"{a} kuivilla oksilla, jotka kalisivat kuin luukasa. Mist\"{a} valtavasta tapahtumasta olikaan aiheutunut t\"{a}m\"{a} ilmi\"{o}, joka tavataan Australiassa usein, kun kokonaisia metsi\"{a} n\"{a}ytt\"{a}\"{a} joutuneen jonkin kulkutaudin uhriksi? Sit\"{a} ei tiedet\"{a}. Vanhimmatkaan alkuasukkaat tai heid\"{a}n jo kauan kuoleman lehdoissa makaavat esi-is\"{a}ns\"{a} eiv\"{a}t koskaan ole n\"{a}hneet niit\"{a} vehrein\"{a}. Glenarvan katseli harmaata taivasta, jota vasten kumipuiden pienimm\"{a}tkin oksat selv\"{a}sti piirtyiv\"{a}t hienoina viiruina. Ayrton kummasteli, ettei hevosia ja juhtia en\"{a}\"{a} ollut sill\"{a} paikalla, mihin h\"{a}n oli ne vienyt. Liekaan sidotut el\"{a}imet eiv\"{a}t toki voineet liikkua kauaksi. Niit\"{a} etsittiin mets\"{a}st\"{a}, mutta l\"{o}yt\"{a}m\"{a}tt\"{a}. H\"{a}mm\"{a}styneen\"{a} Ayrton k\"{a}\"{a}ntyi komeiden mimoosien reunustamaa Snowy-jokea kohti. H\"{a}n p\"{a}\"{a}steli huutoja, jotka olivat hyvin tuttuja h\"{a}nen juhdilleen, mutta n\"{a}m\"{a} eiv\"{a}t vastanneet. Nyt h\"{a}n n\"{a}ytti todella levottomalta, ja h\"{a}nen toverinsa katsoivat h\"{a}nt\"{a} huolestuneina. Tunti kului turhassa etsiskelyss\"{a}, ja Glenarvan aikoi jo palata vankkurien luo, jotka olivat ainakin puolentoista kilometrin p\"{a}\"{a}ss\"{a}, kun h\"{a}nen korvaansa kuului hirnuntaa, ja heti sen j\"{a}lkeen kuultiin mylv\"{a}hdys. --- Tuolla ne ovat! John Mangles huudahti tunkeutuen korkeiden gastrolobium-pensaiden v\"{a}liin, jotka olivat kyllin korkeita k\"{a}tke\"{a}kseen kokonaisen el\"{a}inlauman. Glenarvan, Mulrady ja Ayrton riensiv\"{a}t h\"{a}nen per\"{a}ss\"{a}\"{a}n ja olivat pian yht\"{a} kummissaan kuin h\"{a}nkin. Kaksi h\"{a}rk\"{a}\"{a} ja kolme hevosta makasi maassa \"{a}killisesti kuolleina kuten aikaisemminkin oli sattunut. Raadot olivat jo kylmi\"{a}, ja joukko nuoria korppeja raakkui mimoosien oksilla t\"{a}hystellen t\"{a}t\"{a} odottamatonta saalista. Glenarvan ja h\"{a}nen yst\"{a}v\"{a}ns\"{a} katselivat toisiaan, eik\"{a} Wilson voinut pid\"{a}tt\"{a}\"{a} kirousta, joka p\"{a}\"{a}si h\"{a}nen huuliltaan. --- Mit\"{a} sille mahtaa, Wilson, sanoi lordi Glenarvan, joka tuskin itse jaksoi pysy\"{a} rauhallisena, --- me emme voi sille mit\"{a}\"{a}n. Ottakaa mukaanne elossa oleva juhta ja hevonen, Ayrton. Niiden on nyt p\"{a}\"{a}stett\"{a}v\"{a} meid\"{a}t p\"{a}lk\"{a}h\"{a}st\"{a}. --- Elleiv\"{a}t vankkurit olisi juuttuneet kiinni, John Mangles vastasi, --- n\"{a}m\"{a} kaksi el\"{a}int\"{a} riitt\"{a}isiv\"{a}t pienin p\"{a}iv\"{a}matkoin vet\"{a}m\"{a}\"{a}n ne rannikolle. T\"{a}ytyy siis v\"{a}ltt\"{a}m\"{a}tt\"{a} saada se kirottu peli irti. --- Koetetaan, John, Glenarvan vastasi. --- Palatkaamme leirille, jossa luultavasti jo ollaan levottomia meid\"{a}n pitk\"{a}st\"{a} poissaolostamme. Ayrton irrotti juhdan siteet, Mulrady hevosen, ja sitten palattiin pitkin joen mutkaista rantaa. Puolta tuntia my\"{o}hemmin tiesiv\"{a}t Paganel ja MacNabbs, lady Helena ja neiti Grant, kuinka oli asian laita. --- Totisesti, majuri tuli lausuneeksi, --- onpa paha juttu, Ayrton, ett\"{a} te ette kengitytt\"{a}nyt kaikkia hevosiamme Wimerran luona. --- Miten niin, herra? Ayrton kysyi. --- Kun kaikista hevosista ainoastaan se, jonka annoitte sepp\"{a}nne pidelt\"{a}v\"{a}ksi, on v\"{a}ltt\"{a}nyt yhteisen kohtalon. --- Se on totta, John Mangles sanoi. --- Se on tosiaan omituinen sattuma. --- Sattuma eik\"{a} mit\"{a}\"{a}n muuta, per\"{a}mies vastasi katsoen kiinte\"{a}sti majuriin. MacNabbs puristi huulensa yhteen kuin olisi halunnut pid\"{a}tt\"{a}\"{a} esiin pyrkivi\"{a} sanoja. Glenarvan, Mangles, lady Helena n\"{a}yttiv\"{a}t odottavan, ett\"{a} h\"{a}n lausuisi ajatuksensa loppuun, mutta majuri vaikeni ja meni vankkurien luo, joita Ayrton tarkasteli. --- Mit\"{a} h\"{a}n tarkoitti? Glenarvan kysyi John Manglesilta. --- En tied\"{a}, nuori kapteeni vastasi. --- MacNabbs on muutenkin sellainen mies, joka ei jaarittele turhanp\"{a}iten. --- Ehk\"{a} h\"{a}n tuntee jotakin ep\"{a}luuloa Ayrtonia kohtaan, lady Helena sanoi. --- Ep\"{a}luuloa? Paganel toisti kohauttaen olkap\"{a}it\"{a}\"{a}n. --- Mutta miksi? Glenarvan kysyi. --- Luuleeko h\"{a}n Ayrtonin tappaneen hevosemme ja juhtamme? Mit\"{a} varten? Ayrtonin etuhan on sama kuin meid\"{a}n. --- Sin\"{a} olet oikeassa, rakas Edward, lady Helena sanoi, --- ja min\"{a} lis\"{a}\"{a}n, ett\"{a} h\"{a}n matkamme alusta saakka on antanut meille kielt\"{a}m\"{a}tt\"{o}mi\"{a} todisteita alttiudestaan. --- Ep\"{a}ilem\"{a}tt\"{a}, John Mangles lausui. --- Mutta mit\"{a} merkitsee sitten majurin huomautus? Minun t\"{a}ytyy ottaa siit\"{a} selv\"{a}. --- Luuleeko h\"{a}n Ayrtonin olevan liitossa karanneiden pahantekij\"{o}iden kanssa? Paganel huudahti varomattomasti. --- Keiden karanneiden pahantekij\"{o}iden? neiti Grant kysyi. --- Herra Paganel erehtyy, John Mangles vastasi. --- H\"{a}n tiet\"{a}\"{a} hyvin, ettei sellaisia ole Victorian maakunnassa. --- Ah, seh\"{a}n on totta! my\"{o}nsi Paganel, joka olisi halunnut saada sanansa takaisin. --- Miss\"{a} ajatukseni olivatkaan? Karkulaisiako? Kuka on koskaan kuullut sellaisista puhuttavan Australiassa? Muuten he tuskin ovat p\"{a}\"{a}sseet maihin, kun jo ovat varsin kunniallista v\"{a}ke\"{a}! Ilmasto! Tied\"{a}tteh\"{a}n, neiti Mary, ilmaston siveellinen vaikutus... Tiedemiehen k\"{a}vi samoin kuin vankkureiden --- j\"{a}i kiinni yritt\"{a}ess\"{a}\"{a}n korjata hairahdustaan. Lady Helena katsoi h\"{a}neen, ja se sai Paganel-poloisen t\"{a}ysin ymm\"{a}lle. Mutta kun h\"{a}n ei tahtonut enemp\"{a}\"{a} nolostuttaa ranskalaista, h\"{a}n vei neiti Maryn telttaan, miss\"{a} Olbinett oli kaikkien taiteen s\"{a}\"{a}nt\"{o}jen mukaan valmistamassa aamiaista. --- Minut itseni siet\"{a}isi karkottaa, Paganel sanoi surkealla \"{a}\"{a}nell\"{a}. --- Niin minustakin tuntuu, Glenarvan vastasi. T\"{a}m\"{a} vastaus sanottiin niin vakavasti, ett\"{a} kelpo maantieteilij\"{a} masentui kokonaan. Glenarvan ja John Mangles meniv\"{a}t vankkurien luo. Ayrton ja molemmat matruusit olivat parhaillaan yritt\"{a}m\"{a}ss\"{a} kiskoa niit\"{a} yl\"{o}s syv\"{a}st\"{a} suosta. H\"{a}rk\"{a} ja hevonen, jotka oli valjastettu rinnakkain, vetiv\"{a}t j\"{a}ntereidens\"{a} koko voimalla; vetohihnat pingottuivat \"{a}\"{a}rimmilleen, aisat olivat v\"{a}h\"{a}ll\"{a} katketa ponnistuksissa, Wilson ja Mulrady ty\"{o}nsiv\"{a}t py\"{o}rist\"{a} Ayrtonin kannustaessa huudoilla ja kepill\"{a} ep\"{a}tasaista paria. Mutta raskaat vankkurit eiv\"{a}t hievahtaneet, kuivahtanut savi piti niit\"{a} kiinni kuin sementiss\"{a} ik\"{a}\"{a}n. John Mangles k\"{a}ski kastella savea pehment\"{a}\"{a}kseen sit\"{a}, mutta turhaan; vankkurit eiv\"{a}t hievahtaneetkaan, ja pitk\"{a}n ponnistelun j\"{a}lkeen sek\"{a} miehet ett\"{a} el\"{a}imet vihdoin lep\"{a}siv\"{a}t. Ellei haluttu hajoittaa vankkureita kappaleiksi, t\"{a}ytyi lopettaa niiden kiskominen yl\"{o}s liejusta. Mutta sellaiseen ei ollut ty\"{o}kaluja. Ayrton tahtoi kuitenkin kaikesta huolimatta yritt\"{a}\"{a} uudelleen, kun lordi Glenarvan esti sen. --- Antaa olla, Ayrton, antaa olla! h\"{a}n sanoi. --- Meid\"{a}n t\"{a}ytyy s\"{a}\"{a}st\"{a}\"{a} viimeist\"{a} hevostamme ja juhtaamme. Jos meid\"{a}n on jatkettava matkaamme jalkaisin, toinen kantaa molempia naisia ja toinen muonavarojamme. Ne voivat siis viel\"{a} tehd\"{a} meille suuria palveluksia. --- Hyv\"{a} on, mylord, per\"{a}mies vastasi ja p\"{a}\"{a}sti v\"{a}syneet el\"{a}imet valjaista. --- Nyt, yst\"{a}v\"{a}ni, Glenarvan lis\"{a}si, --- palatkaamme leiriin, harkitkaamme ja tutkikaamme asemaamme, katsokaamme mill\"{a} puolen on hyv\"{a}t, mill\"{a} huonot toiveet ja tehk\"{a}\"{a}mme sitten p\"{a}\"{a}t\"{o}ksemme. Hetkist\"{a} my\"{o}hemmin virkistiv\"{a}t retkeilij\"{a}t itse\"{a}\"{a}n jokseenkin hyv\"{a}ll\"{a} aterialla ja alkoivat keskustella. Jokaista kehotettiin lausumaan mielipiteens\"{a}. Ensiksi oli t\"{a}sm\"{a}llisesti m\"{a}\"{a}ritett\"{a}v\"{a} leiripaikan sijainti. Paganel, joka sai sen teht\"{a}v\"{a}kseen, laati tarkan laskelman. H\"{a}nen vakuutuksensa mukaan retkikunta oli pys\"{a}htynyt 37. leveysasteella, 147$^{\circ}$ 53' pituusasteen kohdalla, Snowy-joen rannalla. --- Mik\"{a} on Twofold-lahden tarkka pituus? Glenarvan kysyi. --- Sataviisikymment\"{a} astetta, Paganel vastasi. --- Ja n\"{a}m\"{a} kaksi astetta seitsem\"{a}n minuuttia tekev\"{a}t...? --- Sataviisikymment\"{a} kilometri\"{a}. --- Ja Melbourneen on...? --- V\"{a}hint\"{a}\"{a}n kolmesataakuusikymment\"{a} kilometri\"{a}. --- Hyv\"{a}. Kun sijaintimme t\"{a}ten on m\"{a}\"{a}ritetty, Glenarvan sanoi, --- mit\"{a} on teht\"{a}v\"{a}? Vastaus oli yksimielinen: piti l\"{a}hte\"{a} rannikolle viipym\"{a}tt\"{a}. Lady Helena ja Mary Grant lupasivat marssia kahdeksan kilometri\"{a} p\"{a}iv\"{a}ss\"{a}. Uljaat naiset olivat valmiit k\"{a}velem\"{a}\"{a}n jalkapatikassa Snowy-joelta Twofold-lahdelle. --- Sin\"{a} olet mainio matkatoveri, rakas Helena, lordi Glenarvan sanoi. --- Mutta onko varmaa, ett\"{a} lahdelle saapuessamme saamme sielt\"{a} kaikkea, mit\"{a} tarvitsemme? --- Ep\"{a}ilem\"{a}tt\"{a}, Paganel vastasi. --- Eden on jo monta vuotta ollut kaupunkina. Sen satamasta on luultavasti hyv\"{a}t yhteydet Melbournen kanssa. Oletan, ett\"{a} kuudenkymmenen kilometrin p\"{a}\"{a}ss\"{a} t\"{a}\"{a}lt\"{a}, Delegeten kunnassa, Victorian rajalla, voimme t\"{a}ydent\"{a}\"{a} retkikunnan ruokavaroja ja saada kulkuneuvoja. --- Ent\"{a} \textit{Duncan}? Ayrton kysyi. --- Ettek\"{o} arvelisi hy\"{o}dylliseksi, mylord, k\"{a}ske\"{a} sit\"{a} saapumaan lahdelle? --- Mit\"{a} te siit\"{a} sanotte, John? Glenarvan kysyi. --- K\"{a}sitt\"{a}\"{a}kseni teid\"{a}n ei siin\"{a} suhteessa tarvitse pit\"{a}\"{a} kiirett\"{a}, mylord, nuori kapteeni vastasi hetken harkittuaan. --- Ehtiih\"{a}n sielt\"{a}kin l\"{a}hett\"{a}\"{a} sanan Tom Austinille ja kutsua h\"{a}net rannikolle. --- Se on totta, Paganel selitti. --- Huomatkaa, John Mangles jatkoi, --- ett\"{a} me olemme Edeniss\"{a} nelj\"{a}n tai viiden p\"{a}iv\"{a}n kuluttua. --- Nelj\"{a}n tai viiden p\"{a}iv\"{a}n! Ayrton sanoi kohottaen p\"{a}\"{a}t\"{a}\"{a}n. --- Sanokaa, ett\"{a} siihen menee viisitoista tai kaksikymment\"{a} p\"{a}iv\"{a}\"{a}, kapteeni, ellette tahdo liian my\"{o}h\"{a}\"{a}n katua erehdyst\"{a}nne. --- Viisitoista tai kaksikymment\"{a} p\"{a}iv\"{a}\"{a} sataanviiteenkymmeneen kilometriin! Glenarvan huudahti. --- V\"{a}hint\"{a}\"{a}nkin, mylord. Nyt on kuljettava Victorian vaikea kulkuisimman osan halki, er\"{a}maan l\"{a}pi, miss\"{a} karjankasvattajien sanojen mukaan ei ole mit\"{a}\"{a}n; se on metsistynytt\"{a}, raivaamatonta aluetta, jonne ei ole voitu perustaa asemia. Siell\"{a} t\"{a}ytyy kulkea eteenp\"{a}in kirves tai soihtu kourassa, ja uskokaa minua: siell\"{a} ei kuljeta nopeasti. Ayrton oli puhunut varmalla \"{a}\"{a}nell\"{a}. Paganel, johon luotiin kysyvi\"{a} katseita, vahvisti p\"{a}\"{a}nny\"{o}kk\"{a}yksell\"{a} per\"{a}miehen sanat. --- Min\"{a} my\"{o}nn\"{a}n n\"{a}m\"{a} vaikeudet, sanoi silloin John Mangles. --- No olkoon! Viidentoista p\"{a}iv\"{a}n kuluttua voi mylord l\"{a}hett\"{a}\"{a} k\"{a}skyns\"{a} \textit{Duncanille}. --- Min\"{a} lis\"{a}isin, Ayrton jatkoi t\"{a}ll\"{o}in, --- ett\"{a} suurimmat vaikeudet eiv\"{a}t johdu tien hankaluuksista. Mutta on p\"{a}\"{a}st\"{a}v\"{a} Snowyn yli ja luultavasti odotettava veden laskemista. --- Odotettava! nuori kapteeni huudahti. --- Eik\"{o} voisi l\"{o}yt\"{a}\"{a} kahlaamoa? --- Enp\"{a} luule, Ayrton vastasi. --- T\"{a}n\"{a} aamuna etsin sellaista turhaan. On harvinaista, ett\"{a} joki on niin tulvillaan t\"{a}h\"{a}n vuodenaikaan, mutta se on onnettomuus, jolle min\"{a} en mit\"{a}\"{a}n mahda. --- Onko t\"{a}m\"{a} Snowy siis kovin leve\"{a}? lady Glenarvan kysyi. --- Leve\"{a} ja syv\"{a}, rouva, Ayrton vastasi, --- puolitoista kilometri\"{a} leve\"{a} ja vuolasvirtainen. Hyv\"{a}k\"{a}\"{a}n uimari ei voisi vaaratta yritt\"{a}\"{a} sen yli. --- Mit\"{a} siit\"{a}, rakennetaan kanootti, huudahti Robert, joka ei pel\"{a}nnyt mit\"{a}\"{a}n. --- Kaadetaan puu, koverretaan se ja soudetaan yli, siin\"{a} kaikki. --- Kapteeni Grantin poika ei joudu pulaan! Paganel sanoi. --- Ja h\"{a}n on oikeassa, John Mangles vastasi. --- Meid\"{a}n on lopulta pakko ryhty\"{a} siihen. Minusta on siis hy\"{o}dyt\"{o}nt\"{a} kuluttaa aikaa turhiin keskusteluihin. --- Mit\"{a} te siit\"{a} ajattelette, Ayrton? Glenarvan kysyi. --- Min\"{a} ajattelen, mylord, ett\"{a} ellemme saa apua, olemme viel\"{a} kuukauden p\"{a}\"{a}st\"{a} Snowyn rannalla. --- Onko teill\"{a} siis parempaa ehdotusta? John Mangles kysyi hiukan k\"{a}rsim\"{a}tt\"{o}m\"{a}n\"{a}. --- On se, ett\"{a} \textit{Duncan} l\"{a}htee Melbournesta ja tulee it\"{a}rannikolle. --- Aina vain \textit{Duncan!} Miten sen saapuminen Twofold-lahteen helpottaisi meid\"{a}n p\"{a}\"{a}sy\"{a}mme sinne? Ayrton mietti pari silm\"{a}nr\"{a}p\"{a}yst\"{a} ennen vastaamistaan ja sanoi sitten v\"{a}ltellen: --- En min\"{a} tahdo tyrkytt\"{a}\"{a} kenellek\"{a}\"{a}n mielipidett\"{a}ni. Ajattelin vain kaikkien parasta, mutta olen valmis l\"{a}htem\"{a}\"{a}n, mill\"{a} hetkell\"{a} vain lordi antaa merkin. Sitten h\"{a}n pani k\"{a}sivarret ristiin rinnalleen. --- Se ei ole mik\"{a}\"{a}n vastaus, Ayrton, Glenarvan huomautti. --- Sanokaa meille ehdotuksenne, ja me keskustelemme siit\"{a}. Mit\"{a} te ehdotatte? Ayrton lausui silloin tyynell\"{a} ja varmalla \"{a}\"{a}nell\"{a}: --- Min\"{a} ehdotan, ett\"{a} emme l\"{a}hde seikkailemaan Snowyn tuolle puolen n\"{a}in huonoin varustein. Meid\"{a}n on odotettava apua juuri t\"{a}ss\"{a}, ja sit\"{a} voi tuoda meille vain \textit{Duncan}. Leiriytyk\"{a}\"{a}mme t\"{a}nne, miss\"{a} meilt\"{a} ei puutu ruokavaroja, ja l\"{a}htek\"{o}\"{o}n yksi meist\"{a} viem\"{a}\"{a}n Tom Austinille m\"{a}\"{a}r\"{a}yst\"{a} pptrjehtia Twofold-lahteen. T\"{a}m\"{a} odottamaton ehdotus her\"{a}tti hiukan h\"{a}mm\"{a}styst\"{a}, eik\"{a} John Mangles salannut paheksuvansa sit\"{a}. --- Sill\"{a} v\"{a}lin, Ayrton jatkoi, --- joko Snowyn vesi laskee, jolloin voidaan l\"{o}yt\"{a}\"{a} kelvollinen kahlaamo, tai ylitett\"{a}v\"{a} virta kanootilla, jonka rakentamiseen meill\"{a} silloin on aikaa. Siin\"{a}, mylord, suunnitelma, jonka alistan teid\"{a}n hyv\"{a}ksytt\"{a}v\"{a}ksenne. --- Hyv\"{a}, Ayrton, Glenarvan vastasi. --- Teid\"{a}n suunnitelmanne ansaitsee vakavaa harkintaa. Sen suurin haitta on, ett\"{a} se aiheuttaa viivytyst\"{a}, mutta se s\"{a}\"{a}st\"{a}\"{a} suuria vaivoja ja kenties vakavia vaaroja. Mit\"{a} ajattelette siit\"{a}, yst\"{a}v\"{a}ni? --- Sanokaa te, MacNabbs, lausui t\"{a}ll\"{o}in lady Helena. --- Keskustelun alusta saakka te olette vain kuunnellut ja olette perin kitsas puhumaan. --- Koska kysytte mielipidett\"{a}ni, majuri vastasi, --- sanon sen teille empim\"{a}tt\"{a}. Ayrton tuntuu minusta puhuneen viisaan ja varovaisen miehen tavoin, ja min\"{a} yhdyn h\"{a}nen ehdotukseensa. T\"{a}t\"{a} vastausta ei juuri ollut odotettu, sill\"{a} t\"{a}h\"{a}n saakka oli MacNabbs aina vastustanut Ayrtonin suunnitelmia. Siksi Ayrtonkin vilkaisi h\"{a}mm\"{a}styneen\"{a} majuriin. Paganel, lady Helena ja matruusit olivat hyvin taipuvia kannattamaan per\"{a}miehen ehdotusta. He eiv\"{a}t empineetk\"{a}\"{a}n MacNabbsin sanojen j\"{a}lkeen. Glenarvan julisti siis Ayrtonin ehdotuksen periaatteessa hyv\"{a}ksytyksi. --- Ja nyt, John, h\"{a}n lis\"{a}si, --- ettek\"{o} tekin katso varovaisuuden vaativan toimimaan n\"{a}in ja majailemaan t\"{a}m\"{a}n joen rannalla kulkuneuvoja odottamassa? --- Miksen, John Mangles vastasi, --- kun vain sanansaattajamme voi p\"{a}\"{a}st\"{a} Snowyn yli, vaikka me itse emme voi. Katsahdettiin per\"{a}mieheen, joka hymyili varmana itsest\"{a}\"{a}n. --- Sanansaattaja ei mene joen yli, h\"{a}n sanoi. --- Ahaa! John Mangles huudahti. --- H\"{a}n palaa yksinkertaisesti Lucknowin tielle, joka vie h\"{a}net suoraan Melbourneen. --- Nelj\"{a}tt\"{a}sataa kilometri\"{a} jalkaisin! nuori kapteeni huomautti. --- Ratsain, Ayrton vastasi. --- Meill\"{a}h\"{a}n on terve hevonen. Se on nelj\"{a}n p\"{a}iv\"{a}n asia. Lis\"{a}t\"{a}\"{a}n siihen kaksi p\"{a}iv\"{a}\"{a} \textit{Duncanin} matkaa varten lahteen ja vuorokausi leirille paluuta varten, niin sanansaattaja on viikon kuluttua t\"{a}\"{a}ll\"{a} laivamiesten kanssa. Majuri hyv\"{a}ksyi p\"{a}\"{a}nny\"{o}kk\"{a}yksell\"{a} Ayrtonin sanat, mik\"{a} ei ollut her\"{a}tt\"{a}m\"{a}tt\"{a} John Manglesin h\"{a}mm\"{a}styst\"{a}. Mutta per\"{a}miehen ehdotus sai puolelleen kaikki \"{a}\"{a}net, eik\"{a} sen j\"{a}lkeen ollut muuta teht\"{a}v\"{a}\"{a} kuin hyvin keksityn suunnitelman toimeenpano. --- Nyt, yst\"{a}v\"{a}ni, Glenarvan sanoi, --- on j\"{a}ljell\"{a} vain sananviej\"{a}n valitseminen. En salaa, ett\"{a} teht\"{a}v\"{a} on vaivalloinen ja vaarallinen. Kuka uhrautuu kumppaniensa puolesta ja l\"{a}htee viem\"{a}\"{a}n viesti\"{a}mme Melbourneen? Wilson, Mulrady, John Mangles, Paganel, jopa Robertkin tarjoutuivat heti. John vaati erityisen hartaasti, ett\"{a} t\"{a}m\"{a} teht\"{a}v\"{a} uskottaisiin h\"{a}nelle. Mutta Ayrton, joka ei viel\"{a} ollut puhunut mit\"{a}\"{a}n, lausui silloin: --- Suvaitkaa, mylord, ett\"{a} min\"{a} l\"{a}hden. Min\"{a} olen tottunut n\"{a}ihin seutuihin. Olen monta kertaa kulkenut pahimmistakin paikoista. Min\"{a} selviydyn siit\"{a}, mist\"{a} joku toinen ei. Yhteiseen etuun vedoten vaadin siis oikeutta l\"{a}hte\"{a} Melbourneen. Sana teilt\"{a} riitt\"{a}\"{a} suosittamaan minua Tom Austinille, ja kuudessa p\"{a}iv\"{a}ss\"{a} otan toimittaakseni \textit{Duncanin} Twofold-lahteen. --- Hyvin puhuttu, Glenarvan vastasi. --- Te olette \"{a}lyk\"{a}s ja rohkea mies, Ayrton, ja te onnistutte. Per\"{a}mies oli ilmeisesti sopivampi kuin kukaan muu t\"{a}h\"{a}n vaikeaan teht\"{a}v\"{a}\"{a}n. Jokainen ymm\"{a}rsi sen ja suostui. John Mangles teki viimeisen vastav\"{a}itteen sanomalla, ett\"{a} Ayrtonin l\"{a}sn\"{a}olo oli v\"{a}ltt\"{a}m\"{a}t\"{o}n \textit{Britannian} tai Harry Grantin j\"{a}lkien l\"{o}yt\"{a}mist\"{a} varten. Mutta majuri huomautti, ett\"{a} retkikunta j\"{a}isi Snowyn rannalle Ayrtonin paluuseen saakka, ettei ollut puhettakaan t\"{a}m\"{a}n t\"{a}rke\"{a}n etsinn\"{a}n jatkamisesta ilnaln h\"{a}nt\"{a}, joten h\"{a}nen poissaolonsa ei mill\"{a}\"{a}n tavoin vahingoittaisi kapteenin parasta. --- Niinp\"{a} niin, l\"{a}htek\"{a}\"{a}, Ayrton, Glenarvan sanoi. --- Pit\"{a}k\"{a}\"{a} kiirett\"{a} ja palatkaa Edenin kautta leirillemme Snowyn rannalle. Tyytyv\"{a}isyyden v\"{a}l\"{a}hdys pilkahti per\"{a}miehen silmiss\"{a}. H\"{a}n k\"{a}\"{a}nsi p\"{a}\"{a}t\"{a}\"{a}n, mutta niin vikkel\"{a}sti kuin h\"{a}n sen tekikin, oli John Mangles sen huomannut. Vaistosta, ei muusta, tunsi John ep\"{a}luulonsa Ayrtonia kohtaan yltyv\"{a}n. Per\"{a}mies ryhtyi siis matkavalmisteluihin molempien matruusien auttamana, joista toinen pani kuntoon h\"{a}nen hevosensa, toinen h\"{a}nen ev\"{a}\"{a}ns\"{a}. T\"{a}ll\"{a} v\"{a}lin Glenarvan kirjoitti Tom Austinille osoitetun kirjeen. H\"{a}n m\"{a}\"{a}r\"{a}si \textit{Duncanin} ensimm\"{a}isen per\"{a}miehen viipym\"{a}tt\"{a} l\"{a}htem\"{a}\"{a}n Twofold-lahteen ja suositti h\"{a}nelle sanantuojaa miehen\"{a}, johon voisi t\"{a}ydellisesti luottaa. Rannikolle saavuttuaan pit\"{a}isi Tom Austinin luovuttaa osa laivan matruuseja Ayrtonin komentoon... Glenarvan oli ehtinyt kirjeess\"{a}\"{a}n t\"{a}lle kohtaa, kun MacNabbs, joka seurasi silmill\"{a}\"{a}n kyn\"{a}nj\"{a}lke\"{a}, kysyi omituisella \"{a}\"{a}nell\"{a}, kuinka h\"{a}n kirjoitti Ayrtonin nimen. --- Niin kuin se lausutaan, Glenarvan vastasi. --- Se on erehdys, majuri huomautti tyynesti. --- Se lausutaan Ayrton, mutta kirjoitetaan Ben Joyce! \gutchapter{ALAND --- ZEALAND.} Ben Joycen nimen mainitseminen vaikutti kuin salamanisku. Ayrton oli \"{a}kki\"{a} k\"{a}\"{a}ntynyt. H\"{a}nen k\"{a}dess\"{a}\"{a}n oli revolveri. Kuului pamaus. Glenarvan kaatui luodin iskem\"{a}n\"{a}. Ulkoa kuului pyssynlaukauksia. John Mangles ja matruusit typertyiv\"{a}t aluksi, mutta yrittiv\"{a}t sitten sy\"{o}ksy\"{a} Ben Joycen kimppuun; rohkea rosvo oli kuitenkin jo kadonnut ja liittynyt kumipuumets\"{a}n reunassa vaanivaan joukkoonsa. Teltta ei suojannut riitt\"{a}v\"{a}sti luodeilta. T\"{a}ytyi per\"{a}yty\"{a}. Glenarvan oli haavoittunut vain liev\"{a}sti ja noussut pystyyn. --- Vankkureihin! John Mangles huusi ja tarttui lady Helenaan ja Mary Grantiin, jotka pian olivat suojassa rattaiden paksun kehikon takana. John, majuri Paganel ja matruusit tarttuivat pyssyihins\"{a} ja valmistautuivat vastaamaan rosvojen tuleen. Glenarvan ja Robert olivat menneet naisten luo, ja Olbinett riensi yhteiseen puolustukseen. T\"{a}m\"{a} kaikki oli tapahtunut parissa silm\"{a}nr\"{a}p\"{a}yksess\"{a}. John Mangles t\"{a}hysti tarkasti mets\"{a}n reunaa. Pamahdukset olivat \"{a}kki\"{a} tauonneet Ben Joycen saapuessa. Syv\"{a} hiljaisuus seurasi r\"{a}tisevi\"{a} laukauksia. Muutamia valkoisia savukiemuroita leijaili viel\"{a} kumipuiden oksien v\"{a}liss\"{a}. Korkeat gastrolobium-t\"{o}yhd\"{o}t olivat liikkumattomia. Hy\"{o}kk\"{a}yksest\"{a} ei en\"{a}\"{a} n\"{a}kynyt merkki\"{a}k\"{a}\"{a}n. Majuri ja John Mangles tekiv\"{a}t tiedusteluretken suurille puille saakka. Sielt\"{a} oli poistuttu. N\"{a}kyi vain paljon askelten j\"{a}lki\"{a}, ja muutamia puoliksi palaneita pyssynpanoksia savusi maassa. Varovaisena miehen\"{a} majuri sammutti ne, sill\"{a} yksikin kipin\"{a} riitti sytytt\"{a}m\"{a}\"{a}n kauhean kulon t\"{a}ss\"{a} kuivassa mets\"{a}ss\"{a}. --- Rosvot ovat poistuneet, John Mangles sanoi. --- Niin ovat, majuri vastasi, --- ja se huolestuttaa minua. Minusta olisi parempi n\"{a}hd\"{a} heid\"{a}t silm\"{a}st\"{a} silm\"{a}\"{a}n. Parempi tiikeri avoimella kent\"{a}ll\"{a} kuin k\"{a}\"{a}rme ruohikossa. Tutkikaamme vankkurien pensaikot l\"{a}hettyvilt\"{a}. Majuri ja John tarkastivat l\"{a}hitienoot. Mets\"{a}n reunasta Snowyn rantaan ei tavattu yht\"{a}\"{a}n rosvoa. Ben Joycen joukko n\"{a}ytti h\"{a}ipyneen tiehens\"{a} kuin petolintuparvi. T\"{a}m\"{a} katoaminen oli liian kummallista, jotta olisi voitu olla t\"{a}ysin turvallisin mielin. Siksi p\"{a}\"{a}tettiin olla varuillaan. Vankkurit olivat kuin saveen muurattuna linnoituksena leirin keskuksessa ja kaksi miest\"{a} piti vahtia aina tunnin kerrallaan. Lady Helenan ja Mary Grantin ensimm\"{a}isen\"{a} huolena oli ollut Glenarvanin haavan sitominen. Miehens\"{a} kaatuessa Ben Joycen luodista oli lady Helena s\"{a}ik\"{a}htyneen\"{a} rient\"{a}nyt h\"{a}nen luokseen. Sitten uljas nainen oli malttanut mielens\"{a} ja taluttanut Glenarvanin vankkureihin. Siell\"{a} paljastettiin haavoittunut olkap\"{a}\"{a}, ja majuri totesi luodin vain repineen ihoa aiheuttamatta mit\"{a}\"{a}n sis\"{a}ist\"{a} vammaa. Luut tai lihakset eiv\"{a}t n\"{a}ytt\"{a}neet vahingoittuneen. Haava vuoti paljon verta, mutta Glenarvan liikutteli sormiaan ja kyyn\"{a}rvarttaan ja rauhoitti n\"{a}in yst\"{a}v\"{a}ns\"{a}. Kun side oli valmis, h\"{a}n ei halunnut, ett\"{a} h\"{a}neen kiinnitett\"{a}isiin sen enemp\"{a}\"{a} huomiota, ja nyt siirryttiin selityksiin. Ayrton oli \"{a}kki\"{a} k\"{a}\"{a}ntynyt. H\"{a}nen k\"{a}dess\"{a}\"{a}n oli revolveri. Kuului pamaus... Retkeilij\"{a}t, lukuunottamatta Mulradya ja Wilsonia, jotka pitiv\"{a}t vahtia ulkona, olivat sijoittuneet vankkureihin niin hyvin kuin taisivat. Majuria pyydettiin puhumaan. Ennen kertomuksensa aloittamista h\"{a}n selitti lady Helenalle ne seikat, joita t\"{a}m\"{a} ei tuntenut, nimitt\"{a}in er\"{a}\"{a}n rosvojoukon karkaamisen Perthist\"{a}, sen ilmestymisen Victorian seuduille ja osallisuuden rautatieonnettomuuteen. H\"{a}n antoi ladylle Seymourissa ostamansa numeron Australian ja Uuden Seelannin Uutisia ja lis\"{a}si, ett\"{a} poliisi oli julistanut palkinnon sille, joka ottaisi kiinni Ben Joycen, pelottavan rosvon, jolle puolentoista vuoden aikana tehdyt rikokset olivat hankkineet surullista kuuluisuutta. Mutta kuinka MacNabbs oli tuntenut per\"{a}mies Ayrtonin Ben Joyceksi? Siin\"{a} oli salaisuus, jonka kaikki pyysiv\"{a}t selitt\"{a}m\"{a}\"{a}n, ja majuri selitti. Jo alusta alkaen oli MacNabbs vaistomaisesti ep\"{a}illyt Ayrtonia. Pari kolme t\"{a}ysin v\"{a}h\"{a}p\"{a}t\"{o}ist\"{a} seikkaa, per\"{a}miehen ja sep\"{a}n v\"{a}lill\"{a} vaihdettu silm\"{a}nisku Wimerra-joella, Ayrtonin vastahakoisuus poiketa kaupunkeihin ja kyliin, h\"{a}nen itsepintainen pyytelyns\"{a}, ett\"{a} \textit{Duncan} komennettaisiin rannikolle, h\"{a}nen hoitoonsa uskottujen el\"{a}inten outo kuolema ja yleens\"{a} suoruuden puute h\"{a}nen k\"{a}yt\"{o}ksess\"{a}\"{a}n, kaikki n\"{a}m\"{a} v\"{a}hitellen kertyneet ilmi\"{o}t olivat her\"{a}tt\"{a}neet majurin ep\"{a}luuloa. H\"{a}n ei kuitenkaan olisi voinut tehd\"{a} suoranaista syyt\"{o}st\"{a} ilman viime\"{o}isi\"{a} tapahtumia. Ruohopensaiden suojassa ry\"{o}mien MacNabbs saapui ep\"{a}ilytt\"{a}vien varjojen luokse, jotka olivat her\"{a}tt\"{a}neet h\"{a}nen huomiotaan vajaan kilometrin p\"{a}\"{a}ss\"{a} leirilt\"{a}. Fosforihohtoiset kasvit loivat himme\"{a}t\"{a} valoa pimeyteen. Kolme miest\"{a} tutki maassa tuoreita j\"{a}lki\"{a}, ja heid\"{a}n joukossaan MacNabbs tunsi Black Pointin sep\"{a}n. --- Ne ne ovat, yksi sanoi. --- Niin ovat, toinen sanoi, --- t\"{a}ss\"{a} on hevosenkeng\"{a}n apila. --- Sama kuin Wimerrasta saakka. --- Kaikki hevoset ovat kuolleet. --- Myrkky\"{a}k\"{a}\"{a}n ei tarvitse hakea kaukaa. --- Sill\"{a} voisi tuhota kokonaisen ratsuv\"{a}en. Hy\"{o}dyllinen kasvi tuo gastrolobium. --- Sitten he vaikenivat, MacNabbs lis\"{a}si, --- ja poistuivat. Min\"{a} en tiennyt viel\"{a} kylliksi. Min\"{a} seurasin heit\"{a}. Pian alkoi keskustelu uudelleen: --- Ovela mies, se Ben Joyce, sepp\"{a} sanoi, --- mainio keksint\"{o} tuo per\"{a}miehen haaksirikko! Jos h\"{a}nen juonensa onnistuu, niin se vasta on onnenpotku! Saakelin Ayrton! --- Sano Ben Joyce, sill\"{a} kyll\"{a} h\"{a}n on nimens\"{a} ansainnut! --- T\"{a}ll\"{o}in roistot poistuivat kumimets\"{a}st\"{a}. Min\"{a} olin saanut kuulla kaiken, mink\"{a} halusinkin, ja palasin leiriin siin\"{a} uskossa, ett\"{a} kaikista rikollisista ei tule kunnon ihmisi\"{a} Australiassa, ellei Paganelilla ole mit\"{a}\"{a}n sit\"{a} vastaan. Majuri vaikeni. H\"{a}nen kumppaninsa miettiv\"{a}t \"{a}\"{a}nett\"{o}min\"{a}. --- Niinp\"{a}, Glenarvan sanoi suuttumuksesta kalpeana, --- Ayrton on tuonut meid\"{a}t t\"{a}nne saakka rosvotakseen ja murhatakseen meid\"{a}t. --- Aivan, majuri vastasi. --- Ja Wimerrasta asti h\"{a}nen joukkonsa seurasi meid\"{a}n j\"{a}lki\"{a}mme ja vakoili meit\"{a} otollista tilaisuutta v\"{a}ijyen? --- Aivan. --- Mutta eik\"{o} se lurjus sitten olekaan \textit{Britannian} matruusi? Onko h\"{a}n siis varastanut Ayrton-nimens\"{a} ja laivapassinsa? Katseet k\"{a}\"{a}ntyiv\"{a}t MacNabbsin puoleen, jonka mieleen n\"{a}iden kysymysten oli t\"{a}ytynyt juolahtaa. --- Kaikki on viel\"{a} h\"{a}m\"{a}r\"{a}n peitossa, h\"{a}n vastasi aina tyynell\"{a} \"{a}\"{a}nell\"{a}\"{a}n, --- mutta k\"{a}sitt\"{a}\"{a}kseni miehen nimi todellakin on Ayrton. Ben Joyce on h\"{a}nen rosvonimens\"{a}. Kiist\"{a}m\"{a}tt\"{a} h\"{a}n tuntee Harry Grantin ja on ollut \textit{Britannian} toisena per\"{a}miehen\"{a}. N\"{a}m\"{a} seikat, jotka Ayrtonin kertomat tarkat yksityiskohdat jo ovat todistaneet, vahvistaa lis\"{a}ksi teille mainitsemani rosvojen keskustelu. \"{A}lk\"{a}\"{a}mme siis eksyk\"{o} turhiin olettamuksiin, vaan pit\"{a}k\"{a}\"{a}mme varmana, ett\"{a} Ben Joyce on Ayrton, kuten Ayrton on Ben Joyce, siis \textit{Britannian} matruusi, josta on tullut rosvojoukon p\"{a}\"{a}llikk\"{o}. MacNabbsin selitys hyv\"{a}ksyttiin keskustelutta. --- Nyt, Glenarvan lausui, --- selitt\"{a}k\"{a}\"{a}, kuinka ja miksi Harry Grantin per\"{a}mies on Australiassa. --- Kuinkako? Sit\"{a} en tied\"{a}, MacNabbs vastasi, --- eik\"{a} poliisi n\"{a}y tiet\"{a}v\"{a}n asiasta sen enemp\"{a}\"{a} kuin min\"{a}k\"{a}\"{a}n. Miksi? Sit\"{a} on minun mahdoton sanoa. Se j\"{a}\"{a} tulevaisuuden selitett\"{a}v\"{a}ksi. --- Poliisi ei tied\"{a} edes, ett\"{a} Ayrton ja Ben Joyce on sama henkil\"{o}, John Mangles huomautti. --- Te olette oikeassa, John, majuri vastasi, --- mutta se tieto olisi omiaan helpottamaan etsiskely\"{a}. --- N\"{a}in ollen, lady Helena sanoi, --- tuo onneton oli tunkeutunut Paddy O'Mooren farmille jossakin rikollisessa tarkoituksessa? --- Niin, ep\"{a}ilem\"{a}tt\"{a}, MacNabbs vastasi. --- H\"{a}n valmisti jotakin juonta irlantilaista vastaan, kun h\"{a}nelle tarjoutui parempi tilaisuus. Sattuma toi meid\"{a}t paikalle. H\"{a}n kuuli Glenarvanin kertomuksen, pullopostin haaksirikosta, ja k\"{a}ytti rohkeana miehen\"{a} sit\"{a} heti hyv\"{a}kseen. P\"{a}\"{a}tettiin l\"{a}hte\"{a} retkelle maitse. Wimerrassa h\"{a}n ilmoitti aikeensa yhdelle miehist\"{a}\"{a}n, Black Pointin sep\"{a}lle, ja toimi niin, ett\"{a} j\"{a}lkemme saattoi helposti tuntea. H\"{a}nen joukkonsa on seurannut meit\"{a}. Myrkkykasvin avulla h\"{a}nen onnistui v\"{a}hitellen tappaa vetojuhtamme ja hevosemme. Sitten, kun katsoi hetken koittaneen, h\"{a}n ajoi vankkurimme Snowyn suohon, jotta h\"{a}nen johtamansa rosvolauma voisi hy\"{o}k\"{a}t\"{a} kimppuumme. Ben Joycen asia oli selvitetty. Majuri oli paljastanut h\"{a}nen menneisyytens\"{a} ja osoittanut h\"{a}nen olevan rohkea ja pelottava pahantekij\"{a}. H\"{a}nen selv\"{a}sti todistetut aikeensa vaativat Glenarvanin puolelta mit\"{a} suurinta valppautta. Onneksi paljastettua rosvoa sai pel\"{a}t\"{a} v\"{a}hemm\"{a}n kuin kavaltajaa. Mutta t\"{a}st\"{a} selv\"{a}st\"{a} tilanteesta koitui raskaat seuraukset. Kukaan ei ollut viel\"{a} ajatellut niit\"{a}. Ainoastaan Mary Grant sivuutti kaiken t\"{a}m\"{a}n keskustelun menneisyydest\"{a} ja ajatteli tulevaisuutta. John Mangles oli ensimm\"{a}inen, joka huomasi h\"{a}nen kalpeutensa ja ep\"{a}toivonsa. H\"{a}n ymm\"{a}rsi, mit\"{a} neidon mieless\"{a} liikkui. --- Neiti Grant! h\"{a}n huudahti. --- Te itkette! --- Mit\"{a} sin\"{a} itket, lapseni? lady Helena kysyi. --- Is\"{a}ni! Voi, hyv\"{a} rouva, is\"{a}ni! neito vastasi. H\"{a}n ei voinut jatkaa. Mutta asia valkeni \"{a}kki\"{a} jokaiselle. Ymm\"{a}rrettiin Maryn suru, mink\"{a} vuoksi h\"{a}nen silm\"{a}ns\"{a} kyyneltyiv\"{a}t, miksi h\"{a}nen is\"{a}ns\"{a} nimi nousi syd\"{a}mest\"{a} huulille. Ayrtonin petoksen paljastuminen tuhosi toiveet. Saadakseen Glenarvanin petetyksi mukaansa oli roisto keksinyt haaksirikkojuttunsa. MacNabbsin kuulemassa keskustelussa olivat rosvot sen selv\"{a}sti sanoneet. \textit{Britannia} ei ollut ikin\"{a} murskautunut Twofold-lahden kallioihin! Harry Grant ei ollut ikin\"{a} noussut maihin Australian mantereelle! Toista kertaa oli asiakirjan erheellinen tulkinta johtanut \textit{Britannian} etsij\"{a}t v\"{a}\"{a}rille j\"{a}ljille! T\"{a}t\"{a} ja molempien lasten surua ajatellen olivat kaikki alakuloisen \"{a}\"{a}nett\"{o}min\"{a}. Kukapa en\"{a}\"{a} olisi voinut l\"{o}yt\"{a}\"{a} lohdutuksen sanaa? Robert itki sisarensa syliss\"{a}. Paganel mutisi kiukkuisella \"{a}\"{a}nell\"{a}: --- Ah, kirottu asiakirja! Voitpa kerskua panneesi n\"{a}in monen kunnon ihmisen p\"{a}\"{a}n pahasti py\"{o}r\"{a}lle! Ja kunnon maantieteilij\"{a} mukiloi raivoissaan otsaansa ja oli v\"{a}h\"{a}ll\"{a} halkaista sen. Glenarvan l\"{a}hti Mulradyn ja Wilsonin luo, jotka olivat vahdissa ulkopuolella. Mets\"{a}nreunan ja joen v\"{a}lisell\"{a} tasangolla vallitsi syv\"{a} hiljaisuus. Suuret liikkumattomat pilvet n\"{a}yttiv\"{a}t murskautuvan toisiinsa taivaalla. T\"{a}ss\"{a} painostavassa ilmassa, syv\"{a}ss\"{a} horroksessa, olisi pieninkin rasahdus kuultu tarkasti, mutta mit\"{a}\"{a}n ei kuulunut. Ben Joycen ja h\"{a}nen joukkonsa oli t\"{a}ytynyt vet\"{a}yty\"{a} jokseenkin kauaksi, sill\"{a} lintuparvet, jotka leikkiv\"{a}t puiden alimmilla oksilla, muutamat kengurut, jotka rauhassa pureksivat nuoria vesoja, eurus-pari, joiden p\"{a}\"{a}t luottavasti pistiv\"{a}t esiin suurten pensaiden lomasta, todistivat, ett\"{a} ihmisen l\"{a}sn\"{a}olo ei h\"{a}irinnyt er\"{a}maan rauhaa. --- Yhteen tuntiin ette siis ole n\"{a}hneet tai kuulleet mit\"{a}\"{a}n? Glenarvan kysyi matruuseiltaan. --- Emme, mylord, Wilson vastasi. --- Rosvojen t\"{a}ytyy olla t\"{a}\"{a}lt\"{a} monen kilometrin p\"{a}\"{a}ss\"{a}. --- Heit\"{a} ei n\"{a}ht\"{a}v\"{a}sti ole ollut kyllin monta voidakseen hy\"{o}k\"{a}t\"{a} meid\"{a}n kimppuumme, Mulrady lis\"{a}si. --- Tuo Ben Joyce on kai halunnut pestata muutamia kaltaisiaan roistoja alppien juurella harhailevien lurjuksien joukosta. --- Se on luultavaa, Mulrady, Glenarvan vastasi. --- Ne roistot ovat pelkureita. He tiet\"{a}v\"{a}t meid\"{a}n olevan aseistettuja, hyvin aseistettuja sittenkin. Ehk\"{a}p\"{a} he odottavat y\"{o}t\"{a} aloittaakseen hy\"{o}kk\"{a}yksens\"{a}. P\"{a}iv\"{a}n laskettua t\"{a}ytyy olla kahta vertaa valppaampia. Kun vain voisimme p\"{a}\"{a}st\"{a} t\"{a}lt\"{a} soiselta tasangolta ja jatkaa matkaamme rannikkoa kohti! Mutta tulviva virta katkaisee tien. Jos voisin saada lautan, joka veisi meid\"{a}t toiselle rannalle, maksaisin siit\"{a} sen painon kultaa! --- Miksei mylord k\"{a}ske meit\"{a} rakentamaan lauttaa? Wilson kysyi. --- Puistahan ei ole puutetta. --- Ei, Wilson, Glenarvan vastasi, --- Snowy ei ole tavallinen joki, se on ylip\"{a}\"{a}sem\"{a}t\"{o}n koski. T\"{a}ll\"{a} hetkell\"{a} John Mangles, majuri ja Paganel saapuivat Glenarvanin luo. He olivat juuri olleet tarkastamassa Snowya. Viime sateiden paisuttama vesi oli viel\"{a} paljon korkeammalla kuin tavallisesti. N\"{a}in oli syntynyt Amerikan koskia muistuttava kuohuva tulva. Oli mahdotonta antautua sen kohiseville laineille ja valtavaan vy\"{o}ryyn, jossa tuhannet py\"{o}rteet aukoivat kuiluun. John Mangles selitti ylityksen olevan mahdotonta. --- Mutta, h\"{a}n lis\"{a}si, --- ei t\"{a}nnek\"{a}\"{a}n auta j\"{a}\"{a}d\"{a} mit\"{a}\"{a}n yritt\"{a}m\"{a}tt\"{a}. Se, mit\"{a} aiottiin tehd\"{a} ennen Ayrtonin kavallusta, on viel\"{a} t\"{a}rke\"{a}mp\"{a}\"{a} nyt j\"{a}lkeenp\"{a}in. --- Mit\"{a} ehdotat, John? Glenarvan kysyi. --- Min\"{a} ehdotan, ett\"{a} apua on saatava, ja koska ei p\"{a}\"{a}st\"{a} Twofold-lahdelle, t\"{a}ytyy menn\"{a} Melbourneen. Meill\"{a} on viel\"{a} yksi hevonen. Antakaa se minulle, mylord, ja min\"{a} l\"{a}hden Melbourneen. --- Mutta se on vaarallinen yritys, John, Glenarvan sanoi. --- Puhumattakaan yli kolmensadan kilometrin matkasta tuntemattoman maan halki ovat polut ja tie ep\"{a}ilem\"{a}tt\"{a} Ben Joycen kumppaneiden vartioimia. --- Tied\"{a}n sen, mylord, mutta tied\"{a}n my\"{o}s, ett\"{a} t\"{a}m\"{a} tilanne ei voi jatkua. Ayrton vaati vain kahdeksan p\"{a}iv\"{a}\"{a} tuodakseen t\"{a}nne \textit{Duncanin} miehet. Min\"{a} aion olla Snowyn rannalla j\"{a}lleen kuudessa p\"{a}iv\"{a}ss\"{a}! No niin, mit\"{a} k\"{a}skette, mylord? --- Ennen kuin Glenarvan lausuu sanansa, Paganel puuttui puheeseen, --- on minun teht\"{a}v\"{a} er\"{a}s huomautus. Melbourneen on kyll\"{a} l\"{a}hdett\"{a}v\"{a}, mutta siihen vaaraan ei John Mangles saa antautua. H\"{a}n on \textit{Duncanin} kapteeni eik\"{a} sen vuoksi saa uhrautua. Min\"{a} l\"{a}hden h\"{a}nen sijastaan. --- Hyvin puhuttu, majuri huomautti. --- Mutta miksi juuri te, Paganel? --- Eik\"{o} siis meit\"{a} lasketakaan mukaan? huudahtivat Mulrady ja Wilson. --- Ja luuletteko te, MacNabbs jatkoi, --- ett\"{a} min\"{a} pelk\"{a}\"{a}n kolmensadan kilometrin matkaa hevosen sel\"{a}ss\"{a}? --- Yst\"{a}v\"{a}ni, Glenarvan sanoi, --- arpa ratkaiskoon, kenen meist\"{a} on l\"{a}hdett\"{a}v\"{a} Melbourneen. Paganel, kirjoittakaa meid\"{a}n nimemme... --- Ei ainakaan teid\"{a}n, mylord, John Mangles sanoi. --- Ja miksei? Glenarvan kysyi. --- Kuinka voisitte erota lady Helenasta, eik\"{a} haavannekaan viel\"{a} ole ummessa! --- Glenarvan, Paganel sanoi, --- te ette voi j\"{a}tt\"{a}\"{a} retkikuntaa. --- Ei, majuri vahvisti. --- Teid\"{a}n paikkanne on t\"{a}\"{a}ll\"{a}, Edward, teid\"{a}n ei sovi l\"{a}hte\"{a}. --- Retki on vaarallinen, Glenarvan vastasi, --- enk\"{a} min\"{a} luovuta osuuttani muille. Kirjoittakaa, Paganel, minun nimeni toverieni nimien joukkoon, ja suokoon taivas, ett\"{a} se avataan ensimm\"{a}isen\"{a}. T\"{a}h\"{a}n tahtoon oli taipuminen. Glenarvanin nimi kirjoitettiin muiden joukkoon. Ryhdyttiin vet\"{a}m\"{a}\"{a}n, ja arpa osui Mulradyyn. Uljas matruusi hurrasi mielihyv\"{a}st\"{a}. --- Mylord, min\"{a} olen valmis l\"{a}htem\"{a}\"{a}n, h\"{a}n sanoi. Glenarvan puristi Mulradyn k\"{a}tt\"{a}. Sitten h\"{a}n palasi vankkurien luo j\"{a}tt\"{a}en majurille ja John Manglesille leirin vartioinnin. Lady Helenalle ilmoitettiin heti, ett\"{a} oli p\"{a}\"{a}tetty l\"{a}hett\"{a}\"{a} sananviej\"{a} Melbourneen ja kenet arpa siihen oli m\"{a}\"{a}r\"{a}nnyt. H\"{a}n lausui Mulradylle sanoja, jotka sy\"{o}pyiv\"{a}t uljaan matruusin syd\"{a}meen. Tiedettiin, ett\"{a} h\"{a}n oli urhea, \"{a}lyk\"{a}s, voimakas, uupumaton, eik\"{a} arpa olisikaan voinut tehd\"{a} parempaa valintaa. Mulradyn l\"{a}ht\"{o} m\"{a}\"{a}r\"{a}ttiin kello kahdeksaksi, illan lyhyen h\"{a}m\"{a}r\"{a}n j\"{a}lkeen. Wilson otti varustaakseen hevosen. H\"{a}n p\"{a}\"{a}tti vaihtaa sen keng\"{a}n, joka sill\"{a} oli vasemmassa takajalassa, ja panna sijalle yhden y\"{o}ll\"{a} kuolleiden hevosten kengist\"{a}. Rosvot eiv\"{a}t silloin voisi tunnistaa Mulradyn j\"{a}lki\"{a} ja seurata h\"{a}nt\"{a}, sill\"{a} heill\"{a} ei ollut hevosia. Wilsonin ollessa n\"{a}iss\"{a} puuhissa, Glenarvan valmisti Tom Austinille l\"{a}hetett\"{a}v\"{a}\"{a} kirjett\"{a}; mutta h\"{a}nen haavoitettu olkansa h\"{a}iritsi h\"{a}nt\"{a}, ja h\"{a}n pyysi Paganelia kirjoittamaan puolestaan. Tiedemies oli vaipunut miettim\"{a}\"{a}n jotakin eik\"{a} n\"{a}ytt\"{a}nyt huomaavan, mit\"{a} h\"{a}nen ymp\"{a}rill\"{a}\"{a}n tapahtui. T\"{a}ytyy tunnustaa, ett\"{a} Paganel keskell\"{a} t\"{a}t\"{a} per\"{a}kk\"{a}isten onnettomuuksien sarjaa mietti vain v\"{a}\"{a}rintulkittua asiakirjaa. H\"{a}n k\"{a}\"{a}nteli sanoja l\"{o}yt\"{a}\"{a}kseen niist\"{a} uuden ajatuksen ja oli syventynyt tulkinnan onkaloihin. Niinp\"{a} h\"{a}n ei kuullut Glenarvanin pyynt\"{o}\"{a}, vaan se t\"{a}ytyi uudistaa. --- Jaha, hyv\"{a} on, Paganel vastasi, --- min\"{a} olen valmis. Ja viel\"{a} puhuessaan Paganel otti konemaisesti muistikirjansa esiin. Rep\"{a}isi siit\"{a} puhtaan lehden ja asettui kyn\"{a} k\"{a}dess\"{a} kirjoittamaan. Glenarvan alkoi sanella seuraavia ohjeita: --- K\"{a}sky Tom Austinille l\"{a}hte\"{a} merelle viipym\"{a}tt\"{a} ja tuoda \textit{Duncan}... Paganel kirjoitti viime mainitun sanan, kun h\"{a}nen katseensa sattumalta osui Australian ja Uuden Seelannin Uutiset lehden numeroon, joka oli pudonnut maahan. Lehti oli niin taitettu, ett\"{a} sen nimest\"{a} n\"{a}kyi vain kaksi viimeist\"{a} tavua. Paganelin kyn\"{a} pys\"{a}htyi, ja h\"{a}n n\"{a}ytti kokonaan unohtaneen Glenarvanin, kirjeen ja sanelun. --- No, Paganel? Glenarvan kysyi. --- Ah! maantieteilij\"{a} huudahti. --- Mik\"{a} teid\"{a}n on? majuri kysyi. --- Ei mik\"{a}\"{a}n, ei mik\"{a}\"{a}n! Paganel vastasi. Sitten h\"{a}n mutisi matalammalla \"{a}\"{a}nell\"{a}: --- \textit{Aland, aland, aland!} H\"{a}n oli noussut pystyyn ja siepannut sanomalehden. H\"{a}n puristi sit\"{a} koettaen pid\"{a}tt\"{a}\"{a} sanoja, jotka pyrkiv\"{a}t h\"{a}nen huulilleen. Lady Helena, Mary, Robert ja Glenarvan katselivat h\"{a}nt\"{a} ymm\"{a}rt\"{a}m\"{a}tt\"{a} mit\"{a}\"{a}n t\"{a}st\"{a} selitt\"{a}m\"{a}tt\"{o}m\"{a}st\"{a} kohtauksesta. Paganel n\"{a}ytti \"{a}kki\"{a} tulleen hulluksi. Mutta t\"{a}t\"{a} kiihtymyst\"{a} ei kest\"{a}nyt kauan. H\"{a}n tyyntyi v\"{a}hitellen; ilo, joka loisti h\"{a}nen katseestaan, sammui; h\"{a}n istui paikalleen ja sanoi tyynell\"{a} \"{a}\"{a}nell\"{a}: --- Olen k\"{a}ytett\"{a}viss\"{a}nne, mylord, milloin tahdotte. Glenarvan ryhtyi jatkamaan kirjeen sanelua, joka tuli lopullisesti t\"{a}h\"{a}n muotoon: --- K\"{a}sky Tom Austinille l\"{a}hte\"{a} merelle viipym\"{a}tt\"{a} ja tuoda \textit{Duncan} 37. leveysasteelle Australian it\"{a}rannikolle... --- Australianko? Paganel kysyi. --- Niinp\"{a} niin, Australian! Sitten h\"{a}n lopetti kirjeen ja ojensi sen Glenarvanin allekirjoitettavaksi. T\"{a}m\"{a}, jota veres haava h\"{a}iritsi, suoritti t\"{a}m\"{a}n muodollisuuden niin hyvin kuin taisi. Kirje suljettiin ja sinet\"{o}itiin. Paganel, jonka k\"{a}si viel\"{a} vapisi liikutuksesta, kirjoitti seuraavan osoitteen: Tom Austin, \textit{Duncanin} per\"{a}mies, Melbourne. Sitten h\"{a}n l\"{a}hti vankkureista levitellen k\"{a}si\"{a}\"{a}n ja toistellen n\"{a}it\"{a} k\"{a}sitt\"{a}m\"{a}tt\"{o}mi\"{a} sanoja: --- Aland! Aland! Zealand!\_ \gutchapter{NELJ\"{A}N P\"{A}IV\"{A}N TUSKA.} Loppup\"{a}iv\"{a} kului mit\"{a}\"{a}n erikoista tapahtumatta. Mulradyn l\"{a}ht\"{o}valmistelut suoritettiin loppuun. Uljas matruusi oli onnellinen voidessaan t\"{a}ll\"{a} tavoin osoittaa uskollisuuttaan lordi Glenarvanille. Paganel oli j\"{a}lleen tyyntynyt ja muuttunut entisekseen. H\"{a}nen katseensa osoitti tosin viel\"{a}, ett\"{a} jokin asia askarrutti h\"{a}nt\"{a} ankarasti, mutta h\"{a}n n\"{a}ytti p\"{a}\"{a}tt\"{a}neen pit\"{a}\"{a} sen salassa. H\"{a}nell\"{a} oli ep\"{a}ilem\"{a}tt\"{a} p\"{a}tev\"{a}t syyt menettelyyns\"{a}, sill\"{a} majuri kuuli h\"{a}nen toistelevan n\"{a}it\"{a} sanoja, kuin itsens\"{a} kanssa kamppaillen: --- Ei, ei! He eiv\"{a}t uskoisi minua! Ja mit\"{a} se muuten hy\"{o}dytt\"{a}isi? On liian my\"{o}h\"{a}ist\"{a}! Tehty\"{a}\"{a}n t\"{a}m\"{a}n p\"{a}\"{a}t\"{o}ksen h\"{a}n ryhtyi antamaan Mulradylle tarpeellisia ohjeita Melbournen matkaa varten ja piirsi h\"{a}nelle matkareitin aivan kuin h\"{a}nell\"{a} olisi ollut kartta silmiens\"{a} edess\"{a}. Kaikki ruokoaavikon polut yhtyiv\"{a}t Lucknowin tiehen. Kuljettuaan suoraan etel\"{a}\"{a}n rannikolle saakka t\"{a}m\"{a} tie teki jyrk\"{a}n k\"{a}\"{a}nteen Melbournea kohti. Piti yh\"{a} vain ratsastaa sit\"{a} pitkin eik\"{a} yritt\"{a}\"{a} oikaista tuntemattomien seutujen halki. Mik\"{a}\"{a}n ei siis ollut yksinkertaisempaa. Mulrady ei voinut eksy\"{a}. Mit\"{a} vaaroihin tuli, niit\"{a} ei ollut en\"{a}\"{a} muutamien kilometrien p\"{a}\"{a}ss\"{a} leirilt\"{a}, jonka l\"{a}hettyvill\"{a} Ben Joycen joukkoineen t\"{a}ytyi piileskell\"{a}. P\"{a}\"{a}sty\"{a}\"{a}n heid\"{a}n ohitseen Mulrady lupasi ripe\"{a}sti j\"{a}tt\"{a}\"{a} rosvot j\"{a}lkeens\"{a} ja suorittaa t\"{a}rke\"{a}n teht\"{a}v\"{a}ns\"{a} hyv\"{a}\"{a}n loppuun. Kello kuusi sy\"{o}tiin yhteinen ateria. Oli rankkasade. Teltta ei antanut riitt\"{a}v\"{a}\"{a} suojaa, ja kaikki olivat kiivenneet vankkureihin. Se oli muuten turvallinen paikka. Savi piti sit\"{a} lujasti kiinni maassa, johon se oli juuttunut kuin linna perustalleen. Asevarastoa oli seitsem\"{a}n pyssy\"{a} ja seitsem\"{a}n revolveria, ja linna saattoi kest\"{a}\"{a} pitk\"{a}n piirityksen, sill\"{a} ampumavaroja tai elintarvikkeita ei puuttunut. Kuuden p\"{a}iv\"{a}n kuluttua ankkuroisi \textit{Duncan} Twofold-lahteen. Kaksikymment\"{a}nelj\"{a} tuntia my\"{o}hemmin saapuisi sen miehist\"{o} Snowyn toiselle rannalle, ja ellei joen yli viel\"{a} p\"{a}\"{a}sisi, rosvojen ainakin olisi pakko per\"{a}yty\"{a} suurempien voimien tielt\"{a}. Mutta ennen kaikkea Mulradyn t\"{a}ytyi onnistua vaarallisessa yrityksess\"{a}\"{a}n. Kello kahdeksan oli tullut hyvin pime\"{a}. Oli l\"{a}hd\"{o}n hetki. Hevonen tuotiin esiin. Sen jalkoihin oli varovaisuuden vuoksi k\"{a}\"{a}ritty liinakangasta, ettei askeleita kuuluisi. Hevonen n\"{a}ytti v\"{a}syneelt\"{a}, ja kuitenkin kaikkien menestys riippui sen jalkojen varmuudesta ja voimasta. Majuri neuvoi Mulradya s\"{a}\"{a}st\"{a}m\"{a}\"{a}n sit\"{a} heti kun h\"{a}n oli rosvojen ulottumattomissa. Parempi oli kulkea hiukan hitaammin, mutta p\"{a}\"{a}st\"{a} varmasti perille. John Mangles antoi matruusilleen revolverin, jonka oli eritt\"{a}in huolellisesti ladannut. Se oli pelottava ase miehen k\"{a}dess\"{a}, joka ei vapise, sill\"{a} kuusi muutamassa sekunnissa ammuttua laukausta aukaisi helposti pahantekij\"{o}iden tukkiman tien. Mulrady nousi satulaan. --- T\"{a}ss\"{a} on kirje, jonka annat Tom Austinille, Glenarvan sanoi h\"{a}nelle. --- H\"{a}n ei saa hukata tuntiakaan. L\"{a}htek\"{o}\"{o}n Twofold-lahteen, ja ellei h\"{a}n tapaa meit\"{a} siell\"{a}, jos n\"{a}et emme ole p\"{a}\"{a}sseet Snowyn yli, tulkoon viipym\"{a}tt\"{a} meid\"{a}n luoksemme. L\"{a}hde nyt, kunnon poikani, ja Jumala sinua suojelkoon! Glenarvan, lady Helena, Mary Grant, kaikki puristivat Mulradyn k\"{a}tt\"{a}. T\"{a}m\"{a} l\"{a}ht\"{o} pime\"{a}ss\"{a} ja sateisessa y\"{o}ss\"{a} vaaralliselle retkelle er\"{a}maan tuntemattomien \"{a}\"{a}rett\"{o}myyksien halki olisi vaikuttanut v\"{a}hemm\"{a}n karaistuun mieleen kuin Mulradyn. --- Hyv\"{a}sti, mylord, h\"{a}n sanoi tyynell\"{a} \"{a}\"{a}nell\"{a} ja katosi pian mets\"{a}nreunaa kulkevaa polkua pitkin. T\"{a}ll\"{a} hetkell\"{a} k\"{a}vi rajuilma kahta ankarammaksi. Kumipuiden korkeat oksat kalisivat pime\"{a}ss\"{a} kolealla \"{a}\"{a}nell\"{a}. Saattoi kuulla kuivien oksien putoilevan m\"{a}rk\"{a}\"{a}n maahan. Moni j\"{a}ttil\"{a}ispuu, joka oli elinvoimaton, mutta oli t\"{a}h\"{a}n saakka pysynyt pystyss\"{a}, kaatui n\"{a}iss\"{a} myrskyvihureissa. Tuuli vonkui puiden natinaa \"{a}\"{a}nekk\"{a}\"{a}mmin ja sekoitti kauheat huokauksensa Snowyn kohinaan. Suuret pilvet, joita se ajoi it\"{a}\"{a}np\"{a}in, painuivat maahan saakka kuin usvariekaleet. Synkk\"{a} pimeys lis\"{a}si viel\"{a} y\"{o}n kamaluutta. Mulradyn l\"{a}hdetty\"{a} retkel\"{a}iset k\"{o}mpiv\"{a}t vankkureihin. Lady Helena ja Mary Grant, Glenarvan ja Paganel olivat etummaisessa osastossa, joka oli tiiviisti suljettu. Toisessa olivat Olbinett, Wilson ja Robert saaneet riitt\"{a}v\"{a}n suojapaikan. Majuri ja John Mangles pitiv\"{a}t vartiota ulkona. Se oli v\"{a}ltt\"{a}m\"{a}t\"{o}n varotoimi, sill\"{a} rosvojen hy\"{o}kk\"{a}ys oli helppo ja siis mahdollinen. Molemmat uskolliset vartijat suorittivat siis vartiopalvelustaan ja kestiv\"{a}t filosofisen tyynesti ne viimat, joilla y\"{o} pieksi heid\"{a}n kasvojansa. He koettivat n\"{a}hd\"{a} salahy\"{o}kk\"{a}yksille otollisen pimeyden l\"{a}pi, sill\"{a} korva ei voinut erottaa mit\"{a}\"{a}n myrskyn pauhinan, tuulen vinkunan, oksien r\"{a}tin\"{a}n, puiden runkojen kaatumisen ja ry\"{o}ppy\"{a}v\"{a}n veden kohinan vuoksi. Silloin t\"{a}ll\"{o}in sattui kuitenkin tyynempi\"{a} hetki\"{a}. Tuuli vaikeni kuin henke\"{a} vet\"{a}\"{a}kseen. Snowy yksin kohisi liikkumattomien kaislojen ja synk\"{a}n kumipuumets\"{a}n v\"{a}liss\"{a}. Hiljaisuus tuntui n\"{a}in\"{a} tyynin\"{a} hetkin\"{a} syvemm\"{a}lt\"{a}. Majuri ja John Mangles kuuntelivat silloin tarkkaavasti. Er\"{a}\"{a}n t\"{a}llaisen keskeytyksen aikana kuului kime\"{a} vihellys. John Mangles riensi majurin luo. --- Kuulitteko? h\"{a}n kysyi t\"{a}lt\"{a}. --- Kuulin, MacNabbs sanoi. --- Oliko se ihminen vai el\"{a}in? --- Ihminen, John Mangles vastasi. Sitten molemmat kuuntelivat. \"{A}kki\"{a} kuului selitt\"{a}m\"{a}t\"{o}n vihellys uudelleen, ja siihen oli vastauksena jotakin laukauksen tapaista, mutta kovin ep\"{a}selv\"{a}sti, sill\"{a} myrsky pauhasi silloin uudella raivolla. MacNabbs ja John Mangles eiv\"{a}t kuulleet toistensa puhetta. He meniv\"{a}t vankkurien taakse tuulensuojaan. T\"{a}ll\"{a} hetkell\"{a} avautui vankkurien nahkakuomu, ja Glenarvan tuli molempien kumppaniensa luokse. H\"{a}n oli kuullut samoin kuin hekin tuon kauhean vihellyksen ja pamahduksen, jonka kaiku oli tuntunut vaunujen kuomussa. --- Mill\"{a} suunnalla? h\"{a}n kysyi. --- Tuolla, John sanoi osoittaen pime\"{a}\"{a} polkua siell\"{a} p\"{a}in, minne Mulrady oli mennyt. --- Kuinka kaukana? --- Tuuli kantoi, John Mangles vastasi. --- Sen t\"{a}ytyi tulla ainakin kilometrin p\"{a}\"{a}st\"{a}. --- L\"{a}htek\"{a}\"{a}mme, Glenarvan sanoi heitt\"{a}en pyssyn olalleen. --- Ei l\"{a}hdet\"{a}, majuri vastasi. --- Se on ansa, jolla meit\"{a} houkutellaan pois vankkurien luota. --- Ent\"{a} jos Mulrady on kaatunut roistojen luodeista, Glenarvan sanoi tarttuen MacNabbsin k\"{a}teen. --- Sen saamme tiet\"{a}\"{a} huomenna, majuri vastasi kylm\"{a}sti p\"{a}\"{a}tetty\"{a}\"{a}n est\"{a}\"{a} Glenarvania tekem\"{a}st\"{a} hy\"{o}dyt\"{o}nt\"{a} virhett\"{a}. --- Te ette saa l\"{a}hte\"{a} leirist\"{a}, mylord, John sanoi, --- min\"{a} menen yksin. --- Ettek\"{a} mene, MacNabbs sanoi tarmokkaasti. --- Tahdotteko siis, ett\"{a} meid\"{a}t tapetaan yksitellen, heikennet\"{a}\"{a}n voimiamme, kunnes olemme noiden roistojen armoilla? Jos Mulrady on joutunut heid\"{a}n uhrikseen, sellaista onnettomuutta emme saa lis\"{a}t\"{a} toisella. Mulrady on l\"{a}htenyt arvan m\"{a}\"{a}r\"{a}\"{a}m\"{a}n\"{a}. Jos arpa olisi osunut minuun h\"{a}nen sijastaan, niin olisin l\"{a}htenyt kuten h\"{a}nkin, mutta en olisi pyyt\"{a}nyt enk\"{a} odottanut mit\"{a}\"{a}n apua. Estetty\"{a}\"{a}n Glenarvania ja John Manglesia majuri oli kaikin puolin oikeassa. Olisi ollut mielet\"{o}nt\"{a} ja lis\"{a}ksi hy\"{o}dyt\"{o}nt\"{a} kiirehti\"{a} matruusin luo, juosta t\"{a}ss\"{a} pime\"{a}ss\"{a} y\"{o}ss\"{a} piileksivien rosvojen eteen. Glenarvanin pieness\"{a} joukossa ei ollut niin monta miest\"{a}, ett\"{a} niit\"{a} olisi voitu viel\"{a} uhrata. Glenarvan ei kuitenkaan n\"{a}ytt\"{a}nyt haluavan hyv\"{a}ksy\"{a} n\"{a}it\"{a} syit\"{a}. H\"{a}n puristi asettaan. H\"{a}n asteli edestakaisin vankkurien ymp\"{a}ri kuunnellen parhaansa mukaan. H\"{a}n koetti l\"{a}p\"{a}ist\"{a} katseellaan t\"{a}m\"{a}n kauhean pimeyden. H\"{a}nt\"{a} kidutti ajatus, ett\"{a} yhteen h\"{a}nen mieheens\"{a} oli sattunut tappava luoti, ett\"{a} mies oli avuton ja huusi turhaan niit\"{a}, joiden vuoksi h\"{a}n oli uhrautunut. MacNabbs ei tiennyt onnistuisiko h\"{a}nen est\"{a}\"{a} Glenarvania vai aikoiko t\"{a}m\"{a} hyv\"{a}n syd\"{a}mens\"{a} kannustamana heitt\"{a}yty\"{a} Ben Joycen luotien eteen. --- Edward, h\"{a}n sanoi, --- rauhoittukaa. Kuulkaa yst\"{a}v\"{a}n puhetta. Ajatelkaa lady Helenaa, Mary Grantia, kaikkia, jotka j\"{a}\"{a}v\"{a}t t\"{a}nne! Ja minne te sitten aiotte menn\"{a}? Mist\"{a} l\"{o}yt\"{a}isitte Mulradyn? H\"{a}nen kimppuunsa on hy\"{o}k\"{a}tty ehk\"{a} kilometrin p\"{a}\"{a}ss\"{a} t\"{a}\"{a}lt\"{a}. Miss\"{a}p\"{a}in? Mit\"{a} polkua menette? T\"{a}ll\"{a} hetkell\"{a} ja kuin vastaukseksi majurin puheeseen kuului ep\"{a}toivoinen huuto. --- Kuunnelkaa! Glenarvan sanoi. Huuto kuului samalta suunnalta, miss\"{a} laukaus oli pamahtanut, alle puolen kilometrin p\"{a}\"{a}st\"{a}. Glenarvan ty\"{o}nsi MacNabbsin luotaan ja oli jo menossa pitkin polkua, kun noin kolmensadan askelen p\"{a}\"{a}ss\"{a} vankkureista kuului uusi huuto: --- Apuun, apuun! Se oli valittava ja ep\"{a}toivoinen \"{a}\"{a}ni. John Mangles ja majuri riensiv\"{a}t sit\"{a} kohti. Muutaman hetken kuluttua he huomasivat pensaikon laidassa ihmisolennon, joka ry\"{o}mi eteenp\"{a}in ja huokaili valittavasti. Se oli haavoittunut Mulrady, kuoleman kieliss\"{a}, ja kun h\"{a}nen kumppaninsa nostivat h\"{a}net maasta, he tunsivat k\"{a}tens\"{a} kastuvan verest\"{a}. Satoi kahta kauheammin, ja tuuli ulvoi kuivien puiden oksissa. Keskell\"{a} rajuilman puuskia Glenarvan, majuri ja John Mangles kantoivat Mulradya. Heid\"{a}n saapuessaan nousivat kaikki. Paganel, Robert, Wilson, Olbinett l\"{a}htiv\"{a}t vankkureista, ja lady Helena luovutti huoneensa Mulrady-paralle. Majuri riisui matruusin takin, joka tihkui verta ja vett\"{a}. H\"{a}n paljasti haavan. Onneton oli saanut oikeaan kylkeens\"{a} tikariniskun. MacNabbs sitoi h\"{a}net huolellisesti. H\"{a}n ei osannut sanoa, oliko ase vioittanut t\"{a}rkeit\"{a} elimi\"{a}. Haavasta pulppusi helakanpunainen ja ep\"{a}tasainen verivirta; haavoittuneen kalpeus ja voimattomuus todisti, ett\"{a} h\"{a}neen oli pahasti sattunut. Majuri pani haavan p\"{a}\"{a}lle, jonka h\"{a}n ensin pesi raikkaalla vedell\"{a}, suuren taulapalasen, sitten pehme\"{a}t\"{a} liinan\"{o}yht\"{a}\"{a} ja kiinnitti ne siteell\"{a}. H\"{a}n sai verenvuodon tyrehtym\"{a}\"{a}n. Mulrady pantiin lep\"{a}\"{a}m\"{a}\"{a}n haavakylki yl\"{o}sp\"{a}in, p\"{a}\"{a} ja rinta korkealla, ja lady Helena sai h\"{a}net juomaan muutamia kulauksia vett\"{a}. Nelj\"{a}nnestunnin kuluttua siihen saakka alallaan maannut haavoittunut liikahti. H\"{a}n raotti silmi\"{a}\"{a}n. H\"{a}nen huulensa mutisivat hajanaisia sanoja, ja pannessaan korvansa l\"{a}helle h\"{a}nen suutaan majuri kuuli h\"{a}nen toistavan: --- Mylord ... kirje ... Ben Joyce... Majuri toisti n\"{a}m\"{a} sanat ja katsoi kumppaneihinsa. Mit\"{a} Mulrady halusi sanoa? Ben Joyce oli hy\"{o}k\"{a}nnyt matruusin kimppuun, mutta mink\"{a} vuoksi? Pelk\"{a}st\"{a}\"{a}n pys\"{a}hdytt\"{a}\"{a}kseen h\"{a}net, est\"{a}\"{a}kseen h\"{a}nt\"{a} saapumasta \textit{Duncanille?} Tuo kirje... Glenarvan tutki Mulradyn taskut. Tom Austinille osoitettua kirjett\"{a} ei en\"{a}\"{a} ollut niiss\"{a}! Y\"{o} kului tuskallisessa levottomuudessa. Pel\"{a}ttiin joka hetki, ett\"{a} haavoittunut kuolisi. H\"{a}n oli ankarassa kuumeessa. Lady Helena ja Mary Grant pysyiv\"{a}t h\"{a}nen luonaan uskollisina hoitajina. Milloinkaan potilasta ei ole hoidettu huolellisemmin eik\"{a} s\"{a}\"{a}liv\"{a}isemmin k\"{a}sin. P\"{a}iv\"{a} koitti. Sade oli lakannut. Suuria pilvi\"{a} vy\"{o}ryi viel\"{a} taivaan syvyyksiss\"{a}. Maa oli t\"{a}ynn\"{a} katkenneita oksia. Vesiry\"{o}ppyjen liottama savi oli vajottanut viel\"{a} lis\"{a}\"{a}. Vankkureihin p\"{a}\"{a}sy k\"{a}vi hankalaksi, mutta ne eiv\"{a}t voineet upota en\"{a}\"{a} syvemm\"{a}lle. John Mangles, Paganel ja Glenarvan l\"{a}htiv\"{a}t p\"{a}iv\"{a}nkoitteessa tiedusteluretkelle leirin ymp\"{a}rist\"{o}\"{o}n. He astelivat pitkin polkua, jossa viel\"{a} n\"{a}kyi veripilkkuja. Ben Joycesta ja h\"{a}nen joukostaan ei n\"{a}kynyt j\"{a}lke\"{a}k\"{a}\"{a}n. He eteniv\"{a}t sinne asti, miss\"{a} hy\"{o}kk\"{a}ys oli tapahtunut. Siell\"{a} lojui maassa kaksi Mulradyn luotien kaatamaa miest\"{a}. Toinen oli Black Pointin sepp\"{a}. H\"{a}nen kuoleman kouristamat kasvonsa olivat kauhistuttavat. Glenarvan ei jatkanut tiedusteluaan kauemmaksi. Varovaisuus kielsi menem\"{a}st\"{a} kovin pitk\"{a}lle. H\"{a}n palasi siis vankkurien luo syv\"{a}sti huolissaan vaikeasta tilanteesta. --- Toisen sanansaattajan l\"{a}hett\"{a}mist\"{a} Melbourneen ei voi ajatella, h\"{a}n sanoi. --- T\"{a}ytyy kuitenkin uskaltaa, mylord, John Mangles vastasi, --- ja min\"{a} yrit\"{a}n p\"{a}\"{a}st\"{a} l\"{a}pi, vaikka se ei matruusilleni onnistunut. --- Ei, John. Sinulla ei ole edes hevosta, joka kantaisi sinua kolmesataa kilometri\"{a}. Mulradyn hevonen, ainoa j\"{a}ljell\"{a} ollut, ei tosiaankaan ollut palannut. Oliko se kaatunut murhaajien luodeista? Harhailiko se eksyneen\"{a} er\"{a}maassa? Olivatko rosvot saaneet sen k\"{a}siins\"{a}? --- Mit\"{a} tapahtuneekin, Glenarvan sanoi, --- me emme en\"{a}\"{a} eroa. Odotetaan viikko tai kaksi, kunnes Snowyn vesi laskee tavalliselle tasolleen. Me p\"{a}\"{a}semme lyhyin p\"{a}iv\"{a}matkoin silloin Twofold-lahdelle ja l\"{a}het\"{a}mme varmempaa tiet\"{a} \textit{Duncanille} k\"{a}skyn saapua rannikolle. --- Se on ainoa keino, Paganel lausui. --- Niinp\"{a}, yst\"{a}v\"{a}ni, Glenarvan toisti, --- nyt ei en\"{a}\"{a} erota. Kukaan ei voi l\"{a}hte\"{a} yksin rosvojen valtaamaan er\"{a}maahan. Jumala pelastakoon vain matruusiparkamme ja suojelkoon meit\"{a} itse\"{a}mme! Glenarvan oli oikeassa molemmissa asioissa; ensinn\"{a}kin kielt\"{a}m\"{a}ll\"{a} kaikki uhkayritykset ja toiseksi p\"{a}\"{a}tt\"{a}m\"{a}ll\"{a} odottaa k\"{a}rsiv\"{a}llisesti Snowyn rannalla ylitysmahdollisuutta. H\"{a}n oli vain noin viidenkymmenen kilometrin p\"{a}\"{a}ss\"{a} Delegetesta, Uuden Etel\"{a}-Walesin ensimm\"{a}isest\"{a} rajakaupungista, josta oli saatavissa kulkuneuvoja Twofold-lahdelle. Sielt\"{a} h\"{a}n s\"{a}hk\"{o}tt\"{a}isi Melbourneen \textit{Duncania} koskevat ohjeet. N\"{a}m\"{a} toimenpiteet olivat viisaita, mutta niihin ryhdyttiin my\"{o}h\"{a}\"{a}n. Ellei Glenarvan olisi l\"{a}hett\"{a}nyt Mulradya retkelle, mit\"{a} onnettomuuksia olisikaan v\"{a}ltetty, puhumattakaan matruusin murhasta! Leirille palatessaan h\"{a}n tapasi toverinsa paremmalla tuulella. He n\"{a}yttiv\"{a}t j\"{a}lleen optimistisilta. --- H\"{a}n voi paremmin! H\"{a}n voi paremmin! Robert huusi juosten lordi Glenarvanin luo. --- Mulradyko? --- Niin, Edward, lady Helena vastasi. --- On tapahtunut k\"{a}\"{a}nne. Majuri on rauhallisempi. Matruusimme j\"{a}\"{a} eloon. --- Miss\"{a} MacNabbs on? --- H\"{a}nen luonaan. Mulrady on halunnut puhua h\"{a}nen kanssaan. Heit\"{a} ei saa h\"{a}irit\"{a}. Tunti sitten oli haavoittunut todella toipunut tajuttomuudestaan, ja kuume oli laskenut. Heti kun Mulradyn taju ja puhekyky palautui, h\"{a}n pyysi tavata Glenarvania tai t\"{a}m\"{a}n poissaollessa majuria. N\"{a}hdess\"{a}\"{a}n h\"{a}nen olevan niin heikkona MacNabbs halusi kielt\"{a}\"{a} kaiken keskustelun; mutta Mulrady oli niin itsepintainen, ett\"{a} majurin t\"{a}ytyi mukautua. Keskustelua oli kest\"{a}nyt jo muutaman minuutin, kun Glenarvan palasi. T\"{a}ytyi siis vain odottaa MacNabbsin kertomusta. Pian avautuikin vankkurien kuomu, ja majuri ilmestyi esiin. H\"{a}n tuli yst\"{a}viens\"{a} luo kumipuun juurelle, mihin teltta oli pystytetty. H\"{a}nen tavallisesti niin tyynet kasvonsa osoittivat h\"{a}nen ajattelevan ankarasti. Kun h\"{a}nen katseensa sattuivat lady Helenaan ja nuoreen neitoon, niist\"{a} n\"{a}kyi s\"{a}\"{a}liv\"{a}\"{a} surua. Glenarvan tiedusteli, miten asianlaita oli, ja majuri kertoi seuraavaa: L\"{a}hdetty\"{a}\"{a}n leirilt\"{a} Mulrady oli ratsastanut Paganelin neuvomaa polkua. H\"{a}n kulki niin nopeasti kuin y\"{o}n pimeys salli. Arvionsa mukaan h\"{a}n oli p\"{a}\"{a}ssyt kolme kilometri\"{a}, kun joukko miehi\"{a} --- h\"{a}nen luullakseen viisi --- juoksi h\"{a}nen hevosensa eteen. Hevonen kavahti pystyyn. Mulrady tempasi revolverinsa ja ampui. H\"{a}nest\"{a} n\"{a}ytti, ett\"{a} kaksi rosvoista kaatui. Laukausten valossa h\"{a}n tunsi Ben Joycen. Mutta siin\"{a} olikin kaikki. H\"{a}n ei ehtinyt ampua asettaan tyhj\"{a}ksi. Ankara isku osui oikeaan kylkeen ja h\"{a}n putosi maahan. H\"{a}n ei kuitenkaan viel\"{a} ollut menett\"{a}nyt tajuntaansa. Murhamiehet luulivat h\"{a}nen kuolleen. H\"{a}n tunsi, ett\"{a} h\"{a}nen taskujaan kopeloitiin. Sitten joku sanoi: --- Minulla on se kirje. --- Anna t\"{a}nne, Ben Joyce vastasi, --- ja nyt on \textit{Duncan} meid\"{a}n! T\"{a}ll\"{a} kohtaa MacNabbsin kertomusta Glenarvan ei voinut olla huudahtamatta. MacNabbs kertoi edelleen: --- Ottakaa te muut hevonen kiinni! Ben Joyce jatkoi. --- Kahden p\"{a}iv\"{a}n kuluttua olen \textit{Duncanin} kannella, kuuden Twofold-lahdella. Siell\"{a} on sovittu paikka. Mylordin joukko on silloin viel\"{a} kiinni Snowyn soissa. Menk\"{a}\"{a} joen yli Kemple-pierin siltaa my\"{o}ten aina rannikolle asti ja odottakaa minua. Min\"{a} keksin kyll\"{a} keinon saada teid\"{a}t laivalle. Niin pian kuin sen miehist\"{o} on meress\"{a}, me hallitsemme \textit{Duncanin} omistajina Intian valtamerelt\"{a}. --- El\"{a}k\"{o}\"{o}n Ben Joyce! huusivat rosvot. Mulradyn hevonen tuotiin paikalle, Joyce l\"{a}hti nelist\"{a}m\"{a}\"{a}n Lucknowin tiet\"{a}, ja h\"{a}nen miehens\"{a} k\"{a}\"{a}ntyiv\"{a}t kaakkoon Snowy-joelle. Vaikka Mulrady oli pahoin haavoittunut, h\"{a}nell\"{a} oli voimaa ry\"{o}mi\"{a} kolmensadan askelen p\"{a}\"{a}h\"{a}n leirist\"{a}, miss\"{a} tapasimme h\"{a}net melkein kuolleena. Siin\"{a} Mulradyn kertomus. Te ymm\"{a}rr\"{a}tte nyt, mink\"{a} vuoksi uljas matruusi tahtoi v\"{a}ltt\"{a}m\"{a}tt\"{a} puhua. N\"{a}m\"{a} tiedot pel\"{a}styttiv\"{a}t Glenarvanin ja h\"{a}nen kumppaninsa. --- Merirosvoja! Merirosvoja! Glenarvan huudahti. --- Minun miehist\"{o}ni murhataan! \textit{Duncan} noiden rosvojen k\"{a}siss\"{a}! --- Niin, sill\"{a} Ben Joyce yll\"{a}tt\"{a}\"{a} laivan, majuri vastasi, --- ja silloin... --- Hyv\"{a} on! Meid\"{a}n on ehditt\"{a}v\"{a} rannikolle ennen noita roistoja! Paganel sanoi. --- Kuinka p\"{a}\"{a}semme Snowyn yli? Wilson kysyi. --- Samoin kuin hekin, Glenarvan vastasi. --- He menev\"{a}t Kemple-pierin siltaa my\"{o}ten, samoin mekin. --- Ent\"{a} Mulrady, kuinka h\"{a}nen k\"{a}y? lady Helena kysyi. --- H\"{a}net kannetaan. Vuorotellen. Voinko j\"{a}tt\"{a}\"{a} miehist\"{o}ni puolustautumatta Ben Joycen joukon valtaan? Snowyn ylitys Kemple-pierin siltaa my\"{o}ten oli mahdollinen, mutta arveluttava. Rosvot saattoivat asettua sillalle sit\"{a} puolustamaan. Heit\"{a} olisi ainakin kolmekymment\"{a} seitsem\"{a}\"{a} vastaan! Mutta on olemassa hetki\"{a}, jolloin ei k\"{a}y laskeminen lukum\"{a}\"{a}r\"{a}\"{a}, vaan on joka tapauksessa ment\"{a}v\"{a} eteenp\"{a}in. --- Mylord, sanoi silloin John Mangles, --- ennen kuin panemme kaiken viimeisen kortin varaan, ennen kuin l\"{a}hdemme siltaa kohti, on paras menn\"{a} tutkimaan se. Min\"{a} otan sen tehd\"{a}kseni. --- Min\"{a} tulen mukaan, John, Paganel lausui. Esitys hyv\"{a}ksyttiin, ja John Mangles ja Paganel valmistautuivat l\"{a}htem\"{a}\"{a}n heti. Heid\"{a}n piti edet\"{a} pitkin Snowyn rantaa siihen saakka, miss\"{a} tulisivat Ben Joycen ilmoittamalle paikalle, ja ennen kaikkea v\"{a}ltt\"{a}\"{a} n\"{a}ytt\"{a}ytym\"{a}st\"{a} rosvoille, joita ep\"{a}ilem\"{a}tt\"{a} liikkui rannalla. Elintarvikkein varustettuina ja hyvin aseistettuina l\"{a}htiv\"{a}t rohkeat miehet retkelle ja katosivat pian rannan korkeiden kaislojen sekaan. Heit\"{a} odotettiin koko p\"{a}iv\"{a}. Iltaan menness\"{a} he eiv\"{a}t viel\"{a} olleet palanneet. Alettiin pel\"{a}t\"{a} pahinta. Vihdoin kello yhdentoista seuduilla Wilson ilmoitti heid\"{a}n palaavan. Paganel ja John Mangles olivat aivan n\"{a}\"{a}nnyksiss\"{a} kuudentoista kilometrin vaelluksesta. --- Silta? Onko sit\"{a}? Glenarvan kysyi rient\"{a}en heit\"{a} vastaan. --- On, liaanisilta, John Mangles sanoi. --- Rosvot ovat siit\"{a} tosiaan menneet yli. Mutta... --- Mutta...? Glenarvan kysyi aavistaen uutta onnettomuutta. --- He ovat polttaneet sillan per\"{a}ss\"{a}\"{a}n! Paganel vastasi. \gutchapter{EDEN.} Nyt ei ollut ep\"{a}toivon, vaan toiminnan aika. Kun Kemple-pierin silta oli h\"{a}vitetty, t\"{a}ytyi p\"{a}\"{a}st\"{a} Snowy-joen yli mill\"{a} muulla keinolla tahansa ja ehti\"{a} ennen Ben Joycen joukkoa Twofold-lahden rannalle. Niinp\"{a} aikaa ei tuhlattukaan turhiin puheisiin, vaan seuraavana eli 16. p\"{a}iv\"{a}n\"{a} tammikuuta l\"{a}htiv\"{a}t John Mangles ja Glenarvan tutkimaan jokea valmistellakseen ylityst\"{a}. Sateen paisuttama kuohuva vesi ei laskenut. Se kohisi hirve\"{a}n\"{a} koskena. Sen uhmaaminen oli sy\"{o}ksymist\"{a} kuoleman kitaan. Glenarvan seisoi liikkumatta, k\"{a}sivarret ristiss\"{a}, p\"{a}\"{a} painuneena. --- Tahdotteko, ett\"{a} koetan p\"{a}\"{a}st\"{a} toiselle rannalle uimalla? John Mangles kysyi. --- En, John, Glenarvan vastasi pid\"{a}tt\"{a}en k\"{a}dell\"{a}\"{a}n rohkeata nuorta miest\"{a}, --- odottakaamme! Ja molemmat palasivat leirille. P\"{a}iv\"{a} kului suuressa levottomuudessa. Kymmenen kertaa Glenarvan k\"{a}vi uudelleen Snowyn rannalla. H\"{a}n koetti keksi\"{a} jotakin rohkeata keinoa p\"{a}\"{a}st\"{a} virran yli. Mutta turhaan. Jos sen uomassa olisi virrannut sulaa laavaa, ei ylimeno olisi ollut mahdottomampi. N\"{a}iden pitkien hukkaan menneiden tuntien aikana lady Helena hoiti majurin neuvojen mukaan Mulradya mit\"{a} huolellisemmin. Matruusi tunsi virkoavansa el\"{a}m\"{a}\"{a}n. MacNabbs vakuutti, ett\"{a} mik\"{a}\"{a}n t\"{a}rke\"{a} elin ei ollut vioittunut. Suuri verenvuoto riitti selitt\"{a}m\"{a}\"{a}n potilaan heikkouden. Niinp\"{a} kun verenvuoto oli tyrehtynyt ja haava sidottu, tarvittiin vain aikaa ja lepoa h\"{a}nen t\"{a}ydelliseksi paranemisekseen. Lady Helena oli vaatinut, ett\"{a} sairas edelleen makaisi vankkurien ensimm\"{a}isess\"{a} osastossa. Mulrady oli siit\"{a} melkein h\"{a}peiss\"{a}\"{a}n. H\"{a}nen suurin huolensa oli ajatus, ett\"{a} h\"{a}nen tilansa saattaisi viiv\"{a}stytt\"{a}\"{a} Glenarvania, ja h\"{a}nelle t\"{a}ytyi luvata, ett\"{a} h\"{a}net j\"{a}tett\"{a}isiin leiriin Wilsonin hoitoon, jos Snowyn ylitys k\"{a}visi mahdolliseksi. Paha kyll\"{a}, t\"{a}m\"{a} ylimeno ei ollut mahdollista sin\"{a} eik\"{a} seuraavana, tammikuun 17. p\"{a}iv\"{a}n\"{a}. Se sai Glenarvanin ep\"{a}toivoiseksi. Lady Helena ja majuri yrittiv\"{a}t turhaan rauhoittaa h\"{a}nt\"{a}, kehottaa k\"{a}rsiv\"{a}llisyyteen. K\"{a}rsiv\"{a}llisyyteen, kun ehk\"{a} t\"{a}ll\"{a} hetkell\"{a} Ben Joyce saapuisi laivan kannelle, kun \textit{Duncan} nosti ankkurinsa ja lis\"{a}si h\"{o}yry\"{a} rient\"{a}\"{a}kseen t\"{a}lle turmionrannalle ja joka hetki toi sit\"{a} l\"{a}hemm\"{a}ksi tuhoa! John Mangles tunsi syd\"{a}mess\"{a}\"{a}n samaa tuskaa kuin Glenarvan. Niinp\"{a} haluten kaikin mokomin ylitt\"{a}\"{a} virta h\"{a}n rakensi kanootin australialaisten malliin suurista kumipuunkuoren palasista. N\"{a}m\"{a} perin kevyet liuskat oli sidottu yhteen puuvanteilla; siit\"{a} tuli kovin hauras vene. Kapteeni ja matruusi koettivat t\"{a}t\"{a} kanoottia seuraavan p\"{a}iv\"{a}n kuluessa. He tekiv\"{a}t kaikki, mit\"{a} notkeus, voima, taito ja rohkeus voi. Mutta heti kun he olivat joutuneet virtaan, alus kaatui, ja he olivat v\"{a}h\"{a}ll\"{a} saada maksaa hengell\"{a}\"{a}n uskaliaan yrityksens\"{a}. Vene katosi virran py\"{o}rteisiin. John Mangles ja Wilson eiv\"{a}t olleet ehtineet kulkea edes reilua kymment\"{a} metri\"{a} sateen ja sulaneen lumen paisuttamassa virrassa, jonka leveys nyt oli yli puolitoista kilometri\"{a}. Samoin kuluivat 19. ja 20. p\"{a}iv\"{a} tammikuuta, eik\"{a} tilanne muuttunut. Majuri ja Glenarvan tekiv\"{a}t pitki\"{a} matkoja joen rantaa yl\"{o}sp\"{a}in l\"{o}yt\"{a}m\"{a}tt\"{a} kahlaamoa. Kaikkialla sama tulviva virta, sama kuohuva koski. Australian alppien koko etel\"{a}rinteen vesim\"{a}\"{a}r\"{a}t ker\"{a}\"{a}ntyiv\"{a}t t\"{a}h\"{a}n ainoaan uomaan. \textit{Duncanin} pelastamisen toivosta t\"{a}ytyi luopua. Viisi p\"{a}iv\"{a}\"{a} oli kulunut Ben Joycen l\"{a}hd\"{o}st\"{a}. Laiva oli luultavasti t\"{a}ll\"{a} hetkell\"{a} rannikolla ja rosvojen k\"{a}siss\"{a}! Nykyinen tilanne ei kuitenkaan voinut kest\"{a}\"{a} kauan. Satunnaiset tulvat menev\"{a}t pian ohi juuri ankaruutensa vuoksi. Aamulla 21. p\"{a}iv\"{a}n\"{a} tammikuuta totesikin Paganel, ett\"{a} vedenkorkeus alkoi v\"{a}het\"{a}. H\"{a}n ilmoitti havaintonsa Glenarvanille. --- Mit\"{a} v\"{a}li\"{a} sill\"{a} nyt on? Glenarvan vastasi. --- Se on liian my\"{o}h\"{a}ist\"{a}. --- Mutta silti emme voi j\"{a}\"{a}d\"{a} t\"{a}nne, majuri huomautti. --- Tosiaan, John Mangles sanoi. --- Huomenna ehk\"{a} ylitys on jo mahdollinen. --- Ent\"{a} pelastaako se onnettoman miehist\"{o}ni? Glenarvan huudahti. --- Kuunnelkaa, mylord, John Mangles vastasi. --- Min\"{a} tunnen Tom Austinin. H\"{a}nen on ollut m\"{a}\"{a}r\"{a} t\"{a}ytt\"{a}\"{a} teid\"{a}n k\"{a}skynne ja l\"{a}hte\"{a} niin pian kuin mahdollista. Mutta kuka tiet\"{a}\"{a}, oliko \textit{Duncan} valmis, oliko sen vauriot korjattu Ben Joycen saapuessa Melbourneen? Ent\"{a} jos laiva ei ole voinut l\"{a}hte\"{a} merelle, jos on tapahtunut p\"{a}iv\"{a}n, kahden my\"{o}h\"{a}styminen? --- Sin\"{a} olet oikeasssa, John! Glenarvan vastasi. --- T\"{a}ytyy p\"{a}\"{a}st\"{a} Twofold-lahdelle. Me olemme vain viidenkymmenen kilometrin p\"{a}\"{a}ss\"{a} Delegetest\"{a}! --- Aivan, Paganel sanoi, --- ja sielt\"{a} saamme nopeita kulkuneuvoja. Kuka tiet\"{a}\"{a}, emmek\"{o} ehdi ajoissa ehk\"{a}isem\"{a}\"{a}n onnettomuuden? --- L\"{a}hdet\"{a}\"{a}n! Glenarvan huudahti. John Mangles ja Wilson ryhtyiv\"{a}t heti rakentamaan suurta lauttaa. Kokemus oli osoittanut, ett\"{a} kaarnan palat eiv\"{a}t voineet kest\"{a}\"{a} virran voimaa. John kaatoi siis kumipuita, joista rakennettiin k\"{o}mpel\"{o}, mutta tukeva lautta. Se oli pitk\"{a}llinen ty\"{o}, ja p\"{a}iv\"{a} kului, ennen kuin se saatiin valmiiksi. Lautta valmistui vasta seuraavana p\"{a}iv\"{a}n\"{a}. Silloin oli Snowyn vesi tuntuvasti laskenut. Koski oli muuttunut virraksi, mutta kuitenkin vuolaaksi. Mutta suuntaamalla viistoon, sit\"{a} m\"{a}\"{a}r\"{a}tyiss\"{a} rajoissa apuna k\"{a}ytt\"{a}en toivoi John p\"{a}\"{a}st\"{a}v\"{a}n toiselle rannalle. Kello puoli yksi mentiin lautalle ja kukin otti mukaansa elintarvikkeita kahdeksi p\"{a}iv\"{a}ksi. J\"{a}\"{a}nn\"{o}s samoin kuin vankkurit ja teltta j\"{a}tettiin. Mulrady oli niin voimistunut, ett\"{a} h\"{a}net voitiin siirt\"{a}\"{a}; h\"{a}nen paranemisensa edistyi nopeasti. Kello yhden aikaan oli kukin paikallaan lautalla, joka oli sidottu kiinni rantaan. John Mangles oli j\"{a}rjest\"{a}nyt aluksen oikealle puolelle Wilsonin hoidettavaksi jonkinlaisen airontapaisen, jonka oli m\"{a}\"{a}r\"{a} pit\"{a}\"{a} lautan pois virrasta, ja hillit\"{a} sen ajelehtimista. Itse seisoi h\"{a}n per\"{a}ss\"{a} arvellen voivansa ohjata ison per\"{a}melan avulla. Lady Helena ja Mary Grant olivat lautan keskell\"{a} Mulradyn luona, Glenarvan, majuri, Paganel ja Robert heid\"{a}n ymp\"{a}rill\"{a}\"{a}n valmiina auttamaan. --- Onko selv\"{a}, Wilson? John Mangles kysyi matruusiltaan. --- On, kapteeni, Wilson vastasi tarttuen airoonsa voimakkaalla k\"{a}dell\"{a}. --- Ole varuillasi ja pid\"{a} meid\"{a}t pois virrasta. John Mangles irrotti lautan ja survaisi sen Snowyn aalloille. Kaikki sujui hyvin noin parisenkymment\"{a} metri\"{a}. Wilson yritti est\"{a}\"{a} lauttaa joutumasta virtaan. Mutta pian olivat py\"{o}rteet temmanneet lautan, joka k\"{a}\"{a}ntyi ymp\"{a}ri airon tai per\"{a}simen voimatta pit\"{a}\"{a} sit\"{a} oikeassa suunnassa. Ponnistuksistaan huolimatta Wilson ja John Mangles olivat heti t\"{a}ysin p\"{a}invastaisessa asennossa kuin piti, mik\"{a} teki airojen k\"{a}ytt\"{a}misen mahdottomaksi. T\"{a}ytyi alistua kohtaloon. Ei ollut mit\"{a}\"{a}n keinoa suoristaa lautan kieppuvaa kulkua. Se py\"{o}ri ymp\"{a}ri huimaavaa vauhtia ja meni virran mukana. John Mangles seisoi kalpeana hampaitaan purren ja katseli kuohuvaa vett\"{a}. T\"{a}ll\"{a} v\"{a}lin oli lautta saapunut keskelle Snowya. Se oli silloin noin kilometrin verran alempana l\"{a}ht\"{o}kohtaansa. Siell\"{a} virta oli tavattoman v\"{a}kev\"{a}, ja kun se rikkoi py\"{o}rteet, lautta hiukan vakavoitui. John ja Wilson tarttuivat airoihinsa, ja heid\"{a}n onnistui suunnata alusta viistoon. Seurauksena oli, ett\"{a} p\"{a}\"{a}stiin l\"{a}hemm\"{a}ksi vasenta rantaa. Ei oltu siit\"{a} en\"{a}\"{a} kuin vajaan sadan metrin p\"{a}\"{a}ss\"{a}, kun Wilsonin airo \"{a}kki\"{a} katkesi. Lautta, jossa ei en\"{a}\"{a} ollut voimaa, joutui virran valtaan. John yritti est\"{a}\"{a} sit\"{a} melansa katkeamisen uhalla. Wilson, jonka k\"{a}det olivat verill\"{a}, riensi auttamaan h\"{a}nt\"{a}. Vihdoin yritys onnistui, ja yli puoli tuntia kest\"{a}neen matkan j\"{a}lkeen lautta t\"{o}rm\"{a}si jyrkk\"{a}\"{a}n rantaan. T\"{a}r\"{a}hdys oli ankara, tukit irtautuivat, k\"{o}ydet katkesivat, vesi tuli kohisten sis\"{a}lle. Matkustajat ehtiv\"{a}t vain tarttua kiinni rannan pensaisiin ja siepata mukaansa Mulradyn ja puoliksi kastuneet naiset. Lyhyesti sanoen, kaikki pelastuivat, mutta suurin osa ev\"{a}it\"{a} ja aseet, majurin kiv\"{a}\"{a}ri\"{a} lukuunottamatta, meniv\"{a}t menojaan lautan rippeiden mukana. Joen yli oli p\"{a}\"{a}sty. Retkikunta oli jokseenkin ilman varusteita viidenkymmenen kilometrin p\"{a}\"{a}ss\"{a} Delegetest\"{a}, keskell\"{a} Victorian maakunnan rajan tuntemattomia er\"{a}maita. Siell\"{a} ei ole uudisasukkaita eik\"{a} karjankasvattajia, sill\"{a} t\"{a}m\"{a} seutu on asumatonta, lukuunottamatta ehk\"{a} julmia ja rosvoilevia varkaita. P\"{a}\"{a}tettiin viipym\"{a}tt\"{a} l\"{a}hte\"{a} eteenp\"{a}in. Mulrady huomasi hyvin olevansa esteen\"{a}; h\"{a}n pyysi saada vaikkapa yksikseen j\"{a}\"{a}d\"{a} odottamaan apua Delegetest\"{a}. Glenarvan ei suostunut. H\"{a}n ei voinut ehti\"{a} Delegeteen ennen kolmea p\"{a}iv\"{a}\"{a} ja rannikolle ennen viitt\"{a}, siis vasta 26. p\"{a}iv\"{a}n\"{a} tammikuuta. Ja \textit{Duncan} oli 16. p\"{a}iv\"{a}n\"{a} l\"{a}htenyt Melbournesta. Mit\"{a}p\"{a} h\"{a}nelle nyt merkitsi muutaman tunnin viivytys? --- Ei, yst\"{a}v\"{a}ni, h\"{a}n sanoi. --- Min\"{a} en j\"{a}t\"{a} ket\"{a}\"{a}n. Tehk\"{a}\"{a}mme paarit, ja me kannamme sinua vuoron per\"{a}\"{a}n. Paarit tehtiin kumipuun oksista, ja Mulrady sijoitettiin niihin, tahtoi tai ei. Glenarvan halusi olla ensimm\"{a}isen\"{a} kantamassa matruusiansa. H\"{a}n tarttui paareihin yhdest\"{a} p\"{a}\"{a}st\"{a}, Wilson toisesta, ja niin l\"{a}hdettiin taivaltamaan. Mik\"{a} surkea n\"{a}ky ja kuinka huonosti olikaan p\"{a}\"{a}ttynyt t\"{a}m\"{a} niin hyvin alkanut retki! Ei oltu en\"{a}\"{a} etsim\"{a}sss\"{a} Harry Grantia. T\"{a}m\"{a} mannermaa, jossa h\"{a}n ei ollut eik\"{a} koskaan k\"{a}ynytk\"{a}\"{a}n, uhkasi tuhota h\"{a}nen etsij\"{a}ns\"{a}. Ja kun h\"{a}nen rohkeat maanmiehens\"{a} saapuisivat Australian rannalle, he eiv\"{a}t tapaisi siell\"{a} edes \textit{Duncania} p\"{a}\"{a}st\"{a}kseen takaisin is\"{a}nmaahansa! Ensimm\"{a}inen p\"{a}iv\"{a} marssittiin \"{a}\"{a}nett\"{o}min\"{a} ja vaivalloisesti. Joka kymmenes minuutti vaihdettiin paarien kantajia. Kaikki matruusin toverit alistuivat nurkumatta t\"{a}h\"{a}n vaivaan, jota ankara kuumuus viel\"{a} suurensi. Iltaan menness\"{a} oli p\"{a}\"{a}sty ainoastaan kahdeksan kilometri\"{a} ja leiriydyttiin er\"{a}\"{a}seen kumipuulehtoon. Haaksirikosta pelastuneet muonan j\"{a}\"{a}nn\"{o}kset sy\"{o}tiin ilta-ateriaksi. T\"{a}stedes oli luotettava vain majurin pyssyyn. Y\"{o} oli huono. Alkoi sataa. Aika tuntui pitk\"{a}lt\"{a} p\"{a}iv\"{a}nnousuun. L\"{a}hdettiin taas liikkeelle. Majuri ei saanut tilaisuutta ampua ainoatakaan laukausta. T\"{a}m\"{a} surkea seutu oli er\"{a}maatakin autiompi, kun ei ollut edes el\"{a}imi\"{a}. Onneksi Robert l\"{o}ysi trapinpes\"{a}n ja siin\"{a} kymmenkunta suurta munaa, jotka Olbinett kypsensi kuumassa tuhkassa. T\"{a}m\"{a} sek\"{a} hiukkanen er\"{a}\"{a}n rotkon pohjalta l\"{o}ydetty\"{a} paisuruohoa oli koko aamiainen 22. p\"{a}iv\"{a}n\"{a} tammikuuta. Kulku k\"{a}vi nyt tavattoman hankalaksi. Hietakentill\"{a} kasvoi ``spinifexi\"{a}'', piikkist\"{a} ruohoa, jota Melbournessa sanotaan piikkisiaksi. Se repi vaatteet rikki ja s\"{a}\"{a}ret verille. Uljaat naiset eiv\"{a}t kuitenkaan valittaneet; he k\"{a}veliv\"{a}t urheasti esimerkki\"{a} antaen ja rohkaisten toinen toistaan sanalla tai katseella. Illalla pys\"{a}hdyttiin Bulla-Bulla-vuoren juurelle Jungalla-puron reunalle. Illallinen olisi ollut laiha, ellei MacNabbs olisi vihdoin saanut ammutuksi suurta rottaa, jonka tieteellinen nimi on ``mus conditor'' ja joka on ravintorikas. Olbinett paistoi sen, ja se olisi maistunut mainettaan viel\"{a} paremmalta, jos se olisi ollut lampaan kokoinen. Piti kuitenkin tyyty\"{a}. Se kalvettiin luita my\"{o}ten. Tammikuun 23. p\"{a}iv\"{a}n\"{a} retkeilij\"{a}t l\"{a}htiv\"{a}t taipaleelle v\"{a}synein\"{a}, mutta yh\"{a} tarmokkaina. Kierretty\"{a}\"{a}n vuorenjuuren he vaelsivat pitkien kenttien yli, joiden ruoho tuntui olevan valaskalanpartaa, sotkuista piikkivyyhte\"{a}, ter\"{a}v\"{a}piikkist\"{a} ryteikk\"{o}\"{a}, miss\"{a} tiet\"{a} t\"{a}ytyi raivata milloin kirveell\"{a}, milloin tulella. T\"{a}n\"{a} aamuna ei ollut puhettakaan aamiaisesta. Ei mik\"{a}\"{a}n voinut olla hedelm\"{a}tt\"{o}m\"{a}mp\"{a}\"{a} kuin t\"{a}m\"{a} kvartsiliuskeita t\"{a}ynn\"{a} oleva seutu. N\"{a}l\"{a}n ohella my\"{o}s jano alkoi vaivata ankarasti, ja polttava kuumuus lis\"{a}si sen tuskaa. Glenarvan seurueineen ei p\"{a}\"{a}ssyt etenem\"{a}\"{a}n kilometri\"{a}k\"{a}\"{a}n tunnissa; ja jos t\"{a}t\"{a} veden ja ravinnon puutetta jatkuisi iltaan, he kaatuisivat kesken matkan en\"{a}\"{a} nousematta. Mutta kun ihmiselt\"{a} puuttuu kaikki, kun h\"{a}n katsoo olevansa t\"{a}ysin avuton, kun h\"{a}n ajattelee hetkens\"{a} tulleen, silloin ilmestyy kaitselmuksen k\"{a}si. Juotavaa tarjosivat kannukasvit, mainiota nestett\"{a} t\"{a}ynn\"{a} olevat pikarintapaiset, joita riippui korallimaisten pensaiden oksilla. Kaikki virkistiv\"{a}t itse\"{a}\"{a}n ja tunsivat elpyv\"{a}ns\"{a}. Ruoka oli samaa, joka el\"{a}tt\"{a}\"{a} alkuasukkaita, kun riistaa, hy\"{o}nteisi\"{a} ja k\"{a}\"{a}rmeit\"{a} ei ole. Paganel l\"{o}ysi er\"{a}\"{a}n puron kuivuneesta uomasta kasvin, jonka erinomaisia ominaisuuksia muuan h\"{a}nen toverinsa Maantieteellisess\"{a} seurassa oli h\"{a}nelle usein kuvannut. Se oli ``nardu'', marsileaceae-heimoon kuuluva salasiitti\"{o}, sama, joka pitensi Burken ja Kingin el\"{a}m\"{a}\"{a} sis\"{a}maan autiomailla. Sen apilaa muistuttavien lehtien alla oli kuivia iti\"{o}it\"{a}. N\"{a}m\"{a} pavun kokoiset iti\"{o}t rikottiin kahden kiven v\"{a}liss\"{a}, ja niist\"{a} saatiin jonkinlaista jauhoa. Siit\"{a} tehtiin karheata leip\"{a}\"{a}, joka tyynnytti n\"{a}l\"{a}n tuskan. Olbinett ker\"{a}si sit\"{a} ison joukon, joten ravinto oli turvattu useaksi p\"{a}iv\"{a}ksi. Seuraavana eli 24. p\"{a}iv\"{a}n\"{a} Mulrady k\"{a}veli osan matkaa itse. H\"{a}nen haavansa oli kokonaan arpeutunut. Delegeten kaupunki oli vain kuudentoista kilometrin p\"{a}\"{a}ss\"{a}, ja illalla leiriydyttiin 149$^{\circ}$ pituusasteen kohdalla Uuden Etel\"{a}-Walesin rajalla. Jo muutaman tunnin oli satanut l\"{a}pitunkevaa vihmasadetta. Ei olisi ollut mit\"{a}\"{a}n suojaa, ellei John Mangles olisi sattumalta l\"{o}yt\"{a}nyt hylj\"{a}tty\"{a} ja heikkokuntoista halonhakkaajah\"{o}kkeli\"{a}. T\"{a}ytyi siis tyyty\"{a} t\"{a}h\"{a}n kurjaan, oksista ja oljista tehtyyn kojuun. Wilson halusi sytytt\"{a}\"{a} tulen paistaakseen narduleip\"{a}\"{a} ja ker\"{a}si maasta kuivia risuja. Mutta kun ne piti sytytt\"{a}\"{a}, se ei onnistunut. Niiden sis\"{a}lt\"{a}m\"{a} suuri alunam\"{a}\"{a}r\"{a} teki ne palamattomiksi. Ne olivat sit\"{a} palamatonta puuta, jonka Paganel oli maininnut merkillisess\"{a} luettelossaan Australian tuotteista. T\"{a}ytyi siis olla ilman tulta ja samoin ilman leip\"{a}\"{a} ja nukkua m\"{a}riss\"{a} vaatteissa, korkeissa puissa piileksivien naurulintujen ik\"{a}\"{a}n kuin pilkatessa onnettomia matkustajia. Glenarvan oli kuitenkin l\"{a}hell\"{a} k\"{a}rsimystens\"{a} loppua. Nyt olikin jo aika. Molemmat nuoret naiset ponnistelivat sankarillisesti, mutta heid\"{a}n voimansa v\"{a}heniv\"{a}t joka tunti. He laahustivat, he eiv\"{a}t en\"{a}\"{a} k\"{a}velleet. Seuraavana p\"{a}iv\"{a}n\"{a} noustiin auringon sarastaessa. Kello yksitoista tuli n\"{a}kyviin Delegete Wellesleyn kreivikunnassa, kahdeksankymmenen kilometrin p\"{a}\"{a}ss\"{a} Twofoldista. Siell\"{a} saatiin pian kulkuneuvot. Ja tuntiessaan olevansa niin l\"{a}hell\"{a} rantaa Glenarvan alkoi j\"{a}lleen toivoa. Jos \textit{Duncan} oli hiukankin my\"{o}h\"{a}stynyt, ehk\"{a}p\"{a} h\"{a}n ehtisi perille ennen sen tuloa. Vuorokauden kuluttua h\"{a}n olisi lahden rannalla! Virkist\"{a}v\"{a}n aterian j\"{a}lkeen l\"{a}htiv\"{a}t retkel\"{a}iset viiden vire\"{a}n hevosen vet\"{a}miss\"{a} postivaunuissa Delegetest\"{a}. Ruhtinaallisen juomarahan toivossa innostuneina ajajat antoivat vaunujen menn\"{a} hyv\"{a}\"{a} tiet\"{a} pitkin huimaa vauhtia. He eiv\"{a}t k\"{a}ytt\"{a}neet kuin pari minuuttia hevosten vaihtoon joka kuudentoista kilometrin p\"{a}\"{a}ss\"{a}. Tuntui kuin Glenarvan olisi saanut heihin samaa intoa, joka h\"{a}ness\"{a} itsess\"{a}\"{a}n hehkui. Koko p\"{a}iv\"{a} kiidettiin n\"{a}in kymmenen kilometri\"{a} tunnissa, koko y\"{o} samoin. Seuraavana p\"{a}iv\"{a}n\"{a} auringon noustessa maininkien kohina ilmoitti Tyynen valtameren olevan l\"{a}hell\"{a}. T\"{a}ytyi ajaa lahden ymp\"{a}ri, jotta p\"{a}\"{a}stiin 37. asteen kohdalle, juuri sille paikalle, miss\"{a} Tom Austinin oli m\"{a}\"{a}r\"{a} odottaa retkel\"{a}isten saapumista. Kun meri n\"{a}kyi, kaikkien katseet k\"{a}\"{a}ntyiv\"{a}t ulapalle t\"{a}hystellen horisonttia. Oliko kaitselmuksen ihmeellisest\"{a} sattumasta \textit{Duncan} siell\"{a} purjehtien pitkin rannikkoa, kuten taannoin Cap Corrientesin kohdalla Argentiinan rannikolla? Ei n\"{a}hty mit\"{a}\"{a}n. Taivas ja vesi yhtyiv\"{a}t n\"{a}k\"{o}piirin rajalla. Ei ainoatakaan purjetta valtameren pinnalla. Yksi toivo oli viel\"{a} j\"{a}ljell\"{a}. Kenties Tom Austin oli katsonut olevan syyt\"{a} laskea ankkuriin Twofold-lahteen, sill\"{a} meri aaltoili hurjasti eik\"{a} alus voi t\"{a}llaisilla rannikoilla tuntea oloaan turvalliseksi. --- Edeniin! Glenarvan m\"{a}\"{a}r\"{a}si. Vaunut k\"{a}\"{a}ntyiv\"{a}t heti oikealla pitkin lahden rantaa kiert\"{a}v\"{a}\"{a} tiet\"{a}, kahdeksan kilometrin p\"{a}\"{a}ss\"{a} sijaitsevaa pient\"{a} Edenin kaupunkia kohti. Ajajat pys\"{a}yttiv\"{a}t l\"{a}helle majakkkaa, joka on sataman suulla. Ulkosatamassa oli muutamia laivoja ankkurissa, mutta yhdenk\"{a}\"{a}n mastossa ei liehunut Malcolmin lippu. Glenarvan, John Mangles, Paganel astuivat ajoneuvoista maahan ja meniv\"{a}t tulliin, tiedustellen virkamiehilt\"{a} viime p\"{a}ivin\"{a} saapuneita laivoja. Yht\"{a}\"{a}n laivaa ei ollut saapunut satamaan viikon kuluessa. --- Ehkei h\"{a}n ole lainkaan l\"{a}htenyt! huudahti Glenarvan, joka ihmissyd\"{a}mess\"{a} helposti tapahtuvasta k\"{a}\"{a}nteest\"{a} ei tahtonut en\"{a}\"{a} antautua ep\"{a}toivoon. --- Kenties olemme saapuneet ennen h\"{a}nt\"{a}! John Mangles pudisti p\"{a}\"{a}t\"{a}\"{a}n. H\"{a}n tunsi Tom Austinin. H\"{a}nen ensimm\"{a}inen per\"{a}miehens\"{a} ei koskaan olisi vitkastellut kymment\"{a} p\"{a}iv\"{a}\"{a}, kun k\"{a}sky oli selv\"{a}. --- Min\"{a} tahdon tiet\"{a}\"{a}, kuinka on asianlaita, Glenarvan sanoi. --- Varmuus on aina ep\"{a}varmuutta parempi. Nelj\"{a}nnestuntia my\"{o}hemmin oli l\"{a}hetetty s\"{a}hk\"{o}sanoma Melbournen laivanvarustajien esimiehelle. Sitten retkel\"{a}iset l\"{a}htiv\"{a}t \textit{Victoria}-hotelliin. Kello kaksi tuotiin lordi Glenarvanille s\"{a}hk\"{o}sanoma. Se oli kirjoitettu seuraavaan muotoon: ``Lordi Glenarvan, Eden, Twofold Bay \textit{Duncan} l\"{a}htenyt 18. p\"{a}iv\"{a}n\"{a} t\"{a}t\"{a} kuuta tuntemattomaan suuntaan. J. Andrew.'' S\"{a}hk\"{o}sanoma putosi Glenarvanin k\"{a}sist\"{a}. Ei ep\"{a}ilyst\"{a}k\"{a}\"{a}n! Kunniallinen skotlantilainen huvipursi oli Ben Joycen k\"{a}siss\"{a} merirosvolaivana. N\"{a}in p\"{a}\"{a}ttyi t\"{a}m\"{a} niin suotuisin entein alkanut retki Australian halki. Kapteeni Grantin ja haaksirikkoisten j\"{a}ljet n\"{a}yttiv\"{a}t olevan auttamattomasti kadonneet; t\"{a}m\"{a} ep\"{a}onnistuminen oli maksanut kokonaisen laivav\"{a}en hengen; lordi Glenarvan oli joutunut tappiolle taistelussaan, ja t\"{a}m\"{a}n urhean etsij\"{a}n, jota yhteen liittoutuneet luonnonvoimat eiv\"{a}t olleet voineet pys\"{a}hdytt\"{a}\"{a} aavikoilla, oli ihmisten kataluus voittanut Australian mantereella. \gutchapter{VIITESELITYKSET: } [1] Venuksen kulku auringonkehr\"{a}n editse tapahtui 1769. T\"{a}m\"{a} harvinainen ilmi\"{o} oli t\"{a}htitieteellisesti perin mielenkiintoinen; sen avulla saatettiin n\"{a}et tarkoin m\"{a}\"{a}ritell\"{a} auringon ja maan v\"{a}linen et\"{a}isyys. [2] Tavattoman ankaria, Intian valtamerell\"{a} puhaltavia tuulia. Niiden suunta ei ole pysyv\"{a}, vaan vaihtelee vuodenaikojen mukaan, ja tavallisesti ne ovat kes\"{a}ll\"{a} p\"{a}invastaisia kuin talvella. [3] Ilmapuntarin normaalikorkeus on 760 millimetri\"{a} [4] Lasissa on kemiallista seosta, joka muuttaa muotoaan tuulen suunnan ja ilmakeh\"{a}n s\"{a}hk\"{o}varauksen mukaan. [5] Merilaki kielt\"{a}\"{a}kin kapteenia k\"{a}ytt\"{a}m\"{a}st\"{a} t\"{a}t\"{a} ep\"{a}toivoista keinoa, jos toinen alus on tulossa sen per\"{a}ss\"{a} samaa reitti\"{a} my\"{o}ten. [6] Jacques Paganel tapasikin Stuartin Skotlantiin palattuaan, mutta ei saanut kauan nauttia t\"{a}m\"{a}n kuuluisan retkeilij\"{a}n seurasta. Stuart kuoli 5. p\"{a}iv\"{a}n\"{a} kes\"{a}kuuta 1866 er\"{a}\"{a}ss\"{a} vaatimattomassa talossa Nottingham-Hilliss\"{a}. [7] Toline, viet\"{a}v\"{a} Echucaan, rautatiekantaja Jeffries Smithin huostassa. Rahti maksettu. [8] On kuitenkin mahdollista, ett\"{a} siirtolaiset ovat erehtyneet. Kultaa sis\"{a}lt\"{a}v\"{a}t kerrostumat eiv\"{a}t todellisuudessa ole l\"{a}hesk\"{a}\"{a}n tyhjentyneet. Viimeisten tietojen mukaan Australiasta arvioidaan Victorian ja Uuden Walesin kultakent\"{a}t viideksi miljoonaksi hehtaariksi; kultasuonia sis\"{a}lt\"{a}v\"{a}n kvartsin painon arvioidaan olevan suunnilleen 20.650 \textit{miljardia} kiloa, ja niiden tyhjent\"{a}miseksi nykyisill\"{a} ty\"{o}v\"{a}lineill\"{a} tarvittaisiin satatuhatta ty\"{o}miest\"{a} kolmensadan vuoden aikana. Rahassa arvioidaan Australian sis\"{a}lt\"{a}m\"{a} kultam\"{a}\"{a}r\"{a} 664 miljardiksi 250 miljoonaksi frangiksi. [9] Norfolkin saari on Australian it\"{a}puolella; sinne hallitus siirt\"{a}\"{a} rikoksen uusijoita ja parantumattomiksi katsottuja karkotusvankeja erikoisvalvontaan. [10] T\"{a}m\"{a}n ilmi\"{o}n huomasi jo Drummond Australiassa sieniss\"{a}, jotka n\"{a}ytt\"{a}v\"{a}t kuuluvan \textit{Agaricus olearicus}-heimoon. \gutchapter{End of Project Gutenberg's Kapteeni Grantia etsim\"{a}ss\"{a}, by Jules Verne} *** END OF THIS PROJECT GUTENBERG EBOOK KAPTEENI GRANTIA ETSIM\"{A}SS\"{A} *** ***** This file should be named 39057-8.txt or 39057-8.zip ***** This and all associated files of various formats will be found in: http://www.gutenberg.org/3/9/0/5/39057/ Produced by Tapio Riikonen Updated editions will replace the previous one---the old editions will be renamed. 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\documentclass[oneside,final,12pt]{book} \usepackage{amssymb} \usepackage{amsmath} \usepackage{xunicode} \usepackage{verbatim} \usepackage{longtable} \usepackage{tabu} \addtolength{\textwidth}{0.3\linewidth} \addtolength{\hoffset}{-0.15\linewidth} \usepackage{hyperref} \usepackage{xstring} \def\rooturl{https://math.bgu.ac.il/} \hyperbaseurl{\rooturl} \let\hhref\href \providecommand{\extrahref}[2][]{\LTRfootnote{\LR{\IfBeginWith*{#2}{http}{\nolinkurl{#2}}{\nolinkurl{\rooturl#2}}}}} \renewcommand{\href}[2]{\IfBeginWith*{#1}{http}{\hhref{#1}{#2}}{\hhref{\rooturl#1}{#2}}\extrahref{#1}} \usepackage{polyglossia} \usepackage{longtable} %% even in English, we sometimes have Hebrew (as in course hours), and we %% can't add it in :preamble, since it comes after hyperref %%\usepackage{bidi} \setdefaultlanguage{english} \setotherlanguage{hebrew} \setmainfont[Ligatures=TeX]{Libertinus Serif} \SepMark{‭.} \robustify\hebrewnumeral \robustify\Hebrewnumeral \robustify\Hebrewnumeralfinal % vim: ft=eruby.tex: \begin{document} \pagestyle{empty} \pagenumbering{gobble} \begin{center} \vspace*{\baselineskip} {\Large BGU Math} \vspace*{\baselineskip} \rule{\textwidth}{1.6pt}\vspace*{-\baselineskip}\vspace*{2pt} \rule{\textwidth}{0.4pt}\\[\baselineskip] {\Huge Colloquium}\\[0.5\baselineskip] {\Large 2015--16--B meetings} \rule{\textwidth}{0.4pt}\vspace*{-\baselineskip}\vspace{3.2pt} \rule{\textwidth}{1.6pt}\\[\baselineskip] \end{center} {\renewcommand{\arraystretch}{1.2} \global\tabulinesep=2mm \begin{longtabu}{|X[-1,l]|X[-2,c]|X[-3,l]|} \hline \textbf{Date} & \textbf{Speaker} & \textbf{Title}\\ \hline \textrm{Mar 8}% % & Sasha Sodin (Tel Aviv University)% & Random matrix valued fields\\ \hline \textrm{Mar 15}% % & Jarek Kedra (U. of Aberdeen)% & On conjugation invariant geometry of groups\\ \hline \textrm{Mar 22}% % & MIcha Sharir (TAU)% & Eliminating cycles, cutting lenses, and bounding incidences\\ \hline \textrm{Mar 29}% % & Mikhail Muzychuk (Netanya Academic College)% & Isomorphism problem for Cayley combinatorial objects\\ \hline \textrm{Apr 5}% % & Minhyong Kim (Oxford)% & Reciprocity laws, Diophantine equations, and fundamental groups\\ \hline \textrm{Apr 12}% % & Tamar Ziegler (Hebrew University)% & Concatenating cubic structures and patterns in primes\\ \hline \textrm{May 3}% % & Ronen Eldan (Weizmann)% & Interplays between stochastic calculus and geometric inequalities\\ \hline \textrm{May 10}% % & Henri Darmon ( McGill)% & Elliptic curves and explicit class field theory\\ \hline \textrm{May 17}% % & Ido Efrat (BGU)% & Absolute Galois groups - old and new results\\ \hline \textrm{May 31}% % & N. Christopher Phillips ( University of Oregon)% & The mean dimension of a homeomorphism and the radius of comparison of its C*-algebra\\ \hline \textrm{Jun 14}% % & Shakhar Smorodinsky (BGU)% & Improved bounds on the Hadwiger Debrunner numbers\\ \hline \textrm{Jun 28}% % & Michael Lin (BGU)% & Positive Ritt contractions on \$L\_p\$\\ \hline \end{longtabu}} % vim: ft=eruby.tex \vfill Meetings are on \textsc{Tuesdays}, \emph{14:30-15:30}, in \textbf{Math -101} (unless otherwise mentioned) To subscribe for email announcements, please visit:\\ \url{http://mlists.cs.bgu.ac.il/mailman/listinfo/math-colloquium@lists.bgu.ac.il} % vim: ft=eruby.tex \end{document} % vim: ft=eruby.tex:

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% 2kol.tex % last edit: 20-NOV-1991 --JH % % Name: two_col.tex Double Column Format for plain TeX. % % Author: % E. Myers and F.E. Paige % clean up and modifications by Jeroen Hellingman % % Description: % % two_col.tex produces double-column output with balanced columns. % Adapted from The TeXBook, pg 417, and The TUGboat, Vol 6, pg 29. % % \setdoublecolumns initializes the double column format, including % setting \hsize and \vsize: % % \setdoublecolumns#1#2#3 initializes double column format % #1 = overall width % #2 = overall height % #3 = column width % % \begindoublecolumns and \enddoublecolumns are used to switch between % single and double column format: % % \begindoublecolumns starts double column format % \enddoublecolumns returns to single column format % and balances columns % \leftcolrule draws a rule across left column % \rightcolrule draws a rule across right column % % % A typical TeX double-column document will contain: % % \setdoublecolumns{width}{height}{colwidth} % in cm, in, pt,... % ... title page, etc ... % ... title, author, etc ... % default is single column % \begindoublecolumns % switch to 2 columns % ... text ... % \enddoublecolumns % switch to 1 column % \leftcolrule % rule left column (optional) % $$ % ... long equation, table, etc ... % across both columns % $$ % \rightcolrule % rule right column (optional) % \begindoublecolumns % again 2 columns % ... text ... % \enddoublecolumns % end % % Since double columns are narrow, the normal TeX spacing will produce % many overfull hboxes. 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\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{*3}{*1} \titlespacing{\subsection}{0pt}{*2}{*0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[greek,ngerman,english]{babel} \usepackage{float} \begin{document} \title{A novel oncotherapy strategy, direct thrombin inhibitors suppress progression, dissemination and spontaneous metastasis in non-small cell lung cancer} \author[1]{Zhao Bing}% \author[1]{Mengfang Wu}% \author[2]{Zhihuang Hu}% \author[1]{Tianfa Wang}% \author[1]{Jinchao Yu}% \author[1]{Yixin Ma}% \author[1]{Qi Wang}% \author[1]{Yanling Zhang}% \author[1]{Di Chen}% \author[1]{Tianyu Li}% \author[3]{Yaran Li}% \author[1]{Min Yu}% \author[2]{Huijie Wang}% \author[1]{Wei Mo}% \affil[1]{Fudan University}% \affil[2]{Fudan University Shanghai Cancer Center}% \affil[3]{Fudan University School of Basic Medical Sciences}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \selectlanguage{english} \begin{abstract} Background and Purpose: Cancer cachexia and cancer-associated thrombosis are potentially fatal outcomes of advanced cancer. Nevertheless, thrombin expression in NSCLC primary tumor tissues and the association between prognosis of NSCLC patients remain largely unknown. Experimental Approach: Clinical pathological analysis was performed to determine the relationship between thrombin and tumor progression. Effect of r-hirudin and DTIP on cancer progression were evaluated. Western blotting, immunohistochemistry, and immunofluorescence were used to explore the inhibition mechanism of r-hirudin and DTIP. Therapeutic effect of combination of DTIP and chemotherapy was determined. Key Results: We illustrated thrombin expression in NSCLC tissues is closely related to clinicopathological features and the prognosis of patients. Thrombin deficiency inhibited tumor progression. The novel thrombin inhibitors, r-hirudin and DTIP, inhibited cell invasion and metastasis in vitro. They inhibited tumor growth and metastasis in orthotopic lung cancer model; inhibited cells invasion and prolonged survival after injection tumor cells via tail vein; they also inhibited angiogenesis and spontaneous metastases from subcutaneously inoculated tumors. The promotional activity of thrombin in invasion and metastasis was abolished in PAR-1 deficient-NSCLC cells. r-hirudin and DTIP inhibit tumor progression through the thrombin-PAR-1-mediated RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B signaling cascades via inhibiting the MMP9 and IL6 expression. DTIP potentiated chemotherapy-induced growth and metastatic inhibition and inhibited chemotherapy-induced resistance in mice. Conclusions and Implications: Thrombin makes a substantial contribution, together with PAR-1, to NSCLC malignancy. We concluded the anticoagulants, r-hirudin and DTIP, could be expanded for anti-tumor therap. Combination therapy of DTIP and chemotherapy might achieve a better therapeutic effect.% \end{abstract}% \sloppy \textbf{Abbreviations} NSCLC: non-small cell lung cancer; OS: overall survival; DTIP: Direct thrombin inhibitor peptide; r-hirudin: recombinant hirudin; PAR-1: Proteinase-activated receptors; GAPDH: Glyceraldehyde-3-phosphate dehydrogenase; gRNA: guide RNA; NF-\selectlanguage{greek}κ\selectlanguage{english}B: nuclear factor \selectlanguage{greek}κ\selectlanguage{english}B; HUVEC: human umbilical vein endothelial cells, VEGF: Vascular endothelial growth factor. \textbf{Introduction} Lung cancer is the leading cause of cancer-related deaths among humans worldwide (Kyu et al., 2018), and non-small cell lung cancer (NSCLC) accounts for approximately 85\% of all lung cancer cases (Yuan, Huang, Chen, Wu \& Xu, 2019). Even when NSCLC is diagnosed at an operable stage and treatment with chemotherapy is applied, the incidence of recurrence and metastasis remains high with a median survival of less than 10-12 months. Most patients initially respond to platinum or gemcitabine-based chemotherapy (Mlak et al., 2016; Pelayo Alvarez, Westeel, Cortes-Jofre \& Bonfill Cosp, 2013; Wang et al., 2018), but usually relapse and acquire chemo-resistant disease, such that the 5-year survival is \textless{} 0.5\% (Morabito et al., 2014). Thus, targeting tumor metastasis and drug-resistant may represent a promising strategy to treat NSCLC (Vyse \& Huang, 2019). It has long been presumed that tumors may take advantage of the hemostatic system. Many significant hemostatic abnormalities have been described in cancer patients, including disseminated intravascular coagulation, hemorrhagic events, and migratory thrombophlebitis (Soff, 2019; Tan et al., 2019). Indeed, hemostatic complications are a common cause of death in patients with cancer(Joseph S. Palumbo, 2000). Previous studies in mice have unequivocally shown that tumor cell-associated tissue factor (Yokota et al., 2014), circulating prothrombin (Horowitz et al., 2011), and several downstream thrombin procoagulant targets (i.e., platelets, fibrinogen, factor XII) strongly promote tumor cell metastatic potential (Joseph S. Palumbo, 2000; Plantureux, Crescence, Dignat-George, Panicot-Dubois \& Dubois, 2018; Yokoyama, Mori \& Matsuura, 2008). However, at the level of primary tumor growth, the contribution of hemostatic factors has been less clear. Thrombin is an allosteric enzyme with an elaborate structure that exerts diverse biological effects by interacting with various receptors on the surface of vascular and nonvascular cells (Lane, Philippou \& Huntington, 2005). Thrombin has also been shown to contribute to tumor progression in manners both coagulation-dependent and coagulation-independent (Xue et al., 2010). A substantial amount of data supports the idea that thrombin plays important roles in tumorigenesis, contributing to inflammation, angiogenesis, and metastatic dissemination of tumor cells through its PAR-1 receptor (Battinelli, Markens, Kulenthirarajan, Machlus, Flaumenhaft \& Italiano, 2014; Reddel et al., 2017; Yokota et al., 2014). Nevertheless, thrombin expression in NSCLC primary tumor tissues and the association with prognosis of NSCLC patients remain largely unknown. PAR-1, the prototypic member of the PAR family, has been shown to respond to a highly select group of serine proteases. Cleavage of PAR-1 by thrombin initiates potent inflammatory responses, including the up-regulation of cell surface adhesion molecules, induction of hyperpermeability (Feistritzer \& Riewald, 2005), and the activation of the nuclear factor \selectlanguage{greek}κ\selectlanguage{english}B (NF-\selectlanguage{greek}κ\selectlanguage{english}B) pathways (Jeffers et al., 2015). At present, chemotherapy is an established multimodal therapy for NSCLC, however, its benefits are limited due to a low response rate or acquired tumor resistance. In the present study, Arnold et. al have shown that PAR-1 in the tumors induces the chemo-resistance of cancer. As thrombin is the prototypical PAR-1 agonist, which indicates that targeting thrombin may be particular effective in combination with routine chemotherapy. Direct Thrombin Inhibitor Peptide (DTIP) and recombinant hirudin (r-hirudin) which are derivatives of wild-type hirudin variant 2, were developed by our group (Mo, Zhang, Chen, Wang \& Song, 2009; Zhao et al., 2017). DTIP and r-hirudin bind to exosite I and to the apolar region of thrombin, while the N-terminal moiety of r-hirudin and DTIP blocks access to the thrombin active site to inhibit the activity of thrombin. r-hirudin has entered phase I clinical trials, and DTIP is a novel antithrombotic agent that could be used to prevent thrombosis without conferring an increased bleeding risk for subcutaneous injection. Here, we investigated the protein levels of thrombin in clinical NSCLC samples, explored the relationship between thrombin expression level and clinicopathological features, prognosis of NSCLC patients. We evaluated the effects of r-hirudin and DTIP on tumor progression, dissemination and spontaneous metastasis in vitro and in vivo. We also demonstrated the presence of thrombin and PAR-1 accounts for the majority of the invasive signal. The novel findings presented here indicate the roles of r-hirudin and DTIP, anticoagulant drugs, could be expanded for anti-tumor therapy. We speculate that the use of r-hirudin and DTIP in combination would be a new breakthrough in cancer treatment. \textbf{Materials and Methods} Materials Thrombin was obtained from Sigma Aldrich (St Louis, MO). ML161 (PAR-1 antagonist) was purchased from TargetMol (Boston, USA). The anti-NF-\selectlanguage{greek}κ\selectlanguage{english}B p65, anti-phospho-NF-\selectlanguage{greek}κ\selectlanguage{english}B p65, anti-I\selectlanguage{greek}κ\selectlanguage{english}B\selectlanguage{greek}α, \selectlanguage{english}anti-phospho-I\selectlanguage{greek}κ\selectlanguage{english}B\selectlanguage{greek}α, \selectlanguage{english}anti-Erk, anti-phospho-Erk, anti-STAT3, anti-phospho-STAT3, anti-Akt, anti-phospho-Akt were purchased from Cell Signaling Technology (Danvers, MA). The antibody specific for thrombin, PAR-1, and CD31 were from Santa Cruz (Santa Cruz Biotechnology, Santa Cruz, CA). The anti-MMP9, anti-IL6 and anti-GAPDH were from Proteintech (Proteintech Group, Chicago, IL). The kit for monitoring the activation of RhoA was obtained from Cytoskeleton (Denver, CO). r-hirudin and DTIP were obtained from our group, and expression and purification of r-hirudin and DTIP has been described previously (Mo, Zhang, Chen, Wang \& Song, 2009; Zhao et al., 2017). \textbf{Patients and tissues} All experiments using human tissues were performed in accordance with the Declaration of Helsinki and approved by the Institutional Review Board of Fudan University. The clinical samples of lung cancer patients were obtained from Fudan University Shanghai Cancer Center (Shanghai, China). The tissues consisted of samples from 132 patients with NSCLC, including 100 cases of adenocarcinoma (ADC), 23 cases of squamous cell carcinoma (SCC), and 9 cases of other types of NSCLC at different stages. On each tissue, healthy lung tissues were also included. \textbf{Wound healing assay} Wound healing was analysed using IBIDI Culture-Inserts (IBIDI GmbH, Martinsried, Germany). Cells were dissociated from plates using 0.05\% (w/v) trypsin and seeded into culture-insert plates at a concentration of 2 \selectlanguage{ngerman}× 10\textsuperscript{4} cells per culture well. After 24 hours of incubation, culture inserts were removed. Photographs of the movement of cells into the scratch area were taken after 24 h using a light microscope. \textbf{Cell migration} Cell migration was measured using transwell inserts (Corning Life Sciences, Tewksbury, MA) according to manufacturer's instructions. Briefly, transwell chambers (8 mm pore size) were coated with 50 \selectlanguage{greek}μ\selectlanguage{english}L of diluted matrigel. Cells suspended in serum-free medium at a density of 1.5\selectlanguage{ngerman}×10\textsuperscript{5} cells/mL were seeded (0.1 ml) in the upper chambers and 0.5 mL medium containing 10\% FBS was added to the lower chambers, and PBS, 10 nmol/L thrombin, 25 nmol/L r-hirudin, 50 nmol/L DTIP, 10 nmol/L thrombin + 25 nmol/L r-hirudin and 10 nmol/L thrombin + 50 nmol/L DTIP were added to both of the upper and lower chambers. After culturing for 24 hours, cells were \selectlanguage{english}fixed in methanol and stained with 0.1\% crystal violet. The cells on the bottom of the filters were counted. \textbf{F-actin staining assay and confocal microscopy} Cells were grown on 35-mm glass-bottom dishes and fixed with 4\% paraformaldehyde for 15 minutes and then permeabilized with 0.5\% Triton X-100 in PBS for 10 minutes. The cells were then blocked with 1\% BSA for 20 minutes. Cells were incubated with YF-488 phalloidin (US Everbright\textsuperscript{(r)}Inc) for 30 minutes and then stained with DAPI for 5 minutes. The cells were observed under a confocal microscope. \textbf{Measuring RhoA activation} Determination of RhoA activations (RhoA-GTP) was monitored using commercially available kits. Briefly, cells were lysed using a cell lysis buffer provided by the manufacturer. Half of the lysates were saved for Western blotting quantitation of total RhoA. The remaining sample was incubated with 20 \selectlanguage{greek}µ\selectlanguage{english}g GST fusion protein RBD (rhotekin Rho-binding domain), at 4 \selectlanguage{ngerman}\textsuperscript{°}C with rotation for 1 h, which is bound to the colored glutathione-sepharose beads. The RBD protein motif binds specifically to the active GTP-bound form of RhoA. Beads were washed, resuspended in loading buffer and proteins were separated on 12\% SDS-PAGE followed by transferring to a PVDF membrane and Western blotting using an anti-RhoA monoclonal antibody as described by the manufacturer. \textbf{Tube formation assay} Ninety-six-well plates were precoated with 50 \selectlanguage{greek}μ\selectlanguage{english}L liquid Matrigel per well. After incubation at 37\selectlanguage{ngerman}\textsuperscript{°}C for 1 hour, HUVESs (1.5 × 10\textsuperscript{4} cells/well), suspended in DMEM medium with PBS, 10 nmol/L thrombin, 25 nmol/L r-hirudin, 50 nmol/L DTIP, 10 nmol/L thrombin + 25 nmol/L r-hirudin and 10 nmol/L thrombin + 50 nmol/L DTIP and were seeded and cultured for 8 hours. Five randomly chosen fields were photographed and counted. \textbf{gRNA design and lentivirus infection} CRSIPR guides targeting \emph{Thrombin} and \emph{PAR-1} of human and mouse sequences were generated and cloned into LentiCRISPRv2 at BsmBI restriction sites. LentiCRISPRv2 and packing constructs were transfected into 293T cells. Virus supernatants were collected 48 h after transfection. A549 and LLC cells were infected with viral supernatants in the presence of polybrene and were then selected in growth media containing puromycin. All the cell lines used have been tested and authenticated by karyotyping. Transfection with the empty plasmid was performed which was used as negative control (NC). A549\emph{\textsuperscript{THR-/-}} , LLC\emph{\textsuperscript{Thr-/-}} , A549\emph{\textsuperscript{PAR-1-/-}} and LLC\emph{\textsuperscript{Par-1-/-}} cell lines were checked by PCR and sequencing. \textbf{Scoring ofimmunostained specimens} Immunostained specimens were reviewed by 2 investigators blinded to the patients' clinical status using a multihead microscope. To evaluate expression of proteins using immunohistochemistry, the intensity of proteins staining was graded by consensus on a scale from 0 to 3 (0 = negative staining; 1 = weakly positive; 2 = moderately positive; 3 = strongly positive). The frequency of positive cells was graded by consensus on a scale from 0 to 4 (0 = less than 1\%; 1 = 1\% to 10\%; 2 = 10\% to 50\%; 3 = 50\% to 80\%, 4 = greater than 80\%). The immunohistochemical scores (HIS) were determined by staining intensity and positive cells. Based on the score of thrombin or PAR-1 in the central positive staining area in tumor section as a cutoff value, the score of thrombin or PAR-1 was classified positive (thrombin+ \textgreater{}2, and PAR-1 high expression \textgreater{}6) and negative (thrombin- \selectlanguage{english}[?]2, and PAR-1 low expression \selectlanguage{english}[?]6). \textbf{Tail vein injections} This animal study was conducted in accordance with the rules and regulations of the IACUC at the Department of Laboratory Animal Science, Fudan University (Shanghai, P.R. China). Lewis lung carcinoma (LLC) cells were collected and resuspended in serum-free medium. C57/BL6 mice were injected through the tail vein with 1x10\textsuperscript{6}cells in 0.1 mL. Fourteen days after injection of cells, the mice were subjected to PET scanning. Mice were euthanized by pentobarbital sodium, and all lungs were dissected or further imaged by fluorescence stereomicroscopy and then were \selectlanguage{english}fixed in Bouin's solution, and the number of metastatic nodules on the lung surface was counted. \textbf{Subcutaneousinoculation of tumors in mice} This animal study was conducted in accordance with the rules and regulations of the IACUC at the Department of Laboratory Animal Science, Fudan University (Shanghai, P.R. China). Tumor cells at a density of 1x10\textsuperscript{6}in 0.1mL serum-free media were injected subcutaneously into the right \selectlanguage{english}flank of mice. The mice were monitored daily for the development of visible tumors. Once a tumor was clearly visible, it was calipered three times each week, and the volume was estimated using the formula V = (LW\textsuperscript{2})/2 where V is volume, L is longest diameter, and W is shortest diameter. Mice were euthanized by pentobarbital sodium, and the tumors were removed, some were \selectlanguage{english}fixed in 4\% paraformaldehyde, and the other tumors were lysed for Western blotting. \textbf{Orthotopic lung cancer model in mice} Mice were anesthetized with chloral hydrate (300 mg/kg) via intraperitoneal injection and placed in the right lateral decubitus position. A total of 1 x 10\textsuperscript{6} cells in 50 \selectlanguage{greek}µ\selectlanguage{english}L RPMI-1640 medium and 50 \selectlanguage{greek}µ\selectlanguage{english}L Matrigel were injected into the left lung parenchyma through the left rib cage. Mice were monitored daily. Mice were euthanized by pentobarbital sodium, and the lung tissues were removed. \textbf{Statistical Analysis} All data are expressed as mean \selectlanguage{ngerman}± SD. Unless otherwise stated, differences between the 2 groups were analyzed by unpaired t test when variances are equal, and 1-way analysis of variance followed by Newman-Keuls test were used for multiple comparisons with Prism 6 (GraphPad Inc). P\textless{}0.05 was considered to be statistically significant. \textbf{Results} \textbf{The expression of thrombin in lung cancer is closely related toclinicopathological features and the prognosis of patients.} Thrombin has also been shown to contribute to tumor progression. However, the expression of thrombin in NSCLC tissues and the relationship between thrombin expression and clinicopathological features and the prognosis of NSCLC patients have not been reported. To confirm the presence of thrombin (prothrombin) in NSCLC, 132 patients with a pathologically confirmed diagnosis of NSCLC were analyzed. We found the expression of thrombin was significantly increased in tumors of all different types of NSCLC tissues compared with their adjacent non-tumor lung tissues (Fig. 1A-C). There was no significant difference in different subtypes of NSCLC (Fig. 1C). To further evaluate the prognostic value of thrombin for NSCLC patients, univariate and multivariate analyses were performed with the clinicopathological characteristic. As shown in Table 1, thrombin expression in tumor tissue was significantly correlated with TNM stage of NSCLC. The 5-year overall survival (OS) rates of thrombin-positive patients were significantly lower than those of thrombin-negative patients (Fig. 1D). Moreover, both the mRNA and protein levels were significantly increased in comparison to normal lung cell line (BEAS-2B) detected by Q-PCR (Fig. 1E) and western blot (Fig. 1F) in three NSCLC cell lines. \textbf{Thrombin plays an important role in the progression of lung cancer.} To observe the role of thrombin in lung cancer cells, we constructed A549\emph{\textsuperscript{THR-/-}} and LLC\emph{\textsuperscript{Thr-/-}} cells. Transwell assay results showed that thrombin depletion inhibited cell migration in A549 and Lewis cells (Fig. 2A-D). IL6 has been demonstrated to be involved in the development, progression and metastasis in several cancers (Huang et al., 2018). Matrix metalloproteinases (MMPs) affects the physical barrier of the tumor microenvironment (TME) and induces metastasis (Lyu, Xiao, Yin, Yang \& He, 2019). We found that the expression levels of MMP9 and IL6 were decreased in thrombin deficient cells, and the expression of MMP9 and IL6 could be restored by adding exogenous thrombin (supplementary Fig. S1). To assess the role of thrombin in vivo, we employed tumor models. In subcutaneous transplanted tumor model, tumor growth inhibition was observed in thrombin deficient group (Fig. 2E-G). In addition, the lung metastases were reduced in thrombin deficient group (Fig. 2H-I). In orthotopic lung tumor model, thrombin deficiency could markedly increase the survival time of mice (Fig. 2J). And the control LLC cells generated massive lung tumor burden in mice. Significantly, the depletion of thrombin led to smaller lung tumor burden (Figure 2K). HE staining of lung sections also revealed bigger tumor area in control mice as compared to the thrombin deficient group (Figure 2L). Thrombin deficiency also inhibited liver metastasis in mice. Together with the in vitro experiments, we concluded that thrombin plays an important role in the progression of lung cancer. \textbf{r-hirudin and DTIP inhibitthrombin-promotedcell migration, invasion and angiogenesis.} To further explore the role of thrombin in the lung cancer, we used exogenous thrombin to treat NSCLC cell lines in vitro. DTIP and r-hirudin which are direct thrombin inhibitors, were developed by our group. A549, Lewis (Fig. 3A) and 95D cells (supplementary Fig. S2A) incubated with 10 nmol/L thrombin displayed a remarkable promotion in the ability to migrate into the blank space compared with the normal control (NC) group. However, r-hirudin and DTIP blocked thrombin-enhanced wound-closure capability of NSCNC cells. Transwell assay results showed that thrombin-driven migration was inhibited by pre-treatment with r-hirudin and DTIP in A549, Lewis (Fig. 3B) and 95D cells (supplementary Fig. S2B). Rho GTPases are well known as regulators of actin cytoskeletal organization and cell motility. Therefore, we examined the effect of r-hirudin and DTIP on the activation of RhoA and the status of actin filament organization. Our findings indicated that r-hirudin and DTIP could suppress the activation of RhoA in thrombin-stimulated A549 cells (Fig. 3C). As illustrated in Fig. 3D, thrombin significantly enhanced the fluorescence intensity of polymerized actin (F-actin) compared with the NS groups. However, r-hirudin and DTIP could decrease the fluorescence intensity in thrombin-stimulated cells. The appearance of membrane ruffles and the formation of lamellipodia were also decreased in r-hirudin- and DTIP-treated cells. (Fig. 3E, 3F and supplementary Fig. S2C). These data demonstrated that r-hirudin and DTIP decreased the amount of F-actin and the formation of lamellipodia in thrombin-stimulated NSCLC cells, which consequently leads to decreased cell motility and migration ability. In previous studies, we found thrombin deficiency could reduce the expression of MMP9 and IL6. Furthermore, the expression of MMP9 and IL6 also could be increased by exogenous thrombin, which could be inhibited by r-hirudin and DTIP (Fig. 3G and supplementary Fig. S3E-G). RhoA could be activated by thrombin (Fig. 3C). CCG, an inhibitor of RhoA, could inhibit thrombin-induced expression of MMP9 and IL6. LPA, an activator of RhoA, could prevent the inhibition induced by r-hirudin and DTIP (Fig. 3G and supplementary Fig. S3E-G). Thrombin has been reported to activate NF-\selectlanguage{greek}κ\selectlanguage{english}B signaling in human pleural mesothelial. The effect of r-hirudin and DTIP on the NF-\selectlanguage{greek}κ\selectlanguage{english}B pathway in thrombin-stimulated NSCLC cells was analyzed. The results indicated that thrombin could activate NF-\selectlanguage{greek}κ\selectlanguage{english}B signaling in NSCLC cells. Compared with the thrombin-treated group, r-hirudin and DTIP exhibited diminished I\selectlanguage{greek}κ\selectlanguage{english}B\selectlanguage{greek}α \selectlanguage{english}and p65 phosphorylation, suggesting that r-hirudin and DTIP can inhibit thrombin-induced NF-\selectlanguage{greek}κ\selectlanguage{english}B activation. CCG could inhibit the thrombin-induced NF-\selectlanguage{greek}κ\selectlanguage{english}B activation, while RhoA or NF-\selectlanguage{greek}κ\selectlanguage{english}B activatiors (LPA and LPS) could prevent the inhibition induced by r-hirudin and DTIP (supplementary Fig. S3A-D). The results indicated that thrombin could activate NF-\selectlanguage{greek}κ\selectlanguage{english}B signaling via RhoA in NSCLC cells. Studies have shown that NF-\selectlanguage{greek}κ\selectlanguage{english}B pathway activation upregulates the expression of cell adhesion molecules and inflammatory cytokines. We also found RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B inhibitor could inhibit thrombin-induced expression of MMP9 and IL6, RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B activator could prevent the inhibition induced by r-hirudin and DTIP (Fig. 3G and supplementary Fig. S3E-G), suggesting that thrombin can regulate the expression of MMP9 and IL6 via RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B pathway. Thrombin is known to promote the release VEGF and induce angiogenesis. Hence, we examined the effects of r-hirudin and DTIP on angiogenesis using a tube formation assay. After thrombin treatment, the tubule formation was promoted, r-hirudin and DTIP significantly inhibit thrombin-induced tube formation (Fig. 3H). These results demonstrated that r-hirudin and DTIP possessed an anti-angiogenic potential. \textbf{r-hirudin and DTIP exert anti-invasive andanti-metastatic abilities in a mouse lung cancer model.} Our aforementioned results suggest anti-metastatic and anti-angiogenic activity of r-hirudin and DTIP in vitro. We further confirmed the effects in vivo. In orthotopic lung tumor model, DTIP could improve the survival time of mice compared with the control group, (Fig. 4A), and mice in r-hirudin or DTIP-treated groups had smaller tumor burden (Fig. 4B), had fewer mice with liver metastases (Fig. 4C). Murine models of experimental metastasis have been used frequently to investigate the effects of anti-haemostatic agents on cancer metastasis. Although such artificial models do not encompass the entire metastatic process, they remain useful for `proof-of-concept'-experiments, focusing on the haematogenous phase of tumor dissemination (Mammadova-Bach et al., 2020; Sjoberg et al., 2019; Vuong et al., 2019). Gross examination of the lungs harvested from r-hirudin- or DTIP-treated mice revealed a median of 21 (n=12) or 20 (n=12) surface pulmonary metastases per animal. In contrast, the lungs harvested from normal saline treated mice (n=16) had confluent metastases that were too numerous to count and were clearly enlarged (Fig. 4D, 4E). Micro-PET scan and histologic analyses revealed scattered small foci of tumor tissue within the lungs harvested from r-hirudin- or DTIP-treated mice, while the lungs harvested from normal saline-treated mice were nearly completely effaced by tumor tissue (Fig. 4F, 4G). We found the number of mice with tumor cells colonized in the liver was largely reduced in the r-hiruin and DTIP group compared with the normal saline group (Fig. 4I, 4J). It is important to note 78\% of control mice (n=9) were dead at 24 days, with all dead at 32 days, whereas 25\% of r-hirudin-treated mice (n=12) and 30\% of DTIP-treated mice (n=10) were dead at 24 days (Fig. 4H). We also examined spontaneous metastasis through subcutaneous inoculation of tumor cells in mice, which involves a more comprehensive process. Treatment of r-hirudin and DTIP for one week inhibited tumor growth slightly (Fig. 5A, 5B). Six of the 9 tumors analyzed from normal saline-treated mice showed signs of panniculus invasion, whereas only 2 of 9 tumors from r-hirudin-treated mice and 2 of 10 tumors from DTIP-treated mice had any noticeable signs of panniculus invasion (Fig. 5C, 5D). And we also administered 1.0 mg/kg DTIP or 0.5 mg/kg r-hirudin for 21 consecutive days after one week of the injection of LLC cells. r-hirudin and DTIP significantly inhibited tumor growth (Fig. 5E-G). The number of mice with lung and liver metastases was largely reduced in r-hirudin or DTIP treated groups (Fig. 5H-K). Tumor angiogenesis was assessed using IHC analysis for CD31. The r-hirudin or DTIP treated groups showed a significant reduction of CD31-positive microvessels versus controls (Fig. 5L). We performed immunohistochemical analysis on tumor samples to determine the expression levels of MMP9 and IL6. There is decreased expression of MMP9 and IL6 after treatment with r-hirudin and DTIP compared with normal saline-treated mice (Fig. 5M). We also examined phosphorylation levels of p65 and the key downstream signaling molecules intratumorally. We observed a marked inhibition of phospho-p65, phospho-Erk, phospho-STAT3, and phospho-Akt levels in the r-hirudin- and DTIP-treated groups (Fig. 5N). Furthermore, we did not find increased bleeding after administration of DTIP, slight subcutaneous hemorrhage was observed after r-hirudin administration for three weeks continuously (data are not shown). These results show that DTIP, a direct thrombin inhibitor, could be extended to anti-cancer therapy. \textbf{PAR-1 is a major determinant in thrombin-promotedmetastatic of lung cancer.} Thrombin is the main activator of PAR-1 (Vu, Hung, Wheaton \& Coughlin, 1991). Overexpression of PAR-1 has been detected in various types of cancers, including ovarian (Grisaru-Granovsky, Salah, Maoz, Pruss, Beller \& Bar-Shavit, 2005), breast cancer (Boire, Covic, Agarwal, Jacques, Sherifl \& Kuliopulos, 2005), lung cancer, prostate cancer (Black et al., 2007), and melanoma. Our previous experimental results also showed PAR-1 was highly expressed in human and mouse tumors compared with normal lung tissues (supplementary Fig. S4). However, we did not find an obvious relationship between the PAR-1 expression levels of tumors and clinical variables, such as the stage of NSCLC differentiation status and disease progression (supplementary Table 1). To observe the role of PAR-1 in thrombin-mediated invasion and metastasis more clearly, we constructed A549\emph{\textsuperscript{PAR-1-/-}} and LLC\emph{\textsuperscript{Par-1-/-}} cells. PAR-1 depletion almost completely abrogated thrombin-promoted cell migration, and the effect of r-hirudin and DTIP on thrombin-induced migration and invasion was abolished (Fig. 6A-D). PAR-1 is a G protein coupled receptor and has been shown to induce cellular invasion through RhoA-dependent signaling. After depleting PAR-1, the activation of RhoA was inhibited and the ability of thrombin to activate RhoA was also inhibited (Fig. 6E). Similar responses were also observed via immunofluorescence staining of F-actin, as PAR-1 depletion decreased the formation of membrane ruffles (Fig. 6F). These data suggest thrombin-enhanced cell motility and migration can be completely abrogated by PAR-1 depletion in vitro. PAR-1 deficiency exhibited diminished I\selectlanguage{greek}κ\selectlanguage{english}B\selectlanguage{greek}α \selectlanguage{english}phosphorylation and p65 phosphorylation (supplementary Fig. S5A). Importantly, thrombin-driven NF-\selectlanguage{greek}κ\selectlanguage{english}B activation were inhibited by pre-treatment with the specific PAR-1 inhibitor ML161 (supplementary Fig. S5A). LPA or LPS could rescue the activation of NF-\selectlanguage{greek}κ\selectlanguage{english}B, but thrombin could not. r-hirudin and DTIP could not inhibit NF-\selectlanguage{greek}κ\selectlanguage{english}B activation induced by LPA or LPS (supplementary Fig. S5B,5C), suggesting r-hirudin and DTIP inhibit thrombin-induced RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B activation via PAR-1 signaling. We also found PAR-1 deficiency exhibited deceased expression of MMP9 and IL6. Besides thrombin, LPA or LPS could increase MMP9 and IL6 expression in PAR-1 deficient cells. r-hirudin and DTIP could not inhibit MMP9 and IL6 expression induced by LPA or LPS (supplementary Fig. S6), suggesting r-hirudin and DTIP inhibit thrombin-induced MMP9 and IL6 expression through RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B activation via PAR-1 signaling. To further analyze the effects of PAR-1 on lung cancer growth and metastasis, we established lung cancer model in mice using LLC cells infected by gRNA-PAR-1 lentivirus (\emph{Par-1\textsuperscript{-/-}} group) or LV-negative control (NC, vehicle group). In orthotopic lung tumor model, PAR-1 deficiency could markedly increase the survival rate and inhibit tumor growth in lung (Fig. 6G-I). In the metastatic colonization model, our results confirmed PAR-1 deficient lung cancer cells lead to less lung metastatic nodes than control cells (supplementary Fig. S7A, 7B), as well as significantly decreased signal intensity in the lungs, as seen on micro-PET scans (supplementary Fig. S7C). In addition, PAR-1 deficiency could markedly increase the survival rate (supplementary Fig. S7D). In subcutaneous tumors, PAR-1 deficient group were significantly smaller than control group (Fig. 6J, 6K). The lung metastases and liver metastases were both largely reduced in PAR-1 deficient group (supplementary Fig. S7E). In addition, based on the results of CD31 staining, we confirmed that CD31-positive microvessels decreased in the PAR-1 deficient tumors (Fig. 6L). We also found the levels of phospho-p65, phospho-Erk, phospho-STAT3, and phospho-Akt were reduced in PAR-1 deficient tumors (supplementary Fig. S7F). Together with the in vitro experiments, we concluded that PAR-1 plays an important role in the thrombin-induced progression of lung cancer. \textbf{DTIP potentiateschemotherapy-induced growth and metastasis inhibition and inhibits chemotherapeutic drug tolerance of NSCLC in mice.} Chemotherapy has been commonly prescribed in the treatment of patients with NSCLC, however, its benefits are limited due to a low response rate or acquired tumor resistance. Arnold et. al have shown that PAR-1 in the tumor induces the chemo-resistance of cancer (Queiroz et al., 2014). Meanwhile, chemotherapy such as gemcitabine, cisplatin, and paclitaxel are associated with a significant increase in the risk of arterial thromboembolic events (Zaborowska-Szmit, Krzakowski, Kowalski \& Szmit, 2020). we hypothesized that DTIP could potentiate chemotherapy-induced inhibition of tumor progression. When combination DTIP and gemcitabine, the tumor volume and tumor weight in the combination treatment group was significantly smaller than that in the groups administered DTIP alone or gemcitabine alone (Fig. 7A-C). The number of mice with lung metastases was largely reduced in the combination treatment group (Fig. 7D, 7E). We also counted the survival rates of mice in different groups. It is important to note 85\% of control mice (n=7) were dead at 60 days, 57\% of r-hirudin-treated mice (n=7) and 50\% of gemcitabine -treated mice (n=8) were dead at 60 days, whereas, 16\% combination -treated mice (n=6) were dead at 60 days (Fig. 7F). Paclitaxel could not significantly inhibit the growth of LLC in vivo. However, when combined with DTIP, the growth (Fig. 7G-I) and metastasis (Fig. 7J, 7K) of LLC were significantly inhibited. Combination of DTIP and cisplatin had a smaller tumor volume (supplementary Fig. S8A-C), but there was no significant difference in metastasis and survival time of mice compared with the group administered cisplatin alone (supplementary Fig. S8D, 8E). In addition, we evaluated the chemotherapy effects in thrombin deficient NSCLC mouse models. We found gemcitabine or paclitaxel treated mice in thrombin deficient group had smaller tumors (supplementary Fig. S9A, 9C) and longer survival time (supplementary Fig. S9B, 9D) compared with control group treated with gemcitabine or paclitaxel. These results indicated that combination therapy of DTIP and chemotherapy might achieve a better therapeutic effect. \textbf{Discussion} Metastasis has been recognized as the main cause of fatal outcomes in lung cancer patients. It is of interest that low-grade intravascular coagulation has been observed in most patients with solid tumors (Rickles, Edwards, Barb \& Cronlund, 1983). Malignant tumors often exhibit hypercoagulability, which is correlated with high levels of activated thrombin (Caine, Stonelake, Lip \& Kehoe, 2002). Studies have shown that exogenous thrombin is capable of enhancing tumor adhesion to platelets (Nierodzik, Kajumo \& Karpatkin, 1992), endothelial cells (Klepfish, Greco \& Karpatkin, 1993), and fibronectin (Chen et al., 2014) in vitro, and revealed that exogenous thrombin promotes tumor growth (Nierodzik et al., 1998). In this study we demonstrated that thrombin expression in tumor tissues was significantly correlated with metastatic potential of NSCLC, postoperative tumor recurrence, and poor prognosis of NSCLC patients. This finding is supported by the fact that a high thrombin expression was significantly associated with the aggressive histopathological characteristics of NSCLC, such as high TNM stage. Thrombin deficiency impairs tumor progression. This indicates that thrombin may serve as an independent predictor for tumor recurrence and prognosis of NSCLC patients, which might be an explanation as to why malignant tumors often exhibit hypercoagulability. To further explore the role of thrombin in the lung cancer, we used exogenous thrombin to treat NSCLC cell lines in vitro. we found that 10 nmol/L thrombin can promote NSCLC cell invasion, angiogenesis, and metastasis in vitro. r-hirudin and DTIP are new bivalent direct thrombin inhibitors that could effectively prevent the formation of thrombosis and embolism (Mo, Zhang, Chen, Wang \& Song, 2009; Zhao et al., 2017). These results showed that r-hirudin and DTIP could inhibit thrombin-induced cell invasion, angiogenesis, and metastasis in vitro. r-hirudin and DTIP inhibit progression, dissemination and spontaneous metastasis in NSCLC mice models, thus prolonging the survival time of mice in lung cancer models. Furthermore, in our studies, we did not find increased bleeding after administration of DTIP, slight subcutaneous hemorrhage was observed after r-hirudin administration for three weeks continuously. These results show that DTIP could be extended to anti-cancer therapy. The cleavage of the thrombin-receptor PAR-1 by thrombin exposes a new N terminus that binds to the receptor to induce trans-membrane signaling (McLaughlin, Shen, Holinstat, Brooks, Dibenedetto \& Hamm, 2005). PAR-1 overexpression has been reported in malignant invasive tumor cell lines (Black et al., 2007; Queiroz et al., 2014). Our data suggested that PAR-1 is highly expressed in human NSCLC tissues, but showed no difference based on subtype and clinical stage. To further explore the role of thrombin in the PAR-1-mediated NSCLC metastasis, we used exogenous thrombin to treat PAR-1 deficient NSCLC cells in vitro, and found that the invasion and metastasis of PAR-1 deficient cell lines was inhibited in vitro and in vivo; thrombin had no effect on their invasive and metastatic. In our study, we showed that thrombin promotes the activation of RhoA through the activation of PAR-1, thereby inducing cytoskeletal rearrangements, actin stress fiber formation, and activation of NF-\selectlanguage{greek}κ\selectlanguage{english}B. Activation of cytosolic NF-\selectlanguage{greek}κ\selectlanguage{english}B leads to expression of MMP9 and inflammatory marker IL6. r-hirudin and DTIP can bind to thrombin specifically and block the thrombin binding to PAR1, thereby inhibiting RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B activation and reducing the expression of MMP9 and IL6 in NSCLC cells, which would be hugely beneficial for suppressing metastasis. Chemotherapy used in NSCLC seem to cause primarily vascular complications, including venous or arterial thromboembolic events. In a nonrandomized study, the addition of low-molecular-weight heparin (LMWH) to standard gemcitabine/cisplatinum chemotherapy significantly improved survival in patients with locally advanced or metastatic pancreatic carcinoma (Icli et al., 2007). The total response rate for patients treated with LMWH was almost 60\%, compared with only 12\% for patients treated with chemotherapy only. In our studies, we found combination therapy of DTIP and chemotherapy results in improved anti-tumor efficacy, and DTIP could potentiate gemcitabine-induced inhibition of lung cancer and inhibit paclitaxel resistance in mice. This approach merits further evaluation in more extensive studies and in NSCLC patients. \textbf{Conclusions} In this study, we not only provide convincing evidence that thrombin plays a crucial role in NSCLC, but also an explanation as to why intravascular coagulation with generation of thrombosis has been observed in most patients with solid tumors. We conclude that thrombin plays an important role in PAR-1-mediated NSCLC invasion and metastasis through RhoA and NF-\selectlanguage{greek}κ\selectlanguage{english}B signaling cascades via promoting the expression of MMP9 and IL6. We conclude that the highly specific, potent, thrombin inhibitor DTIP inhibit tumor spontaneous seeding of the tumor systemically into the vital organs, tumor metastasis in NSCLC. We suggest treatment with DTIP should start immediately after diagnosis (before extensive tumor development) and in conjunction with chemotherapy. \textbf{Acknowledgement} This study was supported by the National Natural Science Foundation of China (NSFC 81902995 and NSFC 81673498) and the Science and Technology Commission of Shanghai Municipality (STCSM 16431904600) and the Project funded by China Postdoctoral Science Foundation (2018M641936). The authors would like to thank the Duoease Scientific Service Center for excellent language editing service and suggestions for figure revision. Conflict of Interest Disclosures None of the authors has a relevant conflict of interest. Contributions ZB, WM, and ZY performed all of the experiments; WT, YJ, MY, WQ, CD, LT and LY participated in the research; ZB and MW designed experiments, analyzed data, and wrote the paper; YM is the supervisor of ZB; HZ and WH collected the clinical samples. All authors read and approved the final manuscript. References Battinelli EM, Markens BA, Kulenthirarajan RA, Machlus KR, Flaumenhaft R, \& Italiano JE (2014). Anticoagulation inhibits tumor cell-mediated release of platelet angiogenic proteins and diminishes platelet angiogenic response. Blood 123\textbf{:} 101-112. Black PC, Mize GJ, Karlin P, Greenberg DL, Hawley SJ, True LD\emph{, et al.} (2007). Overexpression of protease-activated receptors-1,-2, and-4 (PAR-1, -2, and -4) in prostate cancer. 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Yokoyama Y, Mori S, \& Matsuura N (2008). Effect of Platelet Derived Growth Factor on Development and Progression of Breast Cancer. Tumor Biol 29\textbf{:} 77-77. Yuan M, Huang L-L, Chen J-H, Wu J, \& Xu Q (2019). The emerging treatment landscape of targeted therapy in non-small-cell lung cancer. Signal Transduction and Targeted Therapy 4. Zaborowska-Szmit M, Krzakowski M, Kowalski DM, \& Szmit S (2020). Cardiovascular Complications of Systemic Therapy in Non-Small-Cell Lung Cancer. J Clin Med 9. Zhao B, Zhang Y, Huang Y, Yu J, Li Y, Wang Q\emph{, et al.} (2017). A novel hirudin derivative inhibiting thrombin without bleeding for subcutaneous injection. Thromb Haemost 117\textbf{:} 44-56. \textbf{Table 1. Association of thrombin expression with the clinicopathologic characteristics of 132 NSCLC patients} \textbf{Figure 1 The expression of thrombin in lung cancer is closely related to clinicopathological features and the prognosis of patients.}(\textbf{a-c)} Thrombin expression in NSCLC patients. \textbf{(a)}Paraffin sections obtained from patients with resectable NSCLC tissues were stained for thrombin. (\textbf{b)} Score of thrombin expression in adjacent non-tumor lung tissue and in NSCLCs. (\textbf{c)} Thrombin expression in different types of NSCLC. (\textbf{d)} The overall survival rates of thrombin-positive patients and thrombin-negative patients. (\textbf{e)}The mRNA level of thrombin in BEAS-2B, A549, 95D, and PC9 was determined by Q-PCR. (\textbf{f)} The expression of thrombin in BEAS-2B, A549, 95D, and PC9 was determined by western blotting analysis. Right, Summary data of western blotting were given. All the results were expressed as mean \selectlanguage{ngerman}±\selectlanguage{english} SD. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001, NS, not significant. \textbf{Figure 2Thrombin plays an important role in the progression of lung cancer.} (\textbf{a)} Western blot depicting depletion of thrombin in A549 cells transfected with human thrombin gRNA compared with negative control. (\textbf{b)} Representative pictures of A549 cells migrated through the transwell are shown, Right, quantitative analysis of invasive cells. (\textbf{c)} Western blot depicting depletion of thrombin in Lewis cells transfected with mouse thrombin gRNA compared with negative control. (\textbf{d)} Representative pictures of Lewis cells migrated through the transwell are shown, Right, quantitative analysis of invasive cells. (\textbf{e-i)}Thrombin deficient LLC cells and control cells were injected subcutaneously into the right \selectlanguage{english}flank of mice. (\textbf{e)} Serial calipation of tumor volume after transplantation cells into mice. \textbf{(f)} Mice were humanely euthanized, and the tumors were resected 35 days after cell injection.\textbf{(g)} The weight of resected tumors was determined. (\textbf{h)}H\&E stained sections of lung tissue. (\textbf{i)} The number of metastatic nodes per lung was determined. \textbf{(j-l)} In orthotopic lung tumor model, 1 x 10\textsuperscript{6} cells in 50 \selectlanguage{greek}µ\selectlanguage{english}L RPMI-1640 medium and 50 \selectlanguage{greek}µ\selectlanguage{english}L Matrigel were injected into the left lung parenchyma through the left rib cage. (\textbf{j)}Survival rate of mice in different groups. (\textbf{k)} Representative photograph of lungs bearing tumors (left); Gross appearance of representative lung harvested viewed under a fluorescence stereoscope (middle); H\&E stained sections of lung tissue (right). (\textbf{l)} Average tumor area in the lungs was measured. \textbf{(m)}Number of mice with tumor cells in liver. All the results were expressed as mean \selectlanguage{ngerman}±\selectlanguage{english} SD. ANOVA followed by Dunnett's test was applied for multiple comparison. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001, NS, not significant. \textbf{Figure 3 r-hirudin and DTIP inhibit thrombin-promoted cell migration, invasion and angiogenesis in vitro.} (\textbf{a)}A549 and Lewis cells were pretreated with PBS, 10 nmol/L thrombin, 25 nmol/L r-hirudin, 50 nmol/L DTIP, 10 nmol/L thrombin + 25 nmol/L r-hirudin, 10 nmol/L thrombin + 50 nmol/L DTIP for 24 hours. The migration of r-hirudin and DTIP treated A549 and Lewis cells were assessed using wound healing assay. Right, quantitative analysis of wound area. (\textbf{b)} Transwell assay was performed to assess cell migration of A549 and Lewis cells. Right, quantitative analysis of invasive cells. (\textbf{c)} Endogenous GTP-bound form of RhoA was enriched by a pull-down assay and detected by Western blotting. Total RhoA was detected using anti-RhoA antibody. Bottom, summary data of western blotting were given. (\textbf{d)}Representative images of each group stained with phalloidin in A549 cells. (\textbf{e)}Quantification of the F-actin fluorescence intensity. (\textbf{f)}Percentages of ruffle-positive cells in different groups were calculated based on the immunofluorescence. (\textbf{g)} Expression of IL6 and MMP9 in different groups. (\textbf{h)} Effect of r-hirudin and DTIP against HUVEC tube formation on Matrigel. Left, representative photographs of five independent experiments were shown. Right, quantification of the inhibition activity of aspirin on tube formation. All the results were expressed as mean\selectlanguage{english} +-\selectlanguage{english} SD. ANOVA followed by Dunnett's test was applied for multiple comparison. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001, NS, not significant. \textbf{Figure 4 r-hirudin and DTIP exert the ability of Anti-growth and anti-metastasis in orthotopic lung tumor model and lung cancer metastasis model.(a-c)}In orthotopic lung tumor model, 1 x 10\textsuperscript{6} cells were injected into the left lung through the left rib cage, and 1.0 mg/kg DTIP or 0.5 mg/kg r-hirudin was administered for 7 consecutive days after 3 days of the injection of LLC cells. (\textbf{a)}Survival of mice treated with saline, r-hirudin and DTIP after injection of LLC cells into the left lung. (\textbf{b)}Representative photograph of lungs (left); Gross appearance of representative lung harvested viewed under a fluorescence stereoscope (middle); H\&E stained sections of lung tissue (right). (\textbf{c)} Number of NS, r-hirudin, and DTIP treated mice with liver metastasis. \textbf{(d-j)}Tail-vein injection of 1x10\textsuperscript{6} LLC cells was performed in mice. The LLC were engineered to express red fluorescent protein to simplify detection of tumor foci in vivo. Mice that were injected with LLC were immediately treated with saline, 1.0 mg/kg DTIP or 0.5 mg/kg r-hirudin once a day for one week. We randomly divided the mice into two groups, one was sacrificed on the 14th day to observe the metastasis of tumors, and the other group was used to analyze the survival rate of mice. (\textbf{d)}Effect of r-hirudin and DTIP on the formation of metastatic nodes on day 14. Representative photograph of metastatic nodules on lungs (upper). Gross appearance of representative lung harvested from different groups viewed under a fluorescence stereoscope (bottom). (\textbf{e)}The number of metastatic nodes per lung was determined in different groups. (\textbf{f)} Representative micro-PET images of mice 14 days after injection. (\textbf{g)}H\&E stained sections of lung tissue. (\textbf{h)}Survival of mice treated with saline, r-hirudin and DTIP after injection of LLC cells via tail-vein. (\textbf{i)}H\&E stained sections of liver tissue. (\textbf{j)} Number of NS, r-hirudin, and DTIP treated mice with tumor cells in liver. All the results were expressed as mean\selectlanguage{english} +-\selectlanguage{english} SD. Compared with NS group by one-way ANOVA. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05. \textbf{Figure 5 r-hirudin and DTIP could inhibit the progression of tumor.} LLC cells at a density of 1x10\textsuperscript{6} in 0.1mL serum-free media were injected subcutaneously into the right \selectlanguage{english}flank of mice. (\textbf{a-d)} Mice that were injected with LLC cells were immediately treated with normal saline, 0.5 mg/kg r-hirudin or 1.0 mg/kg DTIP for one week. (\textbf{a)}The curve of tumor growth after injection of LLC cells. (\textbf{b)} In vivo imaging of each group at 4 weeks after cell injection. (\textbf{c)} H\&E stained sections of tumor. (\textbf{d)} Number of NS, r-hirudin and DTIP treated mice with panniculus invasion. (\textbf{e-n)} After one week of the injection of LLC cells, mice were administered with normal saline, 1.0 mg/kg DTIP or 0.5 mg/kg r-hirudin for 21 consecutive days. (\textbf{e)} The curve of tumor growth after injection of LLC cells. (\textbf{f)} Weight of resected tumors driven from normal saline-, r-hirudin-, and DTIP-treated groups. (\textbf{g)} In vivo imaging of each group at 45 days after cell injection. (\textbf{h)}Representative photograph of metastatic nodules on lungs (upper). Gross appearance of representative lung harvested from different groups viewed under a fluorescence stereoscope (bottom) (\textbf{i)} Number of NS, r-hirudin and DTIP treated mice with lung metastasis. (\textbf{j)} Representative photograph of metastatic nodules on livers (upper). Gross appearance of representative single liver lobes harvested from different groups viewed under a fluorescence stereoscope (bottom). (\textbf{k)} Number of NS, r-hirudin and DTIP treated mice with liver metastasis. (\textbf{l)} Effect of r-hirudin and DTIP against primary tumor angiogenesis. Left, a typical photograph of immunohistochemical staining of CD31. Right, the histogram represents the number of microvessels. (\textbf{m)} Immunohistochemical analysis was performed on tumor samples to determine the expression of MMP9 and IL6 on tumors from NS, r-hirudin and DTIP treated mice. (\textbf{n)}Inhibition of phosphorylation of p65, Erk, STAT3, and Akt in tumors by r-hirudin and DTIP. Right, summary data of western blotting. All the results were expressed as mean\selectlanguage{english} +-\selectlanguage{english} SD. Compared with NS group by one-way ANOVA. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001. \textbf{Figure 6 PAR-1 is a major determinant in thrombin-promoted progression of lung cancer.}(\textbf{a)}Western blot depicting depletion of PAR-1 in A549 cells transfected with human PAR-1 gRNA compared with negative control. (\textbf{b)}Representative pictures of A549 cells migrated through the transwell are shown, Right, quantitative analysis of invasive cells. (\textbf{c)}Western blot depicting depletion of PAR-1 in Lewis cells transfected with mouse PAR-1 gRNA compared with negative control. (\textbf{d)}Representative pictures of Lewis cells migrated through the transwell are shown, Right, quantitative analysis of invasive cells. (\textbf{e)}GTP-bound form of RhoA was enriched by a pull-down assay and detected by Western blotting. Total RhoA was detected using anti-RhoA antibody. (\textbf{f)} Representative images of each group stained with phalloidin. Right, Measurement of ruffles-positive cells infected with the indicated lentivirus. (\textbf{g-i)} 1 x 10\textsuperscript{6}PAR-1 deficient LLC cells and control cells were injected into the left lung through the left rib cage. (\textbf{g)} Survival of mice in different groups. (\textbf{h)} Representative photograph and H\&E stained sections of lung tissues. (\textbf{i)} Average tumor area in total lungs. (\textbf{j-l)} Tumor cells were injected subcutaneously into the right \selectlanguage{english}flank of mice. (\textbf{j)}Serial calipation of tumor volume after transplantation of LLC\emph{\textsuperscript{Par-1-/-}} and LLC\textsuperscript{NC} cells into mice. (\textbf{k)} In vivo imaging of each group at 5 weeks after cell injection. (\textbf{l)}Representative images of anti-CD31 staining in tumor tissues. Right, the histogram represents the number of microvessels. All the results were expressed as mean\selectlanguage{english} +-\selectlanguage{english} SD. ANOVA followed by Dunnett's test was applied for multiple comparison. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001, NS, not significant. \textbf{Figure 7Combination therapy of DTIP and chemotherapy results in improved anti-tumor efficacy.(a-f)}1x10\textsuperscript{6}LLC cells were subcutaneously injected in the right dorsal region of mice. One week after LLC inoculation, the mice were randomly divided into four groups, normal saline, DTIP (1 mg/kg per day, s.c.), gemcitabine (120 mg/kg once a week; i.p.), and combination DTIP with gemcitabine treatment groups, and then the mice were administered normal saline or DTIP for 21 consecutive days, gemcitabine for 4 consecutive weeks. (\textbf{a)} The curve of tumor growth after injection of LLC cells. (\textbf{b)}Mice were humanely euthanized and the tumors were resected at 45 days after cell injection. (\textbf{c)} Weight of resected tumors was determined in different groups. (\textbf{d)} Representative photograph of metastatic nodules on lungs (upper). H\&E stained sections of representative single lung lobes harvested (bottom). (\textbf{e)}Number of mice with liver metastasis. (\textbf{f)} Survival rate of mice in different groups. (\textbf{g-k)}1x10\textsuperscript{6}LLC cells were subcutaneously injected in the right dorsal region of mice. One week after LLC inoculation, the mice were randomly divided into four groups, normal saline, DTIP (1 mg/kg per day, s.c.), paclitaxel (20 mg/kg every two days; i.p.), and combination DTIP with paclitaxel treatment groups, and then the mice were administered normal saline or DTIP for 21 consecutive days, paclitaxel for 4 consecutive weeks. (\textbf{g)} The curve of tumor growth after injection of LLC cells. (\textbf{h)} Mice were humanely euthanized and the tumors were resected at 42 days after cell injection. (\textbf{i)} Weight of resected tumors was determined in different groups.\textbf{(j)}H\&E stained sections of representative single lung lobes harvested.\textbf{(k)} The number of pulmonary foci in lungs. All the results were expressed as mean\selectlanguage{english} +-\selectlanguage{english} SD. ANOVA followed by Dunnett's test was applied for multiple comparison. *\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.05, **\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.01, ***\emph{p} \selectlanguage{english} \textless{}\selectlanguage{english} 0.001, NS, not significant. Gemcitabine: Gem; paclitaxel: PTX \textbf{Hosted file} \verb`Table 1.docx` available at \url{https://authorea.com/users/354546/articles/478087-a-novel-oncotherapy-strategy-direct-thrombin-inhibitors-suppress-progression-dissemination-and-spontaneous-metastasis-in-non-small-cell-lung-cancer}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig1/fig1} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Fig2/Fig2} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig3/fig3} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig4/fig4} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig5/fig5} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig6/fig6} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/fig7/fig7} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}

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\documentclass[10pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}%ATTENTION codage en utf8 ! \usepackage{fourier} \usepackage[scaled=0.875]{helvet} \renewcommand{\ttdefault}{lmtt} \usepackage{amsmath,amssymb,makeidx} \usepackage{fancybox} \usepackage{tabularx} \usepackage[normalem]{ulem} \usepackage{pifont} \usepackage{textcomp} \newcommand{\euro}{\eurologo{}} \usepackage{pst-plot,pst-text,pstricks-add} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\D}{\mathbb{D}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} %Tapuscrit Olivier Reboux \setlength{\textheight}{23,5cm} \setlength{\voffset}{-1,5cm} \newcommand{\vect}[1]{\mathchoice% {\overrightarrow{\displaystyle\mathstrut#1\,\,}}% {\overrightarrow{\textstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptscriptstyle\mathstrut#1\,\,}}} \renewcommand{\theenumi}{\textbf{\arabic{enumi}}} \renewcommand{\labelenumi}{\textbf{\theenumi.}} \renewcommand{\theenumii}{\textbf{\alph{enumii}}} \renewcommand{\labelenumii}{\textbf{\theenumii.}} \def\Oij{$\left(\text{O},~\vect{\imath},~\vect{\jmath}\right)$} \def\Oijk{$\left(\text{O},~\vect{\imath},~\vect{\jmath},~\vect{k}\right)$} \def\Ouv{$\left(\text{O},~\vect{u},~\vect{v}\right)$} \usepackage{fancyhdr} \usepackage[np]{numprint} \usepackage[frenchb]{babel} \begin{document} \setlength\parindent{0mm} \rhead{\textbf{A. P. M. E. P.}} \lhead{\small BaccalaurŽéat STI Génie mécanique, énergétique, civil} \lfoot{\small{Antilles--Guyane}} \rfoot{\small{20 juin 2011}} \renewcommand \footrulewidth{.2pt} \pagestyle{fancy} \thispagestyle{empty} \begin{center}\textbf{DurŽée : 4 heures} \vspace{0,5cm} {\Large \textbf{\decofourleft~BaccalaurŽéat STI GŽénie mécanique, civil~\decofourright\\Antilles--Guyane 20 juin 2011}} \vspace{0,25cm} L'utilisation d'une calculatrice est autorisŽée. \end{center} \vspace{0.25cm} \textbf{\textsc{Exercice 1} \hfill 5 points} \medskip Dans tout ce qui suit, on désigne par : \setlength\parindent{5mm} \begin{itemize} \item[$\bullet~~$] $\Z$ l'ensemble des entiers relatifs ; \item[$\bullet~~$] $\R$ l'ensemble des nombres réels ; \item[$\bullet~~$] $\Z$ l'ensemble des nombres complexes. \end{itemize} \setlength\parindent{0mm} \medskip \textbf{\textsc{Exercice 1} \hfill 4,5 points} \medskip \emph{Cet exercice est un questionnaire à choix multiple. Pour chacune des questions, trois réponses sont proposées dont une seule est exacte. Indiquer sur votre copie le numéro de la question et la lettre correspondant à la réponse choisie. On ne demande aucune justification.\\ Chaque réponse juste rapporte $0,75$ point; une réponse fausse enlève $0,25 point$ ; une absence de réponse ne rapporte ni n'enlève de point.\\ Si le total des points est négatif, il est ramené à zéro.} \smallskip Le plan complexe est rapporté à un repère orthonormal direct \Ouv. On note i le nombre complexe de module 1 et d'argument $\dfrac{\pi}{2}$. On considère les nombres complexes $z_{1} = 1 - \text{i}\sqrt{3}$ et $z_{2} = - \sqrt{3} + \text{i}$ d'images respectives A et B. \medskip {\small\begin{tabularx}{\linewidth}{|c|m{3cm}|*{3}{>{\centering \arraybackslash}X|}}\cline{3-5} \multicolumn{2}{r|}{}& Réponse a &Réponse b &Réponse c\\ \hline Question 1&Le module de $z_{1}$ et un argument de $z_{1}$ sont respectivement :&2 et $\dfrac{\pi}{3}$&$\sqrt{2}$ et $-\dfrac{\pi}{3}$& 2 et $-\dfrac{\pi}{3}$\\ \hline Question 2 &La forme algébrique de $\dfrac{z_{1}}{z_{2}}$ est :&$\dfrac{1 - \text{i}\sqrt{3} }{- \sqrt{3} + \text{i}}$&$- \dfrac{\sqrt{3}}{2} + \dfrac{1}{2}\text{i}$&$- \dfrac{1}{\sqrt{3}} - \sqrt{3}$\\ \hline Question 3 &Un argument de $\dfrac{z_{2}}{z_{1}}$ est :&$- \dfrac{5\pi}{6}$&$\dfrac{5\pi}{6}$&$\dfrac{\pi}{2}$\\ \hline Question 4 &L'ensemble des points $M$ du plan, d'affixe $z$, tels que $\left|z - z_{1}\right| = 2$ est :&La droite (AB) &Un cercle de centre A &Une demi-droite d'origine A \\ \hline Question 5&L'ensemble des points $M$ du plan, d'affixe $z$, tels que: arg$(z) = \dfrac{\pi}{3} + 2k\pi,\, k \in \Z$ est :& Une droite & Un cercle de centre O&Une demi-droite privée de son origine.\\ \hline Question 6 & On considère dans $\C$ l'équation d'inconnue $z$ : $z^2 -4z + 7 = 0$& L'équation n'a pas de solution &Les solutions sont $2 - \sqrt{3}$ et $2 + \sqrt{3}$& Les solutions sont $2 - \text{i}\sqrt{3}$ et $2 + \text{i}\sqrt{3}$\\ \hline \end{tabularx}} \vspace{0,5cm} \textbf{\textsc{Exercice 2} \hfill 5,5 points} \medskip On désigne par (E) l'équation différentielle : \[y "+ y = 0\] où $y$ est une fonction inconnue deux fois dérivable sur $\R$. \begin{enumerate} \item Résoudre l'équation différentielle (E). \item Déterminer la solution $f$ de (E) vérifiant les conditions $f(0) = \dfrac{1}{2}$ et $f'\left(\dfrac{2\pi}{3}\right) = 0$. \item Vérifier que pour tout nombre réel $x,\, f(x) = \cos \left(x + \dfrac{\pi}{3}\right)$. \emph{On rappelle que pour tous nombres réels $a$ et $b$, on a :} \[\cos (a + b) = \cos a \cos b - \sin a \sin b.\] \item On considère l' équation $cos \left(x + \dfrac{\pi}{3}\right) = 0$ d' inconnue réelle $x$. \begin{enumerate} \item Résoudre cette équation dans $\R$. \item Préciser les solutions appartenant à l'intervalle $]-\pi~;~\pi]$. \item Placer sur le cercle trigonométrique les points dont les affixes ont pour argument une solution de cette équation. \end{enumerate} \end{enumerate} \vspace{0,5cm} \textbf{\textsc{Problème} \hfill 10 points} \medskip \textbf{Partie A} \medskip On considère la fonction $f$ définie sur $\R$ par \[f(x) = \text{e}^x + ax + b \text{e}^{-x}\] où $a$ et $b$ sont des nombres réels que l'on se propose de déterminer dans cette partie. Dans le plan muni d'un repère \Oij, on a représenté ci-dessous la courbe $\mathcal{C}$, représentative de la fonction $f$, et $\mathcal{T}$ la tangente à la courbe $\mathcal{C}$ au point d'abscisse $0$. \smallskip On note $f'$ la fonction dérivée de la fonction $f$. \begin{enumerate} \item Par lecture graphique, donner $f(0)$ et $f'(0)$. \item \begin{enumerate} \item Exprimer $f(0)$ en fonction de $b$. \item En déduire la valeur de $b$. \end{enumerate} \item \begin{enumerate} \item Donner, pour tout réel $x$, l'expression de $f'(x)$. \item Exprimer $f'(0)$ en fonction de $a$ et $b$. \item En utilisant les questions précédentes, déterminer $a$, puis en déduire l'expression de $f(x)$. \end{enumerate} \end{enumerate} \medskip \psset{unit=1.5cm} \begin{center} \begin{pspicture*}(-2,-0.5)(3.5,8.5) \psaxes[linewidth=1.5pt](0,0)(-2,-0.5)(3.5,8.5) \psgrid[gridlabels=0pt,subgriddiv=1,gridcolor=orange] \psplot[plotpoints=8000,linewidth=1.5pt,linecolor=blue]{-1.26}{2.38}{2.71828 x exp x sub 2 2.71828 x exp div add}\uput[r](2,5){$\mathcal{C}$} \psplot[linewidth=1.5pt]{-2}{1.75}{3 2 x mul sub}\uput[l](-1,5){$\mathcal{T}$} \end{pspicture*} \end{center} \bigskip \textbf{Partie B} \medskip \begin{enumerate} \item Questions préliminaires: \begin{enumerate} \item Vérifier que pour tout réel $x$, on a : $\text{e}^{2x} - \text{e}^x - 2 = \left(\text{e}^x - 2\right)\left(\text{e}^x + 1\right)$. \item Résoudre dans $\R$ l'inéquation d'inconnue $x$ : \[\text{e}^{2x} - \text{e}^x - 2 = 0.\] On admet que la fonction $f$ est définie sur $\R$ par $f(x) = \text{e}^x - x + 2\text{e}^{-x}$. \smallskip \end{enumerate} \item Déterminer la limite de $f$ en $- \infty$. \item \begin{enumerate} \item Vérifier que pour tout réel $x$ non nul, on a : $f(x) = x\left(\dfrac{\text{e}^x}{x} - 1 + \dfrac{2}{x\text{e}^x}\right)$. \item En déduire la limite de $f$ en $+ \infty$. \item Calculer la valeur exacte de $f(\ln 2)$ puis en donner une valeur approchée à $10^{-1}$ près. \end{enumerate} \item \begin{enumerate} \item Montrer que pour tout réel $x,\,f'(x) = \dfrac{\text{e}^{2x} - \text{e}^x - 2}{\text{e}^x}$. \item Déterminer le signe de $f'$ à l'aide des questions préliminaires. \item Dresser le tableau de variation de la fonction $f$. \end{enumerate} \end{enumerate} \bigskip \textbf{Partie C} \medskip \begin{enumerate} \item Calculer la valeur exacte de $\displaystyle\int_{0}^1 f(x)\:\text{d}x$. \item \begin{enumerate} \item Tracer sur la figure en annexe la droite $\mathcal{D}$ d'équation $y = 4$. \item Hachurer sur la figure en annexe \textbf{qui sera à rendre avec la copie}, le domaine $\mathcal{S}$ du plan délimité par la courbe $\mathcal{C}$, la droite $\mathcal{D}$ et les droites d'équations $x = 0$ et $x = 1$. \item Calculer, en unités d'aire, la valeur exacte de l'aire du domaine $\mathcal{S}$. \end{enumerate} \end{enumerate} \newpage \begin{center} \textbf{ANNEXE} \vspace{0,5cm} \textbf{à rendre avec la copie} \vspace{1cm} \psset{unit=3cm} \begin{pspicture*}(-0.75,-0.25)(2.25,4.75) \psaxes[linewidth=1.5pt,Dx=0.5,Dy=0.5,comma=true](0,0)(-0.75,-0.25)(2.25,4.75) \psgrid[gridlabels=0pt,subgriddiv=1,gridcolor=orange] \psplot[plotpoints=8000,linewidth=1.5pt,linecolor=blue]{-0.58}{1.85}{2.71828 x exp x sub 2 2.71828 x exp div add}\uput[r](1.4,3.1){$\mathcal{C}$} \end{pspicture*} \end{center} \end{document}

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%Teilweise Erzeugt mit dem LaTeX-Generator: http://latex.sehnot.de %Schriftgröße, Layout, Papierformat, Art des Dokumentes \documentclass[10pt,oneside,a4paper]{scrartcl} %Einstellungen der Seitenränder \usepackage[left=2cm,right=2cm,top=1.5cm,bottom=1.5cm,includeheadfoot]{geometry} %neue Rechtschreibung \usepackage[ngerman]{babel} %Umlaute ermöglichen \usepackage[utf8]{inputenc} %Gesamtseitenzahl \usepackage{lastpage} % Kopf- und Fußzeile \usepackage[automark]{scrpage2} %Quellcode-Listings \usepackage{listings} %Hyperlinks \usepackage{hyperref} %Kopfzeile \ihead{CISCO} \chead{} \ohead{http://kohnlehome.de/netz/ccna-v7.pdf} \setheadsepline{0.5pt} %Fußzeile \setfootsepline{0.5pt} \ifoot{Franz Kohnle} \cfoot{Seite \thepage\ von \pageref{LastPage}} \ofoot{\today} \pagestyle{scrheadings} \begin{document} % Überschrift \begin{center} \LARGE % Schriftgröße \bfseries % Fettdruck \sffamily % Serifenlose Schrift CCNA V7.0 \end{center} \section*{Course \#1} \begin{enumerate} \item Networking Today \item Basic Switch and End Device Configuration \item Protocol Models \item Physical Layer \item Number Systems \item Data Link Layer \item Ethernet Switching \item Network Layer \item Address Resolution \item Basic Router Configuration \item IPv4 Addressing \item IPv6 Addressing \item ICMP \item Transport Layer \item Application Layer \item Network Security Fundamentals \item Build a Small Network \end{enumerate} \newpage \section*{Course \#2} \begin{enumerate} \item Basic Device Configuration \item Switching Concepts \item VLANs \item Inter-VLAN Routing \item STP \item Etherchannel \item DHCPv4 \item SLAAC and DHCPv6 Concepts \item FHRP Concepts \item LAN Security Concepts \footnote{New/significantly changed content} \item Switch Security Configuration \footnotemark[1] \item WLAN Concepts \footnotemark[1] \item WLAN Configuration \footnotemark[1] \item Routing Concepts \item IP Static Routing \item Troubleshoot Static and Default Routes \end{enumerate} \section*{Course \#3} \begin{enumerate} \item Single-Area OSPFv2 Concepts \item Single-Area OSPFv2 Configuration \item Network Security Concepts \footnotemark[1] \item ACL Concepts \item ACLs for IPv4 Configuration \item NAT for IPv4 \item WAN Concepts \item VPN and IPsec Concepts \footnotemark[1] \item QoS Concepts \item Network Management \item Network Design \item Network Troubleshooting \item Network Virtualization \item Network Automation \footnotemark[1] \end{enumerate} \end{document}

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\documentclass[10pt,a4paper,french]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{fourier} %\DeclareSymbolFont{calletters}{OMS}{cmsy}{m}{n} %\DeclareSymbolFontAlphabet{\mathcal}{calletters} %\usepackage{xspace} \usepackage[scaled=0.875]{helvet} \renewcommand{\ttdefault}{lmtt} \usepackage{amsmath,amssymb,amstext} \usepackage{fancybox} \usepackage{tabularx} \usepackage[normalem]{ulem} \usepackage{pifont} \usepackage[euler]{textgreek} \usepackage{textcomp,enumitem,mathcomp} \usepackage[table]{xcolor} \usepackage{lscape} \usepackage{lastpage} \usepackage{graphicx,colortbl} \newcommand{\euro}{\eurologo{}} \usepackage{pst-tree,pst-plot,pst-text,pst-func,pst-math,pst-bspline,pstricks-add} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\D}{\mathbb{D}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} %%% Tapuscrit : Denis Vergès %%% Corrigé : François Hache \usepackage[left=3.5cm, right=3.5cm, top=2cm, bottom=2.cm]{geometry} %\usepackage{esvect} \newcommand{\vect}[1]{\overrightarrow{\,\mathstrut#1\,}} \newcommand{\vectt}[1]{\overrightarrow{\,\mathstrut\text{#1}\,}} \renewcommand{\theenumi}{\textbf{\arabic{enumi}}} \renewcommand{\labelenumi}{\textbf{\theenumi.}} \renewcommand{\theenumii}{\textbf{\alph{enumii}}} \renewcommand{\labelenumii}{\textbf{\theenumii.}} \def\Oij{$\left(\text{O},~\vect{\imath},~\vect{\jmath}\right)$} \def\Oijk{$\left(\text{O},~\vect{\imath},~\vect{\jmath},~\vect{k}\right)$} \def\Ouv{$\left(\text{O},~\vect{u},~\vect{v}\right)$} \usepackage{fancyhdr} \usepackage[dvips]{hyperref} \hypersetup{% pdfauthor = {APMEP}, pdfsubject = {Baccalauréat Général}, pdftitle = {épreuve de spécialité - session 2021 }, allbordercolors = white, pdfstartview=FitH} \usepackage[np]{numprint} %\renewcommand\arraystretch{1.4} \renewcommand{\d}{\,\text{d}\,} % le d de différentiation \newcommand{\e}{\,\text{e}\,} % le e de l'exponentielle \renewcommand{\i}{\text{i\,}} % le i des complexes \newcommand{\ds}{\displaystyle} %\frenchbsetup{StandardLists=true} \usepackage{babel} \DecimalMathComma \begin{document} \setlength\parindent{0mm} \rhead{\textbf{A. P{}. M. E. P{}.}} \lhead{\small Baccalauréat Général Épreuve d'enseignement de spécialité } \lfoot{\small{Corrigé de l'épreuve 1}} \rfoot{\small{session 15 mars 2021}} \pagestyle{fancy} \thispagestyle{empty} \begin{center}{\textbf{\Large\decofourleft~BACCALAURÉAT GÉNÉRAL}~\decofourright\\[6pt] {\large ÉPREUVE D'ENSEIGNEMENT DE SPÉCIALITÉ -- CORRIGÉ}\\[6pt] \textbf{Session 15 mars 2021 Sujet 1}} %\vspace{1cm} % %Durée de l’épreuve : \textbf{4 heures} % %\vspace{1cm} % %\emph{L'usage de la calculatrice avec mode examen actif est autorisé.\\ %L'usage de la calculatrice sans mémoire, \og type collège \fg, est autorisé.} \end{center} %\vspace{0,25cm} % %Le candidat traite \textbf{4 exercices} : les exercices 1, 2 et 3 communs à tous les candidats et un seul des deux exercices A ou B. \bigskip \textbf{\large Exercice 1 \hfill Commun à tous les candidats \hfill 5 points} \medskip Dans une école de statistique, après étude des dossiers des candidats, le recrutement se fait de deux façons : \setlength\parindent{1cm} \begin{itemize} \item[$\bullet~~$] 10\,\% des candidats sont sélectionnés sur dossier. Ces candidats doivent ensuite passer un oral à l'issue duquel 60\,\% d'entre eux sont finalement admis à l'école. \item[$\bullet~~$] Les candidats n'ayant pas été sélectionnés sur dossier passent une épreuve écrite à l'issue de laquelle 20\,\% d'entre eux sont admis à l'école. \end{itemize} \setlength\parindent{0cm} %\bigskip \begin{center} \textbf{Partie I} \end{center} On choisit au hasard un candidat à ce concours de recrutement. On notera: \setlength\parindent{1cm} \begin{itemize} \item[$\bullet~~$] $D$ l'évènement \og le candidat a été sélectionné sur dossier \fg{} ; \item[$\bullet~~$] $A$ l'évènement \og le candidat a été admis à l'école \fg{} ; \item[$\bullet~~$] $\overline{D}$ et $\overline{A}$ les évènements contraires des évènement $D$ et $A$ respectivement. \end{itemize} \setlength\parindent{0cm} \medskip \begin{enumerate} \item On traduit la situation par un arbre pondéré: \begin{center} {%\bigskip \psset{levelsep=3cm,nodesepB=4pt, treesep=10mm} \pstree[treemode=R,nodesepA=0pt]% R pour Right {\TR{}} { \pstree[nodesepA=4pt]{\TR{$D$}\naput{$0,1$}} { \TR{$A$}\naput{$0,6$} \TR{$\overline{A}$}\nbput{$0,4$} } \pstree[nodesepA=4pt]{\TR{$\overline{D}$}\nbput{$0,9$}} { \TR{$A$}\naput{$0,2$} \TR{$\overline{A}$}\nbput{$0,8$} } } } \bigskip \end{center} \item La probabilité que le candidat soit sélectionné sur dossier et admis à l'école est: $P(D\cap A)=0,1\times 0,6=0,06$. \item La probabilité de l'évènement $A$ est $P(A)$. D'après la formule des probabilités totales: $P(A) = P(D\cap A) + P(\overline{D}\cap A) = 0,06 + 0,9\times 0,2 = 0,24$. \item On choisit au hasard un candidat admis à l'école. La probabilité que son dossier n'ait pas été sélectionné est: $P_A(\overline{D}) = \dfrac{P(\overline{D}\cap A)}{P(A)} = \dfrac{0,18}{0,24}=0,75$. \end{enumerate} %\bigskip \begin{center} \textbf{Partie II} \end{center} \begin{enumerate} \item On admet que la probabilité pour un candidat d'être admis à l'école est égale à $0,24$. On considère un échantillon de sept candidats choisis au hasard, en assimilant ce choix à un tirage au sort avec remise. On désigne par $X$ la variable aléatoire dénombrant les candidats admis à l'école parmi les sept tirés au sort. \begin{enumerate} \item On admet que la variable aléatoire $X$ suit une loi binomiale. %Quels sont les paramètres de cette loi? La probabilité pour un candidat d'être admis à l'école est égale à $p=0,24$, et on choisit un échantillon de 7 candidats donc $n=7$. La variable aléatoire $X$ suit donc la loi binomiale $\mathcal{B}\left (7\,;\,0,24\right )$. \item La probabilité qu'un seul des sept candidats tirés au sort soit admis à l'école est: $P(X=1)= \ds\binom{7}{1}\times 0,24^1 \times (1-0,24)^{7-1} \approx 0,32$. \item La probabilité qu'au moins deux des sept candidats tirés au sort soient admis à cette école est: $P(X\geqslant 2) = 1-P(X\leqslant 1) = 1-0,47=0,53$. \end{enumerate} \item Un lycée présente $n$ candidats au recrutement dans cette école, où $n$ est un entier naturel non nul. On admet que la probabilité pour un candidat quelconque du lycée d'être admis à l'école est égale à $0,24$ et que les résultats des candidats sont indépendants les uns des autres. \begin{enumerate} \item La variable aléatoire $Y$ qui donne le nombre d'admis parmi les $n$ candidats présentés suit la loi binomiale $\mathcal{B}\left (n\;;\;0,24\right )$. La probabilité qu'aucun candidat issu de ce lycée ne soit admis à l'école est: $P(Y=0) = \ds\binom{n}{0}\times 0,24^0 \times 0,76^n=0,76^n$. \item On cherche à partir de quelle valeur de l'entier $n$ la probabilité qu'au moins un élève de ce lycée soit admis à l'école est supérieure ou égale à $0,99$. On veut donc que $P(Y\geqslant 1) \geqslant 0,99$ c'est-à-dire $1-P(Y=0) \geqslant 0,99$ ou encore\\ $P(Y=0) \leqslant 0,01$. On résout l'inéquation d'inconnue $n$: $0,76^n \leqslant 0,01$: $0,76^n \leqslant 0,01 \iff \ln\left (0,76^n\right ) \leqslant \ln\left (0,01\right ) \iff n \times \ln\left (0,76\right ) \leqslant \ln\left (0,01\right ) \iff n \geqslant \dfrac{\ln\left (0,01\right )}{\ln\left (0,76\right )}$ Or $\dfrac{\ln\left (0,01\right )}{\ln\left (0,76\right )}\approx 16,8$ donc c'est à partir de 17 élèves que la probabilité qu'au moins un élève de ce lycée soit admis à l'école est supérieure ou égale à $0,99$. \end{enumerate} \end{enumerate} \bigskip \textbf{\large Exercice 2 \hfill Commun à tous les candidats \hfill 5 points} \medskip Soit $f$ la fonction définie sur l'intervalle $]0~;~ +\infty[$ par : $f(x) = \dfrac{\e^x}{x}$. On note $\mathcal{C}_f$ la courbe représentative de la fonction $f$ dans un repère orthonormé. %\medskip \begin{enumerate} \item \begin{enumerate} \item D'après le cours, la limite de la fonction $f$ en $+ \infty$ est $+\infty$. \item On cherche la limite de $f$ en 0: $\left. \begin{array}{@{} r} \ds\lim_{x\to 0} \e^{x} = 1\\[7pt] \ds\lim_{x\to 0\atop x>0} \dfrac{1}{x}= +\infty \end{array} \right \rbrace \implies \ds\lim_{x\to 0 \atop x>0} \dfrac{\e^{x}}{x} = +\infty$ Donc l'axe des ordonnées est asymptote verticale à la courbe $\mathcal{C}_f$. \end{enumerate} \item Pour tout réel $x$ de l'intervalle $]0~;~ +\infty[$, on a : $f'(x)=\dfrac{\e^{x}\times x - \e^{x}\times 1}{x^2} = \dfrac{\e^{x} (x-1)}{x^2}$. \item Pour déterminer les variations de la fonction $f$ sur l'intervalle $]0~;~ +\infty[$, on cherche le signe de $f'(x)$. \begin{center} {\renewcommand{\arraystretch}{1.5} \def\esp{\hspace*{2cm}} $\begin{array}{|c | *{5}{c} |} \hline x & 0 & \esp & 1 & \esp & +\infty \\ \hline x-1 & & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{+} & \\ \hline \e^{x} & & \pmb{+} & \vline\hspace{-2.7pt}{\phantom 0} & \pmb{+} & \\ \hline x^2 & 0 \hfill{} & \pmb{+} & \vline\hspace{-2.7pt}{\phantom 0} & \pmb{+} & \\ \hline f'(x) & \vline\;\vline\hfill{} & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{+} & \\ \hline \end{array}$ } \end{center} $f(1)=\dfrac{\e^{1}}{1}=\e$ On établit le tableau de variations de la fonction $f$: \begin{center} {\renewcommand{\arraystretch}{1.3} \psset{nodesep=3pt,arrowsize=2pt 3} % paramètres \def\esp{\hspace*{1.5cm}}% pour modifier la largeur du tableau \def\hauteur{0pt}% mettre au moins 20pt pour augmenter la hauteur $\begin{array}{|c| l *3{c} c|} \hline x & 0 & \esp & 1 & \esp & +\infty \\ \hline f'(x) & \vline\;\vline\; & \pmb{-} & \vline\hspace{-2.7pt}0 & \pmb{+} & \\ \hline & \vline\;\vline\; \Rnode{max1}{+\infty} & & & & \Rnode{max2}{+\infty} \\ f(x) & \vline\;\vline\; & & & & \rule{0pt}{\hauteur} \\ & \vline\;\vline\; & & \Rnode{min}{\e} & & \rule{0pt}{\hauteur} \ncline{->}{max1}{min} \ncline{->}{min}{max2}\\ \hline \end{array}$ } \end{center} \item Soit $m$ un nombre réel. On cherche, en fonction des valeurs du nombre réel $m$, le nombre de solutions de l'équation $f(x) = m$. Cela revient à chercher le nombre de points d'intersection de la courbe $\mathcal{C}_f$ et de la droite horizontale d'équation $y=m$. \begin{list}{\textbullet}{D'après le tableau de variations:} \item si $m<\e$, l'équation $f(x)=m$ n'admet pas de solution; \item si $m=\e$, l'équation $f(x)=m$ admet une solution unique $x=1$; \item si $m>\e$, l'équation $f(x)=m$ admet deux solutions. \end{list} \item On note $\Delta$ la droite d'équation $y = -x$. On note A un éventuel point de $\mathcal{C}_f$ d'abscisse $a$ en lequel la tangente à la courbe $\mathcal{C}_f$ est parallèle à la droite $\Delta$. \begin{enumerate} \item %Montrer que $a$ est solution de l'équation $\text{e}^x(x - 1) + x^2 = 0$. La tangente en $a$ est parallèle à la droite $\Delta$ si et seulement si le coefficient directeur de la tangente est égal à $-1$, autrement dit quand $f'(a)=-1$. $f'(a)=-1 \iff \dfrac{\e^{a} (a-1)}{a^2}=-1 \iff \e^{a} (x-1) = -a^2 \iff \e^{a}(x-1)+a^2=0$ ce qui veut dire que le nombre $a$ est solution de l'équation $\e^x(x - 1) + x^2 = 0$. \end{enumerate} On note $g$ la fonction définie sur $]0~;~ +\infty[$ par $g(x) = \e^x(x - 1) + x^2 $. On admet que la fonction $g$ est dérivable et on note $g'$ sa fonction dérivée. \begin{enumerate}[resume] \item %Calculer $g'(x)$ pour tout nombre réel $x$ de l'intervalle $[0~;~ +\infty[$, puis dresser le tableau de variations de $g$ sur $]0~;~+\infty[$. $g'(x)= \e^{x}\times (x-1) + \e^{x}\times 1 + 2x = x\e^{x}+2x$ Sur $\R$, $\e^{x}>0$ donc sur $[0~;~+\infty[$, $x\e^{x}+2x \geqslant 0$ donc $g'(x)\geqslant 0$. $\left. \begin{array}{@{} r} \ds\lim_{x\to +\infty} \e^{x} = +\infty\\ \ds\lim_{x\to +\infty} x-1= +\infty\\ \ds\lim_{x\to +\infty} x^2 = +\infty \end{array} \right \rbrace \implies \ds\lim_{x\to +\infty} g(x) = +\infty$ $g(0)=\e^{0}(0-1)+0=-1$ On dresse le tableau de variations de la fonction $g$ sur $[0~;~+\infty[$: \begin{center} {\renewcommand{\arraystretch}{1.3} % augmentation de la hauteur de toutes les lignes \psset{nodesep=3pt,arrowsize=2pt 3} % paramètres \def\esp{\hspace*{3cm}} % pour modifier la largeur du tableau \def\hauteur{0pt} % mettre au moins 12pt pour augmenter la hauteur $\begin{array}{|c| *3{c}|} \hline x & 0 & \esp & +\infty \\ \hline g'(x) & 0 & \pmb{+} & \\ \hline & & & \Rnode{max}{+\infty} \\ g(x) & & & \rule{0pt}{\hauteur} \\ & \Rnode{min}{-1} & & \rule{0pt}{\hauteur} \ncline{->}{min}{max} \ncline[linestyle=dotted, linecolor=red]{alpha}{zero}\\ \hline \end{array}$ } \end{center} \item% Montrer qu'il existe un unique point $A$ en lequel la tangente à $\mathcal{C}_f$ est parallèle à la droite $\Delta$. On complète le tableau de variations de $g$: \begin{center} {\renewcommand{\arraystretch}{1.3} \def\esp{\hspace*{3cm}} \psset{nodesep=3pt,arrowsize=2pt 3} % paramètres $\begin{array}{|c| *3{c}|} \hline x & 0 & \esp & +\infty \\ \hline & & & \Rnode{max}{+\infty} \\ g(x) & & & \\ & \Rnode{min}{-1} & & \ncline{->}{min}{max} \rput*(-2,0.65){\Rnode{zero}{\blue 0}} \rput(-2,1.75){\Rnode{alpha}{\blue a}} \ncline[linestyle=dotted, linecolor=blue]{alpha}{zero}\\ \hline \end{array}$ } \end{center} D'après ce tableau, l'équation $g(x)=0$ admet une solution unique $a$ sur $[0~;~+\infty[$, donc il existe un unique point A en lequel la tangente à $\mathcal{C}_f$ est parallèle à la droite $\Delta$. \end{enumerate} \end{enumerate} \bigskip \textbf{\large Exercice 3 \hfill Commun à tous les candidats \hfill 5 points} %\medskip % %\emph{Cet exercice est un questionnaire à choix multiples. Pour chacune des questions suivantes, une seule des quatre réponses proposées est exacte. \\Une réponse exacte rapporte un point. Une réponse fausse, une réponse multiple ou l'absence de réponse à une question ne rapporte ni n'enlève de point.\\ Pour répondre, indiquer sur la copie le numéro de la question et la lettre de la réponse choisie. \\Aucune justification n'est demandée.} \begin{center} \psset{unit=1cm} \begin{pspicture}(-0.5,-0.5)(9,5) \psline(0,0)(5,0)(8,1.8)%DCB \pspolygon[linestyle=dashed](0,0)(8,1.8)(3,1.8)(0,0)%BADB \psline[linestyle=dashed](5,0)(3,1.8)(4,4)(4,0.95)%CASI \psline(0,0)(4,4)(5,0)(8,1.8)(4,4)%DSCBS \uput[dl](0,0){D}\uput[dr](5,0){C}\uput[ur](8,1.8){B}\uput[ul](3,1.8){A} \uput[u](4,4){S}\uput[d](4,0.95){I} \uput[ul](2,2){K}\uput[ur](4.5,2){L}\uput[ur](6,2.9){M} \psdots[dotstyle=+,dotangle=30,dotscale=1.85](2,2)(4.5,2)(6,2.9) \end{pspicture} \end{center} SABCD est une pyramide régulière à base carrée ABCD dont toutes les arêtes ont la même longueur. Le point I est le centre du carré ABCD. On suppose que : IC = IB = IS $= 1$. Les points K, L et M sont les milieux respectifs des arêtes [SD], [SC] et [SB]. %\medskip \begin{enumerate} \item Les droites suivantes ne sont pas coplanaires: \begin{center} \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~} (DK) et (SD) &\textbf{b.~} (AS) et (IC) &\fbox{\textbf{c.~} (AC) et (SB)} &\textbf{d.~} (LM) et (AD) \end{tabularx} \end{center} \begin{tabular}{@{\hspace*{0.05\linewidth}} | p{0.93\linewidth}} \vspace*{-10pt} \begin{list}{\textbullet}{On procède par élimination.} \item Les droites (DK) et (SD) sont sécantes en D donc coplanaires; on élimine \textbf{a.} \item Les droites (AS) et (IC) sont sécantes en A donc coplanaires; on élimine \textbf{b.} \item Les droites (LM) et (AD) sont toutes deux parallèles à (BC) donc parallèles entre elles; elles sont donc coplanaires; on élimine \textbf{d.} \end{list} \smallskip \textbf{Réponse c.} \end{tabular} \end{enumerate} Pour les questions suivantes, on se place dans le repère orthonormé de l'espace $\left(\text{ I}~;~ \vect{\text{IC}},~\vect{\text{IB}},~\vect{\text{IS}}\right)$. Dans ce repère, on donne les coordonnées des points suivants: \[\text{I}(0~;~0~;~0) \:;\: \text{A}(-1~;~0~;~0) \:;\: \text{B}(0~;~1~;~0) \:;\: \text{C}(1~;~0~;~0); \text{D}(0~;~-1~;~0) \:;\: \text{S}(0~;~0~;~1).\] \begin{enumerate}[resume] \item Les coordonnées du milieu N de [KL] sont: \begin{center} \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~} $\left(\dfrac{1}{4}~;~\dfrac{1}{4}~;~\dfrac{1}{4}\right)$& \fbox{\textbf{b.~}$\left(\dfrac{1}{4}~;~- \dfrac{1}{4}~;~\dfrac{1}{2}\right)$}& \textbf{c.~}$\left(-\dfrac{1}{4}~;~\dfrac{1}{4}~;~\dfrac{1}{2}\right)$& \textbf{d.~}$\left(-\dfrac{1}{2}~;~\dfrac{1}{2}~;~1\right)$ \end{tabularx} \end{center} \begin{tabular}{@{\hspace*{0.05\linewidth}} | p{0.93\linewidth}} \vspace*{-10pt} \begin{list}{\textbullet}{} \item Le milieu K de [SD] a pour coordonnées $\left ( 0~;~-\frac{1}{2}~;~\frac{1}{2}\right )$. \item Le milieu L de [SC] a pour coordonnées $\left ( \frac{1}{2}~;~0~;~\frac{1}{2}\right )$. \item Le milieu N de [KL] a donc pour coordonnées $\left ( \frac{1}{4}~;~-\frac{1}{4}~;~\frac{1}{2}\right )$. \end{list} \smallskip \textbf{Réponse b.} \end{tabular} \medskip \item Les coordonnées du vecteur $\vect{\text{AS}}$ sont: \begin{center} \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~} $\begin{pmatrix}1\\1\\0 \end{pmatrix}$& \fbox{\textbf{b.~} $\begin{pmatrix}1\\0\\1 \end{pmatrix}$}& \textbf{c.~} $\begin{pmatrix}2\\1\\-1 \end{pmatrix}$ & \textbf{d.~} $\begin{pmatrix} 1\\1\\1\end{pmatrix}$ \end{tabularx} \end{center} \begin{tabular}{@{\hspace*{0.05\linewidth}} | p{0.93\linewidth}} \textbf{Réponse b.} \end{tabular} \medskip \item Une représentation paramétrique de la droite (AS) est: {\footnotesize \begin{center} \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~} $\left\{\begin{array}{l c r}x&=&-1-t\\y&=&t\\z&=&-t \end{array}\right.$ $(t \in \R)$&\textbf{b.~} $\left\{\begin{array}{l c r}x&=&-1+2t\\y&=&0\\z&=&1 + 2t \end{array}\right.$ $(t \in \R)$& \fbox{\parbox{2.6cm}{\textbf{c.~} $\left\{\begin{array}{l c r}x&=&t\\y&=&0\\z&=&1+t \end{array}\right.$\\ $(t \in \R)$}} &\textbf{d.~} $\left\{\begin{array}{l c r}x&=&-1-t\\y&=&1+t\\z&=&1-t \end{array}\right.$ $(t \in \R)$ \end{tabularx} \end{center}} \begin{tabular}{@{\hspace*{0.05\linewidth}} | p{0.93\linewidth}} La droite (AS) a pour vecteur directeur $\vectt{AS}\,(1~;~0~;~1)$; la seule représentation qui convienne est la c. \smallskip \textbf{Réponse c.} \end{tabular} \medskip \item Une équation cartésienne du plan (SCB) est: \begin{center} \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~} $y+z-1 =0$ &\fbox{\textbf{b.~}$x+y+z- 1=0$} & \textbf{c.~}$x-y+z=0$& \textbf{d.~}$x+z-1 =0$ \end{tabularx} \end{center} \begin{tabular}{@{\hspace*{0.05\linewidth}} | p{0.93\linewidth}} \vspace*{-10pt} \begin{list}{\textbullet}{On procède par élimination.} \item Le plan d'équation $y+z-1=0$ ne contient pas C\,$(1~;~0~;~0)$; on élimine \textbf{a.} \item Le plan d'équation $x-y+z=0$ ne contient pas S\,$(0~;~0~;~1)$; on élimine \textbf{c.} \item Le plan d'équation $x+z-1=0$ ne contient pas B\,$(0~;~1~;~0)$; on élimine \textbf{d.} \end{list} \smallskip \textbf{Réponse b.} \end{tabular} \end{enumerate} \bigskip \textbf{\Large Exercice au choix du candidat \hfill 5 points} %\medskip % %Le candidat doit traiter un seul des deux exercices A ou B. %Il indique sur sa copie l'exercice choisi: exercice A ou exercice B. %Pour éclairer son choix, les principaux domaines abordés par chaque exercice sont indiqués dans un encadré. \medskip \textbf{\large Exercice A} \medskip \begin{tabularx}{\linewidth}{|X|}\hline \textbf{Principaux domaines abordés : Suites numériques; raisonnement par récurrence ; suites géométriques.}\\ \hline \end{tabularx} \medskip La suite $\left(u_n\right)$ est définie sur $\N$ par $u_0 = 1$ et pour tout $n$, $u_{n+1} = \dfrac{3}{4}u_n + \dfrac{1}{4}n + 1$. %\smallskip \begin{enumerate} \item %Calculer, en détaillant les calculs, $u_1$ et $u_2$ sous forme de fraction irréductible. Pour $n=0$, $u_1=u_{0+1}=\dfrac{3}{4}u_0 + \dfrac{1}{4}\times 0 +1 =\dfrac{3}{4}\times 1 +1 = \dfrac{7}{4}$. Pour $n=1$, $u_1=u_{1+1}=\dfrac{3}{4}u_1 + \dfrac{1}{4}\times 1+1 = \dfrac{3}{4}\times \dfrac{7}{4}+\dfrac{1}{4} +1 = \dfrac{41}{16}$. \end{enumerate} \medskip \parbox{0.5\linewidth}{L'extrait, reproduit ci-contre, d'une feuille de calcul réalisée avec un tableur présente les valeurs des premiers termes de la suite $\left(u_n\right)$.} \hfill \parbox{0.35\linewidth}{ \begin{tabularx}{\linewidth}{|c|*{2}{>{\centering \arraybackslash}X|}}\hline \cellcolor{lightgray}{} & \cellcolor{lightgray}A&\cellcolor{lightgray}B \\ \hline \cellcolor{lightgray}1 &$n$&$u_n$\\ \hline \cellcolor{lightgray}2 &0 &1\\ \hline \cellcolor{lightgray}3 &1 &1,75\\ \hline \cellcolor{lightgray}4 &2 &\np{2,5625}\\ \hline \cellcolor{lightgray}5 &3 &\np{3,421875}\\ \hline \cellcolor{lightgray}6 &4 &\np{4,31640625}\\ \hline \end{tabularx}} \medskip \begin{enumerate}[resume] \item \begin{enumerate} \item La formule, étirée ensuite vers le bas, que l'on peut écrire dans la cellule B3 de la feuille de calcul pour obtenir les termes successifs de $\left(u_n\right)$ dans la colonne B est: \text{= 3/4 * B2 + 1/4 * A2 +1}. \item La suite $\left(u_n\right)$ semble croissante. \end{enumerate} \item \begin{enumerate} \item Soit $\mathcal{P}_n$ la propriété: $n \leqslant u_n \leqslant n + 1$. \begin{list}{\textbullet}{} \item \textbf{Initialisation} Pour $n=0$, $u_0=1$ et $0 \leqslant 1 \leqslant 1$ donc $\mathcal{P}_0$ est vraie. \item \textbf{Hérédité} On suppose $\mathcal{P}_n$ vraie, c'est-à-dire: $n \leqslant u_n \leqslant n+1$ (hypothèse de récurrence). $n \leqslant u_n \leqslant n+1 \iff \dfrac{3}{4}n \leqslant \dfrac{3}{4}u_n \leqslant \dfrac{3}{4}\left (n+1\right )\\[7pt] \phantom{n \leqslant u_n \leqslant n+1} \iff \dfrac{3}{4}n +\dfrac{1}{4} n \leqslant \dfrac{3}{4}u_n +\dfrac{1}{4} n \leqslant \dfrac{3}{4}\left (n+1\right ) +\dfrac{1}{4} n \\[7pt] \phantom{n \leqslant u_n \leqslant n+1} \iff n \leqslant \dfrac{3}{4}u_n +\dfrac{1}{4} n \leqslant n+\dfrac{3}{4}\\[7pt] \phantom{n \leqslant u_n \leqslant n+1} \iff n+1 \leqslant \dfrac{3}{4}u_n +\dfrac{1}{4} n +1 \leqslant n+\dfrac{3}{4} +1 \iff n+1 \leqslant u_{n+1} \leqslant n+\dfrac{7}{4}$ donc $n+1 \leqslant u_{n+1} \leqslant n+2$. On a démontré que la propriété était vraie au rang $n+1$. \item \textbf{Conclusion} La propriété est vraie au rang 0, et elle est héréditaire pour tout $n\geqslant 0$; d'après le principe de récurrence, la propriété est vraie pour tout $n\geqslant 0$. \end{list} On a donc démontré que, pour tout entier naturel $n$, on a: $n \leqslant u_n \leqslant n + 1$. \item% En déduire, en justifiant la réponse, le sens de variation et la limite de la suite $\left(u_n\right)$. \begin{list}{\textbullet}{D'après la question précédente:} \item Pour tout $n$, $n\leqslant u_n \leqslant n+1$ donc $n+1 \leqslant u_{n+1} \leqslant n+2$ donc $n \leqslant u_n \leqslant n+1 \leqslant u_{n+1} \leqslant n+2$ d'où on tire $u_n \leqslant u_{n+1}$ ce qui démontre que la suite $(u_n)$ est croissante. \item Pour tout $n$, $n\leqslant u_n$; or $\ds\lim_{n\to +\infty} n = +\infty$ donc, par comparaison, $\ds\lim_{n\to +\infty} u_n = +\infty$. \end{list} \item% Démontrer que : $\displaystyle\lim_{n \to + \infty} \dfrac{u_n}{n} = 1$. Pour tout $n$, $n\leqslant u_n \leqslant n+1$ donc pour tout $n>0$, on a: $1 \leqslant \dfrac{u_n}{n} \leqslant \dfrac{n+1}{n}$ c'est-à-dire: $1 \leqslant \dfrac{u_n}{n} \leqslant 1+\dfrac{1}{n}$. $\ds\lim_{n \to +\infty} \dfrac{1}{n}=0$ donc $\ds\lim_{n \to +\infty} 1+\dfrac{1}{n}=1$ Donc, d'après le théorème des gendarmes: $\ds\lim_{n\to +\infty} \dfrac{u_n}{n}=1$. \end{enumerate} \item On désigne par $\left(v_n\right)$ la suite définie sur $\N$ par $v_n = u_n - n$ \begin{enumerate} \item% Démontrer que la suite $\left(v_n\right)$ est géométrique de raison $\dfrac{3}{4}$. Pour tout $n$, $v_n=u_n-n$ donc $u_n=v_n+n$. $v_{n+1}=u_{n+1} - (n+1) = \dfrac{3}{4}u_n + \dfrac{1}{4}n+1 -n-1 =\dfrac{3}{4}\left (v_n+n\right ) -\dfrac{3}{4}n =\dfrac{3}{4}v_n +\dfrac{3}{4}n -\dfrac{3}{4}n =\dfrac{3}{4}v_n$ $v_0=u_0-0=1$ Donc la suite $(v_n)$ est géométrique de raison $q=\dfrac{3}{4}$ et de premier terme $v_0=1$. \item %En déduire que, pour tout entier naturel $n$,on a : $u_n = \left(\dfrac{3}{4}\right)^n + n$. On en déduit que, pour tout $n$, $v_n=v_0\times q^n = \left (\dfrac{3}{4}\right )^n$. Comme $u_n=v_n+n$, on a $u_n=\left (\dfrac{3}{4}\right )^n + n$. \end{enumerate} \end{enumerate} \bigskip \textbf{\large Exercice B} \medskip \begin{tabularx}{\linewidth}{|X|}\hline \textbf{Principaux domaines abordés : Fonction logarithme; convexité} \\ \hline \end{tabularx} \medskip On considère la fonction $f$ définie sur l'intervalle $]0~;~ +\infty[$ par : $f(x) = x + 4 - 4\ln (x) - \dfrac{3}{x}$, où ln désigne la fonction logarithme népérien. On note $\mathcal{C}$ la représentation graphique de $f$ dans un repère orthonormé. \medskip \begin{enumerate} \item On détermine la limite de la fonction $f$ en $+\infty$. $f(x) = x\left ( 1- 4\dfrac{\ln(x)}{x}\right ) + 4 - \dfrac{3}{x}$ $\left. \begin{array}{@{} r} \ds\lim_{x\to +\infty} \dfrac{\ln(x)}{x} = 0 \implies \ds\lim_{x\to +\infty} x\left ( 1- 4\dfrac{\ln(x)}{x}\right ) + 4 = +\infty\\ \ds\lim_{x\to +\infty} \dfrac{3}{x}= 0 \end{array} \right \rbrace \implies \ds\lim_{x\to +\infty} f(x) = +\infty$ \item On admet que la fonction $f$ est dérivable sur $]0~;~ +\infty[$ et on note $f'$ sa fonction dérivée. %Démontrer que, pour tout nombre réel $x > 0$, on a : $f'(x) = \dfrac{x^2 - 4x + 3x^2}{x^2}.$ $f'(x)= 1 + 0 - \dfrac{4}{x} +\dfrac{3}{x^2} = \dfrac{x^2 - 4x +3}{x^2}$ \item \begin{enumerate} \item %Donner le tableau de variations de la fonction $f$ sur l'intervalle $]0~;~ +\infty[$. %On y fera figurer les valeurs exactes des extremums et les limites de $f$ en $0$ et en $+ \infty$. % %On admettra que $\displaystyle\lim_{x \to 0} f(x) = - \infty$. On cherche le signe de $f'(x)$ sur $]0~;~+\infty[$: $x^2-4x+3 = (x-1)(x-3)$ \begin{center} { \renewcommand{\arraystretch}{1.5} \def\esp{\hspace*{2cm}} $\begin{array}{|c | l *{6}{c} |} \hline x & 0 & \esp & 1 & \esp & 3 & \esp & +\infty \\ \hline x^2-4x+3 & & \pmb{+} & \vline\hspace{-2.7pt}{0} & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{-} &\\ \hline x^2 & 0 & \pmb{+} & \vline\hspace{-2.7pt}{\phantom 0} & \pmb{+} & \vline\hspace{-2.7pt}{\phantom 0} & \pmb{+} &\\ \hline f'(x) & \vline\;\vline & \pmb{+} & \vline\hspace{-2.7pt}{0} & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{+} & \\ \hline \end{array}$ } \end{center} $f(1)=1+4-4\ln(1)-\dfrac{3}{1}=2$; $f(3) = 3+4-4\ln(3) - \dfrac{3}{3}=6-4\ln(3)\approx 1,69$ On établit le tableau des variations de $f$ en admettant que que $\displaystyle\lim_{x \to 0} f(x) = - \infty$: \begin{center} {\renewcommand{\arraystretch}{1.3} \psset{nodesep=3pt,arrowsize=2pt 3} % paramètres \def\esp{\hspace*{1.5cm}}% pour modifier la largeur du tableau \def\hauteur{20pt}% mettre au moins 20pt pour augmenter la hauteur $\begin{array}{|c|l *5{c} c|} \hline x & 0 & \esp & 1 & \esp & 3 & \esp & +\infty \\ \hline f'(x) & \vline\;\vline\; & \pmb{+} & \vline\hspace{-2.7pt}0 & \pmb{-} & \vline\hspace{-2.7pt}0 & \pmb{+} & \\ \hline & \vline\;\vline\; & & \Rnode{max1}{2} & & & & \Rnode{max2}{+\infty} \\ f (x) &\vline\;\vline\; & & & & & & \rule{0pt}{\hauteur}\\ &\vline\;\vline\; \Rnode{min1}{-\infty} & & & & \Rnode{min2}{6-4\ln(3)\approx 1,61} & & \rule{0pt}{\hauteur} \ncline{->}{min1}{max1} \ncline{->}{max1}{min2} \ncline{->}{min2}{max2} \\ \hline \end{array}$ } \end{center} \item %Par simple lecture du tableau de variations, préciser le nombre de solutions de l'équation $f(x) = \dfrac{5}{3}$. $\bullet~~$$\dfrac{5}{3}\in ]-\infty~;~2]$ donc l'équation $f(x) =\dfrac{5}{3}$ admet une unique solution dans l'intervalle $]0~;~1]$. $\bullet~~$$\dfrac{5}{3} \approx 1,67$ et $f(3) = 6 - 4\ln 3 \approx 1,61$ donc $\dfrac{5}{3} \in [6 - 4\ln 3~;~2]$, donc l'équation $f(x)=\dfrac{5}{3}$ admet une solution unique dans l'intervalle $]1~;~3[$. $\bullet~~$$\dfrac{5}{3} \in [6 - 4\ln 3~;~+ \infty[$, donc $f(x) =\dfrac{5}{3}$ admet une unique solution dans l'intervalle $]0~;~1]$. Conclusion : l'équation $f(x)=\dfrac{5}{3}$ admet donc trois solutions dans $]0~;~+\infty[$. Voir cidessus les valeurs approchées des solutions. \end{enumerate} \begin{center} \psset{unit=1cm,arrowsize=2pt 3} \begin{pspicture*}(-1,-4)(11,5) \psgrid[gridlabels=0pt,subgriddiv=1,gridwidth=0.1pt] \psaxes[linewidth=1.25pt,labelFontSize=\scriptstyle]{->}(0,0)(-1,-3.95)(11,4.95) \psaxes[linewidth=1.25pt,labelFontSize=\scriptstyle](0,0)(-1,-3.95)(11,4.95) \psplot[plotpoints=2000,linewidth=1.25pt,linecolor=red]{0.1}{10}{x 4 add x ln 4 mul sub 3 x div sub} \psline[linecolor=blue,linewidth=0.25pt](0,1.6667)(11,1.6667) \psline[linewidth=0.5pt,linestyle=dashed,ArrowInside=->]{->}(0,1.667)(0.61,1.667)(0.61,0) \psline[linewidth=0.5pt,linestyle=dashed,ArrowInside=->]{->}(0.61,1.667)(2.28,1.667)(2.28,0) \psline[linewidth=0.5pt,linestyle=dashed,ArrowInside=->]{->}(2.28,1.667)(3.78,1.667)(3.78,0) \uput[d](0.61,0){\footnotesize $\approx 0,61$}\uput[d](2.28,0){\footnotesize $\approx 2,28$}\uput[d](3.78,0){\footnotesize $\approx 3,78$}\uput[u](9.5,1.667){\blue $y = \frac{5}{3}$} \uput[u](9.5,4.25){\red $\mathcal{C}_f$} \end{pspicture*} \end{center} \item Pour étudier la convexité de $f$, on détermine le signe de $f''$, la dérivée seconde de $f$. %On justifiera que la courbe $\mathcal{C}$ admet un unique point d'inflexion, dont on précisera les coordonnées. $f'(x)=\dfrac{x^2-4x+3}{x^2}$ donc $f''(x) = \dfrac{(2x-4)\times x^2 - (x^2-4x+3)\times 2x}{x^4} = \dfrac{(2x^2 -4x -2x^2 +8x -6)\times x}{x^4} =\dfrac{4x-6}{x^3}$ \begin{center} \renewcommand{\arraystretch}{1.5} \def\esp{\hspace*{2cm}} $\begin{array}{|c | l *{4}{c} |} \hline x & 0 & \esp & \frac{3}{2} & \esp & +\infty \\ \hline 4x-6 & & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{+} & \\ \hline x^3 &0 & \pmb{+} & \vline\hspace{-2.7pt}{\phantom 0} & \pmb{+} & \\ \hline f''(x) &\vline\;\vline & \pmb{-} & \vline\hspace{-2.7pt}{0} & \pmb{+} & \\ \hline &\vline\;\vline & f \text{ concave} & \vline\hspace{-2.7pt}{\phantom0} & f \text{ convexe} & \\ \hline \end{array}$ \renewcommand{\arraystretch}{1} \end{center} La dérivée seconde s'annule et change de signe pour $x=\dfrac{3}{2}$ donc la courbe $\mathcal{C}_f$ admet un unique point d'inflexion d'abscisse $\dfrac{3}{2}$. $f\left (\dfrac{3}{2}\right) = \dfrac{3}{2} +4 -4\ln\left (\dfrac{3}{2}\right ) -\dfrac{3}{\frac{3}{2}} = \dfrac{11}{2} -4\ln\left (\dfrac{3}{2}\right ) -2 = \dfrac{7}{2} -4\ln\left (\dfrac{3}{2}\right ) $ La courbe $\mathcal{C}$ admet un unique point d'inflexion de coordonnées $\left ( \dfrac{3}{2}~;~\dfrac{7}{2} -4\ln\left (\dfrac{3}{2}\right )\right )$. \end{enumerate} \end{document}

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%!TEX encoding = UTF-8 Unicode \documentclass[10pt]{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{fourier} \usepackage[scaled=0.875]{helvet} \renewcommand{\ttdefault}{lmtt} \usepackage{amsmath,amssymb,makeidx} \usepackage{fancybox} \usepackage{tabularx} \usepackage[normalem]{ulem} \usepackage{pifont} \usepackage{textcomp} \newcommand{\euro}{\eurologo{}} %Tapuscrit : Denis Vergès \usepackage{pst-plot,pst-tree,pst-node,pstricks-add} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\D}{\mathbb{D}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} \setlength{\textheight}{23,5cm} \newcommand{\vect}[1]{\mathchoice% {\overrightarrow{\displaystyle\mathstrut#1\,\,}}% {\overrightarrow{\textstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptstyle\mathstrut#1\,\,}}% {\overrightarrow{\scriptscriptstyle\mathstrut#1\,\,}}} \renewcommand{\theenumi}{\textbf{\arabic{enumi}}} \renewcommand{\labelenumi}{\textbf{\theenumi.}} \renewcommand{\theenumii}{\textbf{\alph{enumii}}} \renewcommand{\labelenumii}{\textbf{\theenumii.}} \def\Oij{$\left(\text{O},~\vect{\imath},~\vect{\jmath}\right)$} \def\Oijk{$\left(\text{O},~\vect{\imath},~\vect{\jmath},~\vect{k}\right)$} \def\Ouv{$\left(\text{O},~\vect{u},~\vect{v}\right)$} \setlength{\voffset}{-1,5cm} \usepackage{fancyhdr} \usepackage[frenchb]{babel} \usepackage[np]{numprint} \begin{document} \setlength\parindent{0mm} \rhead{\textbf{A. P{}. M. E. P{}.}} \lhead{\small Baccalauréat ES/L } \lfoot{\small{Métropole}} \rfoot{\small 21 juin 2013} \renewcommand \footrulewidth{.2pt} \pagestyle{fancy} \thispagestyle{empty} \begin{center} {\Large \textbf{\decofourleft~Baccalauréat ES/L Métropole 21 juin 2013~\decofourright\\(sujet dévoilé)}} \end{center} \vspace{0,25cm} \textbf{\textsc{Exercice 1} \hfill 4 points} \textbf{Commun à tous les candidats} \bigskip Cet exercice est un questionnaire à choix multiples (QCM). Pour chacune des questions posées, une seule des quatre réponses est exacte. Indiquer sur la copie le numéro de la question et la lettre correspondant à la réponse choisie. Aucune justification n'est demandée. Une réponse exacte rapporte 1 point. Une réponse fausse, une réponse multiple ou l'absence de réponse ne rapportent ni n'enlèvent aucun point. \bigskip \begin{enumerate} \item Soit $f$ une fonction définie et dérivable sur $\R$. Le tableau de variations de la fonction $f$ est le suivant : \begin{center} \psset{unit=1cm} \begin{pspicture}(-0.5,0)(6.5,2.5) \psframe(-0.5,0)(6.5,2.5)\psline(-0.5,2)(6.5,2)\psline(0.5,0)(0.5,2.5) \uput[u](0,2){$x$} \uput[u](1,2){$- \infty$} \uput[u](2,2){$- 5$} \uput[u](3.5,2){$- 1$} \uput[u](5,2){$7$} \uput[u](6,2){$+ \infty$} \rput(0,1){$f(x)$} \rput(2,1){$0$}\uput[u](3.5,0){$- 4$}\rput(5,1){$0$} \psline{->}(1,1.5)(3,0.5) \psline{->}(4,0.5)(6,1.5) \end{pspicture} \end{center} \begin{enumerate} \item L'intégrale $\displaystyle\int_{- 1}^7 f(x)\:\text{d}x$ est strictement positive. \item L'intégrale $\displaystyle\int_{- 1}^7 f(x)\:\text{d}x$ est strictement négative. \item L'intégrale $\displaystyle\int_{- 1}^7 f(x)\:\text{d}x$ est nulle. \item Le tableau de variations ne permet pas de connaître le signe de l'intégrale $\displaystyle\int_{- 1}^7 f(x)\:\text{d}x$. \end{enumerate} \item Dans une ville de \np{23000} habitants, la municipalité souhaite connaître l'opinion de ses concitoyens sur la construction d'un nouveau complexe sportif. Afin de l'aider dans sa décision, la municipalité souhaite obtenir une estimation de la proportion de personnes favorables à la construction de ce complexe sportif, au niveau de confiance de 95\,\% avec un intervalle d'amplitude inférieure à 4\,\%. Le nombre minimum de personnes que la municipalité doit interroger est de : \medskip \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~~} $625$ &\textbf{b.~~} $\np{2500}$ &\textbf{c.~~} $920$ &\textbf{d.~~} $874$ \end{tabularx} \medskip \item Soit $f$ la fonction dérivable définie sur $]0~;~+\infty[$ par $f(x) = \dfrac{2 \ln x}{x + 1} - 4$. Dans le plan muni d'un repère, la tangente à la courbe représentative de la fonction $f$ au point d'abscisse $1$ admet pour équation : \medskip \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~~} $y = x + 3$&\textbf{b.~~} $y = x - 5$&\textbf{c.~~} $y = - x - 3$&\textbf{d.~~} $y = 2x - 6$ \end{tabularx} \medskip \item On résout dans $\R$ l'inéquation : $\ln x + \ln 2 \geqslant \ln(3x - 6)$. L'ensemble des solutions est : \medskip \begin{tabularx}{\linewidth}{*{4}{X}} \textbf{a.~~} $]2~;~6]$&\textbf{b.~~} $[6~;~+ \infty[$&\textbf{c.~~} $]0~;~6]$&\textbf{d.~~} $]0~;~4]$ \end{tabularx} \medskip \end{enumerate} \vspace{0,5cm} \textbf{\textsc{Exercice 2} \hfill 5 points} \textbf{Candidats n'ayant pas suivi l'enseignement de spécialité et candidats de L} \bigskip Un industriel étudie l'évolution de la production des jouets sur la machine VP1OOO de son entreprise. En 2000, lorsqu'il l'a achetée, elle pouvait produire \np{120000}~jouets par an. Du fait de l'usure de la machine, la production diminue de 2\,\% par an. On modélise le nombre total de jouets fabriqués au cours de l'année $(2000 + n)$ par une suite $\left(U_{n}\right)$. On a donc $U_{0} = \np{120000}$. \bigskip \begin{enumerate} \item Montrer que, pour tout entier naturel $n :\: U_{n} = \np{120000} \times 0,98^n$. \item \begin{enumerate} \item Quel a été le nombre de jouets fabriqués en 2005 ? \item Déterminer à partir de quelle année, le nombre de jouets fabriqués sera strictement inférieur à \np{100000}. \item Cet industriel décide qu'il changera la machine lorsqu'elle produira moins de \np{90000}~jouets par an. Recopier et compléter les lignes 8 et 9 de l'algorithme ci-dessous afin qu'il permette de déterminer le plus petit entier naturel $n$ tel que $U_{n} < \np{90000}$. \medskip \begin{tabular}{l|l l} 1& \textbf{Variables :} &A est un réel\\ 2 &&$n$ est un entier naturel\\ 3 &&\\ 4 &\textbf{Initialisation :}& Affecter à $A$ la valeur \np{120000}\\ 5 &&Affecter à $n$ la valeur $0$\\ 6&&\\ 7 &\textbf{Traitement :}& Tant que $A \geqslant \np{90000}$\\ 8&& \hspace{0,5cm}$n$ prend la valeur \ldots\\ 9&& \hspace{0,5cm}\ldots\\ 10& &Fin Tant que\\ 11&&\\ 12 &\textbf{Sortie :}& Afficher $n$\\ \end{tabular} \end{enumerate} \item \begin{enumerate} \item Exprimer $1 + 0,98 + 0,98^2 + \cdots + 0,98^n$ en fonction de $n$. \item On pose $S_{n} = U_{0} + U_{1} + U_{2} + \cdots + U_{n}$. Montrer que $S_{n} = \np{6000000} \times \left(1 - 0,98^{n+1}\right)$. \item En déduire le nombre total de jouets fabriqués pendant les $15$~premières années de production. \end{enumerate} \end{enumerate} \vspace{0,5cm} \textbf{\textsc{Exercice 2} \hfill 5 points} \textbf{Candidats ayant suivi l'enseignement de spécialité} \bigskip Dans une entreprise, la société de débit boisson CAFTHÉ installe deux machines : l'une ne sert que du café et l'autre ne sert que du thé. Chaque jour lors de la pause déjeuner, chaque employé de l'entreprise choisit une boisson, et une seule : café ou thé. On suppose que le nombre total d'employés de l'entreprise reste constant au cours du temps. La société CAFTHÉ pense que la machine à café sera toujours la plus utilisée. Une enquête, effectuée sur plusieurs jours, auprès des employés pour connaitre leurs choix de boisson a montré que : $\bullet~~$97\,\% des employés qui choisissent un café un jour donné prennent encore un café le lendemain. $\bullet~~$98\,\% des employés qui choisissent un thé un jour donné prennent encore un thé le lendemain. On admet que cette tendance se poursuit les jours suivants. \medskip Le premier jour, 70\,\% des employés ont choisi un café. On note $C$ l'état \og L'employé choisit un café \fg{} et $T$ l'état \og L'employé choisit un thé \fg. Pour tout entier naturel $n$ non nul, on note : $\bullet~~$$c_{n}$ la probabilité de l'évènement \og un employé, pris au hasard, choisit un café le jour n\fg; $\bullet~~$$t_{n}$ la probabilité de l'évènement \og un employé, pris au hasard, choisit un thé le jour $n$ \fg ; $\bullet~~$$P_{n}$ la matrice $\left(c_{n}\quad t_{n}\right)$ correspondant à l'état probabiliste le jour $n$. \bigskip \begin{enumerate} \item Traduire les données de l'énoncé par un graphe probabiliste de sommets $C$ et $T$. \item Déterminer la matrice $P_{1}$ donnant l'état probabiliste le premier jour. \item La matrice de transition $M$ de ce graphe, en considérant les sommets dans l'ordre $C$ et $T$ est $M = \begin{pmatrix}0,97&0,03\\0,02&0,98\end{pmatrix}$. Déterminer la probabilité, arrondie au centième, qu'un employé choisisse un thé le quatrième jour. \item \begin{enumerate} \item Montrer que l'état stable est $(0,4\quad 0,6)$. \item Est-ce que la société CAFTHÉ avait raison quant à l'utilisation de la machine à café à long terme? \end{enumerate} \item \begin{enumerate} \item Exprimer $P_{n+1}$ en fonction de $P_{n}$. En déduire que pour tout entier $n$, on a $c_{n + 1} = 0,95 \times c_{n} + 0,02$. \item On considère l'algorithme suivant : \medskip \begin{tabular}{|l l} \textbf{Variables :}& $A$ est un réel\\ &$i$ et $n$ sont des entiers naturels\\ \textbf{Entrée :}& Saisir $n$\\ \textbf{Initialisation :} &Affecter à $A$ la valeur $0,70$ \\ \textbf{Traitement :} &Pour $i$ de $1$ à $n$\\ &\hspace{0,5cm}Affecter à $A$ la valeur $0,95 \times A + 0,02$\\ &Fin Pour \\ \textbf{Sortie :} &Afficher $A$ \\ \end{tabular} \medskip En faisant apparaître les différentes étapes, donner la valeur affichée par cet algorithme lorsque la valeur de $n$ est égale à 3. Que permet de déterminer cet algorithme ? \end{enumerate} \end{enumerate} \vspace{0,5cm} \textbf{\textsc{Exercice 3} \hfill 5 points} \textbf{Commun à tous les candidats} \bigskip \emph{Dans cet exercice, sauf indication contraire, les résultats seront donnés sous forme décimale, arrondis éventuellement au millième.} \medskip \emph{Les parties A et B sont indépendantes.} \medskip On s'intéresse à une entreprise chargée de mettre du lait en bouteilles. \bigskip \textbf{Partie A : Étude du processus de mise en bouteille} \medskip La bouteille vide arrive sur un tapis roulant et passe successivement dans 2 machines $M_{1}$ et $M_{2}$. La machine $M_{1}$ remplit la bouteille de lait et la machine $M_{2}$ met le bouchon. Une étude statistique portant sur un grand nombre de bouteilles de lait à la fin de la chaîne a permis d'établir que 5\,\% des bouteilles ne sont pas correctement remplies et que parmi elles 8\,\% ont un bouchon. D'autre part, 4\,\% des bouteilles correctement remplies n'ont pas de bouchon. On choisit une bouteille de lait au hasard à la fin de la chaîne et on note : $\bullet~~$R, l'évènement : \og la bouteille est correctement remplie \fg{} ; $\bullet~~$B, l'évènement: \og la bouteille a un bouchon \fg. \textbf{Rappel des notations :} Si $A$ et $B$ sont deux évènements donnés, $P(A)$ désigne la probabilité que l'évènement $A$ se réalise et $P_{B}(A)$ désigne la probabilité de l'évènement $A$ sachant que l'évènement $B$ est réalisé. $\overline{A}$ désigne l'évènement contraire de l'évènement $A$. \bigskip \begin{enumerate} \item Traduire l'énoncé à l'aide d'un arbre pondéré. \item Déterminer la probabilité que la bouteille soit correctement remplie et qu'elle ait un bouchon. \item Montrer que la probabilité que la bouteille ait un bouchon est égale à $0,916$. \item Sachant que la bouteille a un bouchon, déterminer la probabilité qu'elle soit correctement remplie. \end{enumerate} \bigskip \textbf{Partie B : Production journalière} \medskip Une étude sur les dix premières années a montré que la production journalière de bouteilles de lait dans cette entreprise peut être modélisée par une variable aléatoire $X$ qui suit la loi normale de moyenne \np{2000} et d'écart type $200$. \bigskip \begin{enumerate} \item Calculer la probabilité que la production journalière soit comprise entre \np{1800} et \np{2200}~bouteilles. \item Le service maintenance doit intervenir sur les machines si la production journalière devient inférieure à \np{1600}~bouteilles. Déterminer la probabilité que le service maintenance intervienne sur les machines. \end{enumerate} \medskip \textbf{Rappel :} Si $X$ est une variable aléatoire qui suit la loi normale $\mathcal{N}\left(\mu~;~\sigma^2\right)$ alors : $\bullet~~$$P\left(X \in [\mu - \sigma~;~\mu + \sigma] \right) \approx 0,683$ $\bullet~~$$P\left(X \in [\mu - 2\sigma~;~\mu +2\sigma] \right) \approx 0,954$ $\bullet~~$$P\left(X \in [\mu - 3\sigma~;~\mu + 3\sigma] \right) \approx 0,977$ \vspace{0,5cm} \textbf{\textsc{Exercice 4} \hfill 6 points} \textbf{Commun à tous les candidats} \bigskip Dans un laboratoire, des scientifiques ont étudié pendant 10ans l'effet de la pollution sur une population d'insectes car ils craignaient l'extinction de cette espèce. L'étude a été effectuée sur un échantillon de \np{25000}~insectes. \medskip Les deux parties peuvent être traitées indépendamment l'une de l'autre. \medskip \textbf{Partie A :} \medskip Une étude a permis de montrer que la population d'insectes diminue très rapidement lors des quatre premières années. La population peut être modélisée par la fonction $f$ définie sur l'intervalle [0~;~4] par \[f(t) = 25\text{e}^{-0,5t},\] où $t$ est le temps exprimé en années et $f(t)$ le nombre de milliers d'insectes. \bigskip \begin{enumerate} \item Calculer le pourcentage de diminution du nombre d'insectes la première année. Arrondir à 1\,\%. \item \begin{enumerate} \item Montrer que la fonction $F$ définie sur l'intervalle [0~;~4J par \[F(t) = - 50\text{e}^{-0,5t}\] est une primitive de la fonction $f$ sur l'intervalle [0~;~4]. \item Calculer la valeur exacte de $\displaystyle\int_{2}^4 25\text{e}^{-0,5t}\:\text{d}t$. \item En déduire la population moyenne d'insectes entre le début de la deuxième et le début de la quatrième année. \end{enumerate} \end{enumerate} \medskip \textbf{Partie B :} \medskip Après de longues recherches, un biologiste a mis au point un traitement pour essayer de sauver cette espèce. Ce traitement est administré aux insectes à partir de la quatrième année. L'évolution de la population est alors modélisée par la fonction $g$ définie sur l'intervalle [4~;~10] par : \[g(t) = 20\text{e}^{-0,1t^2} + t - 4,65.\] \begin{enumerate} \item On désigne par $g'$ la fonction dérivée de la fonction $g$. Montrer que pour réel $t$ de l'intervalle [4~;~10], $g'(t) = - 4t\text{e}^{-0,1t^2} + 1$. \item On admet que la fonction $g'$ est continue et strictement croissante sur l'intervalle [4~;~10]. Montrer que l'équation $g'(t) = 0$ a une solution et une seule $\alpha$ dans l'intervalle [4~;~10]. Donner la valeur arrondie au dixième de $\alpha$. \item \begin{enumerate} \item En déduire le signe de $g'(t)$ sur l'intervalle [4~;~10]. \item Donner le sens de variation de la fonction $g$ sur l'intervalle [4~;~10]. \item Que peut-on supposer quant à l'effet du traitement sur la population d'insectes ? \end{enumerate} \end{enumerate} \end{document}

https://ctan.math.washington.edu/tex-archive/info/examples/PSTricks_6_de/15-03-24.ltx

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%% %% Ein Beispiel der DANTE-Edition %% %% %% Copyright (C) 2010 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% %% %% ==== % Show page(s) 1 %% \documentclass[]{exaarticle} \pagestyle{empty} \setlength\textwidth{190.324pt} \setlength\parindent{0pt} \StartShownPreambleCommands \usepackage{pst-plot} \StopShownPreambleCommands \begin{document} \psset{plotpoints=200,unit=0.3,labelFontSize=\scriptstyle} \begin{pspicture}(-8.5,-8.5)(9,9)% Ulrich Dirr \psaxes[Dx=2,dx=2,Dy=2,dy=2,labelsep=.75mm,% arrowlength=1.75,ticksize=2pt,linewidth=0.17mm]% {->}(0,0)(-8.5,-8.5)(9,9) \rput[Br](9,-.7){$x$} \rput[tr](-.3,9){$y$} \rput[Br](-.3,-.7){$0$} \psset{linewidth=.35mm,plotstyle=curve,polarplot} \psplot[linecolor=blue]{0}{720}{8 2.5 x mul sin mul} \end{pspicture} \end{document}

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\contentsline {section}{\numberline {1}Introduction}{1}{section.1} \contentsline {section}{\numberline {2}Usage}{1}{section.2} \contentsline {section}{\numberline {3}Implementation}{2}{section.3} \contentsline {subsection}{\numberline {3.1}\textsf {varioref} and \textsf {prettyref}}{2}{subsection.3.1} \contentsline {subsection}{\numberline {3.2}\textsf {listings}}{5}{subsection.3.2} \contentsline {subsection}{\numberline {3.3}\textsf {natbib}}{9}{subsection.3.3} \contentsline {subsection}{\numberline {3.4}\textsf {algorithm}}{10}{subsection.3.4} \contentsline {subsection}{\numberline {3.5}\textsf {beamer}}{12}{subsection.3.5} \contentsline {subsection}{\numberline {3.6}\textsf {nomencl}}{12}{subsection.3.6} \contentsline {subsection}{\numberline {3.7}Other options}{13}{subsection.3.7} \contentsline {subsection}{\numberline {3.8}Licensing macros}{13}{subsection.3.8}

http://mirrors.concertpass.com/tex-archive/macros/latex/contrib/blowup/blowup-test5.tex

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\listfiles \documentclass[a5paper,twoside]{article} \usepackage{showframe} \usepackage{blowup} \blowUp{paper=a4,pos={inside,top},noscale} \newcommand*\SEITE{% \Huge \noindent A \hfill B \hfill C \vfill \noindent X \hfill Y \hfill Z \newpage} \begin{document} \SEITE \SEITE \SEITE \SEITE \SEITE \end{document} %---------------------------

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\[\delta\left(x-a\right)=x\int_{0}^{\infty}tJ_{\nu}\left(xt\right)J_{\nu}\left(% at\right)\mathrm{d}t,\]

http://dlmf.nist.gov/1.14.E6.tex

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\[(f*g)(t)=\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}F(x)G(x)e^{-itx}dx,\]

https://theanarchistlibrary.org/library/ed-goddard-red-flags-torn.tex

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\documentclass[DIV=12,% BCOR=10mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% twoside,% paper=210mm:11in]% {scrbook} \usepackage[noautomatic]{imakeidx} \usepackage{microtype} \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} \usepackage[shortlabels]{enumitem} \usepackage{tabularx} \usepackage[normalem]{ulem} \def\hsout{\bgroup \ULdepth=-.55ex \ULset} % https://tex.stackexchange.com/questions/22410/strikethrough-in-section-title % Unclear if \protect \hsout is needed. Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand*{\forcelinebreak}{\strut\\*{}} \newcommand*{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment*{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment*{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand*{\Slash}{\slash\hspace{0pt}} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{english} \setmainfont{LinLibertine_R.otf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \setmonofont{cmuntt.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmuntb.ttf,% BoldItalicFont=cmuntx.ttf,% ItalicFont=cmunit.ttf] \setsansfont{cmunss.ttf}[Script=Latin,% Ligatures=TeX,% Scale=MatchLowercase,% Path=/usr/share/fonts/truetype/cmu/,% BoldFont=cmunsx.ttf,% BoldItalicFont=cmunso.ttf,% ItalicFont=cmunsi.ttf] \newfontfamily\englishfont{LinLibertine_R.otf}[Script=Latin,% Ligatures=TeX,% Path=/usr/share/fonts/opentype/linux-libertine/,% BoldFont=LinLibertine_RB.otf,% BoldItalicFont=LinLibertine_RBI.otf,% ItalicFont=LinLibertine_RI.otf] \renewcommand*{\partpagestyle}{empty} % global style \pagestyle{plain} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand*{\captionformat}{} \renewcommand*{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} \frenchspacing % avoid vertical glue \raggedbottom % this will generate overfull boxes, so we need to set a tolerance % \pretolerance=1000 % pretolerance is what is accepted for a paragraph without % hyphenation, so it makes sense to be strict here and let the user % accept tweak the tolerance instead. \tolerance=200 % Additional tolerance for bad paragraphs only \setlength{\emergencystretch}{30pt} % (try to) forbid widows/orphans \clubpenalty=10000 \widowpenalty=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Red Flags Torn} \date{2010} \author{Ed Goddard} \subtitle{A brief sketch of some problems with unions} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Red Flags Torn},% pdfauthor={Ed Goddard},% pdfsubject={A brief sketch of some problems with unions},% pdfkeywords={unions; critique; syndicalism; Black Flag; UK}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Red Flags Torn\par}}% \vskip 1em {\usekomafont{subtitle}{A brief sketch of some problems with unions\par}}% \vskip 2em {\usekomafont{author}{Ed Goddard\par}}% \vskip 1.5em \vfill {\usekomafont{date}{2010\par}}% \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage The ’80s have been back in fashion for a while now. It started ironically: a stonewashed denim jacket at a fancy dress party, a “Frankie Says Relax” t-shirt. But like all ironic jokes, it’s been taken too far. As if getting an economy to match our shoes, we now have rising unemployment, attacks on benefits, and public sector pay cuts. And as it obviously didn’t matter who got in, we thought a Tory government would complete the look with the Labour Party back as the defenders of the poor, even using phrases like “working class” again. We all know that any fightback will not come from the Labour Party (or any other party); it’ll be from workers, public service users, parents, pensioners, students, the unemployed. If we see a mass working class fightback, we can expect the trade union leaders to be there, at the rallies and demonstrations, urging us forward. But looking at the struggles of the past few years, should this fill us with confidence? Are these union leaders behind us? \section{\textbf{Some recent defeats and ‘almosts’}} In 2009, Visteon factories in London and Belfast were occupied. After dragging its heels and giving poor legal advice, Unite encouraged workers to leave the occupied factories. Eventually a deal was done behind closed doors and the union recommended acceptance of a partial offer that left the crucial issue of pensions untouched. In 2008, strikes were prepared across the public sector. Workers in Unison, NUT and PCS all took action against the government’s 2\% pay-cap, sometimes even on the same day. After only two days of strike action Unison, the biggest of the three unions, took its dispute to ACAS. The arbitrating body’s decision being legally binding, this effectively removed its members from the dispute. The other unions soon followed suit. In 2007, as the government threatened 40,000 job cuts at Royal Mail and attacked pay and pensions, wildcat strikes spread across Britain with postal workers refusing to cross each others’ picket lines. The CWU soon called off all action to enter ‘meaningful negotiations’ which lasted weeks and came to no firm conclusion. Demoralised and demobilised posties accepted an agreement basically unchanged from the first one. But the CWU declared victory: they were guaranteed a ‘consultation’ role in the cuts. These are just some examples; you can pick many more from recent and not- so-recent history. And they all raise the question: why are our unions so bad at what we expect them to do? Not being a force for revolution or anything, but bog-standard, Ronseal-advert, doing-what-it-says-on-the-tin, fighting for their members’ interests. \section{\textbf{Union troubles, outside and in..}} Trade union officials will blame the membership, saying they don’t want to fight. This might be true sometimes but didn’t the wildcatting posties want to fight? The Visteon workers, after occupying their factories, didn’t want to fight? There’s more going on than just the ‘workers aren’t up for it’\dots{} It’s not all the unions’ fault. Since the Thatcher years we’ve seen so many new laws restricting strike action that British industrial relations legislation is amongst the most anti-worker in the developed world. Where once wildcat strikes and secondary picketing were common, now they are a rarity. Even things like forcing ballots to be done in secret, posted from home, where workers can’t sense the solidarity of their workmates, is intended to discourage militant action. But there’s a problem with this argument too. These laws were pushed through as a result of working class defeat, a defeat that the unions were complicit in. Unions had been disciplining their members for decades before these laws were even a twinkle in Thatcher’s eye. Whether it be NUM official Will Lawther’s 1947 call to prosecute wildcatting miners “even if there are 50,000 or 100,000 of them” or the UPW slapping members with fines totalling £1,000 and threatening expulsion from the union (thus losing their jobs, as it was a closed shop) for refusing to handle post during the 1977 Grunwick strike, one thing seen time and again is union leaders moving against the militant action of their members. Putting it down to legislation passed in the last 20-30 years does nothing to explain such actions before then. \section{\textbf{Bureaucrats}} So the problems aren’t just external: we can’t just act like proud parents and say they fell in with a bad crowd. The fact is the unions have come to resemble the companies we expect them to fight with highly paid executive decision makers, a downward chain-of-command and a career ladder that goes beyond the union and into the halls of social democratic governing institutions (think-tanks, Labour Party etc). Such a structure needs people to fill it: bureaucrats, who by definition are separate from the lives of the workers they represent. This is true even of former shopfloor militants. Having left the workplace, their everyday experiences are not the same as those they used to work alongside. Their priorities and, more importantly, their material interests are not the same. A victory for a worker means an improvement in working conditions; a victory for a bureaucrat means a seat at the negotiating table. But this seat for the bureaucrat doesn’t necessarily mean any improvement for the worker, as the CWU’s consultation ‘victory’ proves. To say union bureaucrats have different priorities and interests is not just spite. It’s to underline that it’s not about them being “baddies.” Many committed militants become union officials because they want to be employed spreading struggle rather than just working for some arsehole boss. But the trouble is that ‘struggle’ and ‘the union’ are not the same thing and spreading the latter does not mean encouraging the former. This has always been the case. The contradiction between workers and union bureaucrats has been going on in the UK for over a century. One such example was with the anarchist John Turner, an unpaid leader of the United Shop Assistants Union for seven years who in 1898 became a paid national organiser, travelling up and down the country recruiting to the union. Though it grew massively, Turner had also started to change his approach. As conflicts flared up so would branches of the union; but as conflicts died down so did the branches. To keep a stable membership, he introduced sickness and unemployment benefits as perks of union membership. The plan worked. A stable membership was established and by 1910 the Shop Assistants Union was the biggest in the London area. But the nature of the union had changed. And even if Turner couldn’t see it, the workers could. The union bureaucracy became seen by many as an interference with local initiative and in 1909 Turner was accused of playing the “role of one of the most blatant reactionaries with which the Trades Union movement was ever cursed” . The tragedy of John Turner\footnote{More on John Turner can be found in \emph{The slow burning fuse - the lost history of the British anarchists} by John Quail, some of which is online on libcom.org} is not as simple as him ‘selling out’; he remained an anarchist to the day he died. But as a full-time organiser paid by the union his priority began to be perpetuating the union rather than organising conflicts and soon his union was no different from the other unions. This is because in the eyes of a trade union official, the union is not just the means to encourage struggle but the means through which struggle itself happens. Building the union is top priority and stopping things which get the union in trouble (like unofficial action) take on the utmost importance; after all, if the workers get the union into too much trouble, how will struggle happen? Of course, an individual can take on a full-time union job and concentrate on organising conflicts rather than just recruitment. But full-timers aren’t freelancers, their bosses (the union they work for), like any other boss, needs to see results. And ‘results’ doesn’t mean class conflict, it means membership recruitment and retention. Because without members, official trade unionism can’t do what it most needs to. \section{\textbf{Meeting employers half-way}} Criticisms of the bureaucratic nature of the trade unions are not uncommon on the far-left. Many conclude that we need to democratise or ‘reclaim’ the existing unions, while others more radically conclude that we need new unions, controlled by the rank and file. However, this misses the point about what bureaucracies are and why they happen. Unions don’t play this role because they’re bureaucratic, they’re bureaucratic because of the role they play. That is, they try to mediate the conflict between workers and their bosses. The primary way this happens is through monopolising the right to negotiate conditions on behalf of the workforce. What is crucial when trying to do this is maintaining as high a membership as possible, regardless of how detached from the workplace such a union becomes. As union density drops generally, unions solve this problem with endless mergers as high membership figures help maintain their influence with management (not to mention the TUC and the Labour Party). If a union is to secure its place as the negotiator in the workplace, it not only has to win the support of its members but also show bosses that they can get the workforce back to work once an agreement is reached. By having membership figures which they can point at to make sure management recognise them as the body able to negotiate wages and conditions, unions are also able to use this position to retain and attract members. Equally, this influence with the workforce is what’s useful to management. Union bureaucrats offer stability in the workplace, diverting workers’ anger into a complex world of employment law, grievance procedures and casework forms. As Buzz Hargrove, leader of the militant Canadian Auto Workers union, wrote in his autobiography: \begin{quote} “Good unions work to defuse [workers’] anger – and they do it effectively. Without unions, there would be anarchy in the workplace. Strikes would be commonplace, and confrontation and violence would increase. Poor-quality workmanship, low productivity, increased sick time, and absenteeism would be the preferred form of worker protest. “By and large, unions deflect those damaging and costly forms of worker resistance. If our critics understood what really goes on behind the labour scenes, they would be thankful that union leaders are as effective as they are in averting strikes.” \end{quote} The legal restrictions on unions mentioned earlier are often called “anti-union” laws. However when looked at like this, it becomes apparent that these laws are not so much anti-union as anti-worker. If anything, it strengthens the union’s hand by giving it a total monopoly on all legally recognised (and therefore protected) forms of action. The same laws which help employers maintain order in the workplace can also be seen helping the union maintain its half of the bargain with the employers. As a result, pro-union radicals often propose the ‘wink and nod’ strategy: that is, the union officially saying “come on, back to work, the union doesn’t condone this\dots{}” while giving a sly little wink while the boss isn’t looking. But if bosses don’t think a union can keep up its end of the bargain then they won’t recognise them as negotiating “partners.” Why would they? Why would anyone repeatedly reach an agreement with someone else if they knew that person wouldn’t uphold their side of the bargain? In order to function as representatives of the workforce, unions have to play by the rules including, where necessary, policing the workforce and directing militancy into the “proper channels.” The anti-strike laws reinforce this pressure by threatening unions with financial ruin if they don’t rein in legally unprotected actions. This is where the pressure to discipline members comes from. It’s not a question of the right leaders with the right politics or of having the right principles written down in a constitution. It’s not about individuals, it’s about how structures work to fulfill their needs. From John Turner through to today via the French CGT, American CIO, Polish Solidarnosc and countless others, unions have turned, through their role as mediators, away from their origins as expressions of class anger and into organisations disciplining the working class against its own interests. Notably, the unions that avoided this fate are those that adopted explicitly revolutionary perspectives and consciously refused to play a mediating role, such as the Spanish CNT’s refusal to participate in works councils and union elections\footnote{There is of course much to be said about the representative role which the leadership of the CNT took in the Spanish Civil War and the negative effects which this had}. \section{\textbf{So what then?}} This article is just the start of a wider criticism of unions. But where unions seek to act as mediators and representatives they necessitate the creation of bureaucracies to take on this task and bureaucrats, separated as they are from workers’ lives, have different interests from them. They need primarily to maintain their seat at the negotiating table. Therefore it’s no surprise that where gains have been made (even within a union framework) it has been through the threat or actuality of unmediated direct action: from the Lindsey Oil Refinery strikes to the wildcat-prone refuse workers of Brighton to the solidarity of truck drivers not crossing Shell truckers’ picket lines. These strikes, which ended in unqualified victories for the workers, pushed the boundaries of trade union action, breaking anti-strike laws and taking place outside the official union structures (even if organised by lay-reps at local union level). Our task is to encourage this sort of independent activity, to encourage the control of struggles through workplace meetings of all workers affected (regardless of union affiliation) and to encourage the use of direct action to get results. These should be the guiding principles for us in workplace organising. Leave ‘reclaiming the unions’ to the Trots, they can build career ladders for bureaucrats. If union density is what creates militancy then the UK (at 27\%) would be far more militant than France (8\%). Clearly this is not the case. We’re done building new bureaucracies; we need to take action without them. % begin final page \clearpage % if we are on an odd page, add another one, otherwise when imposing % the page would be odd on an even one. \ifthispageodd{\strut\thispagestyle{empty}\clearpage}{} % new page for the colophon \thispagestyle{empty} \begin{center} The Anarchist Library \smallskip Anti-Copyright \bigskip \includegraphics[width=0.25\textwidth]{logo-en} \bigskip \end{center} \strut \vfill \begin{center} Ed Goddard Red Flags Torn A brief sketch of some problems with unions 2010 \bigskip https:\Slash{}\Slash{}libcom.org\Slash{}library\Slash{}red-flags-torn-brief-sketch-some-problems-unions-ed-goddard An article by Ed Goddard, that originally appeared in Black Flag, briefly explaining some of the problems inherent in the official trade unions and the need for workers to take control of their actions out of the hands union bureaucrats. \bigskip \textbf{theanarchistlibrary.org} \end{center} % end final page with colophon \end{document} % No format ID passed.

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\input zb-basic \input zb-matheduc \iteman{ZMATH 2010f.00002} \itemau{Arens, Tilo; Hettlich, Frank; Karpfinger, Christian; Kockelkorn, Ulrich; Lichtenegger, Klaus; Stachel, Hellmuth} \itemti{Mathematics. (Mathematik.)} \itemso{Heidelberg: Spektrum Akademischer Verlag (ISBN 978-3-8274-1758-9/hbk). xiv, 1496~p. (2008).} \itemab Vor mir liegt ein gewaltiges Lehrbuch, sowohl physisch (1500~Seiten im A4-Format) als auch inhaltlich. Die Autoren lassen in sechs Teilen die gesamte Mathematik Revue passieren, die in Ingenieur- oder naturwissenschaftlichen Studieng\"angen verlangt wird. Im einzelnen lauten die \"Uberschriften der Teile: I.~Einf\"uhrung und Grundlagen; II.~Analysis einer reellen Ver\"anderlichen; III.~Lineare Algebra; IV.~Analysis mehrerer reeller Variablen; V.~H\"ohere Analysis; VI.~Wahrscheinlichkeitsrechnung und Statistik. Inhaltlich sind nat\"urlich viele Dinge Standard, allerdings sei bemerkt, dass es Abschnitte zur Tensorrechnung, linearen Optimierung, Funktionalanalysis und Variationsrechnung gibt; ferner f\"uhren die Autoren nicht das Riemannsche Integral, sondern gleich das Lebesguesche Integral ein. Was das Buch auszeichnet, ist einerseits die Vollst\"andigkeit des Inhalts -- die gesamte (Ingenieurs-) Mathematik in einem Band~--, andererseits seine Darstellung. Der Anspruch der Autoren ist es, die Mathematik verst\"andlich zu machen und nicht blo{\ss} Rechenverfahren einzu\"uben, und sie werden diesem Anspruch gl\"anzend gerecht. Also wird so viel wie m\"oglich auch bewiesen (und damit erkl\"art), zumindest solange, wie nicht an den Grundlagen ger\"uhrt wird (der Begriff der Cauchy-Folge erscheint erst auf Seite~1057). Bei der Einf\"uhrung des Lebesgueschen Integrals m\"ussen die Leser allerdings eine Menge Dinge einfach glauben, da die pr\"azise mathematische Argumentation \"uber ihren Horizont hinausginge. Insofern w\"are das Riemannsche Integral als Einstieg intuitiver gewesen. Au{\ss}erdem legen die Autoren Wert darauf, die Leserinnen und Leser vor gewissen Missverst\"andnissen zu warnen, denen Anf\"anger mitunter unterliegen (z.B. $f$ und $f(x)$ zu unterscheiden, vgl. Seite~86). All dies wird unterst\"utzt durch viele Anwendungsbeispiele. Jedes Kapitel schlie{\ss}t mit Aufgaben in jeweils drei Rubriken: Verst\"andnisfragen, Rechenaufgaben, Anwendungsprobleme; Hinweise zum L\"osungsweg und die L\"osung selbst finden sich am Schluss des Buches. Die \"au{\ss}ere Aufmachung des Buchs ist vorbildlich: Druck auf gutem Papier, durchgehend mehrfarbige Abbildungen, eingeschobene K\"asten mit Anwendungen (in gr\"un), Vertiefungen (in violett) und \"Ubersichten (in orange), perfekter Satz mit einer Nullmenge an Tippfehlern. Warnungen erscheinen nat\"urlich in rot! Zus\"atzlich zum gedruckten Buch gibt es die Internetseite \url{http://www.matheweb.de} mit ``Bonusmaterial'' und den vollst\"andig ausgearbeiteten L\"osungswegen (beides inzwischen ebenfalls gedruckt erh\"altlich, vgl.\ Zbl 1200.00002 und Zbl 1200.00003 bzw. ME 2010f.01179 und ME 2010f.01180). Die Autoren und die Mathematik-Programmleitung des Spektrum-Verlags sind zu diesem Werk zu begl\"uckw\"unschen! \itemrv{Dirk Werner (Berlin)} \itemab Liest man die reisserische Werbung f\"ur dieses Buch in der beigef\"ugten Presseinformation des Verlages (``Dieses neuartige Lehrbuch begleitet [den Leser] vom Studienanfang bis ins Berufsleben durch das gesamte praxisrelevante Wissen der Mathematik''), ist man zu Recht erst einmal \"au\ss erst misstrauisch. So einen Unsinn h\"atten die Autoren unbedingt unterbinden m\"ussen, denn niemand kann das ``gesamte Wissen der Mathematik'', auch bei Beschr\"ankung auf ``Praxisrelevantes'' (was soll das sein?) kennen, geschweige denn vermitteln. Bei n\"aherer Lekt\"ure wird man dann aber angenehm \"uberrascht: Den Autoren ist tats\"achlich in einer gewaltigen Anstrengung ein originelles Buch gelungen, und das imponierende Ergebnis (41 Kapitel, 1500 Seiten, 3850 Gramm) kann sich sehen lassen. Einige Worte m\"ogen den Inhalt vermitteln. Im 1. Kapitel werden einf\"uhrende Hinweise zum Sinn und Gebrauch des Buches gegeben und Bemerkungen zum Wesen der Mathematik im allgemeinen sowie der Mathematik f\"ur Ingenieure und Naturwissenschaftler (der Hauptzielgruppe des Werkes) im besonderen gemacht. Das 2. Kapitel (``Logik, Mengen, Abbildungen'') dient der Bereitstellung grundlegender Begriffe und Methoden, das 3. Kapitel (``Rechentechniken'') behandelt Fertigkeiten, die eigentlich jeder Abiturient beherrschen sollte, deren Wiederholung aber wohl sinnvoll ist. Die anschlie\ss enden Kapitel 4 (``Elementare Funktionen''), 5 (``Komplexe Zahlen''), 6 (``Folgen'' ), 7 (``Stetige Funktionen''), 8 (``Reihen''), 9 (``Potenzreihen''), 10 (``Differenzialrechnung''), 11 (``Integrate''), 12 (``Integrationstechniken'') und 13 (``Differenzialgleichungen'') decken wenigstens teilweise den Stoff einer \"ublichen Analysis-I/II-Vorlesung ab. Begriffe, Ergebnisse, Methoden und Anwendungen der Linearen und Multilinearen Algebra werden in den Kapiteln 14 (``Lineare Gleichungssysteme'') , 15 (``Vektorraume''), 16 (``Matrizen und Determinanten''), 17 (``Lineare Abbildungen und Matrizen''), 18 (``Eigenwerte und Eigenvektoren''), 19 (``Analytische Geometrie''), 20 (``Euklidische und unit\"are Vektorraume''), 21 (``Quadriken''), 22 (``Tensorrechnung'') und 23 (``Lineare Optimierung'') vermittelt. Was in einer Analysis-III-Vorlesung \"ublicherweise behandelt wird, steht dann in den Kapiteln 24 (``Funktionen mehrer Variablen''), 25 (``Gebietsintegrale''), 26 (``Kurven und Flachen''), 27 (``Vektoranalysis''), 28 (``Differenzialgleichungssysteme'') und 29 (``Partielle Differenzialgleichungen''), wobei im letztgenannten Kapitel sogar ein kurzer Blick auf numerische Methoden geworfen wird. Einige Aspekte der sogenannten ``H\"oheren Analysis'' werden anschlie\ss end in den Kapiteln 30 (``Fouriertheorie''), 31 (``Funktionalanalysis''), 32 (``Funktionentheorie''), 33 (``Integraltransformationen''), 34 (``Spezielle Funktionen'') und 35 (``Optimierung und Variationsrechnung'') erw\"ahnt. An diesen Kapiteln wird \"ubrigens noch einmal die Absurdit\"at der oben kritisierten Formulierung ``gesamtes praxisrelevantes Wissen'' klar: bei der Darstellung der hier angesprochenen Gebiete auf weniger als 200 Seiten kann nicht mehr herauskommen als einige wenige ``appetizer'' ohne jeglichen Tiefgang. Der letzte Teil ist der Wahrscheinlichkeitsrechnung und Statistik gewidmet, mit der sich bekanntlich ja gerade mathematikfeindliche Naturwissenschaftler und Mediziner ``herumschlagen'' m\"ussen. Dieser Teil besteht aus den Kapiteln 36 (``Deskriptive Statistik''), 37 (``Wahrscheinlichkeit''), 38 (``Zuf\"allige Variable''), 39 (``Spezielle Verteilungen''), 40 (``Sch\"atz- und Testtheorie'') und 41 (``Lineare Regression''). Zum Abschluss werden noch (durchaus sinnvolle) Hinweise zu den Aufgaben gegeben, danach aber (leider, s. das n\"achste Referat Zbl 1200.00003, ME 2010f.01180) sogar vollst\"andige L\"osungen. Was unterscheidet dieses Buch nun von vergleichbaren Werken in der immer mehr ausufernden Literatur f\"ur Studienanf\"anger? Nat\"urlich nicht die Auswahl des Stoffes, sondern vielmehr die Art der Darstellung: viele Bilder, Graphen, Beispiele und Aufgaben, aber auch zahlreiche optisch hervorgehobene Einsch\"ube zur Fixierung, Vertiefung und Wiederholung des Gelernten. Zum Teil ist dies ein didaktisch bew\"ahrtes Prinzip, zum Teil einfach nur ein \"asthetischer Genuss, und auch dieser hat in einem Mathematikbuch durchaus seine Berechtigung. Oft schie\ss en die Autoren aber auch \"uber das Ziel hinaus, etwa bei der Flut \"uberfl\"ussiger Fotos (ein Beispiel von vielen: die Aussage, dass das Fehlen von Regen nicht automatisch Sonnenschein bedeutet, durch ein Foto in Abb. 2.5 ``visualisieren'' zu m\"ussen, ist eine Beleidigung des Lesers). Auch das krampfhafte Bem\"uhen der Autoren, jede Kapitel\"uberschrift noch mit einem Untertitel zu versehen, ist nur manchmal erhellend (z.B. ``Integraltransformationen -- Multiplizieren statt Differenzieren''), manchmal aber irref\"uhrend (z.B. ``Reihen -- Summieren bis zum Letzten''), und manchmal einfach nur albern (z.B. ``Funktionentheorie -- von komplexen Zusammenh\"angen''). Insgesamt kann man dieses Buch aber als gelungen bezeichnen: es deckt ziemlich viel Stoff ab, es ist sehr klar und sorgf\"altig geschrieben, und es zeigt, dass auch viele K\"oche (immerhin 6 Autoren mit v\"ollig unterschiedlichem wissenschaftlichen und didaktischen Hintergrund) den Brei durchaus nicht verderben m\"ussen, sondern sogar au\ss erst genie\ss bar und optisch ansprechend aufbereiten k\"onnen. Der Inhalt ist -- wie die Autoren auch selbst bemerken -- eher auf Studenten der Ingenieurs- und Naturwissenschaften zugeschnitten, aber auch ``richtige'' Mathematikstudenten werden bei der Lekt\"ure sicher profitieren und Freude haben, auch wenn diese vermutlich Beweise vermissen werden, mit denen das Buch geizt. Verdienstvoll ist wie gesagt die Vielzahl (mathematischer!) Skizzen und Bilder, die abstrakte Ergebnisse sch\"on illustrieren und deren druckfertige Herstellung sicher sehr viel Zeit und M\"uhe gekostet hat. Sinnvollerweise sollte jede Universit\"ats- und Fachhochschulbibliothek im deutschsprachigen Raum ein Exemplar dieses Handbuches anschaffen, damit es einem gro\ss en Leserkreis zur Verf\"ung steht. \itemrv{J\"urgen Appell (W\"urzburg)} \itemcc{A15 H65 G75 I15 K15} \itemut{textbooks for non-mathematicians; mathematics for engineers} \itemli{} \end

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\TITLE{\bf Kullback-Leibler情報量とSanovの定理} \def\AUTHOR{黒木玄} \def\DATE{2016年6月16日作成% \thanks{% 最新版は下記URLからダウンロードできる. 飽きるまで継続的に更新と訂正を続ける予定である. 6月16日Ver.0.1(10頁). 数時間かけて10頁ほど書いた. ((中略)) %6月17日Ver.0.2(16頁). 区分求積法による高校レベルの方法に関する %付録\ref{sec:quadrature-by-parts}と %多項分布の場合のSanovの定理の厳密に証明するための\secref{sec:Sanov}を追加した. %そこで紹介した証明は階乗に関するStirlingの公式さえ使わない %極めて初等的な証明である. %6月18日Ver.0.2.1. 小さな追加と訂正. %6月18日Ver.0.3(22頁). Sanovの定理からカノニカル分布の導出について説明した %\secref{sec:Gibbs}を追加した. %たくさんのケアレスミスを訂正した. %6月18日Ver.0.3.1. \secref{sec:binom-Gibbs}の誤植を訂正. %6月19日Ver.0.4(23頁). \exampleref{example:binom-Gibbs}の説明の仕方を変更した. %他にも細かな訂正. %相対R\'enyiエントロピーの定義だけに触れた\remarkref{remark:Renyi-Free}を追加した. %6月21日Ver.0.5(26頁). \remarkref{remark:beta}に %「時間を巻き戻してギャンブルをやり直す話」との関係を追記した. %この文書は\remarkref{remark:beta}から読み始めると読み易いかもしれない. %相対Tsallisエントロピーの定義だけに触れた\remarkref{remark:Tsallis}を追加した. %6月22日Ver.0.6(30頁). %タイトルを「KL情報量の解説」から「KL情報量とSanovの定理」に変更した. %\remarkref{remark:Tsallis}などを別の部分節に分離し, 内容も増やした. %さらにその脚注に相対Tsallisエントロピーの定義の必然性を理解できていないことを %正直に書いた. %細かな手直し. %「加法性」に関する\remarkref{remark:additivity}を追加した. %6月23日Ver.0.7(32頁). %相対エントロピーが多項分布の漸近挙動を記述しているのと同じように %相対Tsallisエントロピーで漸近挙動が記述される多項分布のある拡張 %の構成に関する\secref{sec:Tsallis-multinomial-1}を追加した. %6月24日Ver.0.8(36頁). %KL情報量が「距離」のような性質を持っていることを意味する不等式を扱った %\secref{sec:inequalities}を追加した. %相対Renyiエントロピーと相対Tsallisエントロピー関係の説明を %\secref{sec:entropies}に分離した. %このノートには後でCram\'erの定理の解説も追加する予定. %Cram\'erの定理の上からの評価は自明であり, %下からの評価はカノニカル分布に関する大数の弱法則から導かれる. %7月5日Ver.0.9(39頁). %$\limsup$ と $\liminf$ に関する簡単な解説(\secref{sec:limsup})を追加した. %7月6日Ver.0.10(40頁). %相対Tsallisエントロピーと相性のよい %\secref{sec:Tsallis-multinomial-1}とは異なる多項分布の拡張に関する %\secref{sec:Tsallis-multinomial-2}を追加した. %7月7日(七夕)Ver.0.11(41頁). %相対R\'enyiエントロピーと相対Tsallisエントロピーの負値性に関する %\remarkref{remark:negativities}を追加した. %KL情報量の記号を $D[p|q]$ からより標準的な $D(p||q)$ に書き変えた. %置換し忘れがまだ残っている可能性が高い. %7月7日Ver.0.12(48頁). Cram\'erの定理について解説した\secref{sec:Cramer} %を追加した. %7月10日Ver.0.13(49頁). Cram\'erの定理のガンマ分布への適用例の解説 %(\secref{sec:Cramer-Gamma})をより詳しくした. %\lemmaref{lemma:Cramer}の証明の誤りを訂正した. %7月14日Ver.0.15(58頁). Sanovの定理が %Cram\'erの定理の線形空間に値を持つ確率変数への拡張の %特別な場合になっていることを簡単に解説した %\secref{sec:Sanov-from-Cramer}を追加した. 7月15日Ver.0.16(60頁). $\Psi(\beta)=\log\sum_{i=1}^r e^{-\beta_i}q_i$ のLegendre変換が 相対エントロピーになることを詳しく解説した \secref{remark:Psi-S}を追加した. 7月21日Ver.0.17(62頁). 統計力学の教科書におけるカノニカル分布の導出に関する説明をやり直すための \secref{sec:thermal-reservoir}を追加した. Boltzmann因子 $e^{-\beta(u)E_i}$ は熱浴から出て来る. 8月3日Ver.0.18. 微修正. 9月9日Ver.0.19. 多項分布の中心極限定理のStirlingの公式を使った直接的証明の説明 (\secref{sec:multinomial-limit-theorem})を追加. 9月10日Ver.0.20. \secref{sec:multinomial-limit-theorem}の最後にPearsonのカイ二乗 統計量との関係の説明を追加. 9月12日Ver.0.21. この更新記録を大幅に削除した. 更新の歴史については公開した古い版を参照して欲しい. 9月14日Ver.0.22(71頁). Poisson分布からKullback-Leibler情報量や 多項分布の中心極限定理を出すことに関する\secref{sec:Poisson-KL}を追加した. 9月14日Ver.0.22a: 古い版へのリンクの場所を変えた. 9月14日Ver.0.23(70頁): \secref{sec:multinomial-KL}の最初にStirlingの公式の 簡単な証明を付け加えた. なぜかallowdisplaybreaksを入れたら1頁減った. 9月29日Ver.0.24(72頁): Mcmillanの不等式とその応用に関する\secref{sec:Mcmillan}を 追加した. 10月10日Ver.0.24a(73頁): \secref{sec:Mcmillan}の終わりの方を微小に修正. } %%%%%%%%%% \\[\bigskipamount] {\small \href{http://www.math.tohoku.ac.jp/~kuroki/LaTeX/20160616KullbackLeibler.pdf} {\tt http://www.math.tohoku.ac.jp/{\textasciitilde}kuroki/LaTeX/20160616KullbackLeibler.pdf} }} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\PDFTITLE{Kullback-Leibler} \def\PDFAUTHOR{黒木玄} \def\PDFSUBJECT{確率論} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[12pt,twoside]{jarticle} \usepackage{amsmath,amssymb,amsthm} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\usepackage{hyperref} \usepackage[dvipdfmx]{hyperref} \usepackage{pxjahyper} \hypersetup{% 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\newcommand\sres{s^{\operatorname{res}}} \newcommand\diag{\operatorname{diag}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % enumerate % \renewcommand\labelenumi{(\arabic{enumi})} \renewcommand\labelenumii{(\alph{enumii})} \renewcommand\labelenumiii{(\roman{enumiii})} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % 定理環境 % \newtheoremstyle{jplain}% name {}% space above {}% space below {\normalfont}% body font {}% indent amount {\bfseries}% theorem head font {.}% punctuation after theorem head {4pt}% space after theorem head (default: 5pt) {\thmname{#1}\thmnumber{#2}\thmnote{\hspace{2pt}(#3)}}% theorem head spec %\theoremstyle{plain} % 見出しをボールド、本文で斜体を使う %\theoremstyle{definition} % 見出しをボールド、本文で斜体を使わない \theoremstyle{jplain} \newtheorem{theorem}{定理} \newtheorem*{theorem*}{定理} % 番号を付けない \newtheorem{prop}[theorem]{命題} \newtheorem*{prop*}{命題} \newtheorem{lemma}[theorem]{補題} \newtheorem*{lemma*}{補題} \newtheorem{cor}[theorem]{系} \newtheorem*{cor*}{系} \newtheorem{example}[theorem]{例} \newtheorem*{example*}{例} \newtheorem{axiom}[theorem]{公理} \newtheorem*{axiom*}{公理} \newtheorem{problem}[theorem]{問題} \newtheorem*{problem*}{問題} \newtheorem{summary}[theorem]{要約} \newtheorem*{summary*}{要約} \newtheorem{guide}[theorem]{参考} \newtheorem*{guide*}{参考} \newtheorem{assumption}[theorem]{仮定} \newtheorem*{assumption*}{仮定} % %\theoremstyle{definition} % 見出しをボールド、本文で斜体を使わない \theoremstyle{jplain} \newtheorem{definition}[theorem]{定義} \newtheorem*{definition*}{定義} % 番号を付けない % %\theoremstyle{remark} % 見出しをイタリック、本文で斜体を使わない %\theoremstyle{definition} % 見出しをボールド、本文で斜体を使わない \theoremstyle{jplain} \newtheorem{remark}[theorem]{注意} \newtheorem*{remark*}{注意} % \numberwithin{theorem}{section} \numberwithin{equation}{section} \numberwithin{figure}{section} \numberwithin{table}{section} % % 引用コマンド % \newcommand\secref[1]{第\ref{#1}節} \newcommand\theoremref[1]{定理\ref{#1}} \newcommand\propref[1]{命題\ref{#1}} \newcommand\lemmaref[1]{補題\ref{#1}} \newcommand\corref[1]{系\ref{#1}} \newcommand\exampleref[1]{例\ref{#1}} \newcommand\axiomref[1]{公理\ref{#1}} \newcommand\problemref[1]{問題\ref{#1}} \newcommand\summaryref[1]{要約\ref{#1}} \newcommand\guideref[1]{参考\ref{#1}} \newcommand\definitionref[1]{定義\ref{#1}} \newcommand\remarkref[1]{注意\ref{#1}} % \newcommand\figureref[1]{図\ref{#1}} \newcommand\tableref[1]{表\ref{#1}} \newcommand\fnref[1]{脚注\ref{#1}} % % \qed を自動で入れない proof 環境を再定義 % \makeatletter \renewenvironment{proof}[1][\proofname]{\par %\newenvironment{Proof}[1][\Proofname]{\par \normalfont \topsep6\p@\@plus6\p@ \trivlist \item[\hskip\labelsep{\bfseries #1}\@addpunct{\bfseries.}]\ignorespaces }{% \endtrivlist } \renewcommand{\proofname}{証明} %\newcommand{\Proofname}{証明} \makeatother % % 正方形の \qed を長方形に再定義 % \makeatletter \def\BOXSYMBOL{\RIfM@\bgroup\else$\bgroup\aftergroup$\fi \vcenter{\hrule\hbox{\vrule height.85em\kern.6em\vrule}\hrule}\egroup} \makeatother \newcommand{\BOX}{% \ifmmode\else\leavevmode\unskip\penalty9999\hbox{}\nobreak\hfill\fi \quad\hbox{\BOXSYMBOL}} \renewcommand\qed{\BOX} %\newcommand\QED{\BOX} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \title{\TITLE} \author{\AUTHOR} \date{\DATE} \maketitle \paragraph{古い版} 古い版を以下の場所で公開した: \begin{center} {\small \href {http://www.math.tohoku.ac.jp/~kuroki/LaTeX/20160616KullbackLeibler/} {\tt http://www.math.tohoku.ac.jp/{\textasciitilde}kuroki/LaTeX/20160616KullbackLeibler/} } \end{center} Ver.0.1は10ページしかなかった. \tableofcontents %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \setcounter{section}{-1} % 最初の節番号を0にする \section{はじめに} このノートは次のノートの続編である: \begin{quote} 「ガンマ分布の中心極限定理とStirlingの公式」というタイトルの雑多なノート \\ \href{http://www.math.tohoku.ac.jp/~kuroki/LaTeX/20160501StirlingFormula.pdf} {\tt http://www.math.tohoku.ac.jp/{\textasciitilde}kuroki/LaTeX/20160501StirlingFormula.pdf} \end{quote} このノートで使用するStirlingの公式についてはそのノートを見て欲しい. この雑多なノートは「タイトルにいつわりあり」の雑多な内容のノートになっている. このノートの目標はKullback-Leibler情報量(相対エントロピーの $-1$ 倍)および Boltzmann因子 $\exp(-\sum_\nu \beta_\nu f_{\nu}(k))$ で 記述されるカノニカル分布が 必然的に出て来る理由を説明することである% \footnote{インターネット上での日本語による検索結果を眺めたところ, Kullback-Leibler情報量(相対エントロピーの $-1$ 倍)について 「2つの確率分布の``距離''を表わす量」 「2つの確率分布の違いを表わす量」 のように説明しただけですませているものが目立ち, Kullback-Leibler情報量が自然に出て来るシンプルな理由を十分に説明しているものを 見付けることができなかったのでこの解説ノートを書くことにした. Kullback-Leibler情報量が必然的に出て来る理由は 多項分布の $n\to\infty$ での漸近挙動にKullback-Leibler情報量が 自然に出て来るからである. そのことから, $n\to\infty$ のときの経験分布の挙動を Kullback-Leibler情報量で記述可能になる. その結果の数学的に厳密な定式化はSanovの定理と呼ばれている. この解説ノートを書いたもう一つの理由は, Boltzmann因子, カノニカル分布が出て来る理由を 多項分布の $n\to\infty$ での漸近挙動(もしくはSanovの定理)に基づいて 分かり易く説明している日本語の解説をインターネット上に見付けることが できなかったことである. この解説ノートではBoltzmann因子 $e^{-\beta E_i}$ が出て来る理由も詳しく説明する.}. 最初の方では直観的な説明を重視し, 数学的に厳密な議論は行なわない. 測度論の詳細が必要な議論もしない% \footnote{主に有限集合上の確率分布を扱う.}. 第\ref{sec:Sanov}, \ref{sec:Gibbs}節において 可能な範囲内で数学的に厳密な証明を行なう. \bigskip 以下の文献などを参考にした. \vspace{-7.5mm} \begin{thebibliography}{99} \bibitem{Csiszar2006} Csiszar, Imre. A simple proof of Sanov's theorem. Bull Braz Math Soc, New Series 37(4), 453--459, 2006. \\ \href {http://www.emis.ams.org/journals/em/docs/boletim/vol374/v37-4-a2-2006.pdf} {\tt http://www.emis.ams.org/journals/em/docs/boletim/vol374/v37-4-a2-2006.pdf} \bibitem{Csiszar2008} Csisz\'ar, Imre. Axiomatic characterizations of information measures. Entropy, 2008, 10, 261--273. \href {http://www.mdpi.com/1099-4300/10/3/261/pdf} {\tt http://www.mdpi.com/1099-4300/10/3/261/pdf} %\bibitem{Csiszar-Korner-1986} %Csiszar, Imre and K\"orner, J'anos. %Information Theory: Coding Theorems for Discrete Memoryless Systems. %Cambridge University Press; Second edition (August 15, 2011). %(\href %{https://www.google.co.jp/search?q=%22Information+Theory+Coding+Theorems+for+Discrete+Memoryless+Systems%22+Csiszar+Korner} %{Googleで検索}) \bibitem{Cover-Thomas-2006} Cover, M. Thomas and Thomas, Joy A. Elements of Information Theory. Second Edition, John Wiley \& Sons, Inc., 2006, xxiii+748~pages. (\href {https://www.google.co.jp/search?q=Elements+of+information+theory+Cover+Thomas} {Googleで検索}) \bibitem{Dembo-Zeitouni-1998} Dembo, Amir and Zeitouni, Ofer. Large Deviations Techniques and Applications. Stochastic Modelling and Applied Probability (formerly: Applications of Mathematics), 38, Second Edition, Springer, 1998, 396~pages. (\href {https://scholar.google.co.jp/scholar?q=%22Large+deviations+techniques+and+applications%22+Dembo+Zeitouni} {Googleで検索}) \bibitem{Ellis2008} Ellis, Richard, S. The theory of large deviations and applications to statistical mechanics. Lecture notes for \'Ecole de Physique Les Houches, August 5--8, 2008, 123~pages. \\ \href {http://people.math.umass.edu/~rsellis/pdf-files/Les-Houches-lectures.pdf} {\tt http://people.math.umass.edu/{\textasciitilde}rsellis/pdf-files/Les-Houches-lectures.pdf} \bibitem{Okumura2016} 奥村晴彦. Rで楽しむ統計 (Wonderful R 1). 共立出版 (2016/9/8), 208頁. \\ \href {https://github.com/okumuralab/RforFun} {https://github.com/okumuralab/RforFun} \bibitem{Sanov1958} Sanov,~I.~N. On the probability of large deviations of random variables. English translation of Matematicheskii Sbornik, 42(84):1, pp.~11--44. Institute of Statistics Mimeograph Series No.~192, March, 1958. \\ \href {http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS_1958_192.pdf} {\tt http://www.stat.ncsu.edu/information/library/mimeo.archive/ISMS\_1958\_192.pdf} \bibitem{Suyari2004} Suyari, Hiroki. Mathematical structure derived from the $q$-multinomial coefficient in Tsallis statistics. \arxivref{cond-mat/0401546} \bibitem{Sutari-Scarfone} Suyari, Hiroki and Scarfone, Antonio Maria. $\alpha$-divergence derived as the generalized rate function in Tsallis statistics. 信学技報, vol.~114, no.~138, IT2014-16, pp.~25--30, 2014年7月. \href {http://www.ieice.org/ken/paper/201407178BPp/} {\tt http://www.ieice.org/ken/paper/201407178BPp/} \bibitem{Tasaki} 田崎晴明. 統計力学 I, II. 新物理学シリーズ, 培風館 (2008/12), 合計525ページ. \\ \href {https://www.amazon.co.jp/dp/4563024376} {\tt https://www.amazon.co.jp/dp/4563024376} \\ \href {https://www.amazon.co.jp/dp/4563024384} {\tt https://www.amazon.co.jp/dp/4563024384} \bibitem{vanErven-Harremoes} Tim van Erven and Peter Harremo\"es. R\'enyi divergence and Kullback-Leibler divergence. \arxivref{1206.2459} \bibitem{vanRamon2013} Ramon van Handel. Lecture~3: Sanov's theorem. Stochastic Analytic Seminar (Princeton University), Blog Article, 10 October 2013. \\ \href {https://blogs.princeton.edu/sas/2013/10/10/lecture-3-sanovs-theorem/} {\tt https://blogs.princeton.edu/sas/2013/10/10/lecture-3-sanovs-theorem/} \bibitem{Vasicek1980} Vasicek, Oldrich Alfonso. A conditional law of large numbers. Ann.\ Probab., Volume~8, Number~1 (1980), 142--147. \\ \href {http://projecteuclid.org/euclid.aop/1176994830} {\tt http://projecteuclid.org/euclid.aop/1176994830} \end{thebibliography} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{多項分布からKullback-Leibler情報量へ} \label{sec:multinomial-KL} 多項分布にStirlingの公式を単純に代入するだけで 自然かつ容易にKullback-Leibler情報量(もしくはその $-1$ 倍の相対エントロピー) が現われることを説明したい. \paragraph{準備 (Stirlingの公式)} Stirlingの公式はガンマ函数について知っていれば以下のような計算で容易に証明される. 実際, $x=n+\sqrt{n}\,y=n(1+y/\sqrt{n})$ による置換積分を実行すると \begin{align*} n!=\Gamma(n+1)=\int_0^\infty e^{-x}x^n\,dx =n^n e^{-n}\sqrt{n}\int_{-\sqrt{n}}^\infty e^{-\sqrt{n}\,y}(1+y/\sqrt{n})^n\,dy \end{align*} となり, \begin{align*} \log(e^{-\sqrt{n}\,y}(1+y/\sqrt{n})^n) & =-\sqrt{n}\,y+n\log(1+y/\sqrt{n}) \\ & =-\sqrt{n}\,y+n\left(y/\sqrt{n}-y^2/(2n)+O\left(1/(n\sqrt{n}\,)\right)\right) \\ & = -y^2/2 + O\left(1/\sqrt{n}\right) \end{align*} なので, $n\to\infty$ とすると% \footnote{$e^{-\sqrt{n}\,y}(1+y/\sqrt{n})^n$ は $y<0$ で $n$ について単調増加, $y>0$ で $n$ について単調減少であること から極限と積分の交換を証明できる. Lebesgueの収束定理を使えば容易だが, 使わなくても容易である.}, \begin{align*} \int_{-\sqrt{n}}^\infty e^{-\sqrt{n}\,y}(1+y/\sqrt{n})^n\,dy \longrightarrow \int_{-\infty}^\infty e^{-y^2/2}\,dy = \sqrt{2\pi}. \end{align*} これで次のStirlingの公式が得られた: \begin{align*} & n! = n^n e^{-n}\sqrt{2\pi n}(1+o(1)), %\\ & \qquad \log n! = n \log n - n +\frac{1}{2}\log n + \log\sqrt{2\pi} + o(1). \end{align*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{母集団分布が $q_i$ の多項分布} $q_i\geqq 0$, $\sum_{i=1}^r q_i=1$ とする. 1回の独立試行で状態 $i$ が確率 $q_i$ で得られる状況を考える. $q=(q_1,\ldots,q_r)$ を{\bf 母集団分布}と呼ぶことにする. そのような試行を $n$ 回繰り返したとき, 状態 $i$ が生じた回数を $k_i$ と書く($k_i$ は確率変数である). そのとき状態 $i$ が生じた割合 $k_i/n$ (これを{\bf 経験分布}と呼ぶことにする) が $n\to\infty$ でどのように振る舞うかを調べよう. これは, サイコロ(歪んでいてもよい)を $n$ 回ふったときの $i$ の目が出た割合の分布 (経験分布)が $n\to\infty$ でどのように振る舞うかを調べる問題だと言ってよい. 大数の法則によって $n\to\infty$ で $k_i/n\to q_i$ となるが, 後で条件付き確率を考えたいので母集団分布から離れた分布が 経験分布として現われる確率がどのように減衰するかを知りたい. \secref{sec:Boltzmann-factors}では 条件付き確率を考えることによってBoltzmann因子が得られることを説明する. 我々はこれから母集団分布 $q=(q_1,\ldots,q_r)$ を任意に固定し, 経験分布 $(k_1/n,\ldots,k_r/n)$ の確率分布を考え, その $n\to\infty$ での様子を調べることになる. $n$ 回の独立試行で状態 $i$ が $k_i$ 回得られる確率は, $\sum_{i=1}^r k_i=n$ のとき \[ \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r} \tag{$*$} \] になり, 他のとき $0$ になる(多項分布). $p_i\geqq 0$, $\sum_{i=1}^r p_i=1$ と仮定する. $n$ 回の独立試行で状態 $i$ が得られた割合 $k_i/n$ がほぼ $p_i$ になるとき, 経験分布はほぼ $p_i$ になると言うことにする. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{サンプルサイズを大きくしたときの多項分布の漸近挙動} \label{sec:log} $n\to\infty$ のとき経験分布がほぼ $p_i$ になる確率がどのように振る舞うか を知りたい. そこで $n\to\infty$ のとき, $k_i$ たちが \[ k_i= np_i+O(\log n) = np_i\left(1 + O\left(\frac{\log n}{n}\right)\right) \tag{$**$} \] を満たしていると仮定し, 上の確率($*$)がどのように振る舞うかを調べよう. この仮定のもとで $\log(k_i/n)=\log p_i+O((\log n)/n)$ が成立することに注意せよ% \footnote{Taylor展開 $\log(1+x)=x-x^2/2+x^3/3-x^4/4+\cdots$ より.}. Stirlingの公式と $\sum_{i=1}^r k_i=n$ より \begin{align*} & \log n! = n\log n - n + O(\log n) = \sum_{i=1}^r k_i\log n - \sum_{i=1}^r k_i + O(\log n), \\ & \log k_i! = k_i\log k_i - k_i + O(\log k_i) = k_i\log k_i - k_i + O(\log n), \\ & \log q_i^{k_i} = k_i\log q_i. \end{align*} これらを上の確率($*$)の対数に代入すると $k_i$ の項はキャンセルする. さらに($**$)を代入すると次が得られる: \begin{align*} \log\left(\frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r}\right) & = - n\sum_{i=1}^r \frac{k_i}{n}\left(\log\frac{k_i}{n}-\log q_i\right) + O(\log n) \\ & = -n\sum_{i=1}^r p_i(\log p_i - \log q_i)+O(\log n) \\ & = -n\sum_{i=1}^r p_i\log\frac{p_i}{q_i}+O(\log n). \end{align*} 同様の計算を区分求積法を用いた高校レベルの計算で実行することもできる (\secref{sec:quadrature-by-parts}). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Kullback-Leibler情報量と相対エントロピーの定義} \secref{sec:log}の結果は \[ D(p||q)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i} \] とおくと次のように書き直される: \[ \log\left(\frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r}\right) =-n D(p||q) + O(\log n). \] 左辺は経験分布 $k_i/n$ がほぼ $p_i$ になる確率の対数を意味していることに注意せよ. $D(p||q)$ を{\bf Kullback-Leibler 情報量}(カルバック・ライブラー情報量) もしくは{\bf Kullback-Leibler divergence}と呼ぶ. Kullback-Leibler情報量の $-1$ 倍 \[ S(p||q) = -D(p||q) = - \sum_{i=1}^r p_i\log\frac{p_i}{q_i} \] を{\bf 相対エントロピー}と呼ぶことにする. 相対エントロピーは本質的に $n$ が大きなときの 「母集団分布が $q_i$ のとき経験分布がほぼ $p_i$ となる確率の対数の $n$ 分の1」 である. 対数を取る前の公式は次の通り: \[ (\text{$n$ 回の独立試行で経験分布がほぼ $p_i$ になる確率}) =\exp(-n D(p||q) + O(\log n)). \] もしも $D(p||q)>0$ ならば, $n$ を十分に大きくすれば $O(\log n)$ の項は $n D(p||q)$ の項と比較して 無視できる量になるので, この確率は $\exp(-n D(p||q))$ の部分でほぼ決まっていると考えてよい. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Kullback-Leibler情報量の基本性質} \label{sec:KL-prop} Kullback-Leibler情報量 $D(p||q)=\sum_{i=1}^r p_i\log(p_i/q_i)$ は 函数 $f(x)=x\log x$ を用いて, $D(p||q)=\sum_{i=1}^r f(p_i/q_i)q_i$ と表わされるので, $D(p||q)$ の $p=(p_1,\ldots,p_r)$ の函数としての性質を 調べるためには函数 $f(x)=x\log x$ の性質を調べればよい. $f'(x)=\log x + 1$, $f''(x)=1/x>0$ なので函数 $f(x)$ は下に狭義凸である. ゆえに函数 $f(x)$ はその接線の函数で下から押さえられる. 特に $f(x)\geqq f(1)+f'(1)(x-1)=x-1$ (等号の成立と $x=1$ は同値). ゆえに \begin{align*} & D(p||q) =\sum_{i=1}^r f\left(\frac{p_i}{q_i}\right)q_i \geqq \sum_{i=1}^r\left(\frac{p_i}{q_i}-1\right)q_i =0, \\ & \text{等号の成立は $p_i=q_i$ ($i=1,\ldots,r$) と同値.} \end{align*} さらに $f(x)$ が下に狭義凸であることより, $D(p||q)$ も $p$ の函数として下に狭義凸であることもわかる. このようにKullback-Leibler情報量の値は $0$ 以上になり, 最小値 $0$ が実現することと分布 $p_i$ が母集団分布 $q_i$ に 等しくなることは同値である. ゆえに, 分布 $p_i$ が母集団分布 $q_i$ に等しくないとき, $D(p||q)>0$ となるので, 経験分布がほぼ $p_i$ になる確率は $n\to\infty$ で $n$ について指数函数的に $0$ に収束する. したがって, $n\to\infty$ で経験分布 $k_i/n$ は母集団分布 $q_i$ に近付く. これは{\bf 大数の法則}の成立を意味している. Kullback-Leibler情報量は母集団分布 $q_i$ のもとで分布 $p_i$ が経験分布として どれだけ確率的に実現し難いかを表わしている. 異なる分布が実現する確率の比は $n\to\infty$ で Kullback-Leibler情報量の差の $-n$ 倍の指数函数のように振る舞う. ゆえにKullback-Leibler情報量がほんの少しでも違っていれば, Kullback-Leibler情報量がより大きな方の分布は 相対的にほとんど生じないということもわかる. ゆえに, ある条件を課して分布 $p_i$ が生じる条件付き確率を考える場合には, 課した条件のもとでKullback-Leibler情報量が最小になる分布に 経験分布は(条件付き確率の意味で)近付くことになる ({\bf 条件付き大数の法則}, {\bf 条件付き極限定理}). この法則を{\bf 最小Kullback-Leibler情報量の原理}と呼ぶ. $n$ が非常に大きなとき, ある条件のもとで経験的に実現される分布は 課した条件のもとでKullback-Leibler情報量が最小の分布になる. 相対エントロピーはKullback-Leibler情報量の $-1$ 倍だったので, 条件付きで分布 $p_i$ が経験的に生じる確率を考える場合には 課した条件のもとで相対エントロピーが最大になる分布に 経験分布が近付くことになる. この言い換えを{\bf 最大相対エントロピーの原理}と呼ぶ. $n$ が大きなとき、ある条件のもとで経験的に実現される分布は 課した条件のもとで相対エントロピーが最大になるような分布である. 補足. 説明の簡素化のために 条件 $B$ が成立しているとき条件 $A$ が常に成立していると仮定する. このとき, 条件 $A$ のもとで条件 $B$ が成立する確率(条件付き確率)は, 条件 $B$ が成立する確率を条件 $A$ が確率で割ったものと定義される. このように条件付き確率は確率の商で定義される. だから, 確率の商が $n\to\infty$ でどのように振る舞うかを確認できれば, 条件付き確率がどのように振る舞うかがわかる. 上の議論ではこの考え方を使った. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{二項分布の場合の計算例} \label{sec:binom-Sanov} $r=2$, $q_1=q$, $q_2=1-q$ の「コイン投げ」(もしくは「丁半博打」)の場合を考える. この場合に多項分布は二項分布になる. このとき, $p_1=p$, $p_2=1-p$ とおくと, Kullback-Leibler情報量は次のように表わされる: \[ D(p||q)=p\log \frac{p}{q}+(1-p)\log\frac{1-p}{1-q}. \] これは $p=q$ で最小値 $0$ になり, $p$ が $q$ から 離れれば離れるほど大きくなる. Kullback-Leibler情報量は分布の経験的な生じ難さを表わす量なので $q$ から遠い $p$ ほど経験的に生じ難くなる. しかも $p$ が経験的に生じる確率は $n\to\infty$ で $\exp(-nD(p||q)+O(\log n))$ と振る舞う. ゆえに, 複数の $p$ の生じる確率を比較すると, $D(p||q)$ が相対的に大きな $p$ が生じる確率は $n\to\infty$ で比の意味で相対的に $0$ に近付く. 以上を踏まえた上で次の問題について考えよう. \medskip {\bf 問題}\enspace $n$ は非常に大きいと仮定する. $n$ 回のコイン投げの結果表が出た割合が $a$ 以上になったとする. このとき表の割合はどの程度になるだろうか? \medskip 大数の法則より, $n\to\infty$ で表の割合は $q$ に近付く. ゆえに $0\leqq a<q$ のとき, 表の割合が $a$ 以上であるという条件は $n\to\infty$ で常に実現することになる. だから, $0\leqq a<q$ のとき, 表の割合が $a$ 以上の場合に制限{\bf しても}, $n$ が大きければ表の割合はほぼ $q$ に等しくなっていると考えられる. 問題は $q<a\leqq 1$ の場合である. そのとき, $n$ が大きくなればなるほど, 表の割合が $a$ 以上になる確率は $0$ に近付く. 上の問題は表の割合が $a$ 以上になる場合に制限したときに 表の割合がほぼ $p$ になる確率(条件付き確率)が どのように振る舞うかという問題になる. この場合には上で計算したKullback-Leibler情報量が役に立つ. $p\geqq a$ という条件のもとでの $D(p||q)$ の最小値は $p=a$ で 実現される. ゆえに条件付き大数の法則より, $n\to\infty$ で経験分布は $p=a$ に近付く. $q<a\leqq 1$ のとき, 表の割合が $a$ 以上の場合に制限{\bf すると}, $n$ が大きければ表の割合はほぼ $a$ に等しくなっていると考えられる. 以上の結果から以下の公式が成立していることもわかる: \[ \lim_{n\to\infty} \frac{1}{n}\log\sum_{k/n\geqq a} \binom{n}{k}q^k(1-q)^{n-k} =-\inf_{p\geqq a} D(p||q) = \begin{cases} -D(q||q)=0 & (0\leqq a\leqq q), \\ -D(a||q) & (q<a\leqq 1). \end{cases} \] 対数を使わない形式でこの公式を書き下すと, \[ \sum_{k/n\geqq a} \binom{n}{k}q^k(1-q)^{n-k} = \exp\left(-n\inf_{p\geqq a}D(p||q) + o(n)\right). \] 左辺は表の割合が $a$ 以上になる確率である. $n\to\infty$ のとき確率には $D(p||q)$ が最小になる分布だけが強く効いて来る. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{max-plus代数への極限やLaplaceの方法との関係} 実数または $-\infty$ の $a,b$ に対して演算 \[ (a,b)\mapsto\max\{a,b\}, \qquad (a,b)\mapsto a+b \] を考えたもの(半環(semiring), 半体(semifield)と呼ばれている)を {\bf max-plus代数}と呼ぶ. (max-plus代数は{\bf 超離散化}や{\bf tropical mathematics} や各種{\bf 正値性を扱う問題}などに登場する重要な``代数''である. 体は加減剰余が自由にできる``代数''のことであるが, 半体は加乗除は自由にできるが引算は自由に できない``代数''のことである. 引算が自由にできなくても意味のある面白い数学を作れる.) 大雑把には, $\max$ は $0$ 以上の実数の足算に対応しており, $+$ は掛算に対応していて, $-\infty$ は足算の単位元 $0$ に対応している. その対応は $\log$ を取って極限を取ることによって与えられる. すなわち, 次の公式が成立している: \[ \lim_{n\to\infty}\frac{1}{n}\log(e^{na}+e^{nb})=\max\{a,b\}, \qquad \lim_{n\to\infty}\frac{1}{n}\log(e^{na}e^{nb})=a+b. \] 後者は自明である. 前者の公式は次のようにして確かめられる. $a\geqq b$ と仮定すると, $b-a\leqq 0$ となるので, $e^{n(b-a)}$ は有界になり, \[ \frac{1}{n}\log(e^{an}+e^{nb}) =\frac{1}{n}\log\left(e^{na}\left(1+e^{n(b-a)}\right)\right) =a+\frac{1}{n}\log\left(1+e^{n(b-a)}\right) \to a \quad (n\to\infty) \] となる. これで前者の公式も示された. より一般に次が成立している: \[ \lim_{n\to\infty}\frac{1}{n}\log\sum_{i=1}^r \exp(na_i+O(\log n)) = \max\{a_1,\ldots,a_r\}. \] このように $\exp(na_i+O(\log n))$ のように振る舞う量の和の対数の $1/n$ 倍では $n\to\infty$ のとき最大の $a_i$ の部分のみが効いて来る. 対数を使わない方の公式を書き下すと, \[ \sum_{i=1}^r \exp(na_i+O(\log n)) = \exp(n\max\{a_1,\ldots,a_r\}+o(n)) \qquad (n\to\infty). \] これは積分の場合のLaplaceの方法の類似であるとみなされる. 積分の場合は次の通り. 適切な設定のもとで次が成立している: \[ \int_\alpha^\beta \exp\biggl(-nf(x)+O(\log n)\biggr)\,dx = \exp\left(-n\inf_{\alpha\leqq x\leqq\beta} f(x) + o(n)\right) \qquad (n\to\infty). \] $f(x)$ が $\alpha<x=x_0<\beta$ で一意的な最小値を持ち, $f''(x_0)>0$ ならば, \[ \int_\alpha^\beta e^{-nf(x)}g(x)\,dx = e^{-nf(x_0)}g(x_0)\sqrt{\frac{2\pi}{n f''(x_0)}}\,(1+o(1)) \qquad (n\to\infty). \] このような漸近挙動の計算の仕方は{\bf Laplaceの方法}と呼ばれている. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{区分求積法による高校レベルの計算でKL情報量を出す方法} \label{sec:quadrature-by-parts} 多項分布の $n\to\infty$ での漸近挙動を以下のようにして, 区分求積法を使った高校数学っぽい方法で調べることもできる. $q_i\geqq 0$, $\sum_{i=1}^r q_i=1$ とし, 非負の整数 $a,b_i$ は $\sum_{i=1}^r b_i=a$ をみたしているとし, \[ p_i=\frac{b_i}{a}=\frac{Nb_i}{Na} \]とおく. このとき \[ \lim_{N\to\infty}\frac{1}{Na} \log\left(\frac{(Na)!}{(Nb_1)!\cdots(Nb_r)!}q_1^{Nb_1}\cdots q_r^{Nb_r}\right) =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \tag{$*$} \] これの右辺は相対エントロピー(Kullback-Leibler情報量の $-1$ 倍)である. すなわち \[ \lim_{N\to\infty} \left(\frac{(Na)!}{(Nb_1)!\cdots(Nb_r)!}q_1^{Nb_1}\cdots q_r^{Nb_r}\right)^{1/(Na)} =\frac{1}{(p_1/q_1)^{p_1}\cdots (p_r/q_r)^{p_r}}. \] 区分求積法でこれを証明してみよう. 公式($*$)を示せばよい. $N\to\infty$ のとき \begin{align*} & \frac{1}{Na} \log\left(\frac{(Na)!}{(Nb_1)!\cdots(Nb_r)!}q_1^{Nb_1}\cdots q_r^{Nb_r}\right) \\ & =\frac{1}{Na} \left( \sum_{k=1}^{Na}\log k -\sum_{i=1}^r\sum_{k=1}^{Nb_i}\log k +\sum_{i=1}^rNb_i\log q_i \right) \\ & =\frac{1}{Na} \left( \sum_{k=1}^{Na}\log \frac{k}{Na} -\sum_{i=1}^r\sum_{k=1}^{Nb_i}\log \frac{k}{Na} +\sum_{i=1}^rNb_i\log q_i \right) \\ & =\frac{1}{Na}\sum_{k=1}^{Na}\log \frac{k}{Na} -\sum_{i=1}^r\frac{1}{Na}\sum_{k=1}^{Nb_i}\log \frac{k}{Na} +\sum_{i=1}^r p_i\log q_i \\ & \to \int_0^1 \log x\,dx - \sum_{i=1}^r\int_0^{p_i}\log x\,dx + \sum_{i=1}^r p_i\log q_i \\ & =[x\log x-x]_0^1 -\sum_{i=1}^r[x\log x-x]_0^{p_i} +\sum_{i=1}^r p_i\log q_i %\\ & =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \end{align*} 2つ目の等号で括弧の内側に \( Na\log(Na)-\sum_{i=1}^rNb_i\log(Na)=0 \) を挿入した. それによって区分求積法を適用できる形に変形できた. 以上の結果は次が成立することを意味している: $N\to\infty$ のとき \[ (\text{$Na$ 回の試行で経験分布が $p_i=b_i/a$ になる確率})^{1/(Na)}\to\frac{1}{(p_1/q_1)^{p_1}\cdots(p_r/q_r)^{p_r}}. \] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Kullback-Leibler情報量と多項分布の中心極限定理の関係} \label{sec:multinomial-limit-theorem} この部分節は連続ツイート \begin{center} \href {https://twitter.com/genkuroki/status/773390919450132481} {\tt https://twitter.com/genkuroki/status/773390919450132481} \end{center} の内容をまとめ直したものである. \paragraph{基本になる公式の導出} $q_i,p_i>0$, $\sum_{i=1}^r q_i=\sum_{i=1}^r p_i=1$, $k_i$ は正の整数で $\sum_{i=1}^r k_i=n$ であるとする. 多項分布における確率 \begin{align*} \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \end{align*} が, $k_i=np_i+\eps_i$, $p_i=q_i+x_i/\sqrt{n}$, $\eps_i=o(\sqrt{n})$ のとき% \footnote{実際には $|\eps_i|\leqq 1/2$ (特に $\eps_i=O(1)$)に取れる.}, $n\to\infty$ でどのように振る舞うかを調べたい. そこで階乗 $n!$, $k_i!$ にStirlingの公式 \begin{align*} n! = n^n e^{-n}\sqrt{2\pi n}(1+O(1/n)), \qquad k_i! = k_i^{k_i} e^{-k_i}\sqrt{2\pi k_i}(1+O(1/n)) \end{align*} を代入すると \begin{align*} \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} = \frac {n^n e^{-n}\sqrt{2\pi n}(1+O(1/n))} {k_1^{k_1} e^{-k_1}\sqrt{2\pi k_1}\cdots k_r^{k_r} e^{-k_r}\sqrt{2\pi k_r}}. \end{align*} 分子の $e^{-n}$ と分母の $e^{-k_i}$ たちは $\sum_{i=1}^r k_i=n$ より キャンセルして消える. $n^n=n^{k_1}\cdots n^{k_r}$ と $k_i=(k_i/n)n$ を代入して整理すると \begin{align*} \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} = \left(\frac{k_1/n}{q_1}\right)^{-k_1}\cdots\left(\frac{k_r/n}{q_r}\right)^{-k_r} \frac{1+O(1/n)}{\sqrt{(2\pi n)^{r-1}(k_1/n)\cdots(k_r/n)}}. \tag{$*$} \end{align*} この公式が以下の議論の基本になる. この公式($*$)をよく眺めれば多項分布の中心極限定理と Kullback-Leibler情報量の関係がわかる% \footnote{公式($*$)に $n$ が大きなときの多項分布の様子に関する情報が ほぼすべて含まれていると考えてよい.}. \paragraph{多項分布の中心極限定理} 多項分布の多次元正規分布による近似を得るためには \begin{align*} k_i = np_i + \eps_i, \qquad p_i = q_i + \frac{x_i}{\sqrt{n}}, \qquad \eps_i = o(\sqrt{n}) \end{align*} を($*$)に代入すればよい% \footnote{実際には $|\eps_i|\leqq 1/2$ に取れる.}. $\sum_{i=1}^r k_i=n$ と $\sum_{i=1}^r q_i=\sum_{i=1}^r p_i=1$ より, $\sum_{i=1}^r \eps_i=0$, $\sum_{i=1}^r x_i=0$ となり, \begin{align*} & \frac{k_i}{n} =q_i\left(1+\frac{x_i}{\sqrt{n}\,q_i}+\frac{\eps_i}{nq_i}\right) =q_i(1+o(1)), \qquad k_i = nq_i + \sqrt{n}\,x_i+\eps_i, \\ & \log\left(\frac{k_i/n}{q_i}\right)^{-k_i} =-(nq_i+\sqrt{n}\,x_i+\eps_i) \log\left(1+\frac{x_i}{\sqrt{n}\,q_i}+\frac{\eps_i}{nq_i}\right) \\ & \qquad =-(nq_i+\sqrt{n}\,x_i+\eps_i) \left( \frac{x_i}{\sqrt{n}\,q_i}+\frac{\eps_i}{nq_i} +\frac{1}{2} \left(\frac{x_i}{\sqrt{n}\,q_i}+\frac{\eps_i}{nq_i}\right)^2 +o\left(\frac{1}{n}\right) \right) \\ & \qquad =-\sqrt{n}\,x_i-\eps_i+\frac{x_i^2}{2q_i}+o(1) \end{align*} なので, $\sum_{i=1}^r(\sqrt{n}\,x_i+\eps_i)=0$ より, \begin{align*} \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} = \frac {\displaystyle\exp\left(\frac{1}{2}\sum_{i=1}^r\frac{x_i^2}{q_i}\right)} {\sqrt{(2\pi n)^{r-1}q_1\cdots q_r}} \times(1+o(1)). \end{align*} ゆえに $dk_i=\sqrt{n}\,dx_i$ たちを両辺に沿えると, \begin{align*} \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \,dk_1\cdots dk_{r-1} = \frac {\displaystyle\exp\left(\frac{1}{2}\sum_{i=1}^r\frac{x_i^2}{q_i}\right)} {\sqrt{(2\pi)^{r-1}q_1\cdots q_r}} \,dx_1\cdots dx_{r-1} \times(1+o(1)). \end{align*} $\sum_{i=1}^r k_i=1$, $\sum_{i=1}^r x_i=0$ であることに注意せよ. この結果は多項分布が $n$ が大きいときに多次元正規分布で近似できることを意味している (多項分布の中心極限定理). \paragraph{KL情報量の導出} Kullback-Leibler情報量を得るためには, ($*$)の両辺の対数を取って, \begin{align*} k_i = np_i + o(n) = np_i(1+o(1)) \end{align*} を代入して $o(n)$ の項を無視すればよい. $k_i=np_i+o(n)=np_i(1+o(1))$ のとき \begin{align*} \log\left(\frac{k_i/n}{q_i}\right)^{-k_i} =-(np_i+o(n))\log\left(\frac{p_i(1+o(1))}{q_i}\right) =-np_i\log\frac{p_i}{q_i}+o(n) \end{align*} でかつ $\log n=o(n)$ なので \begin{align*} \log\left(\frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r}\right) =-n\sum_{i=1}^r p_i\log\frac{p_i}{q_i} + o(n) =-n D(p||q)+o(n). \end{align*} ここで $D(p||q)$ はKullback-Leibler情報量である. \paragraph{KL情報量と多項分布の中心極限定理の関係} もしもぴったり $k_i=np_i$ ならばKullback-Leibler情報量は($*$)の右辺の因子 \begin{align*} \left(\frac{k_1/n}{q_1}\right)^{-k_1}\cdots\left(\frac{k_r/n}{q_r}\right)^{-k_r} \end{align*} の対数の $-1/n$ 倍に一致する. $k_i=np_i+o(n)$ の場合には, Kullback-Leibler情報量は この因子の対数の $-1/n$ 倍の $n\to\infty$ での極限に一致する. そして多項分布の多次元正規分布による近似の 指数函数部分もこの因子から得られるのであった. したがって多項分布を近似する多次元正規分布の指数函数部分の対数の $-1$ 倍 \begin{align*} \frac{1}{2}\sum_{i=1}^r \frac{x_i^2}{q_i} \end{align*} はKullback-Leibler情報量から得られるはずである. Kullback-Leibler情報量 $D(p||q)$ は $p_i=q_i$ のとき最小値 $0$ になるのであった. その点で $n D(p||q)$ をTaylor展開した結果の2次の部分から 多項分布を近似する多次元正規分布の確率密度函数の指数函数部分の対数の $-1$ 倍が得られる. そのことを確認しよう. まず $\sum_{i=1}^r x_i=0$ と制限せずに $nD(p||q)$ に $p_i=q_i+x_i/\sqrt{n}$ を代入して, $x_i$ たちについて展開すると \begin{align*} nD(p||q) & =\sum_{i=1}^r (nq_i+\sqrt{n}\,x_i)\log\left(1+\frac{x_i}{\sqrt{n}\,q_i}\right) \\ & =\sum_{i=1}^r (nq_i+\sqrt{n}\,x_i) \left( \frac{x_i}{\sqrt{n}\,q_i}-\frac{x_i^2}{2nq_i^2}+o\left(\frac{1}{n}\right) \right) \\ & =\sum_{i=1}^r \left( \sqrt{n}\,x_i+\frac{x_i^2}{2q_i}+o(1) \right). \end{align*} ここで $\sum_{i=1}^r x_i=0$ を使うと, \begin{align*} nD(p||q) = \frac{1}{2}\sum_{i=1}^r \frac{x_i^2}{q_i} + o(1). \end{align*} このことから多項分布の多次元正規分布による近似は $p_i$ たちが $q_i$ たちに近いときに Kullback-Leibler情報量のTaylor展開の3次以上の項を無視することに相当すること がわかる. \paragraph{Pearsonのカイ2乗統計量との関係} 多項分布における \begin{align*} \sum_{i=1}^n \frac {((\text{$i$ の個数の観測値})-(\text{$i$ の個数の期待値}))^2} {(\text{$i$ の個数の期待値})} =\sum_{i=1}^r \frac{(k_i-nq_i)^2}{nq_i} \end{align*} をPearsonのカイ2乗統計量と呼ぶ. これに $k_i=nq_i+\sqrt{n}\,x_i+o(\sqrt{n})$ を代入して整理すると, \begin{align*} \sum_{i=1}^r \frac{(k_i-nq_i)^2}{nq_i} =\sum_{i=1}^r \frac{x_i^2}{q_i} + o(1). \end{align*} ゆえに $n$ が大きいとき, Pearsonのカイ2乗統計量は多項分布を近似する 多次元正規分布にしたがう $x_i$ たちに関する $\sum_{i=1}^r x_i^2/q_i$ で 近似される. 多項分布を近似する多次元正規分布の確率密度函数の指数函数部分 は $\exp\left(-(1/2)\sum_{i=1}^r x_i^2/q_i\right)$ の形をしているので あった. このことから, $n$ が大きいとき, Pearsonのカイ2乗統計量は カイ2乗分布に近似的にしたがうことがわかる. 多項分布($r$ 項分布)を近似する多次元正規分布の確率密度函数は 条件 $\sum_{i=1}^r x_i=0$ で定義される $r-1$ 次元の台を持つので, そのカイ2乗分布の自由度は $r-1$ になる. \begin{remark*}[カイ2乗分布とは] $Z_1,\ldots,Z_s$ は標準正規分布にしたがう独立な確率変数であるとする. 各々の $Z_i$ について $f(Z_i)$ の期待値は \begin{align*} E[f(Z_i)] = \int_\R f(z_i)\frac{e^{-z_i^2/2}}{\sqrt{2\pi}}\,dz_i \end{align*} と表わされる. このとき確率変数 $Y=\sum_{i=1}^s Z_i^2$ が したがう確率分布を自由度 $s$ の{\bf カイ二乗分布}と呼ぶ. カイ二乗分布における期待値は次のように表わされる: \begin{align*} E[f(Y)] = \int_0^\infty f(y) \frac{e^{-y/2}y^{s/2-1}}{\Gamma(s/2)2^{s/2}}\,dy. \end{align*} 実際, \begin{align*} E[f(Y)] &=\text{const.} \int_{\R^s} f\left(\sum_{i=1}^s z_i^2\right)e^{-\sum_{i=1}^s z_i^2/2}\,dz_1\cdots dz_s \\ & =\text{const.} \int_0^\infty f(r^2)e^{-r^2/2}r^{s-1}\,dr %\\ & =\text{const.} \int_0^\infty f(y)e^{-y/2}y^{s/2-1}\,dy. \end{align*} 2つ目の等号で $r^2=\sum_{i=1}^s z_i^2$ とおき, 積分を $r$ と球面上の積分に書き変えた. 球面の面積は半径の $s-1$ 乗に比例するので $r^{s-1}$ の因子が出る. 球面上の積分を実行し, 出て来た定数を const.\ に繰り込んだ. 3つ目の等号で $y=r^2$ とおいた. 定数倍 const.\ は全確率の総和が $1$ になるという条件から自動的に決まる. $A=[a_{ij}]$ は固有値がすべて正の $s$ 次実対称行列であるとし, その逆行列を $A^{-1}=[b_{ij}]$ と書くことにする. $(X_1,\ldots,X_s)$ は($s$ 次元の台を持つ)確率密度函数 \begin{align*} \frac{\exp\left(-\frac12\sum_{i,j=1}^s b_{ij}x_ix_j\right)}{\sqrt{\det(2\pi A)}} \end{align*} が定める多次元正規分布に従う確率変数であるとする. このとき, 確率密度函数の指数函数部分の対数の $-2$ 倍に対応する確率変数 \begin{align*} Y=\sum_{i,j=1}^s b_{ij}X_i X_j \end{align*} も自由度 $s$ のカイ二乗分布にしたがう. すなわち, {\bf 台の次元が $s$ の多次元正規分布の確率密度函数の指数函数部分の 対数の $-2$ 倍に対応する確率変数は自由度 $s$ のカイ二乗分布にしたがう.} このことからカイ2乗分布は一般の多次元正規分布に付随する(最も)基本的な 確率分布であると考えることができる. 上の $Y$ が自由度 $s$ のカイ二乗分布にしたがう理由は以下の通り. 本質的に正値実対称行列の線形代数である. 実対称行列 $A$ はある直交行列 $U=[u_{ij}]$ と対角行列 $D=\diag(\alpha_1,\ldots,\alpha_s)$ によって $A=UDU^{-1}=UDU^T$ と表わされる. $A$ の固有値 $\alpha_i$ はすべて正なので $\sqrt{D}=\diag(\sqrt{\alpha_1},\ldots,\sqrt{\alpha_s})$, $C=U\sqrt{D}$ とおくと, $A=CC^T$ となる. そのとき $A^{-1}=(C^{-1})^T C^{-1}$ なので \begin{align*} Y =\sum_{i,j=1}^s b_{ij}X_i X_j =X^TA^{-1}X =(C^{-1}X)^T (C^{-1}X). \end{align*} ここで $X$ は確率変数 $X_i$ を第 $i$ 成分とする列ベクトルである. すなわち, 確率変数の列ベクトル $Z=[Z_i]$ を $Z=C^{-1}X$ と定めると, \begin{align*} Y = Z^T Z = \sum_{i=1}^s Z_i^2. \end{align*} $Z_i$ たちが独立で各々が標準正規分布にしたがうことを示せれば, $Y$ が自由度 $s$ のカイ2乗分布にしたがうことがわかる. そのためには $Z_i$ たちの分散共分散行列が単位行列になることを示せば十分である. $Z_i$ たちの分散共分散行列の定義は $E[ZZ^T]$ であり, $X_i$ たちの分散共分散行列は $E[XX^T]=A=CC^T$ なので \begin{align*} E[ZZ^T]=E[(C^{-1}X)(C^{-1}X)^T]=C^{-1}E[XX^T](C^T)^{-1} =C^{-1}CC^T(C^T)^{-1}=E. \end{align*} これで示すべきことがすべて示された. \qed \end{remark*} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Poisson分布とKullback-Leibler情報量の関係} \label{sec:Poisson-KL} この部分節は文献 \cite{Okumura2016} のp.80におけるポアソン分布を使った説明 の数学的正当化に関する \begin{center} \href {https://twitter.com/genkuroki/status/775549559405555713} {\tt https://twitter.com/genkuroki/status/775549559405555713} \end{center} 以降の連続ツイートの内容をまとめ直したものである. \paragraph{Poisson分布} $\lambda>0$ であるとする. 確率変数 $K$ がパラメーター $\lambda$ の Poisson分布にしたがうとは, $k=0,1,2,\ldots$ に対する $K=k$ の確率が \begin{align*} P(K=k)=e^{-\lambda}\frac{\lambda^k}{k!} \end{align*} となっていることである. 確率の総和が $1$ になることは \begin{align*} \sum_{k=0}^\infty P(K=k) =e^{-\lambda}\sum_{k=0}^\infty\frac{\lambda^k}{k!} =e^{-\lambda}e^\lambda =1 \end{align*} と確かめられる. Poisson分布は二項分布の極限として得られる. $0<q<1$ に対する二項分布の確率 $n!/(k!(n-k)!)\cdot q^k(1-q)^{n-k}$ に $q=\lambda/n$ を代入すると, \begin{align*} & \frac{n(n-1)\cdots(n-k+1)}{k!} \left(\frac{\lambda}{n}\right)^k\left(1-\frac{\lambda}{n}\right)^{n-k} =\left(1-\frac{\lambda}{n}\right)^n\frac{\lambda^k}{k!} \times A_n, \\ & A_n =\frac{(1-0/n)(1-1/n)\cdots(1-(k-1)/n)}{(1-\lambda/n)^k} \to 1 \qquad (n\to\infty) \end{align*} となる. これで, 二項分布は $nq=\lambda$ が一定のままで $n\to\infty$ とするとPoisson分布に収束することがわかった. Poisson分布の確率 $P(K=k)$ は単位時間で $k$ 回のイベントが起こる確率で あると解釈される. Poisson分布の期待値 $E[K]$ と分散 $E[K^2]-E[K]^2$ は次のように計算される: \begin{align*} & E[K] = \sum_{k=0}^\infty k P(K=k) = e^{-\lambda}\sum_{k=0}^\infty k \frac{\lambda^k}{k!} = e^{-\lambda}\sum_{k=1}^\infty \frac{\lambda^k}{(k-1)!} = e^{-\lambda}\lambda e^\lambda = \lambda, \\ & E[K(K-1)] = e^{-\lambda}\sum_{k=2}^\infty \frac{\lambda^k}{(k-2)!} =e^{-\lambda}\lambda^2 e^\lambda =\lambda^2 \\ & E[K^2]-E[K]^2 = E[K]+\lambda^2-\lambda^2 = E[K] = \lambda. \end{align*} Poisson分布のモーメント母函数 $E[e^{tK}$ は次のように計算される: \begin{align*} E[e^{tK}] = e^{-\lambda}\sum_{k=0}^\infty e^{tk}\frac{\lambda^k}{k!} = e^{-\lambda}e^{\lambda e^t} = e^{\lambda(e^t-1)}. \end{align*} 特にPoisson分布はパラメーター $\lambda$ について再生性を持つ% \footnote{独立な確率変数 $X$, $Y$ がそれぞれパラメーター $\lambda_X$, $\lambda_Y$ のPoisson分布にしたがうとき, $X+Y$ はパラメーター $\lambda_X+\lambda_Y$ の Poisson分布にしたがう.}. ゆえに, 中心極限定理より, $K_\lambda$ がパラメーター $\lambda$ のPoisson分布にしたがう確率変数であるとき, $(K_\lambda-\lambda)/\sqrt{\lambda}$ は $\lambda\to\infty$ で 標準正規分布にしたがう確率変数に弱収束する. したがって, 独立な確率変数たち $K_{i,\lambda_i}$ が それぞれパラメーター $\lambda_i$ のPoisson分布にしたがうとき, \begin{align*} \sum_{i=1}^s \frac{(K_{i,\lambda_i}-\lambda_i)^2}{\lambda_i} \end{align*} は $\lambda_i$ たちを同意に大きくする極限で自由度 $s$ のカイ2乗分布に したがう確率変数に弱収束する. $O_i=K_{i,\lambda_i}$ を観測度数と解釈し, $E_i=\lambda_i$ を期待度数と解釈すると, 上の量は \begin{align*} \sum_{i=1}^s \frac{(O_i-E_i)^2}{E_i} \end{align*} と書き直され, よくPearsonのカイ二乗統計量として使われるスタイルになる. \paragraph{Poisson分布の中心極限定理} Poisson分布の中心極限定理のStirlingの定理を使った直接的証明の概略を説明しよう. $f(x)$ は $\R$ 上の実数値有界連続函数であるとする. $K_\lambda$ はパラメーター $\lambda$ のPoisson分布にしたがう確率変数であるとし, $X_\lambda=(K_\lambda-\lambda)/\sqrt{\lambda}$ とおく. このとき \begin{align*} E[f(X_\lambda)] & =e^{-\lambda}\sum_{k=0}^\infty f\left(\frac{k-\lambda}{\sqrt{\lambda}}\right)\frac{\lambda^k}{k!} =\sum_{x\in\Z_{\geqq-\lambda}/\sqrt{\lambda}} f(x)\frac{\lambda^{\lambda+\sqrt{\lambda}\,x}e^{-\lambda}}{(\lambda+\sqrt{\lambda}\,x)!} \\ & =\sum_{x\in\Z_{\geqq-\lambda}/\sqrt{\lambda}} f(x) \frac {\lambda^{\lambda+\sqrt{\lambda}\,x}e^{-\lambda}(1+O(1/\lambda)))}{(\lambda+\sqrt{\lambda}\,x)^{\lambda+\sqrt{\lambda}\,x} e^{-\lambda-\sqrt{\lambda}\,x} \sqrt{2\pi(\lambda+\sqrt{\lambda}\,x)}} \\ & =\sum_{x\in\Z_{\geqq-\lambda}/\sqrt{\lambda}} f(x) \left(1+\frac{x}{\sqrt{\lambda}}\right)^{-(\lambda+\sqrt{\lambda}\,x)} e^{\sqrt{\lambda}\,x} \frac{1+O(1/\lambda)}{\sqrt{2\pi(1+x/\sqrt{\lambda})}}\frac{1}{\sqrt{\lambda}} \\ & =\sum_{x\in\Z_{\geqq-\lambda}/\sqrt{\lambda}} f(x) \frac{e^{-x^2/2}(1+O(1/\sqrt{\lambda}))}{\sqrt{2\pi(1+x/\sqrt{\lambda})}}\frac{1}{\sqrt{\lambda}} \\ & \longrightarrow \int_{-\infty}^\infty f(x)\frac{e^{-x^2/2}}{\sqrt{2\pi}}\,dx \qquad (\lambda\to\infty). \end{align*} 3つ目の等号でStirlingの公式を使った. 5つ目の等号で \begin{align*} & -(\lambda+\sqrt{\lambda}\,x)\log\left(1+\frac{x}{\sqrt{\lambda}}\right)+\sqrt{\lambda}\,x =-(\lambda+\sqrt{\lambda}\,x) \left( \frac{x}{\sqrt{\lambda}}-\frac{x^2}{2\lambda}+O\left(\frac{1}{\lambda\sqrt{\lambda}}\right) \right) +\sqrt{\lambda}\,x \\ & =-\sqrt{\lambda}\,x+\frac{x^2}{2}-x^2+\sqrt{\lambda}\,x +O\left(\frac{1}{\lambda\sqrt{\lambda}}\right) =-\frac{x^2}{2} +O\left(\frac{1}{\sqrt{\lambda}}\right) \end{align*} を使った. \paragraph{Poisson分布から多項分布へ} $q_i>0$, $\sum_{i=1}^r q_i=1$ と仮定する. 多項分布における確率は \begin{align*} \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r} =n!\prod_{i=1}^r \frac{q_i^{k_i}}{k_i!} \end{align*} と書ける. ただし, $k_i$ たちの動く範囲は $\sum_{i=1}^r k_i=n$ に制限されている. したがって, $\lambda_i=nq_i$ とおくと, \begin{align*} n!\prod_{i=1}^r \frac{q_i^{k_i}}{k_i!} =\frac{n!}{n^n e^{-n}} \prod_{i=1}^r \left( e^{-nq_i}\frac{(nq_i)^{k_i}}{k_i!} \right) =\frac{n!}{n^n e^{-n}} \prod_{i=1}^r \left( e^{-\lambda_i}\frac{\lambda_i^{k_i}}{k_i!} \right). \end{align*} この式中の積の因子はパラメーター $\lambda_i=nq_i$ のPoisson分布の 確率の式の形をしている. このことから, 多項分布は独立なPoisson分布の積を $\sum_{i=1}^r k_i=n$ で制限したものになっていることがわかる. \paragraph{単独のPoisson分布からKL情報量の各項へ} 単独のPoisson分布からKullback-Leibler情報量の「各項」が出て来ることを 説明しよう. パラメーター $\lambda$ のPoisson分布の確率にStirlingの公式を適用すると, \begin{align*} e^{-\lambda}\frac{\lambda^k}{k!} =\frac{e^{-\lambda}\lambda^k}{k^k e^{-k}\sqrt{2\pi k}(1+O(1/k))} =\left(\frac{k}{\lambda}\right)^{-k}e^{k-\lambda}\frac{1+O(1/k)}{\sqrt{2\pi k}}. \end{align*} この形の式が基本になる. この式の右辺の最初の二つの因子の積の対数は \begin{align*} \log\left(\left(\frac{k}{\lambda}\right)^{-k}e^{k-\lambda}\right) =-k\log\frac{k}{\lambda}+k-\lambda. \end{align*} これはほとんどKullback-Leibler情報量の各項の形をしている. さらにそれらしく見えるようにするためには, $k=np$, $\lambda=nq$ を代入して \begin{align*} -k\log\frac{k}{\lambda}+k-\lambda =-n\left(p\log\frac{p}{q}-(p-q)\right) \end{align*} と変形すればよい. 右辺の括弧の中にKullback-Leibler情報量の各項の形の 式が現れている. $p\log(p/q)$ は $p=q$ で最小にならないが, そこから $p-q$ を引いた結果は $p=q$ で最小になる. Poisson分布の中心極限定理 は $-k\log(k-\lambda)+k-\lambda$ の $k=\lambda$ におけるTaylor展開 \begin{align*} -k\log\frac{k}{\lambda}+k-\lambda =-\frac{1}{1\cdot2}\frac{(k-\lambda)^2}{\lambda} +\frac{1}{2\cdot3}\frac{(k-\lambda)^3}{\lambda^2} -\frac{1}{3\cdot4}\frac{(k-\lambda)^4}{\lambda^3} +\cdots \end{align*} を二次の項までで切る近似をすればよい. より正確に述べると, このTaylor展開に $k=\lambda+\sqrt\lambda\,x$ を代入して, $\lambda\to\infty$ の極限を考える. $k=\lambda+\sqrt\lambda\,x$ のとき \begin{align*} -k\log\frac{k}{\lambda}+k-\lambda \longrightarrow -\frac{x^2}{2} \qquad (\lambda\to\infty). \end{align*} このことから, $k=\lambda+\sqrt\lambda\,x$ のとき, $k/\lambda=1+x/\sqrt{\lambda}$, $dk=\sqrt{\lambda}\,dx$ より \begin{align*} e^{-\lambda}\frac{\lambda^k}{k!}\,dk =\left(\frac{k}{\lambda}\right)^{-k}e^{k-\lambda}\frac{1+O(1/k)}{\sqrt{2\pi k}}\,dk \longrightarrow \frac{e^{-x^2}}{\sqrt{2\pi}}\,dx \qquad (\lambda\to\infty) \end{align*} となることもわかる. これでPoisson分布の中心極限定理は, Poisson分布から得られるKL情報量の各項のTaylor展開を二次までで切る近似を することによって得られることがわかった. $-k\log(k/\lambda)+k-\lambda$ の $k=\lambda$ におけるTaylor展開の二次の項 に現われる $(k-\lambda)^2/\lambda$ は $O=(\text{観測度数})=k$, $E=(\text{期待度数})=\lambda$ とおくと \begin{align*} \frac{(k-\lambda)^2}{\lambda} =\frac{((\text{観測度数})-(\text{期待度数}))^2}{(\text{期待度数})} =\frac{(O-E)^2}{E} \end{align*} と統計学の教科書でよく見るスタイルで書ける. Poisson分布の中心極限定理から, $E$ が大きなとき, $(O-E)^2/E$ は近似的に自由度 $1$ のカイ二乗分布に従うことがわかる. \paragraph{複数のPoisson分布の積からKL情報量へ} 単独のPoisson分布からKullback-Leibler情報量の各項が得られたので, 複数のPoisson分布の積からKullback-Leibler情報量そのものが得られる. 単独のPoisson分布に関する計算より \begin{align*} \prod_{i=1}^r\left(e^{-\lambda_i}\frac{\lambda_i^{k_i}}{k_i!}\right) =\prod_{i=1}^r \left( \left(\frac{k_i}{\lambda_i}\right)^{-k_i}e^{k_i-\lambda_i}\frac{1+O(1/k_i)}{\sqrt{2\pi k_i}} \right). \end{align*} そして, $k_i=np_i$, $\lambda_i=nq_i$ とおくと \begin{align*} \log\prod_{i=1}^r \left( \left(\frac{k_i}{\lambda_i}\right)^{-k_i}e^{k_i-\lambda_i} \right) &=-\sum_{i=1}^r\left(k_i\log\frac{k_i}{\lambda_i}+k_i-\lambda_i\right) \\ & =-n\sum_{i=1}^r\left(p_i\log\frac{p_i}{q_i}-(p_i-q_i)\right). \end{align*} ゆえに $\sum_{i=1}^r p_i=\sum_{i=1}^r q_i$ と仮定すると \begin{align*} \log\prod_{i=1}^r \left( \left(\frac{k_i}{\lambda_i}\right)^{-k_i}e^{k_i-\lambda_i} \right) =-n\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \end{align*} 右辺はちょうどKullback-Leibler情報量の $-n$ 倍の形をしている. Kullback-Leibler情報量は多項分布の確率の $n\to\infty$ での漸近挙動から 得られるのであった. そのことを 「多項分布がPoisson分布の積を $\sum_{i=1}^r k_i=n$ という条件で 制限することによって得られること」を用いて示すこともできる. Poisson分布の積と多項分布の関係より, $q_i>0$, $\sum_{i=1}^r q_i=1$, $\lambda_i=nq_i$, $\sum_{i=1}^r k_i=n$ とすると, \begin{align*} \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r} &=\frac{n!}{n^n e^{-n}} \prod_{i=1}^r \left( e^{-\lambda_i}\frac{\lambda_i^{k_i}}{k_i!} \right) \\ & = \sqrt{2\pi n}(1+O(1/n)) \prod_{i=1}^r \frac{(k_i/\lambda_i)^{-k_i} e^{k_i-\lambda_i}}{\sqrt{2\pi k_i}(1+O(1/k_i))}. \end{align*} Stirlingの公式を用いた. この式が基本になる. さらに $k_i=np_i$ とおくと, \begin{align*} \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r} =\frac{1+O(1/n)}{\sqrt{(2\pi n)^{r-1}\prod_{i=1}^r p_i}} \prod_{i=1}^r\left(\frac{p_i}{q_i}\right)^{-np_i}. \end{align*} したがって, \begin{align*} \log\left(\frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r}\right) =-n\sum_{i=1}^r p_i\log\frac{p_i}{q_i} + O(\log n). \end{align*} 右辺にKullback-Leibler情報量 $D(p||q)=\sum_{i=1}^r p_i\log(p_i/q_i)$ が現れた. \paragraph{複数のPoisson分布の積から多項分布の中心極限定理へ} 上の設定をそのまま引き継ぐ. \begin{align*} & \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r} = \sqrt{2\pi n}(1+O(1/n)) \prod_{i=1}^r \frac{(k_i/\lambda_i)^{-k_i} e^{k_i-\lambda_i}}{\sqrt{2\pi k_i}(1+O(1/k_i))}, \\ & \log((k_i/\lambda_i)^{-k_i}e^{k_i-\lambda_i}) =-k_i\log(k_i/\lambda_i)+k_i-\lambda_i =-\frac{1}{2}\frac{(k_i-\lambda_i)^2}{\lambda_i} +\frac{1}{6}\frac{(k_i-\lambda_i)^3}{\lambda_i^2} -\cdots \end{align*} より, \[ k_i =\lambda_i+\sqrt{\lambda_i}\,x_i =nq_i+\sqrt{nq_i}\,x_i, \qquad x_i=\frac{k_i-\lambda_i}{\sqrt{\lambda_i}}=\frac{k_i-nq_i}{\sqrt{nq_i}} \] とおくと, $dk_i=\sqrt{nq_i}\,dx_i$ なので \begin{align*} \frac{n!}{k_1!\cdots k_r!} q_1^{k_1}\cdots q_r^{k_r}\,dk_1\cdots dk_{r-1} \longrightarrow \frac {\exp\left(-\frac{1}{2}\sum_{i=1}^r x_i^2\right)} {\sqrt{(2\pi)^{r-1}q_r}} \,dx_1\cdots dx_{r-1} \qquad (n\to\infty). \end{align*} このようにPoisson分布を経由して多項分布の中心極限定理を出すこともできる. 以上のような見方をすると, {\bf 多項分布よりもPoisson分布の方が基本的な分布である} ように見えて来る. 多項分布は複数のPoisson分布の積を $\sum_{i=1}^r k_i=n$ という条件で制限することによって得られる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{条件付き大数の法則からBoltzmann因子へ} \label{sec:Boltzmann-factors} 条件付き大数の法則(最小Kullback-Leibler情報量の原理, 最大相対エントロピーの原理) からBoltzmann因子で記述される分布が自然に得られることを説明したい. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{問題の設定} 母集団分布が $q=(q_1,\ldots,q_r)$ の多項分布の設定に戻る. $n$ 回の独立試行によって各々の $i$ について 状態 $i$ が生じた割合 $k_i/n$ がほぼ $p_i$ に等しいとき, 経験分布がほぼ $p=(p_1,\ldots,p_r)$ に等しくなると言うことにする. その確率について \[ (\text{$n$ 回で経験分布がほぼ $p$ になる確率}) = \exp(-n D(p||q) + O(\log n)) \qquad (n\to\infty) \] が成立しているのであった. 次の問題を考える: 分布 $p=(p_1,\ldots,p_r)$ に $s$ 個の条件 \[ \sum_{i=1}^r f_{\nu,i}p_i \approx c_\nu \qquad (\nu=1,2,\ldots,s) \tag{$*$} \] を課す. ただし, $\R^r$ のベクトルたち $(1,1,\ldots,1),(f_{\nu,1},\ldots,f_{\nu,r})$ ($\nu=1,\ldots,s$) は一次独立であると仮定しておく. 経験分布がこの条件を満たす分布 $p$ にほぼ 等しい場合に制限したとき, 経験分布の確率分布は $n\to\infty$ で どのように振る舞うか? たとえば, 状態 $i$ のエネルギーが $E_i$ の場合に \[ \sum_{i=1}^r E_i p_i \approx U \] という条件 (すなわちエネルギーの経験的平均値がほぼ $U$ に等しくなっているという条件) を課したとき, 経験分布が $n\to\infty$ でどのように振る舞うか? たとえば, サイコロを振って $i$ の目が出たら, 賞金を $E_i$ ペリカ もらえるとき, \[ \sum_{i=1}^r E_i p_i \approx U \] という条件 (すなわち1回あたりの賞金の経験的平均値がほぼ $U$ ペリカに等しくなっているという条件) を課したとき, 経験分布が $n\to\infty$ でどのように振る舞うか? 以上の2つの例では $s=1$ である. 複数の条件を課せば $s>1$ となる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Boltzmann因子の導出} 条件($*$)のもとでの経験分布の条件付き確率は $n\to\infty$ で, 条件 $\sum_{i=1}^r p_i=1$ と条件($*$)のもとで Kullback-Leibler情報量 $D(p||q)=\sum_{i=1}^r p_i\log(p_i/q_i)$ が 最小値になる分布 $p=(p_1,\ldots,p_r)$ に集中することになる. その条件付き最小値問題を解くためにLagrangeの未定乗数法を使おう. (Kullback-Leibler情報量が $p$ について下に狭義凸な函数であったことを思い出そう.) そのために \[ L = \sum_{i=1}^r p_i \log\frac{p_i}{q_i} + (\lambda-1)\left(\sum_{i=1}^r p_i-1\right) + \sum_{\nu=1}^s\beta_\nu\left(\sum_{i=1}^r f_{\nu,i}p_i - c_\nu \right) \] とおく. ここで $\lambda-1$, $\beta_\nu$ が未定乗数である. 未定乗数と $p_i$ で $L$ を偏微分した結果がすべて $0$ になるという 方程式 \begin{align*} & 0=\frac{\d L}{\d\lambda} = \sum_{i=1}^r p_i - 1, \tag{1} \\ & 0=\frac{\d L}{\d\beta_\nu} = \sum_{i=1}^r f_{\nu,i}p_i - c_\nu \qquad (\nu=1,\ldots,s), \tag{2} \\ & 0=\frac{\d L}{\d p_i} = \log\frac{p_i}{q_i} + \lambda + \sum_{\nu=1}^s \beta_\nu f_{\nu,i} \qquad (i=1,\ldots,r) \tag{3} \end{align*} を解けばよい. (3)より, \[ p_i = \exp\left(-\lambda-\sum_{\nu=1}^s \beta_\nu f_{\nu,i} \right)q_i \] これを(1)に代入すると, \[ Z:= e^\lambda = \sum_{i=1}^r e^{-\sum_{\nu=1}^s \beta_\nu f_{\nu,i}}q_i, \qquad p_i = \frac{1}{Z}e^{-\sum_{\nu=1}^s \beta_\nu f_{\nu,i}}q_i \tag{4} \] となることがわかる. この $Z$ は{\bf 分配函数}と呼ばれる. このように $p_i$ と $Z=e^\lambda$ は $\beta_\nu$ たちの函数になっている. $\beta_\nu$ たちは(4)を(2)に代入することによって決定される. $\exp\left(-\sum_{\nu=1}^s \beta_\nu f_{\nu,i}\right)$ を {\bf Boltzmann因子}と呼ぶことにする. Boltzmann因子は母集団分布 $q_i$ と条件付きの経験分布 $p_i$ が どれだけ異なるかを記述している. このようにして求められた分布 $p_i$ を{\bf カノニカル分布}と呼ぶことにする. 条件($*$)が成立している場合に制限した場合の経験分布は, $n\to\infty$ で以上で求めた分布 $p=(p_1,\ldots,p_r)$ に近付く (条件付き大数の法則より). $n$ が巨大ならば経験分布はカノニカル分布の形をしているとしてよい. たとえば $s=1$, $f_{1,i}=E_i$, $c_1=U$, $\beta_1=\beta$ のとき, \begin{align*} p_i = \frac{1}{Z}e^{-\beta E_i}q_i, \qquad Z = \sum_{i=1}^r e^{-\beta E_i}q_i, \qquad -\frac{\d\log Z}{\d\beta} = \frac{1}{Z} \sum_{i=1}^r E_i e^{-\beta E_i}q_i = U. \end{align*} これらの公式は $q_i$ たちが互いにすべて等しい場合には 統計力学におけるBoltzmann因子を用いた確率分布の記述に一致している. カノニカル分布に対する相対エントロピー $S(p||q)=-D(p||q)=-\sum_{i=1}^r p_i\log(p_i/q_i)$ の別の表示を求めよう: $\log(p_i/q_i)=-\sum_{\nu=1}^s\beta_\nu f_{\nu,i}-\log Z$, $\sum_{i=1}^r p_i=1$, $\sum_{i=1}^r f_{\nu,i}p_i=c_\nu$ なので \begin{align*} S(p||q) = \sum_{\nu=1}^s \beta_\nu c_\nu + \log Z. \end{align*} たとえば $s=1$, $f_{1,i}=E_i$, $c_1=U$, $\beta_1=\beta$ のとき \[ S(p||q) = \beta U + \log Z. \] {\bf 自由エネルギー} $F$ を $F=-\beta^{-1}\log Z$ と定義すると, \[ S(p||q) = \beta(U-F) \] この公式は, Boltzmann定数が含まれていない点を除けば, 統計力学を知っている人達にとってお馴染みの公式だろう% \footnote{Boltzmann定数が $1$ になる単位系を採用することもできる.}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{母分布が連続型の場合から連続型の指数型分布族が得られること} 母集団分布が確率密度函数 $q(x)$ で与えられている場合を考えよう. この場合には $n$ 回の独立試行の結果得られる経験分布の確率密度函数が ほぼ $p(x)$ になる確率の対数の $1/n$ 倍は $n\to\infty$ で \[ S(p||q)=-D(p||q) = -\int p(x)\log\frac{p(x)}{q(x)}\,dx \] に近付くと考えられる. 分布 $p(x)$ に以下の条件を課す: \[ \int f_\nu(x)p(x)\,dx = c_\nu \qquad (\nu=1,\ldots,s). \] 前節と同様にして, この条件のもとで $D(p||q)$ を最小にする 確率密度函数 $p(x)$ を求めると次のようになることがわかる: \begin{align*} & p(x)=\frac{1}{Z}e^{-\sum_{\nu=1}^s \beta_\nu f_\nu(x)}q(x), \\ & Z=\int e^{-\sum_{\nu=1}^s \beta_\nu f_\nu(x)}q(x)\,dx, \\ & -\frac{\d\log Z}{\d\beta_\nu} = \frac{1}{Z}\int f_\nu(x) e^{-\sum_{\nu=1}^s \beta_\nu f_\nu(x)}q(x) \,dx = c_\nu. \end{align*} このようにな形の連続型確率分布の族を{\bf 連続型の指数型分布族}と呼ぶ. 積分が和の場合には{\bf 離散型の指数型分布族}と呼ばれる. たとえば以下の確率分布はすべて指数型分布族に含まれている. \paragraph{二項分布:} $0<\theta<1$ のとき, $-\beta=\log\theta-\log(1-\theta)$ とおくと, $k=0,1,\ldots,n$ について \begin{align*} %& p_k = \binom{n}{k} \theta^k(1-\theta)^{n-k} =\frac{e^{-\beta k}q_k}{Z}, \qquad %\\ & q_k = \binom{n}{k}\frac{1}{2^n}, \qquad Z = \frac{1}{2^n(1-\theta)^n}. \end{align*} この場合と条件付き大数の法則の関係については \exampleref{example:binom-Gibbs}も参照せよ. \paragraph{多項分布:} $\theta_i\geqq 0$, $\theta_r>0$, $\sum_{i=1}^r\theta_i=1$ であるとし, $-\beta_i=\log\theta_i-\log\theta_r$ とおくと, \\ $k_1+\cdots+k_r=n$ のとき \begin{align*} & p_{k_1,\ldots,k_r} = \frac{n!}{k_1!\cdots k_r!}\theta_1^{k_1}\cdots \theta_r^{k_r} =\frac{e^{-\sum_{i=1}^{r-1}\beta_i k_i}q_{k_1,\ldots,k_r}}{Z}, \\ & q_{k_1,\ldots,k_r} =\frac{n!}{k_1!\cdots k_r!}\frac{1}{r^n}, \qquad Z=\frac{1}{r^n\theta_r^n} \end{align*} \paragraph{正規分布:} \[ p(x) = \frac{e^{-(x-\mu)^2/(2\sigma^2)}}{\sqrt{2\pi}} = \frac{e^{-(1/(2\sigma^2))x^2+(\mu/\sigma^2)x}}{Z}, \qquad Z=e^{\mu^2/(2\sigma^2)}\sqrt{2\pi\sigma^2}. \] $\mu=0$, $\sigma=1$ の場合については\secref{sec:normal-Gibbs}も参照して欲しい. 正規分布の確率密度函数 $p(x)$ は平均 $\mu$ と分散 $\sigma^2$ を指定したときに, すなわち $\int_\R p(x)\,dx=1$, \[ \int_\R x\,p(x)\,dx=\mu, \qquad \int_\R x^2\,p(x)\,dx = \sigma^2+\mu^2 \] という条件のもとで, エントロピー \[ S(p) = -\int_\R p(x)\log p(x)\,dx \] が最大になる $p(x)$ として特徴付けられる. \paragraph{Gamma分布:} $x>0$ において \[ p(x)=\frac{e^{-x/\tau}x^{\alpha-1}}{\tau^{\alpha}\Gamma(\alpha)} =\frac{e^{-x/\tau+(\alpha-1)\log x}}{Z}, \qquad Z=\tau^{\alpha}\Gamma(\alpha). \] Gamma分布の確率密度函数 $p(x)$ は $\int_\R p(x)\,dx=1$, \[ \int_0^\infty x\,p(x)\,dx=c_1, \qquad \int_0^\infty (\log x)\, p(x)\,dx = c_2 \] という条件のもとでエントロピー \[ S(p(x)] = - \int_0^\infty p(x)\log p(x)\,dx \] が最大になる $p(x)$ として特徴付けられる. 以下も同様である. \paragraph{第二種Beta分布:} $x>0$ において \[ p(x) =\frac{1}{B(\alpha,\beta)}\frac{x^{\alpha-1}}{(1+x)^{\alpha+\beta}} =\frac{e^{(\alpha-1)\log x-(\alpha+\beta)\log(1+x)}}{Z}, \qquad Z=B(\alpha,\beta). \] \paragraph{自由度 $n$ の $t$ 分布を $1/\sqrt{n}$ でスケールしたもの:} 自由度 $n$ の $t$ 分布の確率密度は \[ \rho(t)\,dt = \frac{1}{c_n} \left(1+\frac{t^2}{n}\right)^{-(n+1)/2}\,dt, \qquad c_n=\sqrt{n}B(1/2,n/2) =\frac{\sqrt{n\pi}\,\Gamma(n/2)}{\Gamma((n+1)/2)} \] であった. $p(x)\,dx=\rho(\sqrt{n}\,x)\,d(\sqrt{n}\,x)$, $\beta=(n+1)/2$ とおくと \[ p(x) =\frac{1}{Z}\frac{1}{(1+x^2)^{(n+1)/2}} =\frac{e^{-\beta\log(1+x^2)}}{Z}, \qquad Z=B(1/2,n/2). \] \paragraph{第一種Beta分布:} $0<x<1$ について \[ p(x) =\frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} =\frac{e^{(\alpha-1)\log x+(\beta-1)\log(1-x)}}{Z}, \quad Z=B(\alpha,\beta). \] \paragraph{Poisson分布:} \[ p_k = \frac{e^{-\lambda}\lambda^k}{k!} =\frac{e^{-(\log\lambda)k}q_k}{Z}, \quad q_k=\frac{e}{k!}, \quad Z=e^{\lambda+1}. \] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{標準正規分布の導出例} \label{sec:normal-Gibbs} 例として $s=1$, $f_1(x)=x^2$, $c_1=1$, $q(x)=1$ の場合にどうなるかを 計算してみよう% \footnote{$q(x)=1$ なのでこの場合に $q(x)$ は確率密度函数にならない. しかし, 以下の計算の結論は正しい.}. この場合に上の結果は, $n$ 回の独立試行の結果得られた $x^2$ の 経験的期待値 $(x_1^2+\cdots+x_n^2)/n$ について \[ \frac{x_1^2+\cdots+x_n^2}{n}=1 \] という条件を課したとき, $n\to\infty$ で $x$ の経験的分布がどうなるかを求めることに等しい. 上の公式を使うと \[ p(x)=\frac{1}{Z}e^{-\beta x^2}, \qquad Z=\int_\R e^{-\beta x^2}\,dx=\sqrt{\pi}\beta^{-1/2}, \qquad -\frac{\d\log Z}{\d\beta}=\frac{1}{2\beta}=1. \] ゆえに $\beta=1/2$, $Z=\sqrt{2\pi}$, $p(x)=e^{-x^2/2}/\sqrt{2\pi}$ となる. すなわち $n\to\infty$ で得られる分布は標準正規分布になる. この結果は $\R^n$ 内の半径の2乗が $n$ の原点を中心とする $n-1$ 次元球面上の 一様分布の $1$ 次元部分空間への射影が $n\to\infty$ で標準正規分布に 収束することを意味している. すなわち次の公式が成立している: \[ \lim_{n\to\infty}\int_{\sqrt{n}\,S^{n-1}} f(x_1)\,\mu_n(dx) =\int_\R f(x)\frac{e^{-x^2/2}}{\sqrt{2\pi}}\,dx. \] ここで $\sqrt{n}\,S^{n-1}$ は原点を中心とする半径 $\sqrt{n}$ の $n-1$ 次元球面 \[ \{\,(x_1,\ldots,x_n)\in\R^n\mid x_1^2+\cdots+x_n^2=n\,\} \] を表わし, $\mu_n$ はその上の一様確率分布であり, $f(x_1)$ の $x_1$ は球面上の点 $(x_1,\ldots,x_n)$ の射影である. この極限の公式は通常の多変数の微積分の計算で直接に確認できる% \footnote{次の雑多なノートのMaxwell-Boltzmann則の節にその直接的な計算が書いてある. \\ \href{http://www.math.tohoku.ac.jp/~kuroki/LaTeX/20160501StirlingFormula.pdf} {\tt http://www.math.tohoku.ac.jp/{\textasciitilde}kuroki/LaTeX/20160501StirlingFormula.pdf}}. 以上の計算例を見れば, 指数型分布族に属する他の確率分布 がどのような条件を課したときに自然に現われるかも理解できると思う. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{多項分布の場合のSanovの定理} \label{sec:Sanov} 多項分布の場合のSanovの定理の主張を明確に述べて厳密に証明しておくことにする. Stirlingの公式さえ使わない易しい証明を紹介する. この節の証明はブログ記事 \cite{vanRamon2013} で 解説されている証明と本質的に同じものである. そのブログには参考になる解説がたくさんある. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sanovの定理の主張} 有限集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の集合を $\cP$ と書く: \[ \cP = \{\,p=(p_1,\ldots,p_r)\in\R^r\mid p_1,\ldots,p_r\geqq 0,\ p_1+\cdots+p_r=1 \,\}. \] $\cP$ は $r-1$ 次元の閉単体である. たとえば $r=3$ のとき $\cP$ は正三角形になる. 確率分布 $q=(q_1,\ldots,q_r)\in\cP$ を任意に取って固定する. 確率変数 $X_1,X_2,\ldots$ は集合 $\{1,2,\ldots,r\}$ に値を持つ確率変数列であり, 独立で同分布 $q=(q_1,\ldots,q_r)$ にしたがっていると仮定する. $q=(q_1,\ldots,q_r)$ を{\bf 母集団分布}と呼ぶ. 集合 $A$ に対してその元の個数を $\# A$ と書き, 条件 $A$ が満たされる確率を $P(A)$ と書くことにする. (後で条件 $A$ のもとでの $B$ の条件付き確率を $P(B|A)$ と書く.) 各々の $i=1,\ldots,r$ に対して $X_1,\ldots,X_n$ に含まれる $i$ の個数が $k_i$ 個になる確率は \[ P\biggl( \#\{\,k=1,2,\ldots,n\mid X_k=i\,\}=k_i\ \text{for each $i=1,\ldots,r$} \biggr) = \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \] となる. 可能な $(k_1,\ldots,k_r)$ の組合せは $k_i=0,1,\ldots,n$, $k_1+\cdots+k_r=n$ を満たしていなければいけない. このような $(k_1,\ldots,k_r)$ に対する $(k_1/n,\ldots,k_r/n)$ 全体の集合 を $\cP_n\subset\cP$ と書くことにする: \[ \cP_n = \left\{\left.\,\left(\frac{k_1}{n},\ldots,\frac{k_r}{n}\right) \,\right|\, k_i=0,1,\ldots,n,\ k_1+\cdots+k_r=n \,\right\}. \] このとき $\cP_n$ の元の個数は $(n+1)^r$ 以下になる. ($\#\cP_n\leqq(n+1)^r$ を後で自由に利用する.) $X_1,\ldots,X_n$ に対応する $\cP_n$ の 元 $P_n=(k_1/n,\cdots,k_r/n)$ を{\bf 経験分布}と呼ぶ. 経験分布 $P_n$ は $\cP_n$ に値を持つ確率変数である. 確率分布の組 $(p,q)\in\cP^2$ の函数 $D(p||q)$ を次のように定める: \[ D(p||q)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \] $p_i$ や $q_i$ が $0$ になる場合には $0\log 0=0$, $-\log 0=\infty$ という約束のもとで値を定めておく. $D(p||q)$ を{\bf Kullback-Leibler情報量} もしくは{\bf Kullback-Leiblerダイバージェンス}と呼ぶ. \begin{theorem}[Sanov] \label{theorem:Sanov} 以上の設定のもとで以下が成立している% \footnote{$\liminf$, $\limsup$ について\secref{sec:limsup}に簡単な解説を書いておいた.}: \begin{enumerate} \item[(1)] $A$ が $\cP$ の{\bf 開}部分集合ならば \[ \liminf_{n\to\infty}\frac{1}{n}\log P(P_n\in A)\geqq -\inf_{p\in A} D(p||q). \] \item[(2)] $A$ が $\cP$ の部分集合ならば% \footnote{我々が扱っている場合には $A$ は任意の部分集合であっても問題ない. しかし, 無限次元の場合には $A$ は{\bf 閉}部分集合だと仮定することが重要になるらしい.} \[ \limsup_{n\to\infty}\frac{1}{n}\log P(P_n\in A)\leqq -\inf_{p\in A}D(p||q). \] \item[(3)] $\cP$ の部分集合 $A$ の開核の閉包が $A$ を含むならば \[ \lim_{n\to\infty}\frac{1}{n}\log P(P_n\in A)= -\inf_{p\in A}D(p||q). \] \end{enumerate} このように経験分布の $n\to\infty$ での漸近挙動は Kullback-Leibler情報量 $D(p||q)$ の $\inf$ で記述される. \qed \end{theorem} \begin{example}[二項分布の場合] $r=2$ とし, $q_1=q$, $q_2=1-q$, $p_1=p$, $p_2=1-p$ とおくと, \[ D(p||q) = p\log\frac{p}{q}+(1-p)\log\frac{1-p}{1-q}. \] これは $p=q$ のとき最低値 $0$ になり, $p$ が $q$ から離れるとこれの値は減少する. $0\leqq a<b\leqq 1$ であるとし, $A=(a,b)=(\text{$a$ から $b$ までの開区間})$ とおく. このとき \[ P(P_n\in A) =\sum_{a<k/n<b}\binom{n}{k}q^k(1-q)^{n-k} \] なので \[ \lim_{n\to\infty} \frac{1}{n}\log\sum_{a<k/n<b}\binom{n}{k}q^k(1-q)^{n-k} =-\inf_{a<p<b}D(p||q) = \begin{cases} -D(b||q) & (b<q), \\ -D(q||q)=0 & (a\leqq q\leqq b), \\ -D(a||q) & (q<a) \end{cases} \] となる. これがSanovの定理の非自明な応用の最も簡単な場合である. \qed \end{example} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sanovの定理の証明の準備} 次の補題が後でStirlingの公式の代わりに使われる. \begin{lemma} \label{lemma:l!/k!} 非負の整数 $k,l$ に対して \[ \frac{l!}{k!} \geqq k^{l-k}. \] \end{lemma} \begin{proof} $l\geqq k$ のとき \[ \frac{l!}{k!} =(k+1)(k+2)\cdots l \geqq k^{l-k}. \] $l\leqq k$ のとき \[ \frac{l!}{k!} =\frac{1}{(l+1)(l+2)\cdots k} \geqq \frac{1}{k^{k-l}} =k^{l-k}. \] これで示すべきことが示された. \qed \end{proof} 次の補題が証明できればSanovの定理の証明は易しい. 次の補題の証明にはStirlingの公式を使わない. \begin{lemma} \label{lemma:types} 任意の $p\in\cP_n$ に対して \[ \frac{1}{(n+1)^r}e^{-n D(p||q)} \leqq P(P_n=p) \leqq e^{-n D(p||q)}. \] \end{lemma} \begin{proof} $p=(p_1,\ldots,p_r)=(k_1/n,\ldots,k_r/n)\in\cP_n$ のとき, \begin{align*} &\! -nD(p||q)=-\sum_{i=1}^r k_i\log p_i+\sum_{i=1}^rk_i\log q_i, \\ & e^{-n D(p||q)} =\frac{q_1^{k_1}\cdots q_r^{k_r}}{p_1^{k_1}\cdots p_r^{k_r}}, %\\ & \qquad P(P_n=p) =\frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r}. \end{align*} ゆえに, この補題の結論は次と同値である: \[ \frac{1}{(n+1)^r}\ \leqq \frac{n!}{k_1!\dots k_r!}p_1^{k_1}\cdots p_r^{k_r} \leqq 1. \] 上からの評価の方(右側の不等式)は多項分布の知識より自明である. (多項分布における確率が $1$ 以下であることを意味しているに過ぎない.) 以下で下からの評価(左側の不等式)を証明しよう. $l_i=0,1,\ldots,n$, $l_1+\cdots+l_r=n$ と仮定する. このとき, $p_i=k_i/n$ なので \[ \frac{n!}{l_1!\dots l_r!}p_1^{l_1}\cdots p_r^{l_r} \leqq \frac{n!}{k_1!\dots k_r!}p_1^{k_1}\cdots p_r^{k_r} \tag{$*$} \] が成立しているはずである. なぜならば多項分布において 確率が最大になるのは経験分布(今の場合は $l_i/n$)が 母集団分布(今の場合は $p_i=k_i/n$)に等しくなるときだからである. 実際, \lemmaref{lemma:l!/k!}より, \begin{align*} \frac{(右辺)}{(左辺)} & =\frac{l_1!}{k_1!}\cdots \frac{l_r!}{k_r!}\cdot k_1^{k_1-l_1}\cdots k_r^{k_r-l_r} %\\ & \geqq k_1^{l_1-k_1}\cdots k_r^{l_r-k_r}\cdot k_1^{k_1-l_1}\cdots k_r^{k_r-l_r} =1. \end{align*} これで($*$)が証明された. ゆえに, 多項定理より \[ 1 =\sum_{l_1+\cdots+l_r=n} \frac{n!}{l_1!\dots l_r!}p_1^{l_1}\cdots p_r^{l_r} \leqq (n+1)^r \frac{n!}{k_1!\dots k_r!}p_1^{k_1}\cdots p_r^{k_r} \] 両辺を $(n+1)^r$ で割れば下からの評価が得られる. \qed \end{proof} \begin{remark} 以上の結果の一部分は以下のように拡張される. $f(n)$ は $f(0)=0$ を満たす非負の整数 $n$ の単調増加函数であるとし, \[ f(n)! = f(1)f(2)\cdots f(n), \qquad f(0)!=1 \] と定める. これを $f$ 階乗と呼ぶことにする. このとき非負の整数 $k,l$ に対して, \[ \frac{f(l)!}{f(k)!}\geqq f(k)^{l-k}. \] 実際, $l\geqq k$ のとき \[ \frac{f(l)!}{f(k)!}=f(k+1)f(k+2)\cdots f(l)\geqq f(k)^{l-k} \] となり, $l\leqq k$ のとき \[ \frac{l!}{k!}=\frac{1}{f(l+1)f(l+2)\cdots f(k)}\geqq \frac{1}{f(k)^{k-l}}=f(k)^{l-k}. \] $k_i\in\Z_{\geqq 0}$ $p_i=f(k_i)/f(n)$ とおくと, $l_i\in\Z_{\geqq 0}$ のとき, \[ \frac{f(n)!}{f(l_1)!\cdots f(l_r)!}p_1^{l_1}\cdots p_r^{l_r} \leqq \frac{f(n)!}{f(l_1)!\cdots k_r)!}p_1^{k_1}\cdots p_r^{k_r}. \] なぜならば \begin{align*} \frac{(\text{右辺})}{(\text{左辺})} & =\frac{f(l_1)!}{f(k_1)!}\cdots \frac{f(l_r)!}{f(k_r)!}\cdot f(k_1)^{k_1-l_1}\cdots f(k_r)^{k_r-l_r} \\ & \geqq f(k_1)^{l_1-k_1}\cdots f(k_r)^{l_r-k_r}\cdot f(k_1)^{k_1-l_1}\cdots f(k_r)^{k_r-l_r} =1. \end{align*} $f(n)$ が特別な場合にはこの類似をさらにたどることができると思われる. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sanovの定理の証明} \begin{proof}[\theoremref{theorem:Sanov}の証明] 下からの評価(1)を示そう. $A$ は有限集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の空間 $\cP$ (これは $r-1$ 次元単体になる)の開部分集合であるとする. $\bigcup_{n=1}^\infty\cP_n=\cP\cap\Q^r$ は $\cP$ の中で稠密である. $A$ は $\cP$ の開部分集合なので分布列 $p_n\in\cP_n\cap A$ で \[ \lim_{n\to\infty} D(p_n||q)=\inf_{p\in A} D(p||q) \] をみたすものを取れる. 以上の状況で \[ P(P_n\in A) =\sum_{p\in\cP_n\cap A}P(P_n=p) \geqq P(P_n=p_n) \geqq \frac{1}{(n+1)^r}e^{-nD(p_n||q)}. \] 最後の不等号で\lemmaref{lemma:types}の下からの評価を使った. これより \[ \frac{1}{n}\log P(P_n\in A) \geqq - D(p_n||q) - \frac{r}{n}\log(n+1) \] となることがわかる. したがって, $n\to\infty$ とすることによって, \[ \liminf_{n\to\infty}\frac{1}{n}\log P(P_n\in A) \geqq - \inf_{p\in A}D(p||q). \] これで(1)が証明された. 上からの評価(2)を示そう. $A$ は有限集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の空間 $\cP$ の任意の部分集合であるとする. このとき \[ P(P_n\in A) =\sum_{p\in\cP_n\cap A}P(P_n=p) \leqq \sum_{p\in\cP_n\cap A}e^{-nD(p||q)} \leqq (n+1)^r e^{-n\inf_{p\in A}D(p||q)}. \] 最初の不等号で\lemmaref{lemma:types}の上からの評価を使った. これより \[ \frac{1}{n}\log P(P_n\in A) \leqq -\inf_{p\in A}D(p||q) + \frac{r}{n}\log(n+1) \] となることがわかる. したがって, $n\to\infty$ とすることによって, \[ \limsup_{n\to\infty}\frac{1}{n}\log P(P_n\in A) \leqq - \inf_{p\in A}D(p||q). \] これで(2)が証明された. (3)を示そう. $A$ の開核を $B$ と書き, $B$ の閉包を $C$ と書き, $A\subset C$ と仮定する. \\ $B\subset A\subset C$ より $-\inf_{p\in B}D(p||q)\leqq -\inf_{p\in A}D(p||q)\leqq -\inf_{p\in C}D(p||q)$. $C$ が $B$ の閉包であること $D(p||q)$ が $p$ の連続函数であることより, $-\inf_{p\in C}D(p||q)=-\inf_{p\in B}D(p||q)$. ゆえに $-\inf_{p\in B}D(p||q)=-\inf_{p\in A}D(p||q)=-\inf_{p\in C}D(p||q)$. したがって(1),(2)から(3)が導かれる. これで\theoremref{theorem:Sanov}が証明された. \qed \end{proof} \begin{remark} 以上の証明では階乗に関するStirlingの近似公式を使っていない. 証明で本質的に使った事柄は次の二つだけである. \begin{enumerate} \item[(1)] 上からの評価のために次の事実を使った: \\ $p_i\geqq 0$, $p_1+\cdots+p_r=1$ のとき \[ \frac{n!}{k_1!\cdots k_r!}p_1^{k_1}\cdots p_r^{k_r}\leqq 1 \quad (k_i\in\Z_{\geqq 0},\ k_1+\cdots+k_r=n). \] これは多項分布において「確率は1以下であること」を意味している. それを意味する不等式は, 左辺を $k_i$ たちを動かして足し上げた結果 が多項定理より $1$ になること \[ \sum_{k_1+\cdots+k_r=n} \frac{n!}{k_1!\cdots k_r!}p_1^{k_1}\cdots p_r^{k_r} = (p_1+\cdots+p_r)^r = 1 \] から, ただちに得られる. \item[(2)] 下からの評価のために次の事実を使った: \\ $k_i\in\Z_{\geqq 0}$, $k_1+\cdots+k_r=n$, $p_i=k_i/n$ のとき, \[ \frac{n!}{l_1!\cdots l_r!}p_1^{l_1}\cdots p_r^{l_r} \leqq \frac{n!}{k_1!\cdots k_r!}p_1^{k_1}\cdots p_r^{k_r} \quad (l_i\in\Z_{\geqq 0},\ l_1+\cdots+l_r=n) \] これは多項分布において 「確率が最大になるのは分布が母集団分布に等しくなるときであること」 を意味している. その不等式は次の易しい不等式($k,l$ の大小関係によらずに成立している) からただちに得られる: \[ \frac{l!}{k!}\geqq k^{l-k} \qquad (k,l\in\Z_{\geqq 0}). \] 実際, この不等式を使うと, $p_i=k_i/n$ より \begin{align*} \frac{(\text{右辺})}{(\text{左辺})} & = \frac{l_1!}{k_1!}\cdots\frac{l_r!}{k_r!} \frac{k_1^{k_1}}{k_1^{l_1}}\cdots\frac{k_r^{k_r}}{k_r^{l_r}} %\\ & \geqq k_1^{l_1-k_1}\cdots k_r^{l_r-k_r}\cdot k_1^{k_1-l_1}\cdots k_r^{k_r-l_r} =1. \end{align*} \end{enumerate} 以上の2つの結果は多項分布について知っていれば当然知っているはずの事柄である. たったそれだけの事実から多項分布版のSanovの定理は証明されるのである. \lemmaref{lemma:types}の証明を逆にたどってKullback-Leibler情報量が 出て来るところまでの議論を繰り返そう. $k_i\in\Z_{\geqq 0}$, $k_1+\cdots+k_r=n$, $p_i=k_i/n$ と仮定する. 上の(2)を $l_i$ 達について足し上げることによって \[ 1 =\sum_{l_1+\cdots+l_r=n} \frac{n!}{l_1!\cdots l_r!}p_1^{l_1}\cdots p_r^{l_r} \leqq (n+1)^r \frac{n!}{k_1!\cdots p_r!}p_1^{k_1}\cdots p_r^{k_r}. \] これの両辺を $(n+1)^r$ で割って得られる不等式と上の(1)を合わせると \[ \frac{1}{(n+1)^r} \leqq \frac{n!}{k_1!\cdots k_r!}p_1^{k_1}\cdots p_r^{k_r} \leqq 1 \] を得る. $q_i\in\Z_{\geqq 0}$, $q_1+\cdots+q_r=1$ であるとし, この不等式全体を $p_1^{k_1}\cdots p_r^{k_r}$ で割って, $q_1^{k_1}\cdots q_r^{k_r}$ をかけると \[ \frac{1}{(n+1)^r} \frac{q_1^{k_1}\cdots q_r^{k_r}}{p_1^{k_1}\cdots p_r^{k_r}} \leqq \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \leqq \frac{q_1^{k_1}\cdots q_r^{k_r}}{p_1^{k_1}\cdots p_r^{k_r}}. \] $k_i=np_i$ より, この時点ですでにKullback-Leibler情報量 \[ D(p||q)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i} \] が見えている: \[ \log\frac{q_1^{k_1}\cdots q_r^{k_r}}{p_1^{k_1}\cdots p_r^{k_r}} = \log\left( \left(\frac{q_1}{p_r}\right)^{p_1} \cdots \left(\frac{q_r}{p_r}\right)^{p_r}\right)^n = -nD(p||q). \] したがって \[ \frac{1}{(n+1)^r}e^{-nD(p||q)} \leqq \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \leqq e^{-nD(p||q)}. \] この不等式が\lemmaref{lemma:types}の結論であった. そしてこの不等式を用いて多項分布の $n\to\infty$ での様子を調べれば ただちにSanovの定理(\theoremref{theorem:Sanov})が得られるのであった. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Sanovの定理を使ったカノニカル分布の導出} \label{sec:Gibbs} \secref{sec:Sanov}の記号をそのまま引き継ぐ. たとえば $\cP$ は有限集合 $\{1,2,\ldots,r\}$ 上の確率分布 $p=(p_1,\ldots,p_r)$ 全体の集合であるとし, 母集団分布 $q=(q_1,\ldots,q_r)\in\cP$ を任意に取って固定する. $n$ 回の独立試行の結果, 状態 $i$ が生じた回数を $k_i$ と書くと, 状態 $i$ の生じた割合は $k_i/n$ である. 経験分布 $P_n=(k_1/n,\ldots,k_r/n)$ は $\cP$ に値を持つ確率変数になる% \footnote{サイコロの目のように試行ごとに値が確率的に変化する変数 を確率変数と呼ぶ. 経験分布 $P_n$ の値は $n$ 回の独立試行をやり直すごとに 確率的に変化するので, $P_n$ は確率変数だとみなされる.}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{分配函数とエネルギーの期待値} \label{sec:Z-U} $E=(E_1,\ldots,E_r)\in\R^r$ であるとし, \[ E_1=\cdots=E_a<E_{a+1}\leqq\cdots\leqq E_{r-b}<E_{r-b+1}=\cdots=E_r \] かつ $q_1,q_r>0$ であると仮定しておく (あとで分配函数の対数凸性などを保証するための仮定). $E_i$ たちを状態 $i$ の{\bf エネルギー}と呼ぶ% \footnote{ギャンブルが好きな人はエネルギーを サイコロで $i$ の目が出たときにもらえる賞金だと思ってよい.}. $\beta\in\R$ に対して 分布 $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))\in\cP$ と函数 $Z(\beta)$ を \[ p_i(\beta)=\frac{e^{-\beta E_i}q_i}{Z(\beta)}, \qquad Z(\beta)=\sum_{i=1}^r e^{-\beta E_i}q_i, \qquad \] によって定める. さらに函数 $U(\beta)=\bra E \ket_\beta$ を \[ U(\beta) =\bra E\ket_\beta =\sum_{i=1}^r E_i p_i(\beta) =-\frac{\d}{\d\beta}\log Z(\beta) \] と定める. $\beta$ を{\bf 逆温度}と呼び, $e^{-\beta E_i}$ を{\bf Boltzmann因子}と呼び, $p(\beta)$ を{\bf カノニカル分布}と呼び, 函数 $Z(\beta)$ を{\bf 分配函数}と呼び, 函数 $U(\beta)$ を{\bf エネルギーの期待値}と呼ぶ. $\log Z(\beta)$ は $\beta$ に関する下に狭義凸な函数である. なぜならば \[ \left(\frac{\d}{\d\beta}\right)^2\log Z(\beta) =\frac{Z''(\beta)Z(\beta)-Z'(\beta)^2}{Z(\beta)^2} \] であり, $a_i=e^{-\beta E_i}q_i\geqq 0$ とおくと, 最初の方の仮定から $a_1,a_r>0$ かつ $E_1<E_r$ なので \begin{align*} & Z''(\beta)Z(\beta)-Z'(\beta)^2 = \sum_{i,j} E_i^2 a_i a_j - \sum_{i,j}E_i a_i E_j a_j \\ & \qquad =\frac{1}{2}\sum_{i,j}(E_i^2+E_j^2)a_ia_j -\frac{1}{2}\sum_{i,j}2E_iE_ja_ia_j =\frac{1}{2}\sum_{i,j}(E_i-E_j)^2 a_ia_j >0 \end{align*} となり, ゆえに \[ \left(\frac{\d}{\d\beta}\right)^2\log Z(\beta) > 0 \] となるからである. したがって, エネルギーの期待値 \[ U(\beta)=-\frac{\d}{\d\beta}\log Z(\beta) \] は $\beta$ の狭義単調減少函数である. 次に $U(\beta)$ の値の様子を調べよう. まず $p(0)=q$ より \begin{align*} U(0)= \sum_{i=1}^r E_i q_i. \end{align*} 次に $\beta\to\infty$ のとき \begin{align*} U(\beta) = \frac {\sum_i E_i e^{-\beta E_i}q_i} {\sum_i e^{-\beta E_i}q_i} = \frac {e^{-\beta E_1}\sum_i E_i e^{-\beta(E_i-E_1)}q_i} {e^{-\beta E_1}\sum_i e^{-\beta(E_i-E_1)}q_i} \to \frac {e^{-\beta E_1}\sum_{i=1}^a E_i q_i} {e^{-\beta E_1}\sum_{i=1}^a q_i} =E_1. \end{align*} 最後に $\beta\to-\infty$ のとき \begin{align*} U(\beta) = \frac {\sum_i E_i e^{-\beta E_i}q_i} {\sum_i e^{-\beta E_i}q_i} = \frac {e^{-\beta E_r}\sum_i E_i e^{\beta(E_r-E_i)}q_i} {e^{-\beta E_r}\sum_i e^{\beta(E_r-E_i)}q_i} \to \frac {e^{-\beta E_r}\sum_{i=r-b+1}^r E_i q_i} {e^{-\beta E_r}\sum_{i=r-b+1}^r q_i} =E_r. \end{align*} 以上によって, $E_r\geqq U\geqq E_1$ と $-\infty\leqq\beta\leqq\infty$ は $U=U(\beta)$ によって一対一に対応していることがわかる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{条件付き確率分布のカノニカル分布への収束} 経験分布 $p=(p_1,\ldots,p_r)\in\cP$ について, 条件 $\sum_{i=1}^r E_i p_i\approx U(\beta)$ のもとで, $n\to\infty$ のとき条件付き確率分布がカノニカル分布 $p(\beta)$ に 収束することを示したい. 以下では, 数学的に厳密な取り扱いをするために, 条件 $\sum_{i=1}^r E_i p_i\approx U(\beta)$ の代わりに, 任意に $a>0$ を取って以下のように条件を課す: \begin{itemize} \item $\beta\geqq 0$ のとき, 条件 \( \displaystyle U(\beta)-a \leqq \sum_{i=1}^r E_i p_i \leqq U(\beta) \) を課す. \item $\beta\geqq 0$ のとき, 条件 \( \displaystyle U(\beta)\leqq \sum_{i=1}^r E_i p_i \leqq U(\beta)+a \) を課す. \end{itemize} 後で $a>0$ の取り方は議論の本質に無関係であることがわかる. この条件のもとでの条件付き確率を考えるために $\{1,2,\ldots,r\}$ 上の確率分布全体の集合 $\cP$ の部分集合 $A$ を \[ A = \begin{cases} \left\{\,p\in\cP \,\left|\, U(\beta)-a \leqq \sum_{i=1}^r E_i p_i \leqq U(\beta) \right.\right\} & (\beta\geqq 0), \\ \left\{\, p\in\cP \,\left|\, U(\beta)\leqq \sum_{i=1}^r E_i p_i \leqq U(\beta)+a \right.\right\} & (\beta\leqq 0) \end{cases} \] と定める. 条件 $P_n\in A$ のもとでの条件付き確率 \[ P(P_n\in B|P_n\in A)=\frac{P(P_n\in A\cap B)}{P(P_n\in A)} \qquad (B\subset\cP) \] が $n\to\infty$ でカノニカル分布 $p(\beta)$ に集中することを Sanovの定理(\theoremref{theorem:Sanov})を使って証明したい. そのために, 任意に $\eps>0$ を取って, $\cP$ の部分集合 $B$ を次のように定める: \[ B = \{\,p\in\cP \mid ||p-p(\beta)||<\eps \,\}. \] ここで $||\cdot||$ はEuclidノルムである. $B$ は $p(\beta)$ の $\eps$ 開近傍である. 以上の設定のもとで, $n\to\infty$ で条件付き確率分布が カノニカル分布 $p(\beta)$ に集中することを意味する \[ P(P_n\in B|P_n\in A)\to 1 \qquad (n\to\infty) \tag{$*$} \] を示すことが以下の目標である. Kullback-Leibler情報量 $D(p||q)$ の定義を $\cP$ の部分集合 $C$ に \[ D(C||q) = \inf_{p\in P}D(p||q) \] と拡張しておく. Sanovの定理より, $\cP$ の部分集合 $C$ の開核の閉包が $C$ を含むとき \[ P(P_n\in C) = \exp(-n D(C||q) + o(n)). \] 上で定めた $\cP$ の部分集合 $A$, $B$, $A\cap B$ の開核の閉包は それぞれ $A$, $B$, $A\cap B$ を含む. さらに $B$ の $A$ での補集合 $B'=A\setminus B$ も同様である. ゆえに \[ P(P_n\in B'|P_n\in A) =\frac{P(P_n\in B')}{P(P_n\in A)} =\exp(-n(D(B'||q)-D(A||q))+o(n)). \] これが $n\to\infty$ で $0$ に収束することと目標である($*$)は同値である. もしも条件 $p\in A$ のもとで $p=p(\beta)$ が $D(p||q)$ が唯一の最小点 になるならば, $B'=A\setminus B$ の閉包に $p(\beta)$ が含まれないことより, $D(B'||q)>D(A||q)=D(p(\beta)||q)$ となり, $n\to\infty$ で $P(P_n\in B'|P_n\in A)\to 0$ となることがわかる. $D(p||q)$ は $p$ の函数として下に狭義凸であり, $A$ は $\cP$ の凸部分集合なので, 条件 $p\in A$ のもとでの $D(p||q)$ が $p=p(\beta)$ で 最小になるならば, $p=p(\beta)$ は唯一の最小点になる. ゆえに条件 $p\in A$ のもとで $D(p||q)$ が $p=p(\beta)$ で 最小になることを示せば($*$)の証明が終了する. 以下でそのことを証明しよう. カノニカル分布 $p(\beta)$ は \[ \sum_{i=1}^r E_i p_i(\beta) = U(\beta) \] を満たしているので, $p(\beta)\in A$ である. さらに% \footnote{相対エントロピー $S(p||q)=-D(p||q)$ を用いて公式を 書き直すと $S(p||q)=\beta U(\beta) + \log Z(\beta)$ になる. この手の公式は統計力学を知っている人達にはお馴染みのものだろう.} \begin{align*} D(p(\beta)||q) & =\sum_{i=1}^r p_i(\beta)\log\frac{p_i(\beta)}{q_i} =\sum_{i=1}^r p_i(\beta)\log\frac{e^{-\beta E_i}}{Z(\beta)} \\ & =\sum_{i=1}^r p_i(\beta)(- \beta E_i - \log Z(\beta)) =-\beta U(\beta)-\log Z(\beta). \tag{$\%$} \end{align*} これが条件 $p\in A$ のもとでの $D(p||q)$ の最小値であることを示したい. すなわち $p\in A$ のとき $D(p||q)\geqq D(p(\beta)||q)$ となることを示したい. $p\in A$ と仮定する. このとき, $A$ の定義より, $\beta\geqq 0$ のとき $\sum_{i=1}^r E_i p_i\leqq U(\beta)$ となり, $\beta\leqq 0$ のとき $\sum_{i=1}^r E_i p_i\geqq U(\beta)$ となるので, $\beta$ の符号によらずに \[ \beta\sum_{i=1}^r E_i p_i \leqq \beta U(\beta). \tag{$\#$} \] が成立している. \secref{sec:Z-U}の計算より, $\beta>0$ と $U(\beta)<\sum_{i=1}^r E_i q_i$ は同値であり, $\beta<0$ と $U(\beta)>\sum_{i=1}^r E_i q_i$ は同値である. 集合 $A$ を定義するときに用いた $a>0$ は以下の議論には関係しない. Kullback-Leibler情報量 $D(p||q)$ は以下のように変形される: \begin{align*} D(p||q) & =\sum_{i=1}^r p_i\log\frac{p_i}{q_i} =\sum_{i=1}^r p_i\log\left(\frac{p_i}{p_i(\beta)}\frac{p_i(\beta)}{q_i}\right) %\\ & =\sum_{i=1}^r p_i\log\frac{p_i}{p_i(\beta)} +\sum_{i=1}^r p_i\log\frac{p_i(\beta)}{q_i} \\ & =D(p||p(\beta))+\sum_{i=1}^r p_i\log\frac{e^{-\beta E_i}}{Z(\beta)} %\\ & =D(p||p(\beta))+\sum_{i=1}^r p_i(-\beta E_i-\log Z(\beta)) \\ & =D(p||p(\beta))-\beta\sum_{i=1}^r E_i p_i - \log Z(\beta). \end{align*} ゆえに, 不等式($\#$)とカノニカル分布のKullback-Leibler情報量 $D(p(\beta)||q)$ の表示($\%$)とKullback-Leibler情報量が常に $0$ 以上であることより, \[ D(p||q) \geqq D(p||p(\beta)) -\beta U(\beta)-\log Z(\beta) = D(p||p(\beta)) + D(p(\beta)||q) \geqq D(p(\beta)||q). \] これで条件 $p\in A$ のもとで $D(p||q)$ は $p=p(\beta)$ で最小になることがわかった. 目標の($*$)が証明された. \begin{remark}[不等式($\#$)について] \label{remark:beta} 以上の議論は本質的に不等式 ($\#$) の仮定だけに基づく. 統計力学の文脈では $\beta$ は絶対温度のBoltzmann定数倍の逆数を意味する. その場合には $\beta>0$ となるので不等式 ($\#$) は \[ (\text{エネルギーの平均値})=\sum_{i=1}^r E_i p_i\leqq U(\beta) \] を意味する. この型の条件でカノニカル分布が特徴付けられることについては 田崎 \cite{Tasaki}の第9-2-1節(p.319)も参照せよ. カノニカル分布が経験的に自然に得られることを示すためには, $\sum_{i=1}^r E_i p_i\approx U(\beta)$ という強い条件を 仮定する必要はなく, 不等式 ($\#$) を仮定するだけでよい. この点についてもう少し詳しくコメントしておく. \secref{sec:Z-U}で計算した通り, $U(0)$ は母集団分布でのエネルギーの期待値 $\sum_{i=1}^r E_i q_i$ になる. そして $\beta>0$ を大きくすると $U(\beta)$ は最小エネルギー準位 $\min\{E_1,\ldots,E_r\}$ に近付き, $\beta<0$ を小さくすると $U(\beta)$ は最大エネルギー準位 $\max\{E_1,\ldots,E_r\}$ に近付く. $\beta=\infty$ で状態は最小エネルギー状態(基底状態)にはりつくようになり, $\beta=-\infty$ で状態は最大エネルギー状態にはりつくようになる. 統計力学において $\beta$ は絶対温度の逆数であり, $\beta=\infty$ は絶対零度に対応し, $\beta=0$ は絶対温度無限大に対応している. 我々が扱っている場合には $\beta$ は負にもなりえる. その場合には対応する絶対温度も負の値になる. 絶対温度の高さを逆温度 $\beta$ の低さで測ることにすれば, 負の絶対温度は 絶対温度無限大よりも高温であるとみなされる. 我々が扱っているのは次のような状況であると考えられる. $r$ 種類の目が出るルーレットを回して, $i$ の目が出たら賞金を $E_i$ ペリカもらえるゲームを考える. ($E_i<0$ の場合には $|E_i|$ ペリカ支払うことにすればギャンブルになる.) $i$ の目が出る確率は $q_i$ であるとする. そのようなゲーム1回あたりの賞金の期待値は $U_0=\sum_{i=1}^r E_i q_i$ になる. 大数の法則よりそのようなゲームをたくさん繰り返せば 1回あたりの賞金の平均値は $U_0$ に近付く. まず $U>U_0$ であると仮定する. ゲームをたくさん繰り返して(回数は $n$ 回とする). ゲーム1回あたりの賞金の平均値が $U$ 未満で終わったならば, 時間を巻き戻して何度でも $n$ 回分のゲームをやり直せると仮定する. そのようにしてゲーム1回あたりの賞金の平均値が ゲーム自体の期待値である $U_0$ より大きい $U$ 以上になったら 時間を巻き戻すのを止める. このとき, $n$ 回のゲーム中 $i$ の目が出た割合 $p_i$ は ($n$ が大きなとき)どのような値になる可能性が高いだろうか? ゲーム1回あたりの賞金の平均値が $U_0$ から離れれば離れるほど そのような状況が生じる確率は下がるので, ゲーム1回あたりの賞金の平均値はほぼ $U$ (すなわち $U$ よりほんの少し大きな数値) になってしまう可能性が高いだろう. そのときの $i$ の目が出た割合 $p_i$ を計算すると, $U$ が定める $\beta$ に対応するカノニカル分布 $p_i(\beta)$ に 近くなる可能性が高いというのがこの節において数学的にきちんと証明したことである. この場合には $U>U_0$ なので $\beta<0$ となる. すなわち必要ならば時間を巻き戻すことによって, ゲーム自体の賞金期待値よりも高い賞金を求めると, 対応する絶対温度は負の値になってしまうと解釈される. 絶対温度が正の値の状況を作り出すには, $U<U_0$ であると仮定し, 必要ならば時間を巻き戻して, ゲーム1回あたりの賞金の平均値が $U$ 以下になるようにすればよい. そのとき, ゲーム1回あたりの賞金の平均値が $U_0$ から離れれば離れるほど そのような状況が生じる確率は下がるので, ゲーム1回あたりの賞金の平均値はほぼ $U$ になる可能性が高く, $i$ の目が出た割合は $U$ に対応するカノニカル分布 $p_i(\beta)$ に近くなる可能性が高い. この場合には $U<U_0$ なので $\beta>0$ となり, 絶対温度は正の値になる. つまり, 時間を巻き戻して, ゲーム自体の期待値よりも低い賞金を得るように すると絶対温度は正の値になるとされるのである. 以上の説明を読めばカノニカル分布の導出で使った不等式 ($\#$) の向きが どのように自然であるかがわかると思う. 上の議論と\secref{sec:binom-Sanov}の最後の方の 極限の計算と比較してみよ. \secref{sec:binom-Sanov}では「丁半博打」のケースを扱っていると考えられる. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{まとめと二項分布もカノニカル分布の例になっていること} \label{sec:binom-Gibbs} 以上の結果は次のようにまとめられる. \begin{theorem}[条件付き大数の弱法則, 条件付き極限定理] \label{theorem:Gibbs} 母集団分布は $q=(q_1,\ldots,q_r)\in\cP$ であるとする. $X_1,X_2,\ldots$ は独立で同分布 $q$ にしたがう $\{1,2,\ldots,r\}$ に値を持つ確率変数列であるとする. $X_1,X_2,\ldots,X_n$ の中に含まれる $i$ の個数を $k_i$ と書き, $P_n=(k_1/n,\ldots,k_r/n)$ とおく. $P_n$ は分布の集合 $\cP$ に値を 持つ確率変数になる. $E_i\in\R$ は\secref{sec:Z-U}の通りとする. $E_1<U<E_r$ であるとし, $\beta\in\R$, $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))\in\cP$, $Z(\beta)$ を以下の条件で定める: \begin{align*} p_i(\beta)=\frac{e^{-\beta E_i}q_i}{Z(\beta)}, \quad Z(\beta)=\sum_{i=1}^r e^{-\beta E_i}q_i, \quad -\frac{\d}{\d\beta}\log Z(\beta) = \sum_{i=1}^r E_i p_i(\beta) = U. \end{align*} $p(\beta)$ を{\bf カノニカル分布}と呼ぶ. $0<a\leqq\infty$ とし, 分布の集合 $A_U\subset\cP$ を \[ A_U = \begin{cases} \left\{\,p\in\cP \,\left|\, U-a \leqq \sum_{i=1}^r E_i p_i \leqq U \right.\right\} & (\beta\geqq 0), \\ \left\{\, p\in\cP \,\left|\, U\leqq \sum_{i=1}^r E_i p_i \leqq U+a \right.\right\} & (\beta\leqq 0) \end{cases} \] と定める. このとき $\sum_{i=1}^r E_i p_i(\beta)=U$ なので $p(\beta)\in A_U$ である. 任意に $\eps>0$ を取り, $p(\beta)$ の $A_U$ における $\eps$ 開近傍 を $B_\eps(p(\beta))$ と書く. このとき, $n\to\infty$ で \[ P(P_n\in B_\eps(p(\beta))|P_n\in A_U) = \frac{P(P_n\in B_\eps(p(\beta)))}{P(P_n\in A_U)} \to 1. \] すなわち経験分布 $P_n$ は $n\to\infty$ で カノニカル分布 $p(\beta)$ に(確率)収束する. \qed \end{theorem} \begin{example} \label{example:binom-Gibbs} 確率 $\theta$ に対応する一般の二項分布が 確率 $1/2$ の二項分布を母集団分布とする場合のカノニカル分布として 自然に現われることを説明しよう. この例は母集団分布が一様分布でない場合のカノニカル分布の簡単な例になっている. 有限集合 $\{0,1,\ldots,r\}$ に値を持つ 確率変数 $X$ は確率 $1/2$ に対応する対称な二項分布にしたがうと仮定する: \[ P(X=i)=\binom{r}{i}\frac{1}{2^r} \qquad (i=0,1,\ldots,r). \] $X_1,X_2,\ldots$ は独立で $X$ と同じ分布を持つ確率変数の列であるとする. $X_1,X_2,\ldots,X_n$ の中に含まれる $i$ の個数を $k_i$ と書き, $P_n=(k_0/n,k_1/n,\ldots,k_r/n)$ とおくと, $P_n$ は $\{0,1,\ldots,r\}$ 上の確率分布に値を持つ確率変数になる. 大数の法則より, 何も条件を付けずに $n\to\infty$ とすると, $P_n$ は対称な二項分布に近付く. $E_i=i$ の場合にカノニカル分布が何になるかを計算してみよう. そのとき, 分配函数は二項定理より \[ Z(\beta) =\sum_{i=0}^r e^{-\beta E_i}q_i =\sum_{i=0}^r \binom{r}{i}\left(\frac{e^{-\beta}}{2}\right)^i\left(\frac{1}{2}\right)^{r-i} =\frac{(e^{-\beta}+1)^r}{2^r} \] となるので, カノニカル分布は \[ p_i(\beta) =\frac{e^{-\beta E_i}q_i}{Z(\beta)} =\binom{r}{i}\frac{e^{-\beta i}}{(e^{-\beta}+1)^r} =\binom{r}{i} \left(\frac{e^{-\beta}}{e^{-\beta}+1}\right)^i \left(\frac{1}{e^{-\beta}+1}\right)^{r-i} \] と二項分布になる. つまり, \[ p_i(\beta)=\binom{r}{i}\theta^i(1-\theta)^{r-i}, \qquad \theta=\frac{e^{-\beta}}{e^{-\beta}+1}. \] このとき, \[ -Z'(\beta)=\frac{r e^{-\beta}(e^{-\beta}+1)^{r-1}}{2^r} \] なので, ``エネルギーの期待値''は \[ U(\beta) =-\frac{\d}{\d\beta}Z(\beta) =\frac{-Z'(\beta)}{Z(\beta)} =\frac{r e^{-\beta}}{e^{-\beta}+1} =r\theta \] と確率 $\theta$ に対応する二項分布における $i$ の期待値になる. 確率 $1/2$ に対応する対称な二項分布については コイン投げの状況を想像すると分かり易いだろう. コインを投げたとき表になる確率が $1/2$ である状況を考える. そのようなコインを $r$ 回投げて表の出た回数 $i$ と表が出た割合 $i/r$ を 記録する行為を $n$ 回繰り返したとしよう. ただし $n$ は非常に大きいとする. 記録には表の出た回数 $i$ と表が出た割合 $i/r$ が それぞれ $n$ 個ずつ記録されている. その記録を見ると次が成立していたとする% \footnote{大数の(弱)法則より, $\theta$ が $1/2$ から離れている確率 は $n\to\infty$ で $0$ に近付く. ここではそのような稀なケースが生じた場合を想定している.}: \[ (\text{表の出た割合 $i/r$ の平均値}) =\sum_{i=0}^r \frac{i}{r} p_i \approx \theta. \tag{$*$} \] このとき $p_i=k_i/n$ たちはどのような値になっている可能性が高いだろうか? 「経験分布 $p=(p_0,p_1,\ldots,p_r)$ は確率 $\theta$ に対応する二項分布にほぼ等しくなっている可能性が高い」というのが, \theoremref{theorem:Gibbs}をすぐ上の計算に適用したときの結論になる. 上で計算したカノニカル分布 $p(\beta)$ (確率 $\theta$ に対応する二項分布)は, \theoremref{theorem:Gibbs}より, \[ (\text{表が出た回数 $i$ の期待値}) =\sum_{i=0}^r i p_i =\sum_{i=0}^r E_i p_i \approx U(\beta) = r\theta \] を満たす分布 $p=(p_0,p_1,\ldots,p_r)$ に制限した場合の 経験分布 $P_n$ が $n\to\infty$ で近付く先になっている. この条件は上の($*$)と同値である. 表の出る割合が $\theta$ になるという条件で制限を付ければ 確率 $\theta$ に対応する二項分布が経験分布として自然に現われる. {\bf 結論.}\enspace 表の出る確率が $1/2$ の公平なコインを $r$ 回投げて表の出た回数を数えること をたくさん繰り返し, $r$ 回中表の出た回数が大量に記録されたリストを作ったとする. そのときもしもその記録において $r$ 回中表の出た割合の平均値が $\theta$ に なっているならば% \footnote{$\theta$ が $1/2$ から離れると, $n$ が大きなときそのようなリストが得られる確率はほぼ $0$ になるが, そのような稀な状況が生じてしまった場合についても考えている.}, そのリストにはあたかも「表の出る確率が $\theta$ の二項分布の記録が残っている」 かのように見えてしまうことになる. \qed \end{example} \begin{remark} \exampleref{example:binom-Gibbs}の 議論を一般化するとほぼ自明に以下のようなことが成立していることがわかる. 母集団分布 $q_i$ は最初から $E_i$ に関するカノニカル分布の形をしていると仮定する: \[ q_i = \frac{e^{-\beta_0 E_i}q_{0,i}}{Z_0}, \qquad Z_0 = \sum_{i=1}^r e^{-\beta_0 E_i}q_{i,0}. \] ここで $q_{0,i}\geqq 0$, $\sum_{i=1}^r q_{0,i}=1$, $E_1,\ldots,E_r\in\R$ の最大値 $E_1$ と最大値 $E_r$ は異なり, $q_1,q_r>0$ であると仮定する. このとき, この母集団分布と $E_i$ たちに対応するカノニカル分布 $p(\beta)$ も 母集団分布と同じ形のカノニカル分布になる: \[ p_i(\beta) = \frac{e^{-(\beta_0+\beta)E_i}q_{0,i}}{Z_0 Z(\beta)}, \qquad Z_0Z(\beta) = Z_0\sum_{i=1}^r e^{-\beta E_i}q_i = \sum_{i=1}^r e^{-(\beta_0+\beta)E_i} q_{0,i}. \] 二項分布は離散型の指数型分布族に含まれているので \exampleref{example:binom-Gibbs}のようなことが成立するのである. 他の指数型分布族に含まれる確率分布についても同様のことが成立する. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{付録: Kullback-Leibler情報量に関する不等式} \label{sec:inequalities} Cover-Thomas \cite{Cover-Thomas-2006} は情報理論に関する有名な教科書である. 情報量とエントロピー一般に関する詳しい解説を読みたい人はその本を参照すればよい. 以下では主にこの教科書を参照しながら, Kullback-Leibler情報量が「距離」のような 性質を持っていることを意味する不等式を扱う. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{準備: Jensenの不等式} \label{sec:Jensen} 函数 $f(X)$ を数 $E[f(X)]$ に対応させる汎函数 $E[\ \cdot\ ]$ は 以下の条件を満たしていると仮定する: \begin{enumerate} \item 線形性: 函数 $f(X)$, $g(X)$ と数 $\alpha,\beta$ に対して, \\ \qquad $E[\alpha f(X)+\beta g(X)]=\alpha E[f(X)]+\beta E[g(X)]$. \item 短調性: $f(X)\geqq g(X)$ が常に成立しているならば $E[f(X)]\geqq E[g(X)]$. \item 規格化条件: $E[1]=1$. \end{enumerate} 規格化条件と短調性より, 数 $\alpha$ に対して $E[\alpha]=\alpha$ となることがわかる. このような $E[\ \cdot\ ]$ を期待値汎函数と呼ぶ. たとえば $p_i\geqq 0$, $\sum_{i=1}^r p_i=1$ のとき, $E[f(X)]=\sum_{i=1}^r f(x_i)p_i$ は期待値汎函数である. 他にも $\rho(x)\geqq 0$, $\int_a^b \rho(x)\,dx=1$ のとき, $E[f(X)]=\int_a^b f(x)\rho(x)\,dx$ も期待値汎函数である. このとき以下の不等式が成立している({\bf Jensenの不等式}): \begin{itemize} \item $f(X)$ が上に凸ならば $E[f(X)]\leqq f(E[X])$. \item $f(X)$ が下に凸ならば $E[f(X)]\geqq f(E[X])$. \end{itemize} 以下で前者のみを証明しよう. 後者は $-f(X)$ に前者を適用すれば得られる. \begin{proof}[前者の証明] 函数 $f(X)$ は上に凸であると仮定し, $\mu=E[X]$ とおく. このとき上に凸な函数 $f(X)$ の $X=\mu$ での``接線''を $a(X-\mu)+f(\mu)$ と書くと, \[ f(X)\leqq a(X-\mu)+f(\mu) \] となるので, \[ E[f(X)]\leqq E[a(X-\mu)+f(\mu)]=a(E[X]-\mu)+f(\mu)=f(E[X]). \] 2つ目の等号で期待値汎函数の短調性を使い, 2つ目の等号でその線形性と規格化条件を使った% \footnote{$E[f(X)]=\sum_{i=1}^r f(x_i)p_i$ の場合のJensenの不等式は $r$ に関する数学的帰納法で証明することもできるが, 期待値汎函数の公理だけを使って 証明する方が不等式が成立する理由が分かりやすいと思う.}. \qed \end{proof} \begin{remark} 上の証明から, $f(X)$ が上に狭義凸ならば, $X$ の分布が $\mu=E[f(X)]$ に集中していない 限り(ほとんど確実に $f(X)=\mu$ が成立していない限り), 等号を含まない強い不等式が成立していることがわかる. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{対数和不等式とその応用} \label{sec:log-sum} 次の不等式はたとえば \cite{Cover-Thomas-2006}, p.31, Theorem 2.7.1 (Log sum inequality) に書いてある. \paragraph{対数和不等式} $0$ 以上の $a_i$, $b_i$ に対して, \[ \sum_{i=1}^n a_i \log\frac{a_i}{b_i}\geqq A\log\frac{A}{B}, \qquad A=\sum_{i=1}^n a_i, \quad B=\sum_{i=1}^n b_i. \] 等号の成立と $a_i/b_i$ が互いにすべて等しいことは同値である. いつものように $0\log 0=0$, $a\log(a/0)=\infty$ と約束しておく. \begin{proof} $a_i>0$, $b_i>0$ の場合のみを証明すれば十分である. (一般の場合はその場合の極限として証明される.) $f(x)=x\log x$ とおくと, $f'(x)=\log x + 1$, $f''(x)=1/x$ なので $f(x)$ は $x>0$ で 下に狭義凸である. これにJensenの不等式を適用しよう. そのために $q_i=b_i/B$ とおく. このとき \begin{align*} \frac{1}{B}\sum_{i=1}^n a_i \log\frac{a_i}{b_i} & =\sum_{i=1}^n \frac{b_i}{B} \frac{a_i}{b_i}\log\frac{a_i}{b_i} =\sum_{i=1}^n q_i f\left(\frac{a_i}{b_i}\right) \\ & \geqq f\left(\sum_{i=1}^n q_i \frac{a_i}{b_i}\right) =f\left(\sum_{i=1}^n \frac{b_i}{B} \frac{a_i}{b_i}\right) =f\left(\frac{A}{B}\right) =\frac{A}{B}\log\frac{A}{B}. \end{align*} $f(x)$ の狭義凸性より, 等号が成立することと $a_i/b_i$ が互いにすべて等しいことが同値であることもわかる. \qed \end{proof} この不等式を使えば特に $p_i$, $q_i$ が非負でそれぞれの総和が $1$ のとき \[ D(p||q)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i}\geqq 1\log\frac{1}{1}=0 \] が得られる({\bf Kullback-Leibler情報量の非負性}). さらに, 集合 $\{1,2,\ldots,r\}$ の分割 \[ \{1,2,\ldots,r\} = A_1\sqcup\cdots\sqcup A_s \] に対して, $\{\,A_1,\ldots,A_s\,\}$ 上の確率分布 $P=(P_1,\ldots,P_s)$, $Q_j=(Q_1,\ldots,Q_s)$ を \[ P_j = \sum_{i\in A_j} p_i, \qquad Q_j = \sum_{i\in A_j} q_i \] と定めると, 対数和不等式より \[ D(p||q) = \sum_{j=1}^s\sum_{i\in A_j} p_i\log\frac{p_i}{q_i} \geqq \sum_{j=1}^s P_i\log\frac{P_j}{Q_j} =D(P||Q). \] 要するに, {\bf 細部の情報を忘れるとKullback-Leibler情報量は小さくなる}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Kullback-Leibler情報量で $L^1$ 距離を上からおさえられこと} 集合 $\{1,2,\ldots,r\}$ 上の確率分布 $p=(p_1,\ldots,p_r)$, $q=(q_1,\ldots,q_r)$ のあいだの $L^1$ 距離 $||p-q||_{L^1}$ を \[ ||p-q||_{L^1} = \sum_{i=1}^r |p_i-q_i| \] と定める. 確率分布 $p$ に関する確率を \[ p(A)=\sum_{i\in A} p_i \qquad(A\subset\{1,2,\ldots,r\}) \] と書くと, \[ ||p-q||_{L^1}=2(p(A)-q(A)), \qquad A = \bigl\{\, i\in\{1,2,\ldots,r\} \,\big|\, p_i\geqq q_i\,\bigr\}. \tag{$\#$} \] なぜならば \begin{align*} ||p-q||_{L^1} & =\sum_{i\in A} (p_i-q_i) + \sum_{i\in A^c}(q_i-p_i) =p(A)-q(A)+q(A^c)-p(A^c) \\ & =p(A)-q(A)+(1-q(A))-(1-p(A)) =2(p(A)-q(A)). \end{align*} 以上の記号を以下においてそのまま用いる. \paragraph{KL情報量で $L^1$ 距離を上からおさえられること:} \[ D(p||q) \geqq \frac{1}{2}||p-q||_{L^1}^2. \tag{$*$} \] この不等式を証明したい. \begin{proof}[$\mathbf{r=2}$ の場合の($*$)の証明] $0<a<1$, $0<b<1$ のとき \[ a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b}\geqq 2(a-b)^2 \] となることを示せばよい. そのために左辺から右辺を引いた結果を $f(b)$ と書く: \[ f(b) = a\log\frac{a}{b}+(1-a)\log\frac{1-a}{1-b} - 2(a-b)^2. \] このとき \begin{align*} f'(b) =-\frac{a}{b}+\frac{1-a}{1-b}-4(b-a) =(b-a)\left(\frac{1}{b(1-b)}-4\right). \end{align*} $b(1-a)\leqq 1/4$ より, $1/(b(1-b))-4\geqq 0$ となる. ゆえに $f(b)$ の符号は $b-a$ の符号に等しい. すなわち $f(b)$ は $b<a$ で単調減少し, $b>a$ で単調増加する. したがって $f(p)=0$ なので $f(b)\geqq 0$ となることがわかる. \qed \end{proof} \begin{proof}[一般の場合の($*$)の証明] 集合 $A$ は($\#$)の通りであるとし, 集合 $\{1,2,\ldots,r\}$ の分割 $\{A, A^c\}$ 上の 確率分布 $P=(a,1-a)$, $Q=(b,1-b)$ を $a=p(A)$, $b=q(A)$ と定める. このとき 細部の情報を忘れるとKullback-Leibler情報量が小さくなること(\secref{sec:log-sum})より \begin{align*} D(p||q) \geqq D(P||Q) \geqq 2(a-b)^2=2(p(A)-q(B))^2=\frac{1}{2}||p-q||_{L^1}^2. \end{align*} ここで2つ目の不等号で上で証明した $r=2$ の場合の結果を使い, 最後に($\#$)を使った. \qed \end{proof} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Pithagorian theorem} \label{sec:Pythagorian} $\cP=\{\,p=(p_1,\ldots,p_r)\in\R^r_{\geqq 0}\mid p_1+\cdots+p_r=1\,\}$ とおき, $\cP$ を集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の集合とみなす. $\cP$ は $r-1$ 次元単体である. 次の不等式は \cite{Cover-Thomas-2006}, p.367, Theorem 11.6.1 にある. \paragraph{Pythagorian theorem} $E$ は $\cP$ の凸閉部分集合であるとし, $q\in\cP\setminus E$ であるとする. $p^*=(p^*_1,\ldots,p^*_r)\in E$ は $D(p||q)$ を $E$ 上で最小化する $p$ であるとする: \[ D(p^*||q) = \min_{p\in E} D(p||q). \] このとき \[ D(p||q) \geqq D(p||p^*) + D(p^*||q) \qquad (p\in E). \] この不等式とKullback-Leibler情報量の非負性より, $D(p||q)\to D(p^*||q)$ ならば $p\to p^*$ となることが導かれる. \begin{proof}[Pythegorian theoremの証明] $p^*$ と $p$ を通る直線上のKullback-Leibler情報量の値の $p^*$ における 微係数を見ればこの不等式が証明される. $t\in\R$ に対して \begin{align*} & p(t) =(p_1(t),\ldots,p_r(t))= tp+(1-t)p^*, \qquad p_i(t)=t p_i+(1-t)p^*_i, \\ & f(t) = D(p(t)||q) = \sum_{i=1}^r (t p_i+(1-t)p^*_i)\log\frac{t p_i+(1-t)p^*_i}{q_i} \end{align*} とおく. このとき \begin{align*} f'(t) & =\sum_{i=1}^r\left( (p_i-p^*_i)\log\frac{t p_i+(1-t)p^*_i}{q_i} + (p_i-p^*_i) \right) \\ & =\sum_{i=1}^r(p_i-p^*_i)\log\frac{t p_i+(1-t)p^*_i}{q_i}. \end{align*} 2つ目の等号で $\sum_{i=1}^r p_i=\sum_{i=1}^r p^*_i=1$ となることを使った. $p(0)=p^*\in E$, $p(1)=p\in E$ であり, $E$ は凸だったので $p(t)\in E$ ($0\leqq t\leqq 1$). $p^*$ は $D(p||q)$ を $E$ 上で最小化する $p$ だったので, $f'(0)\geqq 0$ となる. ゆえに \begin{align*} 0 & \leqq f'(0) = \sum_{i=1}^r (p_i-p^*_i)\log\frac{p^*_i}{q_i} %\\ & = \sum_{i=1}^r p_i\log\left(\frac{p_i}{q_i}\frac{p^*_i}{p_i}\right) - \sum_{i=1}^r p^*_i\log\frac{p^*_i}{q_i} \\ & = \sum_{i=1}^r p_i\log\frac{p_i}{q_i} - \sum_{i=1}^r p_i\log\frac{p_i}{p^*_i} - \sum_{i=1}^r p^*_i\log\frac{p^*_i}{q_i} = D(p||q) - D(p||p^*) - D(p^*||q). \end{align*} これで示したい不等式が示された. \qed \end{proof} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{付録: Cram\'erの定理} \label{sec:Cramer} 完璧に論理的に厳密な解説をするつもりはないので 厳密な証明に興味がある人は注意して欲しい. 目標は統計力学のformulationとの対応を明瞭になるようなスタイルで Cram\'erの定理の証明の概略を説明することである. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Cram\'erの定理の設定と主張} \label{sec:Cramer-theorem} $H$ は平均値を持つ確率変数であるとし, その平均値を \[ U_0 = E[H] \] と書く. $H$ のモーメント母函数% \footnote{確率論の教科書では, 通常, 確率変数 $H$ のモーメント母函数を $M(t)=E[e^{tH}]$ と定義するが, ここでは統計力学との対応を見易くするために $t=-\beta$ とおき, 統計力学における分配函数と同じ記号 $Z(\beta)$ をモーメント母函数に割り振った.}: \[ Z(\beta) = E[e^{-\beta H}]. \] は正の幅を持つ区間上で有限の値を持つと仮定する. $U(\beta)$ を次のように定める: \[ U(\beta) = \frac{E[He^{-\beta H}]}{Z(\beta)} = -\frac{\d}{\d\beta}\log Z(\beta). \] $H_1,H_2$ 独立な確率変数達で $H$ と同じ分布にしたがうならば, $Z(\beta)$ が有限になる開区間において, \begin{align*} & \left(\frac{\d}{\d\beta}\right)^2\log Z(\beta) =-\frac{\d}{\d\beta}U(\beta) =\frac{Z''(\beta)Z(\beta)-Z'(\beta)^2}{Z(\beta)^2}, \\ & Z''(\beta)Z(\beta)-Z'(\beta)^2 =\frac{1}{2} E[(H_1-H_2)^2e^{-\beta(H_1+H_2)}] \geqq 0 \end{align*} となるので, $\log Z(\beta)$ は下に凸な函数になり, $U(\beta)$ は単調減少函数になる. 特に, $U(0)=U_0=E[H]$ となり, $\beta\geqq 0$ のとき $U(\beta)\leqq U_0$ となり, $\beta\leqq 0$ のとき $U(\beta)\geqq U_0$ となる. $\log Z(\beta)$ のLegendre変換 $S(u)$ とその $-1$ 倍 $D(u)$ を次のように定める: \begin{align*} & S(u) = \inf_{\beta\in\R}(\beta u + \log Z(\beta)), \\ & D(u)=-S(u)=\sup_{\beta\in\R}(-\beta u-\log Z(\beta)) \qquad (u\in\R). \end{align*} $S(u)$ は $u$ に関する一次函数(特に下に凸な函数)の族の各点ごとの下限で 定義された函数なので, $S(u)$ は上に凸な函数になる. $0 u -\log Z(0)=0$ なので \[ S(u)\leqq 0, \qquad D(u)\geqq 0 \qquad (u\in\R) \] となる. さらに $Z(\beta)$ が有限な開区間において, \[ \frac{\d}{\d\beta}(\beta u + \log Z(\beta)) = u - U(\beta) \] なので, $U(\beta)=u$ となる $\beta=\beta(u)$ が存在するならば, \[ S(u) = \beta(u)u + \log Z(\beta(u)), \qquad S(U(\beta)) = \beta U(\beta) + \log Z(\beta) \] となる. 簡単のためこのような $\beta=\beta(u)$ が常に取れると仮定する. これらの公式より $S(u)$ は{\bf カノニカル分布の相対エントロピー}に対応し, $D(u)=-S(u)$ は{\bf カノニカル分布のKullback-Leibler情報量}に対応することがわかる. 特に \[ S(U(0))=0, \qquad D(U(0))=0 \] となるので, $S(u)$ は $u=U(0)=E[H]$ で最大値 $0$ になり, $D(u)$ は同点で最小値 $0$ になる. $S(u)$ (もしくは $D(u)$)は $u\geqq U(0)=E[H]$ で単調減少(もしくは単調増加)し, $u\leqq U(0)=E[H]$ で単調増加(もしくは単調減少)する. $U(\beta)$ は単調減少函数なので, $u\leqq U(0)=E[H]$ のとき $\beta(u)\geqq 0$ となり, $u\geqq U(0)=E[H]$ のとき $\beta(u)\leqq 0$ となる. ゆえに次が成立している: \[ S(u)= \begin{cases} \inf_{\beta\geqq 0} (\beta u + \log Z(\beta)) & (u\leqq U(0)=E[H]), \\ \inf_{\beta\leqq 0} (\beta u + \log Z(\beta)) & (u\geqq U(0)=E[H]). \\ \end{cases} \tag{$\#$} \] $D(u)$ についても同様の表示が存在する. $u$ が $H$ の平均値 $U(0)=E[H]$ 以上と以下の場合で 上限もしくは下限を取る範囲 $\beta$ の範囲を半分に制限できる. \begin{theorem}[Cram\'erの定理] \label{theorem:Cramer} 以上の設定のもとで, $H_1,H_2,\ldots$ は独立同分布な確率変数列であり, $H$ と同じ分布にしたがうと仮定する. このとき以下が成立している: \begin{enumerate} \item[(1)] $F$ が $\R$ の閉部分集合ならば \[ \limsup_{n\to\infty}\frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F\right) \leqq \sup_{u\in F}S(u) =-\inf_{u\in F}D(u). \] \item[(2)] $G$ が $\R$ の開部分集合ならば \[ \liminf_{n\to\infty}\frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in G\right) \geqq \sup_{u\in G}S(u) = -\inf_{u\in G}D(u). \] \item[(3)] $A$ が $\R$ の部分集合であり, $A$ の開核 $G$ の閉包 $F$ が $A$ を含み, $\sup_{u\in G}S(u)=\sup_{u\in F}S(u)$ が成立しているならば \[ \lim_{n\to\infty}\frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in A\right) = \sup_{u\in A}S(u) = -\inf_{u\in A}D(u). \] \end{enumerate} このように, 標本平均 $(H_1+\cdots+H_n)/n$ が集合 $A$ に 含まれる確率の $n\to\infty$ での漸近挙動は カノニカル分布の相対エントロピーに対応する量 $S(u)$ (もしくはカノニカル分布のKullback-Leibler情報量に対応する量 $D(u)$) の $A$ における上限(もしくは下限)で記述される. \qed \end{theorem} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Cram\'erの定理の証明} \label{sec:Cramer-proof} \begin{lemma}[Cram\'erの定理の本質的部分] \label{lemma:Cramer} \secref{sec:Cramer-theorem}の設定のもとで以下が成立している. \begin{enumerate} \item[(1)] $u$ が $H$ の平均値 $U(0)=E[H]$ 以上と以下の場合において, それぞれ \begin{align*} & \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \geqq u \right) \leqq S(u) \qquad (u\geqq U(0)=E[H]), \\ & \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \leqq u \right) \leqq S(u) \qquad (u\leqq U(0)=E[H]). \end{align*} この結果を適用するときに, $u\geqq U(0)=E[H]$ で $S(u)$ は単調減少し, $u\leqq U(0)=E[H]$ で $S(u)$ は単調増加することに注意せよ. \item[(2)] 任意の $\delta>0$ に対して \[ \liminf_{n\to\infty} \frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\delta,u+\delta)\right) \geqq S(u). \] \end{enumerate} (1)の上からの評価は特別なアイデア抜きに容易に証明される. (2)の下からの評価は``カノニカル分布に関する大数の弱法則''を 使って証明される. \qed \end{lemma} \begin{proof} (1)の上からの評価を証明しよう. まず, $u\leqq U(0)=E[H]$ と仮定する. $H_1+\cdots+H_n \leqq nu$ のとき $1$ で他のとき $0$ になる函数を $1_{H_1+\cdots+H_n \leqq nu}$ と書くと, $\beta\geqq 0$ のとき \begin{align*} P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \leqq u\right) & = E[1_{H_1+\cdots+H_n \leqq nu}] \\ & \leqq E\left[ 1_{H_1+\cdots+H_n \leqq nu} e^{-\beta(H_1+\cdots+H_n-nu)} \right] \\ & \leqq E\left[ e^{-\beta(H_1+\cdots+H_n-nu)} \right] \\ & = e^{n\beta u} Z(\beta)^n =e^{n(\beta u+\log Z(\beta))}. \end{align*} ゆえに $u\leqq U(0)=E[H]$, $\beta\geqq 0$ のとき \[ \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \leqq u\right) \leqq \beta u+\log Z(\beta). \] したがって\secref{sec:Cramer-theorem}の($\#$)より \[ \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \leqq u\right) \leqq \inf_{\beta\geqq 0}(\beta u+\log Z(\beta))=S(u). \] 次に, $u\geqq U(0)=E[H]$ と仮定して, 上と同様の議論を行なう. $H_1+\cdots+H_n \geqq nu$ のとき $1$ で他のとき $0$ になる函数を $1_{H_1+\cdots+H_n \geqq nu}$ と書くと, $\beta\leqq 0$ のとき \begin{align*} P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \geqq u\right) & = E[1_{H_1+\cdots+H_n \geqq nu}] \\ & \leqq E\left[ 1_{H_1+\cdots+H_n \geqq nu} e^{-\beta(H_1+\cdots+H_n-nu)} \right] \\ & \leqq E\left[ e^{-\beta(H_1+\cdots+H_n-nu)} \right] \\ & = e^{n\beta u} Z(\beta)^n =e^{n(\beta u+\log Z(\beta))}. \end{align*} ゆえに $u\geqq U(0)=E[H]$, $\beta\leqq 0$ のとき \[ \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \geqq u\right) \leqq \beta u+\log Z(\beta). \] したがって\secref{sec:Cramer-theorem}の($\#$)より \[ \frac{1}{n}\log P\left(\dfrac{1}{n}\sum_{k=1}^n H_k \geqq u\right) \leqq \inf_{\beta\leqq 0}(\beta u+\log Z(\beta))=S(u). \] これで(1)の上からの評価が証明された. (2)の下からの評価を証明しよう. (2)は``カノニカル分布に関する大数の弱法則''から導かれる. 確率変数 $H$ の確率分布は $\R$ 上の確率測度 $\mu$ が定める確率分布に したがっているとする. 確率測度 $\mu_\beta$ を \[ \mu_\beta(dx) = \frac{e^{-\beta x}\mu(dx)}{Z(\beta)} \] と定め, この確率測度の定める確率分布を{\bf カノニカル分布}と呼ぶことにする. カノニカル分布に関する期待値と確率をそれぞれ $E_\beta[\ ]$, $P_\beta(\ )$ と書く. 確率変数 $H$ のカノニカル分布に関する平均は \[ E_\beta[H]=\frac{E[H e^{-\beta H}]}{Z(\beta)}=U(\beta) \] になる. 以下では $u=U(\beta)$, $\delta>0$ と仮定する. このとき $S(u)$ の定義より, \[ S(u) = \beta u + \log Z(\beta). \] $\delta$ 以下の任意の $\eps>0$ を取る. カノニカル分布に関する大数の弱法則より \[ \lim_{n\to\infty} P_\beta\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\eps,u+\eps)\right) =1. \] そして, カノニカル分布での確率と母集団分布での確率のあいだに以下の関係がある: \begin{align*} P_\beta\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\eps,u+\eps)\right) & =\frac {E[1_{H_1+\cdots+H_n\in(nu-n\eps,nu+n\eps)}\,e^{-\beta(H_1+\cdots+H_n)}]} {Z(\beta)^n} \\ & \leqq Z(\beta)^{-n} E[1_{H_1+\cdots+H_n\in(nu-n\eps,nu+n\eps)}\, e^{-n\beta u + n|\beta|\eps}] \\ & =e^{-n(\beta u+\log Z(\beta)-|\beta|\delta)} P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\eps,u+\eps)\right) \\ & \leqq e^{-n(\beta u+\log Z(\beta)-|\beta|\delta)} P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\delta,u+\delta)\right). \end{align*} 以上の結果を合わせると \begin{align*} P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\delta,u+\delta)\right) \geqq e^{n(\beta u+\log Z(\beta)-|\beta|\eps)}(1+o(1)) \qquad (n\to\infty). \end{align*} ゆえに両辺の対数の $1/n$ 倍の $n\to\infty$ での極限を取ることによって次を得る: \begin{align*} \liminf_{n\to\infty} \frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\delta,u+\delta)\right) \geqq \beta u + \log Z(\beta) -|\beta|\eps = S(u)-|\beta|\eps. \end{align*} $\eps>0$ はいくらでも小さくできるので, \[ \liminf_{n\to\infty} \frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k \in (u-\delta,u+\delta)\right) \geqq S(u). \] これで(2)も示された. \qed \end{proof} \begin{proof}[\theoremref{theorem:Cramer}の証明] (1)の上からの評価を証明しよう. $F$ は $\R$ の閉部分集合であるとし, \[ F_+=\{\,u\in F\mid u\geqq U(0)=E[H]\,\}, \qquad F_-=\{\,u\in F\mid u\leqq U(0)=E[H]\,\} \] とおく. これらも $\R$ の閉部分集合なので, $F_-$ の最大値 $u_-$ と　$F_+$ の最小値 $u_+$ が存在する. $S(u)$ は $u\geqq U(0)=E[H]$ で単調減少し, $u\leqq U(0)=E[H]$ で単調増加するので \[ \sup_{u\in F_+}S(u) = S(u_+), \quad \sup_{u\in F_-}S(u) = S(u_-), \quad \sup_{u\in F}S(u) = \max\{S(u_+),S(u_-)\}. \] ゆえに\lemmaref{lemma:Cramer} (1)より, \begin{align*} & \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F_+\right) \leqq \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\geqq u_+\right) \leqq S(u_+), \\ & \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F_-\right) \leqq \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\leqq u_-\right) \leqq S(u_-), \\ & P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F\right) \leqq e^{n S(u_+)}+e^{n S(u_-)} \leqq 2e^{n \sup_{u\in F}S(u)}. \end{align*} したがって \begin{align*} \limsup_{n\to\infty} \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F\right) \leqq \sup_{u\in F}S(u). \end{align*} これで(1)が示された. (2)の下からの評価を証明しよう. $G$ は $\R$ の開部分集合であると仮定する. 任意に $\eps>0$ を取ると, ある $u\in G$ で \[ S(v)\geqq \sup_{u\in G}S(u)-\eps \] を満たすものが存在する. $G$ は開部分集合なので, ある $\delta>0$ で $(v-\delta,v+\delta)\subset G$ を満たすものを取れる. このとき, \lemmaref{lemma:Cramer} (2)より \begin{align*} \liminf_{n\to\infty} \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in G\right) & \geqq \liminf_{n\to\infty} \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in (v-\delta,v+\delta)\right) \\ & \geqq S(v) \geqq \sup_{u\in G} S(u)-\eps. \end{align*} したがって \[ \liminf_{n\to\infty} \frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in G\right) \geqq \sup_{u\in G} S(u). \] これで(2)も示された. 最後に(3)を示そう. $A$ は $\R$ の部分集合であるとし, $A$ の開核を $G$ と書き, $G$ の閉包を $F$ と書く. $A\subset F$ と仮定する. このとき $G\subset A\subset F$ なので \begin{align*} & \sup_{u\in G}S(u) \leqq \liminf_{n\to\infty}\frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in G\right) \leqq \liminf_{n\to\infty}\frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in A\right) \\ & \leqq \limsup_{n\to\infty}\frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in A\right) \leqq \limsup_{n\to\infty}\frac{1}{n}\log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in F\right) \leqq \sup_{u\in F}S(u), \\ & \sup_{u\in G}S(u)\leqq \sup_{u\in A}S(u)\leqq \sup_{u\in F}S(u). \end{align*} ゆえに $\sup_{u\in G}S(u)=\sup_{u\in F}S(u)$ ならば \[ \lim_{n\to\infty}\frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n H_k\in A\right) = \sup_{u\in A}S(u). \] これで示すべきことがすべて示された. \qed \end{proof} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{カノニカル分布の相対エントロピーとの関係} $q=(q_1,\ldots,q_r)$ は有限集合 $\{1,\ldots,r\}$ 上の 確率分布であるとする: \[ q_i\geqq 0, \qquad q_1+\cdots+q_r=1. \] 確率変数 $H$ すなわち有限集合 $\{1,\ldots,r\}$ 上の函数 $H(i)=E_i\in\R$ を考える. このとき \[ Z(\beta)=E[e^{-\beta H}] = \sum_{i=1}^r e^{-\beta E_i}q_i. \] カノニカル分布 $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))$ は \[ p_i(\beta)=\frac{e^{-\beta E_i}q_i}{Z(\beta)} \] と定義され, \[ U(\beta)=E_\beta[H]=\sum_{i=1}^r E_i p_i(\beta) =\frac{1}{Z(\beta)}\sum_{i=1}^r E_i e^{-\beta E_i}q_i. \] ゆえに \begin{align*} S(U(\beta)) & =\beta U(\beta)+\log Z(\beta) =-(-\beta U(\beta)-\log Z(\beta)) \\ & =-\sum_{i=1}^r p_i(\beta)(-\beta E_i-\log Z(\beta)) =-\sum_{i=1}^r p_i(\beta)\log\frac{p_i(\beta)}{q_i} =S(p(\beta)||q). \end{align*} すなわち, $\log Z(\beta)$ のLegendre変換で定義された $S(u)$ に $u=U(\beta)$ を代入した結果は カノニカル分布の相対エントロピーに一致する. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{ガンマ分布の場合の例} \label{sec:Cramer-Gamma} 確率変数 $H$ が 形状 $\alpha>0$, スケール $\tau>0$ のガンマ分布にしたがうとは \[ E[f(H)]= \frac{1}{\Gamma(\alpha)\tau^\alpha} \int_0^\infty f(x)e^{-x/\tau}x^{\alpha-1}\,dx \] が成立することである. このとき $\beta>-1/\tau$ ならば \begin{align*} & Z(\beta)=E[e^{-\beta H}] =\frac{1}{\Gamma(\alpha)\tau^\alpha} \int_0^\infty e^{-(1+\tau\beta)x/\tau}x^{\alpha-1}\,dx =\frac{1}{(1+\tau\beta)^\alpha}, \\ & U(\beta) = \frac{(1+\tau\beta)^\alpha}{\Gamma(\alpha)\tau^\alpha} \int_0^\infty e^{-(1+\tau\beta)x/\tau}x^\alpha \,dx = \frac{(1+\tau\beta)^\alpha}{\Gamma(\alpha)\tau^\alpha} \frac{\Gamma(\alpha+1)\tau^{\alpha+1}}{(1+\tau\beta)^{\alpha+1}} = \frac{\tau\alpha}{1+\tau\beta}>0. \end{align*} ここでよく使われる次の公式を使った% \footnote{使った公式はガンマ函数の定義から置換積分によって容易に示される. $U(\beta)$ に関する公式は $U(\beta)=-(\d/\d\beta)\log Z(\beta)$ を 使えばより簡単に得られる.}: \[ \int_0^\infty e^{-c x}x^{s-1}\,dx = \frac{\Gamma(s)}{c^s} \qquad (s,c>0). \] ゆえに \begin{align*} S(U(\beta)) & =\beta U(\beta)+\log Z(\beta) =\frac{\tau\alpha\beta}{1+\tau\beta} -\alpha\log(1+\tau\beta) \\ & =\alpha - \frac{\alpha}{1+\tau\beta}-\alpha\log(1+\tau\beta). \end{align*} これに $U(\beta)=u>0$ と \[ 1+\tau\beta = \frac{\tau\alpha}{u}, \qquad \beta=\frac{\alpha}{u}-\frac{1}{\tau} \] を代入すると, \[ S(u) = \alpha-\frac{u}{\tau}-\alpha\log\frac{\tau\alpha}{u} %= \alpha-\frac{u}{\tau}+\alpha\log\frac{u}{\tau\alpha} = \alpha-\alpha\log\alpha -\left(\frac{u}{\tau}-\alpha\log\frac{u}{\tau}\right). \] $S(u)$ は $u=U(0)=\tau\alpha$ で最大値 $0$ になる. $H_1,H_2,\ldots$ が独立同分布な確率変数列で各々 が $H$ と同じ形状 $\alpha$, スケール $\tau$ のガンマ分布にしたがうとき, ガンマ分布の再生性より% \footnote{$H_1+\cdots+H_n$ のモーメント母函数は は $H$ のモーメント母函数の $n$ 乗 $Z(\beta)^n=(1+\tau\beta)^{-n\alpha}$ に等しい. これは形状 $n\alpha$, スケール $\tau$ のガンマ分布のモーメント母函数に一致する. このことから $H_1+\cdots+H_n$ が形状 $n\alpha$, スケール $\tau$ のガンマ分布 にしたがうことがわかる. 直接的な計算によってもそのことを示せる. $H$, $K$ は独立な確率変数であり, それぞれ形状 $\alpha$, $\beta$, スケール $\tau$ のガンマ分布にしたがうならば \begin{align*} E[f(H+K)] & =\frac{1}{\Gamma(\alpha)\Gamma(\beta)\tau^{\alpha+\beta}} \int_0^\infty\left( \int_0^\infty f(x+y) e^{-(x+y)/\tau} x^{\alpha-1}y^{\beta-1} \,dy \right)\,dx \\ & =\frac{1}{\Gamma(\alpha)\Gamma(\beta)\tau^{\alpha+\beta}} \int_0^\infty\left( \int_x^\infty f(t) e^{-t/\tau} x^{\alpha-1}(t-x)^{\beta-1} \,dt \right)\,dx \\ & =\frac{1}{\Gamma(\alpha)\Gamma(\beta)\tau^{\alpha+\beta}} \int_0^\infty f(t) e^{-t/\tau} \left( \int_0^y x^{\alpha-1}(t-x)^{\beta-1} \,dx \right)\,dy \\ & =\frac{1}{\Gamma(\alpha)\Gamma(\beta)\tau^{\alpha+\beta}} \int_0^\infty f(t) e^{-t/\tau} \left( \int_0^1 t^{\alpha-1}u^{\alpha-1}t^{\beta-1}(1-u)^{\beta-1} t\,du \right)\,dy \\ & =\frac{B(\alpha,\beta)}{\Gamma(\alpha)\Gamma(\beta)\tau^{\alpha+\beta}} \int_0^\infty f(t)e^{-t/\tau}t^{\alpha+\beta-1}\,dt \\ & =\frac{1}{\Gamma(\alpha+\beta)\tau^{\alpha+\beta}} \int_0^\infty f(t)e^{-t/\tau}t^{\alpha+\beta-1}\,dt \end{align*} 2つ目の等号で $y=t-x$ とおいて $y$ から $t$ に積分変数を置換し, 4つ目の等号で $x=tu$ とおいて $x$ から $u$ に積分変数を変換した. これより $H+K$ が形状 $\alpha+\beta$, スケール $\tau$ のガンマ分布に したがうことがわかる. ガンマ分布は形状について再生性を持つと言う. }, $H_1+\cdots+H_n$ は形状 $n\alpha$, スケール $\tau$ の ガンマ分布にしたがうので, \begin{align*} E\left[f\left(\frac{1}{n}\sum_{k=1}^n H_k\right)\right] =\frac{1}{\Gamma(n\alpha)\tau^{n\alpha}} \int_0^\infty f\left(\frac{y}{n}\right)e^{-y/\tau}y^{n\alpha-1}\,dy. \end{align*} ゆえに $0\leqq a<b$ のとき \begin{align*} P\left(a<\frac{1}{n}\sum_{k=1}^r H_k<b\right) = \frac{1}{\Gamma(n\alpha)\tau^{n\alpha}} \int_{na}^{nb}e^{-y/\tau}y^{n\alpha-1}\,dy = \frac{n^{n\alpha}}{\Gamma(n\alpha)} \int_{a/\tau}^{b/\tau} e^{-nx}x^{n\alpha-1}\,dx. \end{align*} 2つ目の等号で $y=n\tau x$ とおいた. Cram\'erの定理より, \begin{align*} \lim_{n\to\infty} \left( \frac{1}{n}\log \frac{n^{n\alpha}}{\Gamma(n\alpha)} \int_{a/\tau}^{b/\tau} e^{-nx}x^{n\alpha-1}\,dx \right) = \sup_{a<u<b}S(u)= \begin{cases} S(b) & (b/\tau<\alpha), \\ 0 & (a/\tau\leqq \alpha\leqq b/\tau), \\ S(a) & (\alpha<a/\tau). \end{cases} \end{align*} Stirlingの公式より $-\log\Gamma(n\alpha)=-n\alpha\log n+n(\alpha-\alpha\log\alpha)+o(n)$ なので, これは次の公式と同値である($A=a/\tau$, $B=b/\tau$): \begin{align*} & \lim_{n\to\infty}\frac{1}{n} \log \left( \int_A^B e^{-nx}x^{n\alpha-1}\,dx \right) \\ & \qquad =\sup_{a/\tau<x<b/\tau}\left(\alpha\log x-x\right) = \begin{cases} \alpha\log B-B & (B<\alpha), \\ \alpha\log\alpha-\alpha & (A\leqq \alpha\leqq B), \\ \alpha\log A-A & (\alpha<A). \end{cases} \end{align*} この公式は \[ e^{-nx}x^{n\alpha-1} =\exp\left(n(\alpha\log x - x) + o(n)\right) \] にLaplaceの方法を適用することによって直接に示される. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Sanovの定理が拡張されたCram\'erの定理の特別な場合であること} \label{sec:Sanov-from-Cramer} 以下の説明は厳密ではない. まず, 複数の逆温度を持つ場合に拡張されたCram\'erの定理について大雑把に説明しよう. $\R^r$ の標準内積を $\bra\ ,\ \ket$ と書く. $X$ は $\R^r$ に値を持つ確率変数であるとし, $\beta=(\beta_1,\ldots,\beta_r)\in\R^r$ に関する分配函数とMassieu函数を \[ Z(\beta)=E[e^{-\bra\beta,X\ket}], \qquad \Psi(\beta)=\log Z(\beta) \] と定める. $\Psi(\beta)$ は $\beta\in\R^r$ に関する下に凸な函数になる. 実際 $a=(a_1,\ldots,a_r)\in\R^r$ に対して $\d_a=\sum_{i=1}^r a_i\d/\d\beta_i$, $X_a=\bra a,X\ket$ とおくと \begin{align*} \d_a^2\Psi(\beta) & =\frac {E[X_a^2e^{\bra\beta,X\ket}]\,E[e^{-\bra\beta,X\ket}]-E[X_a e^{-\bra\beta,X\ket}]^2} {Z(\beta)^2} %\\ & =\frac {E[(X_a-Y_a)^2e^{\bra\beta,X+Y\ket}]} {2Z(\beta)^2} \geqq 0. \end{align*} ここで $Y$ は $X$ と独立で $X$ と同じ分布にしたがう確率変数である. (もしも $X_a$ が定数になるならば $\d_a^2\Psi(\beta)=0$ となることに注意せよ.) $p\in\R^r$ の函数 $S(p)$ を次のように定める($\Psi(\beta)$ のLegendre変換): \[ S(p)=\inf_{\beta\in\R^r}(\bra\beta,p\ket + \Psi(\beta)). \] $\bra\beta,p\ket + \Psi(\beta)$ を $\beta_i$ で偏微分した結果を $0$ とおくと \[ p_i = -\frac{\d}{\d\beta_i}\Psi(\beta) = -\frac{\d}{\d\beta_i}\log Z(\beta) = \frac{E[X_ie^{-\bra\beta,X\ket}]}{Z(\beta)}=:p_i(\beta). \] ここで $X_i$ は $X$ の第 $i$ 成分である (確率変数列中の $i$ 番目の確率変数ではないことに注意せよ). これで $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))$ が定まった. この条件を満たす $\beta$ を $\beta(p)=(\beta_1(p),\ldots,\beta_r(p))$ と書く. (この辺はかなり荒っぽい議論になっている. 実際にはそれなりに細かい注意が必要になる.) このとき \[ S(p(\beta))=\bra\beta,p(\beta)\ket+\Psi(\beta), \qquad S(p)=\bra\beta(p),p\ket+\Psi(\beta(p)). \] $X^{(1)},X^{(2)},\ldots$ は独立同分布の $\R^r$ 確率変数列であるとし, $X$ と同じ確率分布にしたがうと仮定し, $A\subset\R^r$ とする. このとき適切な条件のもとで \[ \lim_{n\to\infty} \frac{1}{n} \log P\left(\frac{1}{n}\sum_{k=1}^n X^{(k)}\in A\right) =\sup_{p\in A} S(p) \] が成立する(拡張されたCram\'erの定理). Sanovの定理は拡張されたCram\'erの定理の特別な場合であることを説明しよう. 有限集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の集合を $\cP\subset\R^r$ と書く: \[ \cP= \{\,p=(p_1,\ldots,p_r)\in\R^r\mid p_1,\ldots,p_r\geqq 0,\ p_1+\cdots+p_r=1\,\}. \] ベクトル $e_i\in\R^r$ を第 $i$ 成分だけが $1$ で他が $0$ であると定める. このとき $e_i\in\cP$ である. $q=(q_1,\ldots,q_r)\in\R^r$ を任意に固定し, $X$ は確率 $q_i$ で値 $e_i$ になる確率変数であるとする. この場合に上で説明した拡張されたCram\'erの定理を適用するとSanovの定理が得られる. そのためにはこの場合に \[ S(p)=-\sum_{i=1}^r p_i\log\frac{p_i}{q_i} = S(p||q) \] となることを示せばよい. この場合には \begin{align*} Z(\beta) =\sum_{i=1}^r e^{-\bra\beta,e_i\ket}q_i =\sum_{i=1}^r e^{-\beta_i}q_i, \qquad \Psi(\beta)=\log Z(\beta). \end{align*} この $\Psi(\beta)$ のLegendre変換が相対エントロピー $S(p||q)$ になることを示したい. 上で説明したように, \[ p_i = p_i(\beta) = -\frac{\d}{\d\beta_i}\Psi(\beta) = -\frac{\d}{\d\beta_i}\log Z(\beta) = \frac{e^{-\beta_i}q_i}{Z(\beta)}. \] なので, 対数を取ることによって \begin{align*} \Psi(\beta) & =\log Z(\beta) =\sum_{i=1}^r p_i\log Z(\beta) \\ & =\sum_{i=1}^r p_i(-\beta_i+\log q_i-\log p_i) =-\bra\beta,p\ket-\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \end{align*} ゆえに, 上の方で説明した $S(p)$ に関する公式を使うと, \[ S(p) =\bra\beta,p\ket+\Psi(\beta) =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i} =S(p||q). \] このようにCram\'erの定理の線形空間に値を持つ確率変数への拡張の 特別な場合としてSanovの定理が得られる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{$\Psi(\beta)=\log\sum_{i=1}^r e^{-\beta_i}q_i$ のLegendre変換は相対エントロピー} \label{remark:Psi-S} 有限集合 $\{1,2,\ldots,r\}$ 上の確率分布全体の集合を $\cP\subset\R^r$ と書く: \[ \cP= \{\,p=(p_1,\ldots,p_r)\in\R^r\mid p_1,\ldots,p_r\geqq 0,\ p_1+\cdots+p_r=1\,\}. \] 簡単のため, 確率分布 $q=(q_1,\ldots,q_r)\in\cP$ は $q_i>0$ ($i=1,\ldots,r$) を満たしていると仮定する. (以下の計算は $q\in\cP$ であっても, $q_i$ たちがすべて正の実数ならば成立している.) 多変数の分配函数 $Z(\beta)$ とMassieu函数 $\Psi(\beta)$ と 確率分布 $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))\in\cP$ を次のように定める: \[ Z(\beta)=\sum_{i=1}^r e^{-\beta_i}q_i, \qquad \Psi(\beta)=\log Z(\beta), \qquad p_i(\beta)=-\frac{\d}{\d\beta_i}\Psi(\beta)=\frac{e^{-\beta_i}q_i}{Z(\beta)} \] ここで $\beta=(\beta_1,\ldots,\beta_r)\in\R^r$ である. これらの基本性質をまとめておこう. $\Psi(\beta)$ は前節で一般の場合に証明しておいたように下に凸な函数である. $e=(1,\ldots,1)\in\R^r$ とおく. このとき \[ Z(\beta+\lambda e)=e^{-\lambda} Z(\beta), \qquad \Psi(\beta+\lambda e)=\Psi(\beta)-\lambda, \qquad p(\beta+\lambda e)=p(\beta). \] 特に確率分布 $p(\beta)$ は $\beta$ の $e$ 方向の変化で一定である. 任意の確率分布 $p=(p_1,\ldots,p_r)\in\cP$ に対して, $\beta\in\R^r$ を \[ p_i=e^{-\beta_i-\lambda}q_i \qquad (\text{$\lambda\in\R$ は任意定数}) \] によって定めると, 上に述べたことより $p=p(\beta)$ となる: \begin{align*} & e^{-\beta_i}q_i=e^\lambda p_i, \qquad Z(\beta)=\sum_{i=1}^r e^{-\beta_i}q_i=\sum_{i=1}^r e^\lambda p_i = e^\lambda, \qquad p_i(\beta)=\frac{e^{-\beta_i}q_i}{Z(\beta)}=p_i. \end{align*} ゆえに $p(\beta)$ の像は $\cP$ 全体に一致する. $p=(p_1,\ldots,p_r)\in\R^r$ に対して $\beta\in\R^r$ の函数 $f(\beta)$ を \[ f(\beta)=\bra\beta,p\ket+\Psi(\beta) \] と定める. $f(\beta)$ は下に凸な函数なので, もしも $f(\beta)$ が最小値を持つならば, その最小点で $f(\beta)$ の偏微分係数はすべて $0$ になる. $f(\beta)$ の偏導函数は \[ \frac{\d}{\beta_i}f(\beta) =\frac{\d}{\d\beta_i}\sum_{i=1}^r\beta_i p_i+\frac{\d}{\d\beta_i}\Psi(\beta) =p_i-p_i(\beta) \] となるので, $f(\beta)$ が最小値を持つための必要十分条件 は $p\in\cP$ となることである. それ以外のとき $f(\beta)$ は 最小値を持たず $\inf_{\beta\in\R^r}f(\beta)=-\infty$ となる. したがって, $\Psi(\beta)$ のLegendre変換 $S(p)$ を \[ S(p)=\inf_{\beta\in\R^r}(\bra\beta,p\ket+\Psi(\beta)) \] と定めると, $S(p)$ の定義域は $\cP$ に一致する (定義域の外での値は $-\infty$ になると考える). $p\in\cP$ のとき, $p=p(\beta(p))$ を満たす $\beta(p)\in\R^r$ を任意に取ると ($\beta(p)$ の取り方には $e$ 方向の平行移動に関する不定性がある), \[ S(p)=\bra\beta(p),p\ket+\Psi(\beta(p)). \] $\beta=\beta(p)$ を上のように $p_i=e^{-\beta_i-\lambda}q_i$ のように取ると \[ \beta_i = -\log\frac{p_i}{q_i}-\lambda, \qquad Z(\beta)=e^\lambda, \qquad \Psi(\beta)=\lambda \] なので \begin{align*} S(p) & =\sum_{i=1}^r \left(-\log\frac{p_i}{q_i}-\lambda\right)p_i+\lambda =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i} =S(p||q). \end{align*} このように $\Psi(\beta)$ のLegendre変換は相対エントロピー $S(p||q)$ に一致する. $S(p)$ は上に凸な函数になる. 逆に $S(p)$ のLegendre変換 \[ F(\beta)=\sup_{p\in\cP}(-\bra\beta,p\ket + S(p)) \] が $\Psi(\beta)$ に一致することも直接の計算によって確認しておこう (下半連続な凸函数については常にこうなる). 函数 $g(p)$ を \[ g(p)=-\bra\beta,p\ket + S(p) \] と定める. $g(p)$ は $p$ に関して上に凸な函数である. $g(p)$ の $\cP$ 上での最大値問題を考えたい. Lagrangeの未定乗数法を使うために $p$ と $\lambda$ の函数 $L$ を \[ L =g(p)-(\lambda-1)\left(\sum_{i=1}^r p_i-1\right) =-\bra\beta,p\ket + S(p)-(\lambda-1)\left(\sum_{i=1}^r p_i-1\right) \] と定める. このとき \begin{align*} -\frac{\d L}{\d\lambda} & = \sum_{i=1}^r p_i-1, \\ \frac{\d L}{\d p_i} & =-\beta_i-\log\frac{p_i}{q_i}-1-(\lambda-1) =-\beta_i-\log\frac{p_i}{q_i}-\lambda. \end{align*} これより, $\sum_{i=1}^r p_i=1$ という条件のもとで $g(p)$ が最大になるのは \[ e^\lambda = \sum_{i=1}^r e^{-\beta_i}q_i = Z(\beta), \quad p_i = e^{-\lambda-\beta_i}q_i = \frac{e^{-\beta_i}q_i}{Z(\beta)}, \quad \log Z(\beta) = \lambda = -\beta_i-\log\frac{p_i}{q_i} \] のときであることがわかる. このとき, \begin{align*} \Psi(\beta) & =\log Z(\beta) =\lambda=\sum_{i=1}^r p_i\lambda =\sum_{i=1}^r p_i\left(-\beta_i-\log\frac{p_i}{q_i}\right) =-\bra\beta,p\ket+S(p) =F(\beta). \end{align*} すなわち $S(p)$ のLegendre変換 $F(\beta)$ は $\Psi(\beta)$ に一致する. 以上の結果は次のようにまとめられる. \begin{prop} $q=(q_1,\ldots,q_r)$ の成分はすべて正の実数であるとする. $\R^r$ 上の下に凸な函数 $\Psi(\beta)$ と $\cP$ 上の上に凸な函数 $S(p)$ を次のように定める: \[ \Psi(\beta)=\log \sum_{i=1}^r e^{-\beta_i}q_i, \qquad S(p)=-\sum_{i=1}^r p_i\log\frac{p_i}{q_i}. \] これらは互いに相手のLegendre変換になっている. すなわち \[ S(p)=\inf_{\beta\in\R^r}(\bra\beta,p\ket+\Psi(\beta)), \qquad \Psi(\beta)=\sup_{p\in\cP}(-\bra\beta,p\ket+S(p)). \] が成立している. \qed \end{prop} \begin{remark} 上の命題の書き換え. $\cP$ 上の函数 $D(p)$ を \[ D(p)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i} \] と定めると, $D(p)$ も $\Psi(\beta)$ と同様に下に凸な函数になり, \[ D(p)=\sup_{\beta\in\R^r}(-\bra\beta,p\ket-\Psi(\beta)), \qquad \Psi(\beta)=\sup_{p\in\cP}(-\bra\beta,p\ket-D(p)) \] が成立している. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{付録: 統計力学との関係?} \label{sec:statistical-mechanics} この節では数学的に厳密な議論をするつもりはない. 十分に理解していることを書くつもりもない. このノートの内容と``標準的な''統計力学の関係について, 筆者が理解を深めるために書いたラフなスケッチを以下に記録しておく. 2016年7月13日: まず, Cram\'erの定理の一般化に関する\secref{sec:generalized-Cramer}を書いた. 2016年7月14日: 統計力学の教科書におけるカノニカル分布の導出の仕方を紹介した \secref{sec:canonical-distribution-in-physics}を書いた. 2016年7月21日: 統計力学の教科書におけるカノニカル分布の導出の説明をやり直すための \secref{sec:thermal-reservoir}を書いた. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{パラメーターに関する分配函数の漸近挙動を仮定した場合} \label{sec:generalized-Cramer} 確率変数の独立同分布の仮定を 確率変数のあるパラメーターに関する漸近挙動に関する仮定に置き換えることによって, Cram\'erの定理に関する\secref{sec:Cramer}とほぼ同じ議論を繰り返そう. $H_\lambda$ はパラメーター $\lambda$ を持つ確率変数であるとし, $H_\lambda$ の確率分布は $\R$ 上の確率測度 $\mu_\lambda$ で記述されているとする: \[ E[f(H_\lambda)] = \int_\R f(x)\,\mu_\lambda(dx). \] パラメーター $\lambda$ は系のサイズ(例えば体積 $V$)を表わし, $H_\lambda$ は系の全エネルギーを表わしていると考える. 分配函数 $Z(\beta,\lambda)$ とその対数 $\Psi(\beta,\lambda)$ (Massieu函数)を 次のように定義する: \[ Z(\beta,\lambda)=E[e^{-\beta H_\lambda}], \qquad \Psi(\beta,\lambda)=\log Z(\beta,\lambda). \] さらに $\R$ 上の確率測度(カノニカル分布) \[ \mu_{\beta,\lambda}(dx)=\frac{e^{-\beta x}\,\mu_\lambda(dx)}{Z(\beta,\lambda)} \] の定める確率と期待値を それぞれ $P_\beta(\ \ )$, $\bra\ \ \ket_\beta=E_\beta[\ \ ]$ と書く. $\Psi(\beta,\lambda)=\log Z(\beta,\lambda)$ は $\lambda\to\infty$ で \[ \Psi(\beta,\lambda) =\lambda(\psi(\beta)+\eta_\lambda(\beta)), \qquad \eta_\lambda(\beta)=o(1), \quad \eta_\lambda'(\beta)=o(1), \quad \eta_\lambda''(\beta)=o(1) \] と振る舞うと仮定する. このとき \begin{align*} \bra H_\lambda\ket_\beta =\frac{E[H_\lambda e^{-\beta H_\lambda}]}{Z(\beta,\lambda)} =-\frac{\d}{\d\beta}\Psi(\beta,\lambda) =-\lambda(\psi'(\beta)+o(1)) \end{align*} なので \[ u(\beta)=-\psi'(\beta) \] とおくと \[ \left\bra \frac{H_\lambda}{\lambda} \right\ket_\beta = u(\beta) + o(1) \to u(\beta) \qquad (\lambda\to\infty). \] さらに, 確率測度 $\mu_{\beta,\lambda}$ に関する $H_\lambda$ の分散は, $Z=Z(\beta.\lambda)$ と書くと, \begin{align*} 0 \leqq & \Bigl\bra (H_\lambda-\bra H_\lambda\ket_\beta)^2 \Bigr\ket_\beta =\bra H_\lambda^2 \ket_\beta - (\bra H_\lambda \ket_\beta)^2 =\frac{Z_{\beta\beta}Z-(Z_\beta)^2}{Z^2} \\ & =\left(\frac{\d}{\d\beta}\right)^2\Psi(\beta,\lambda) =\lambda(\psi''(\beta)+o(1)) \end{align*} に等しい. (この公式より $\Psi(\beta,\lambda)$ が $\beta$ の函数として 下に凸なこともわかる. 以下では $\psi(\beta)$ も下に凸であると仮定する.) ゆえに \[ \left(\text{$\dfrac{H_\lambda}{\lambda}$ の $\mu_{\beta,\lambda}$ に関する分散}\right) = \frac{\psi''(\beta)}{\lambda}+o\left(\frac{1}{\lambda}\right) =O\left(\frac{1}{\lambda}\right) \to 0 \qquad (\lambda\to\infty). \] 以上をまとめると, 確率測度 $\mu_{\beta,\lambda}$ (カノニカル分布)のもとで の $H_\lambda/\lambda$ が``大数の法則''を満たしていることがわかる. すなわち, 確率測度 $\mu_{\beta,\lambda}$ のもとでの $H_\lambda/\lambda$ の分布 は $\lambda\to\infty$ で $u(\beta)=-\psi'(\beta)$ に集中し, $\lambda$ が大きいとき, その分散(ゆらぎの大きさの2乗) は $\psi''(\beta)/\lambda$ 程度になる. $\Psi(\beta,\lambda)$ は $\beta$ の函数として下に凸なので, $\bra H_\lambda\ket_\beta=-\Psi_\beta(\beta,\lambda)$ は $\beta$ について 単調減少函数である. $\psi(\beta)$ も下に凸になると仮定したので, $u(\beta)=-\psi'(\beta)$ も単調減少函数になる. 以下では簡単のため $\beta\geqq 0$ と仮定し, $u=u(\beta)=-\psi'(\beta)\leqq u(0)$ とおき, \[ s(u)=\beta u + \psi(\beta) \] と定める. $U=U(\beta,\lambda)=\bra H_\lambda \ket_\beta$, \[ S(U,\lambda)=\beta U + \Psi(\beta,\lambda) \] とおくと, $\lambda\to\infty$ において $U=\lambda(u+o(1))$, $\Psi(\beta,\lambda)=\lambda(\psi(\beta)+o(1))$ なので, \[ S(U,\lambda)=\lambda(\beta u+\psi(\beta)+o(1))=\lambda s(u)+o(\lambda) \qquad (\lambda\to\infty). \] さらに, \[ \mu_\lambda(dx)=q_\lambda(x)\,dx \] のとき, \[ p_{\beta,\lambda}(x)=\frac{e^{-\beta x}q_\lambda(x)}{Z(\beta,\lambda)} \] とおくと, \[ \mu_{\beta,\lambda}(dx) = \frac{e^{-\beta x}q_\lambda(x)}{Z(\beta,\lambda)}\,dx = p_{\beta,\lambda}(x)\,dx \] なので, $S(U,\lambda)$ は次のように変形される: \begin{align*} S(U(\beta,\lambda),\lambda)) & =\int_\R (\beta x + \log Z(\beta,\lambda))p_{\beta,\lambda}(x)\,dx \\ & =-\int_\R \log\left(\frac{e^{-\beta x}}{Z(\beta,\lambda)}\right)\,p_{\beta,\lambda}(x)\,dx =-\int_\R p_{\beta,\lambda}(x)\log\left(\frac{p_{\beta,\lambda}(x)}{q_\lambda(x)}\right)\,dx. \end{align*} すなわち $S(U,\lambda)$ はカノニカル分布の相対エントロピーであり, $s(u)$ はサイズ $\lambda\to\infty$ におけるカノニカル分布の 相対エントロピー密度($1$ サイズあたりの相対エントロピー)である. まず $P(H_\lambda/\lambda\leqq u)$ の $\lambda\to\infty$ における上からの評価を示そう. \begin{align*} P\left(\frac{H_\lambda}{\lambda}\leqq u\right) & =E[1_{H_\lambda\leqq \lambda u}] %\\ & \leqq E\left[1_{H_\lambda\leqq \lambda u} e^{-\beta(H_\lambda-\lambda u)}\right] \\ & \leqq E[e^{-\beta(H_\lambda-\lambda u)}] =e^{\lambda\beta u}Z(\beta,\lambda) =e^{\lambda\beta u+\Psi(\beta,\lambda)}. \end{align*} ここで $1_{H_\lambda\leqq\lambda u}$ は $H_\lambda\leqq\lambda u$ のとき $1$ になり, 他のとき $0$ になる函数を表わしている. 1つ目の不等号では \( 1_{H_\lambda\leqq \lambda u} \leqq 1_{H_\lambda\leqq \lambda u} e^{-\beta(H_\lambda-\lambda u)} \) ($\beta\geqq 0$ より)を使い, 2つ目の不等号では \( 1_{H_\lambda\leqq \lambda u} e^{-\beta(H_\lambda-\lambda u)} \leqq e^{-\beta(H_\lambda-\lambda u)} \) を使った. ゆえに $\Psi(\beta,\lambda)=\lambda(\psi(\beta)+o(1))$ より \begin{align*} \log P\left(\frac{H_\lambda}{\lambda}\leqq u\right) =\lambda(\beta u + \psi(\beta)+o(1)) =\lambda(s(u)+o(1)). \end{align*} 両辺を $\lambda$ で割って $\lambda\to\infty$ とすると \[ \limsup_{\lambda\to\infty} \frac{1}{\lambda}P\left(\frac{H_\lambda}{\lambda}\leqq u\right)\leqq s(u). \] 次に下からの評価を示そう. $0<\eps\leqq\delta$ と仮定する. 確率測度 $\mu_{\beta,\mu}$ に関する $H_\lambda/\lambda$ の分布は $\lambda\to\infty$ で $u=u(\beta)$ に集中するので(``大数の法則''), \[ P_\beta\left(\frac{H_\lambda}{\lambda}\in(u-\eps,u+\eps)\right) =e^{o(1)}\to 1 \qquad (\lambda\to\infty). \] さらに, $\beta\geqq 0$ より, \begin{align*} P_\beta\left(\frac{H_\lambda}{\lambda}\in(u-\eps,u+\eps)\right) & =\frac {E\left[ 1_{H_\lambda\in(\lambda u-\lambda\eps,\lambda u+\lambda\eps)}\, e^{-\beta H_\lambda} \right]} {Z(\beta,\lambda)} \\ & \leqq Z(\beta,\lambda)^{-1} E\left[ 1_{H_\lambda\in(\lambda u-\lambda\eps,\lambda u+\lambda\eps)}\, e^{-\lambda\beta u+\lambda\beta\eps} \right] \\ & = e^{-\lambda\beta u+\lambda\beta\eps-\Psi(\beta,\lambda)} P\left(\frac{H_\lambda}{\lambda}\in(u-\eps,u+\eps)\right) \\ & = e^{-\lambda\beta u+\lambda\beta\eps-\lambda(\psi(\beta)+o(1))} P\left(\frac{H_\lambda}{\lambda}\in(u-\eps,u+\eps)\right) \\ & \leqq e^{-\lambda(s(u)-\beta\eps+o(1))} P\left(\frac{H_\lambda}{\lambda}\in(u-\delta,u+\delta)\right). \end{align*} したがって $\lambda\to\infty$ において \[ P\left(\frac{H_\lambda}{\lambda}\in(u-\delta,u+\delta)\right) \geqq e^{\lambda(s(u)-\beta\eps+o(1))+o(1)} = e^{\lambda(s(u)-\beta\eps)+o(\lambda)}. \] 両辺の大数の $1/\lambda$ 倍の $\lambda\to\infty$ での極限を取ることによって \[ \liminf_{\lambda\to\infty} \frac{1}{\lambda} P\left(\frac{H_\lambda}{\lambda}\in(u-\delta,u+\delta)\right) \geqq s(u)-\beta\eps. \] $\eps>0$ はいくらでも小さくできるので, \[ \liminf_{\lambda\to\infty} \frac{1}{\lambda} P\left(\frac{H_\lambda}{\lambda}\in(u-\delta,u+\delta)\right) \geqq s(u). \] 以上によって, \secref{sec:Cramer}で証明したCram\'erの定理の本質的部分に 対応する不等式が得られた. よって, \secref{sec:Cramer}と同様の議論を 繰り返すことによって, 次が成立していることがわかる: \[ \lim_{\lambda\to\infty} \frac{1}{\lambda} P\left(\frac{H_\lambda}{\lambda}\leqq u\right) = s(u). \] このようにエネルギー密度 $H_\lambda/\lambda$ が $u=u(\beta)$ 以下の確率の $\lambda\to\infty$ での漸近挙動は, カノニカル分布の相対エントロピー密度 $s(u)$ で記述される. しかし, これだけだとあまりわかった気になれない. 標準的な統計力学に書いてあるカノニカル分布の導出 との関係はどうなっているのだろうか? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{統計力学の教科書におけるカノニカル分布の導出 (1)} \label{sec:canonical-distribution-in-physics} 以下の議論は本質的に田崎 \cite{Tasaki}, pp.~105--106 と同じ議論のつもりである. ただし, 我々は「等確率の原理」(等重率の原理)を仮定せずに議論を進めているので, 「状態数」を「確率」に置き換えて考える. その結果エントロピーではなく, 相対エントロピーを考えることになる. (等確率の原理の仮定のもとでは状態数で確率が決まる. エントロピーは状態数の対数であり, 相対エントロピーは確率の対数である.) $H_{N,V}$ は体積 $V$ と粒子の個数 $N$ に依存する系の全エネルギーを意味する 確率変数であるとする(これは物理のノートではなく, 数学のノートなので等確率の原理を仮定しない). $U_0(N,V)=E[H_{N,V}]$ とおく. $n=N/V$ が一定の条件のもとで $V\to\infty$ とするとき, $U_0(N,V)=V u_0(n)+o(V)$ が成立していると仮定する. ($U_0(N,V)=\infty$, $u_0(n)=\infty$ であってもよい.) $V\to\infty$ で大数の法則 $P(|H_{N,V}/V-u_0(n)|\leqq\eps)\to 1$ ($\eps>0$) が成立しているならば, $H_{N,V}/V$ の分布は $u_0(n)$ に集中する. したがって $U$ が $U_0(N,V)$ から (もしくは $u$ が $u_0(n)$ から) 離れれば離れるほど確率が小さくなる傾向になり, 十分小さな $U$ と $u$ について確率は単調増加函数になる. (物理的に典型的な状況では状態数(したがって確率)はエネルギーの単調増加函数になる.) {\bf 相対エントロピー} $S(U,N,V)$ を エネルギー $H_{N,V}$ が $U$ 以下になる確率の対数と定める: \[ S(U,N,V) = \log P(H_{N,V}\leqq U) \qquad (U\leqq U_0(N,V)). \] $S(U,N,V)$ は $U$ に関する単調増加函数になる. よくある状況ではエネルギーが $U$ 程度になる確率 は $V$ が大きなとき $P(H_{N,V}\leqq U)$ でよく近似される (\cite{Tasaki}, p.~105 の「$\delta$ を消す議論」を見よ. さらにこのノートの\secref{sec:Boltzmann-factors} と\secref{sec:Gibbs}の議論を比較してみよ.). エネルギー密度 $u$ と個数密度 $n$ を次のように定める: \[ u=\frac{U}{V}, \qquad n=\frac{N}{V}. \] 相対エントロピーは以下を満たしていると仮定する. (\cite{Tasaki}, p.~76の(3.2.29)式も見よ.) \begin{assumption} \label{assumption:S} 相対エントロピー $S(U,N,V)$ は $U$ に関して上に凸な函数であると仮定する. さらに $S(U,N,V)$ は $V\to\infty$ で以下の漸近挙動を持つ: \[ S(U,N,V) = V\,s(u,n) + \eta(u,n,V), \qquad u=\frac{U}{V}, \quad n=\frac{N}{V} \] と $\eta(u,n,V)$ を定めると, %$k=0,1,2,\ldots$ に対して, %\[ %\left(\frac{\d}{\d u}\right)^k \epsilon(u,n,V) = o(V) %\qquad (V\to\infty). %\] \[ \eta(u,n,V)=o(V), \qquad \eta_u(u,n,V)=o(V) \qquad (V\to\infty). \] 特に \[ \lim_{V\to\infty}\frac{1}{V}S(U,N,V) =\lim_{V\to\infty}\frac{1}{V}\log P(H_{N,V}\leqq U) =s(u,n) \] が成立しており, $U=Vu$, $\d/\d U=V^{-1}\d/\d u$ より, \begin{align*} & S_U(U,N,V) =\frac{1}{V}(V s_u(u,n)+\eta_u(u,n,V)) =s_u(u,n)+o(1). \tag{$\sharp$} \end{align*} さらに $s_u(u,n)$ の $u$ に関する連続性も仮定しておく. $s(u,n)$ を(体積無限大の極限における){\bf 相対エントロピー密度}と呼ぶ. $s(u,n)$ も $u$ について上に凸な単調増加函数になると仮定する. 逆温度函数 $\beta(u,n)\geqq 0$ を \begin{align*} \beta(u,n) & =s_u(u,n) =S_U(U,N,V)+o(1) \end{align*} と定める. {\bf \secref{sec:generalized-Cramer}の議論は固定された $\lambda=V$ のケースで 以上の仮定が(ほぼ)成立しているような設定を与えていると考えられる.} \qed \end{assumption} 田崎 \cite{Tasaki}, pp.~105--106の議論によれば, カノニカル分布は本質的に \[ \lim_{V\to\infty}\frac{P(H_{N,V}\leqq U-E)}{P(H_{N,V}\leqq U)} =e^{-\beta(u,n)E} \tag{$*$} \] を示すことによって導出される. これは次と同値である: \[ \log\frac{P(H_{N,V}\leqq U-E)}{P(H_{N,V}\leqq U)} =-\beta(u,n)E+o(1) \qquad (V\to\infty). \] これは次のように示される. 平均値の定理より, $0<\theta<1$ を満たすある $\theta$ が存在して, \begin{align*} \log\frac{P(H_{N,V}\leqq U-E)}{P(H_{N,V}\leqq U)} & =S(U-E,N,V)-S(U,N,V) \\ & =-E\, S_U(U-\theta E,N,V) \\ & =-E\left( s_u\left(u-\frac{\theta E}{V},n\right) + o(1) \right) \\ & =-E\, s_u(u,n) + o(1) \\ & =-\beta(u,n)E + o(1). \qquad (V\to\infty). \end{align*} 2つ目の等号で平均値の定理を用い, 3つ目の等号で($\sharp$)を使い, 4つ目の等号で $s_u(u,n)$ が連続であるという仮定を使った. ($*$)の形式で導出された「Boltzmann因子」は以下のように解釈される. 熱浴と注目する系が接触しているような系を考える. 注目する系のサイズは一定であるとし, 熱浴のサイズが無限大になる極限を考える. 熱浴の側に注目して各種確率を計算する. $U$ は系全体のエネルギーであり, $E$ は注目する系のエネルギーだとすると, $U-E$ は熱浴のエネルギーになる. 熱浴のエネルギーが $U-E$ 程度になる確率は $V$ が大きなとき $P(H_{N,V}\leqq U-E)$ で 近似される. 注目する系のエネルギーが $E$ になる確率は $P(H_{N,V}\leqq U-E)$ に比例するだろう. したがって($*$)より, 注目する系のエネルギーが $E$ である確率は $V$ が大きなとき近似的に Boltzmann因子 $e^{-\beta(u,n)E}$ に比例する. しかし, これでもまだわかった気になれない. 以上の解釈のより正確な定式化はどうなっているのだろうか? 十分な理解に達するためには 「熱浴を含めた全体の系と注目する部分系」という設定を直接扱う必要がありそうだ. \secref{sec:normal-Gibbs}における標準正規分布の導出は 本質的に統計力学におけるMaxwell-Boltzmann分布の導出に等しい. その議論における「全体の系」は半径 $\sqrt{n}$ の $n-1$ 次元球面上の一様分布 (全エネルギー一定という条件で定義される高次元球面上の一様分布)であり, 「注目する部分系」はその分布の1次元部分空間への射影であり, 「熱浴」は残りの自由度である. そして全体の系のサイズを大きくする極限が $n\to\infty$ の極限に対応する. この設定を一般化しなければいけない. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{統計力学の教科書におけるカノニカル分布の導出 (2)} \label{sec:thermal-reservoir} 前節の議論をやり直す. 以下, $H,H_k,\Hres, \Htot$ などはすべて確率変数であるとする. 熱浴(thermal reservoir, heat bath)に接している注目する系を考える. 熱浴の体積を表わすパラメーターを $V$ と書く. 粒子数 $N$ は省略して書くことにする. 注目する系のエネルギーを $H$ と書き, 熱浴のエネルギーを $\Hres_V$ と書くと, 注目する系と熱浴を合わせた全体の系のエネルギーは $\Htot_V=H+\Hres_V$ と表わされる と仮定する. 熱浴と注目する系を合わせた全体の系において, \[ P(H=E_i\ \text{and}\ \Htot_V\leqq U) = P(H=E_i)\,P(\Hres_V\leqq U-E_i) \tag{1} \] が成立していると仮定する. 熱浴と無関係に注目する系は確率 $q_i$ で状態 $i$ になり, 状態 $i$ のエネルギーは $E_i$ であるとする. $H$ は確率 $q_i$ で値 $E_i$ になる確率変数である: \[ P(H=E_i)=q_i. \tag{2} \] 等重率の原理(等確率の原理)を仮定した場合には すべての状態 $i$ が等確率で実現されると考えるが, 応用先を物理的な統計力学に限定したくないので 等重率の原理を仮定しない. (以下の議論が示すようにBoltzmann因子の導出に等重率の原理は関係しない.) 熱浴は $V\to\infty$ で次の漸近挙動を満たしていると仮定する: \[ \Sres(U,V) :=\log P(\Hres_V\leqq U) =V\sres(u) + o(V), \qquad u=\frac{U}{V}. \] $\Sres(U,V)$ を熱浴のエントロピーと呼び, $u=U/V$ をエネルギー密度と呼び, $\sres(u)$ を熱浴のエントロピー密度と呼ぶ($C^1$ 級と仮定). $o(V)$ の部分の $u$ による導函数達も $o(V)$ であると仮定する. このとき, $U=Vu$ より $\d/\d U=(1/V)\d/\d u$ なので, 平均値の定理より, 各 $E$ ごとにある $\theta$ で $0<\theta<1$ を満たすものが存在して, \begin{align*} \log P(\Hres_V\leqq U-E) & =\Sres(U-E,V) =\Sres(U,V)-E\frac{\d\Sres}{\d U}(U-\theta E,V) \\ & =\Sres(U,V) -E\frac{1}{V}\frac{\d}{\d u}\left(V\sres\left(u-\frac{\theta E}{V}\right)+o(V)\right) \\ & =\Sres(U,V)-E\frac{\d\sres}{\d u}(u) + o(1). \end{align*} すなわち, {\bf 熱浴の逆温度} $\beta(u)$ を \[ \beta(u) = \frac{\d\sres}{\d u}(u) \] と定めると, \[ P(\Hres_V\leqq U-E)=P(\Hres_V\leqq U)\, e^{-\beta(u)E+o(1)} \qquad (V\to\infty). \] 以上の仮定と結論を, (1),(2)を使ってまとめると, \[ P(H=E_i\ \text{and}\ \Htot_V\leqq U) = P(\Hres_V\leqq U)\, q_i e^{-\beta(u)E_i + o(1)}. \] さらに \begin{align*} P(\Htot_V\leqq U) & =\sum_i P(H=E_i\ \text{and}\ \Htot_V\leqq U) %\\ & =P(\Hres_V\leqq U)\sum_i q_i e^{-\beta(u)E_i + o(1)}. \end{align*} したがって, 条件付き確率を \[ P(\, H=E_i \mid \Htot_V\leqq U\,) = \frac{P(H=E_i\ \text{and}\ \Htot_V\leqq U)}{P(\Htot\leqq U)} \] と書くと, \[ P(\, H=E_i \mid \Htot_V\leqq U \,) = \frac {q_i e^{-\beta(u)E_i+o(1)}} {\sum_j q_j e^{-\beta(u)E_j+o(1)}} \to \frac {q_i e^{-\beta(u)E_i}} {\sum_j q_j e^{-\beta(u)E_j}} \qquad (V\to\infty). \] すなわち, 全体のエネルギーが $U$ 以下であるという条件のもとで, 注目する系のエネルギーが $E_i$ である条件付き確率の 熱浴の体積無限大での極限は次のようになる: \[ \lim_{V\to\infty} P(\, H=E_i \mid \Htot_V\leqq U \,) = \frac {q_i e^{-\beta(u)E_i}} {\sum_j q_j e^{-\beta(u)E_j}}. \] このようにして得られる注目する系に関する確率分布 を逆温度 $\beta(u)$ の{\bf カノニカル分布}と呼ぶ. 熱浴の漸近挙動から得られる因子 $e^{-\beta(u)E_i}$ を{\bf Boltzmann因子}と呼ぶ. \begin{example} $H_1,H_2,\ldots$ は独立同分布な確率変数で穏当な条件を満たすものであるとし, $V=n=1,2,3,\ldots$ とおき, $\Htot_n=H_1+H_2+\cdots+H_n$, $H=H_1$, $\Hres_n=H_2+\cdots+H_n$ と おくと, Sanovの定理もしくはCram\'erの定理によって, 以上の議論の設定を満たしている. この場合の熱浴は独立同分布な試行の繰り返しだと解釈される. 上の方の議論は独立同分布の試行の繰り返しとみなせるような 特殊な場合でなくても, 熱浴の体積無限大での漸近挙動に関する一般的な前提から Boltzmann因子 $e^{-\beta(u)E_i}$ で記述されるカノニカル分布が 普遍的に得られることを示している. \qed \end{example} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{付録: 他の種類のエントロピーについて} \label{sec:entropies} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{自由エネルギーやMassieu函数との関係} \label{sec:free-energy} \begin{remark}[モーメント母函数とキュムラント母函数] 確率分布 $q_i$ のもとで確率変数 $X:i\mapsto X_i$ のモーメント母函数 $M_X(t)$ は \[ M_X(t)=\sum_{i=1}^r e^{tX_i}q_i \] と定義される. これは $X=E$, $t=-\beta$ のとき分配函数 \[ Z(\beta)=\sum_{i=1}^r e^{-\beta E_i}q_i \] に一致する. 確率論の教科書に書いてあるモーメント母函数(積率母函数)は 分配函数と本質的に同じものだと思ってよい. 確率論の教科書によればモーメント母函数の対数 \[ K_X(t) = \log M_X(t) \] は確率変数 $X$ のキュムラント母函数(cumulant generating function)と呼ばれている. 自由エネルギーの定義 \[ F(\beta)=-\frac{1}{\beta}\log Z(\beta) \] は本質的にキュムラント母函数の定義に一致している. より正確には逆温度 $\beta$ で割る前の \[ {\mathcal F}(\beta)=\log Z(\beta) \qquad (\text{より正確には右辺はそのBoltzmann定数倍}) \] の方がキュムラント母函数の直接の対応物になる. こちらの $\mathcal F(\beta)$ は{\bf Massieu函数}と呼ばれている. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{相対R\'enyiエントロピー} \label{sec:Renyi} \begin{remark}[相対R\'enyiエントロピー] \label{remark:Renyi-Free} 2つの確率分布 $p=(p_1,\ldots,p_r)$, $q=(q_1,\ldots,q_r)$ に対して, {\bf 相対R\'enyiエントロピー} $S_\beta(p||q)$ が \[ S_\beta(p||q) = - \frac{1}{\beta-1}\log \sum_{i=1}^r \left(\frac{p_i}{q_i}\right)^\beta q_i = - \frac{1}{\beta-1}\log \sum_{i=1}^r p_i^\beta q_i^{1-\beta} \] と定義される. これの $\beta-1$ 倍を $\beta$ で微分すると \[ \frac{\d}{\d\beta}((\beta-1)S_\beta(p||q)) = -\frac {\sum_{i=1}^r p_i^\beta q_i^{1-\beta}\log(p_i/q_i)} {\sum_{i=1}^r p_i^\beta q_i^{1-\beta}} \] なので, さらに $\beta=1$ とすると, \[ \left.\frac{\d}{\d\beta}\right|_{\beta=1}((\beta-1)S_\beta(p||q)) =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i} =S(p||q) \] と相対エントロピーが出て来る. ゆえに \[ S_1(p||q) := \lim_{\beta\to 1}S_\beta(p||q) = S(p||q). \] 相対R\'enyiエントロピーは相対エントロピーのワンパラーメータ―変形になっている と考えられる. $q_i=1$ の場合のR\'enyiエントロピーの定義を知っていれば 相対R\'enyiエントロピーの定義は誰でも容易に思い付くと思われる. 相対R\'enyiエントロピーの定義は分配函数 \[ Z(\beta;p,q) =\sum_{i=1}^r \left(\frac{p_i}{q_i}\right)^\beta q_i =\sum_{i=1}^r e^{-\beta E_i}q_i, \qquad E_i = -\log\frac{p_i}{q_i} \] に付随する自由エネルギー $F(\beta:p,q)$ とMassieu函数 ${\mathcal F}(\beta;p,q)$ の定義 \begin{align*} & F(\beta;p,q)=-\beta^{-1}\log Z(\beta;p,q), \\ & {\mathcal F}(\beta;p,q)=\log Z(\beta;p,q) \qquad\qquad (\text{Boltzmann定数倍は略}) \end{align*} と本質的に同じである: \[ (\beta-1)S_\beta(p||q) = \beta F(\beta;p,q) = -{\mathcal F}(\beta;p,q) = -\log Z(\beta;p,q). \] R\'enyi divergence (相対R\'enyiエントロピーの $-1$ 倍)の基本性質の まとめが \cite{vanErven-Harremoes} にある. $(\beta-1)S_\beta(p||q)=-\log Z(\beta;p,q)$ は $\beta$ の函数として上に凸である: \begin{align*} & \left(\frac{\d}{\d\beta}\right)^2(-\log Z(\beta;p,q)) =-\frac{\sum_{i,j=1}^r (E_i-E_j)^2 e^{-\beta(E_i+E_j)}q_i q_j}{2Z(\beta)^2} \leqq 0 \\ & (\text{等号成立は $p_i=q_i$ ($i=1,\ldots,r$) と同値}). \end{align*} そして, $(\beta-1)S_\beta(p||q)=-\log Z(\beta;p,q)$ の $\beta=1$ での値が $-\log Z(1;p,q)=-\log 1=0$ であることと, $(\beta-1)S_\beta(p||q)=-\log Z(\beta;p,q)$ の $\beta=1$ での微係数 が相対エントロピー $S(p||q)$ に等しいという上の計算結果より, \[ (\beta-1)S_\beta(p||q)\leqq(\beta-1)S(p||q). \] 右辺は左辺の接線の式である. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{相対Tsallisエントロピー} \label{sec:Tsallis} \begin{remark}[相対Tsallisエントロピー] \label{remark:Tsallis} 確率分布 $p=(p_1,\ldots,p_r),q=(q_1,\ldots,q_r)$ に対して, $Z(\beta;p,q)$ を次のように定める: \[ Z(\beta;p,q) = \sum_{i=1}^r e^{-\beta E_i} q_i = \sum_{i=1}^r \left(\frac{p_i}{q_i}\right)^\beta q_i = \sum_{i=1}^r p_i^\beta q_i^{1-\beta}, \qquad E_i = -\log\frac{p_i}{q_i}. \] 各 $E_i$ は2つの確率分布 $p$ と $q$ の各 $i$ ごとの違いを表わしている. カノニカル分布 $p(\beta)=(p_1(\beta),\ldots,p_r(\beta))$ を \[ p_i(\beta) =\frac{e^{-\beta E_i}q_i}{Z(\beta;p,q)} =\frac{p_i^\beta q_i^{1-\beta}}{Z(\beta;p,q)} \] と定めると, 逆温度 $\beta$ は $q_i=p_i(0)$ と $p_i=p_i(1)$ を 補間するパラメーターになっている. このとき, 相対R\'enyiエントロピー $S_\beta(p||q)$ は \[ S_\beta(p||q) =\frac{\log Z(\beta;p,q)}{1-\beta} =\frac{1}{1-\beta}\log\sum_{i=1}^r p_i^\beta q_i^{1-\beta} \] と表わされ, 相対エントロピー $S(p||q)$ は \[ S(p||q) =-\left.\frac{\d}{\d\beta}\right|_{\beta=1} \log Z(\beta;p,q) =-\left.\frac{\d}{\d\beta}\right|_{\beta=1} Z(\beta;p,q) =-\sum_{i=1}^r p_i\log\frac{p_i}{q_i} \] と表わされる. 2つ目の等号で $Z(1;p,q)=1$ を使った. 次の演算を $x$ に関する $q$ 差分作用素と呼ぶ: \[ D_{x,q}f(x) = \frac{f(x)-f(qx)}{(1-q)x}. \] $q\to 1$ で $q$ 差分 $D_{x,q}f(x)$ は微分 $\d f(x)/\d x$ に収束する. 上の相対エントロピーの式の $\log Z(\beta;p,q)$ ではなく $Z(\beta;p,q)$ を 用いた表示における $\beta$ に関する微分を $q$ 差分で置き換えることによって% \footnote{筆者は2016年6月22日の段階でその必然性をまったく理解できていない.}, {\bf 相対Tsallisエントロピー}が次のように定義される% \footnote{筆者は(相対)Tsallisエントロピーの定義の必然性をまったく理解していない. (相対)R\'enyiエントロピーは本質的に分配函数の対数(自由エネルギー, Massieu函数)なので そのようなものを考えることの必然性を納得できるが, (相対)Tsallisエントロピーについてはよくわからない. } ($q$ 差分の $q$ を次の式では $\alpha$ と書く): \[ T_\alpha(p||q) = -\left. D_{\beta,\alpha}\right|_{\beta=1}Z(\beta;p,q) = -\frac{Z(1;p,q)-Z(\alpha;p,q)}{1-\alpha} = -\frac{1-\sum_{i=1}^r p_i^\alpha q_i^{1-\alpha}}{1-\alpha}. \] $\alpha\to 1$ で $\alpha$ 差分は通常の微分に収束するので, 相対Tsallisエントロピーは相対エントロピーに収束する. そのことは \begin{align*} & T_\alpha(p||q) =-\sum_{i=1}^r\frac{(p_i/q_i)-(p_i/q_i)^\alpha}{1-\alpha}q_i, %\\ & \qquad \lim_{\alpha\to 1}\frac{x-x^{\alpha}}{1-\alpha} = \left.\frac{\alpha}{\d\alpha}\right|_{\alpha=1}x^\alpha = x \log x. \end{align*} より, 直接にも確かめられる. 相対Tsallisエントロピーは相対エントロピーの定義 における $x\log x$ を $(x-x^\alpha)/(1-\alpha)$ で置き換えたものだと言える. 相対Tsallisエントロピーを相対R\'enyiエントロピーで次のように表わすこともできる: \[ T_\beta(p||q) = \frac{Z(\beta;p,q)-1}{1-\beta} = \frac{\exp((1-\beta)S_\beta(p||q))-1}{1-\beta}. \] 逆に相対R\'enyiエントロピーを相対Tsallisエントロピーによって \[ S_\beta(p||q) = \frac{\log Z(\beta;p,q)}{1-\beta} = \frac{\log(1+(1-\beta)T_\beta(p||q))}{1-\beta} \] と表わすこともできる. 相対Tsallisエントロピーと相対R\'enyiエントロピーの 違いは $x-1$ と $\log x=\log(1+(x-1))$ の違いであると考えることもできる. 以上のように, 相対エントロピー, 相対R\'enyiエントロピー, 相対Tsallisエントロピー はどれも分配函数 $Z(\beta;p,q)$ からの派生物である. \qed \end{remark} \begin{remark*}[相対Tsallisエントロピーと相対R\'enyiエントロピーの関係] 相対Tsallisエントロピー $T_\beta(p||q)$ と相対R\'enyiエントロピー $S_\beta(p||q)$ はどちらも \[ Z_\beta(p||q) = \sum_{i=1}^r p_i^\beta q_i^{1-\beta} \] を用いて \[ T_\beta(p||q) = - \frac{Z_\beta(p||q)-1}{\beta-1}, \qquad S_\beta(p||q) = - \frac{\log Z_\beta(p||q)}{\beta-1}. \] と表わされる. $\beta>1$ (もしくは $\beta<1$)の場合はどちらも $Z_\beta(p||q)$ の単調減少函数(もしくは単調増加函数)なので, それらを最大化することは $Z_\beta(p||q)$ を最小化(もしくは最大化)することと同値になる. さらに \[ e_{\beta-1}(x)=(1+(\beta-1)x)^{1/(\beta-1)}, \qquad \ell_{\beta-1}(x)=\frac{x^{\beta-1}-1}{\beta-1} \] が互いに相手の逆函数になることより, \[ Z_\beta(p||q)^{1/(\beta-1)} =e_{\beta-1}(-T_\beta(p||q)) =\exp(-S_\beta(p||q)). \] この意味で相対Tsallisエントロピーと相対R\'enyiエントロピーの違いは ちょうど $e_{\beta-1}(x)$ と $\exp(x)$ の違いになっている. もちろん, この事実は最初から \[ T_\beta(p||q) = - \ell_{\beta-1}\left( Z_\beta(p||q)^{1/(\beta-1)} \right), \qquad S_\beta(p||q) = - \log\left( Z_\beta(p||q)^{1/(\beta-1)} \right) \] と書いておけば自明なのであるが. \qed \end{remark*} \begin{remark}[負値性] \label{remark:negativities} $p_i,q_i\geqq 0$, $\sum_{i=1}^r p_i=\sum_{i=1}^r=q_i=1$ であるとし, $\beta >0$ であると仮定する. 相対エントロピー, 相対R\'enyiエントロピー, 相対Tsallisエントロピーはそれぞれ \begin{align*} & S(p||q) = - \sum_{i=1}^r p_i\log\frac{p_i}{q_i} \\ & S_\beta(p||q) = - \frac{1}{\beta-1}\log\sum_{i=1}^r p_i^\beta q_i^{1-\beta}, \\ & T_\beta(p||q) = -\frac{\sum_{i=1}^r p_i^\beta q_i^{1-\beta}-1}{\beta-1} \end{align*} と定義されたのであった. $\ell_{\beta-1}(x)$ を \[ \ell_{\beta-1}(x)=\frac{x^{\beta-1}-1}{\beta-1} \] と定めると, 相対Tsallisエントロピーは \[ T_\beta(p||q) = -\sum_{i=1}^r p_i\ell_{\beta-1}\left(\frac{p_i}{q_i}\right) \] と表わされる. $S(p||q)$, $S_\beta(p||q)$, $T_\beta(p||q)$ がすべて $0$ 以下 であることを示そう. \paragraph{相対エントロピー} $f(x)=x\log x$ とおくと, $f'(x)=\log x+1$, $f''(x)=1/x$ より $f(x)$ は 下に凸な函数であり, $f(1)=0$, $f'(1)=1$ より, $f(x)\geqq x-1$ となる. ゆえに \begin{align*} S(p||q) = -\sum_{i=1}^r f\left(\frac{p_i}{q_i}\right)q_i \leqq -\sum_{i=1}^r \left(\frac{p_i}{q_i}-1\right)q_i = 0. \end{align*} \paragraph{相対Tsallisエントロピー} $g(x)=x\ell_{\beta-1}(x)$ とおくと, $g'(x)=\ell_{\beta-1}(x)+x^{\beta-1}$, $g''(x)=\beta x^{\beta-2}$ と $\beta>1$ より, $g(x)$ は下に凸な函数であり, $g(1)=0$, $g'(1)=1$ より, $g(x)\geqq x-1$ となる. ゆえに \begin{align} T_\beta(p||q) = -\sum_{i=1}^r g\left(\frac{p_i}{q_i}\right)q_i \leqq -\sum_{i=1}^r \left(\frac{p_i}{q_i}-1\right)q_i = 0. \end{align} \paragraph{相対R\'enyiエントロピー} $\beta>1$ という仮定より, $S_\beta(p||q)\leqq 0$ を示すためには \[ \sum_{i=1}^r p_i^\beta q_i^{1-\beta} = \sum_{i=1}^r \left(\frac{p_i}{q_i}\right)^\beta q_i \geqq 1 \] を示せばよい. $h(x)=x^\beta$ とおくと, $h'(x)=\beta x^{\beta-1}$, $h''(x)=\beta(\beta-1)x^{\beta-2}$ と $\beta>1$ より, $h(x)$ は下に凸な函数であり, $h(1)=1$, $h'(1)=\beta$ より $h(x)\geqq 1+\beta(x-1)$ となる. ゆえに \begin{align*} \sum_{i=1}^r \left(\frac{p_i}{q_i}\right)^\beta q_i \geqq \sum_{i=1}^r \left(1+\beta\left(\frac{p_i}{q_i}-1\right)\right) q_i =1 \end{align*} これで示すべきことがすべて示された. 以上の議論においてJensenの不等式を使えばほんの少しだけ近道できる. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{加法性(示量性)について} \begin{remark}[加法性について] \label{remark:additivity} $\nu=1,2$ に対する 有限集合 $R_\nu=\{1,2,\ldots,r_\nu\}$ 上の 確率分布 $p_\nu=(p_{\nu,1},\ldots,p_{\nu,r_\nu})$, $p_\nu=(p_{\nu,1},\ldots,p_{\nu,r_\nu})$ に対して, 相対エントロピーと相対R\'enyiエントロピーは \begin{align*} & S(p_\nu||q_\nu) = -\sum_{i=1}^{r_\nu} p_{\nu,i}\log\frac{p_{\nu,i}}{q_{\nu,i}}, \\ & S_\beta(p_\nu||q_\nu) = \frac{\log Z_\beta(p_\nu||q_\nu)}{1-\beta}, \qquad Z_\beta(p_\nu||q_\nu) = \sum_{i=1}^{r_\nu} p_{\nu,i}^\beta q_{\nu,i}^{1-\beta} \end{align*} となる. 直積集合 $R_1\times R_2=\{\,(i,j)\mid i\in R_1,\ j\in R_2\,\}$ 上の確率分布が $(i,j)\mapsto p_{1,i}p_{2,j}$, $(i,j)\mapsto q_{1,i}q_{2,j}$ によって定義される. この直積集合上の確率分布の組に対する 相対エントロピーと相対R\'enyiエントロピーの定義を書き下すと次のようになる: \begin{align*} & S(p_1,p_2||q_1,q_2) = -\sum_{i,j} p_{1,i}p_{2,j}\log\frac{p_{1,i}p_{2,j}}{q_{1,i}q_{2,j}}, \\ & S_\beta(p_1,p_2||q_1,q_2) = \frac{\log Z_\beta(p_1,p_2||q_1,q_2)}{1-\beta}, \qquad Z_\beta(p_1,p_2||q_1,q_2) = \sum_{i,j} (p_{1,i}p_{2,j})^\beta (q_{1,i}q_{2,j})^{1-\beta}. \end{align*} このとき次の{\bf 加法性}が成立している: \[ S(p_1,p_2||q_1,q_2) = S(p_1||q_2) + S(p_2||q_2), \qquad S_\beta(p_1,p_2||q_1,q_2) = S_\beta(p_1||q_2) + S_\beta(p_2||q_2). \] 後者は \[ Z_\beta(p_1,p_2||q_1,q_2) = Z_\beta(p_1||q_1)\, Z_\beta(p_2||q_2) \] と同値である. 証明は以下の通り: \begin{align*} S(p_1,p_2||q_1,q_2) & = -\sum_{i,j}p_{1,i}p_{2,j}\log\frac{p_{1,i}}{q_{1,i}} -\sum_{i,j}p_{1,i}p_{2,j}\log\frac{p_{2,j}}{q_{2,j}} \\ & = -\sum_{i}p_{1,i}\log\frac{p_{1,i}}{q_{1,i}} -\sum_{j}p_{2,j}\log\frac{p_{2,j}}{q_{2,j}} %\\ & = S(p_1||q_1) + S(p_2||q_2), \\ Z_\beta(p_1,p_2||q_1,q_2) & = \sum_{i,j} (p_{1,i}p_{2,j})^\beta (q_{1,i}q_{2,j})^{1-\beta} = \sum_{i,j} p_{1,i}^\beta q_{1,i}^{1-\beta}\cdot p_{2,j}^\beta q_{2,j}^{1-\beta} \\ & = \sum_i p_{1,i}^\beta q_{1,i}^{1-\beta}\cdot \sum_j p_{2,j}^\beta q_{2,j}^{1-\beta} = Z_\beta(p_1||q_1)\, Z_\beta(p_2||q_2). \end{align*} 相対Tsallisエントロピー \begin{align*} T_\beta(p_\nu||q_\nu)=\frac{Z_\beta(p_\nu||q_\nu)-1}{1-\beta}, \qquad T_\beta(p_1,p_2||q_1,q_2)=\frac{Z_\beta(p_1,p_2||q_1,q_2)-1}{1-\beta} \end{align*} は加法性を満たしていないが, \[ T_\beta(p_1,p_2||q_1,q_2) =T_\beta(p_1||q_1)+T_\beta(p_2||q_2) +(1-\beta)T_\beta(p_1||q_1)\,T_\beta(p_2||q_2) \] を満たしている. 証明は次の通り: \begin{align*} & T_\beta(p_1,p_2||q_1,q_2)-T_\beta(p_1||q_1]-T_\beta(p_2||q_2) \\ & =\frac {Z_\beta(p_1||q_1)\,Z_\beta(p_2||q_2)-1-(Z_\beta(p_1||q_1)-1)-(Z_\beta(p_2||q_2)-1)} {1-\beta} \\ & =\frac {Z_\beta(p_1||q_1)\,Z_\beta(p_2||q_2)-Z_\beta(p_1||q_1)-Z_\beta(p_2||q_2)+1} {1-\beta} \\ & =\frac{(Z_\beta(p_1||q_1)-1)(Z_\beta(p_2||q_2)-1)}{1-\beta} \\ & =(1-\beta)\,T_\beta(p_1||q_1)\,T_\beta(p_2||q_2). \end{align*} これは $q$ 数 $(x)_q=(1-q^x)/(1-q)$ に関する公式 \[ (x+y)_q = (x)_q + (y)_q + (q-1)\,(x)_q\,(y)_q \] に似ている. Tsallisエントロピー% \footnote{相対Tsallisエントロピーの定義で $q_i=1$ とするとTsallisエントロピー の定義が得られる.} に関係した数学的構造に関する議論および 文献については \cite{Suyari2004} を参照せよ. そこでは $n\to\infty$ の漸近挙動にTsallisエントロピーが現われる 多項係数の類似物が扱われている. \qed \end{remark} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{相対Tsallisエントロピーを漸近挙動に含む多項分布の拡張(1)} \label{sec:Tsallis-multinomial-1} Suyari \cite{Suyari2004} は 多項{\bf 係数}のある拡張の $n\to\infty$ の漸近挙動がTsallisエントロピーで 記述されることを示した. 以下ではその結果を多項{\bf 分布}と{\bf 相対}Tsallisエントロピーの場合に拡張する% \footnote{ほぼ自明な拡張でしかない.}. 以下では細かいことを気にせずに大雑把な素描を行なう. 以下ではパラメーター $h$ とパラメーター $\beta$ のあいだには \[ h=\beta-1, \qquad h+1=\beta \] という関係があると仮定する. パラメーター $h=\beta-1$ による指数函数の拡張 $e_h(x)$ と対数函数の拡張 $\ell_h(x)$ を \[ e_h(x) = (1+hx)^{1/h}, \qquad \ell_h(x) = \frac{x^h-1}{h} \] と定める. これらは互いに相手の逆函数になっており, $h\to 0$ ($\beta\to 1$)で通常の指数函数と対数函数に収束する. この記号法を使うと, \secref{sec:Tsallis}で導入した相対Tsallisエントロピー $T_\beta(p||q)$ を 次のように表わせる% \footnote{これを相対Tsallisエントロピーの定義だと思ってもよい. この形式の定義では, 相対Tsallisエントロピー $T_\beta(p||q)$ が 相対エントロピー $S(p||q)=-\sum_{i=1}^r p_i\log(p_i/q_i)$ の パラメーター $h=\beta-1$ による拡張になっていることが分かり易い.}: \[ T_\beta(p||q) = -\sum_{i=1}^r p_i\,\ell_h\left(\frac{p_i}{q_i}\right). \] なぜならば \begin{align*} -\sum_{i=1}^r p_i\,\ell_h\left(\frac{p_i}{q_i}\right) & =-\frac{1}{h}\sum_{i=1}^r \left(p_i\left(\frac{p_i}{q_i}\right)^h-p_i\right) =-\frac{1}{\beta-1}\sum_{i=1}^r(p_i^\beta q_i^{1-\beta}-p_i) \\ & =-\frac{\sum_{i=1}^r p_i^\beta q_i^{1-\beta}-1}{\beta-1} =\frac{1-\sum_{i=1}^r p_i^\beta q_i^{1-\beta}}{\beta-1} =T_\beta(p||q). \end{align*} これが漸近挙動に現われるような多項分布の拡張を構成することが以下の目標である. 通常の多項分布における確率は \[ a(n;k)=\frac{n!}{k_1\cdots k_r}q_1^{k_1}\cdots q_r^{k_r} \qquad \left(k=(k_1,\ldots,k_r),\ k_i\geqq 0,\ k_1+\cdots+k_r=n\right) \] であり, これの対数は次のように表わされる: \[ \log a(n;k) = \sum_{\nu=1}^n\log\nu - \sum_{i=1}^r\sum_{\nu_i=1}^{k_i} \log\left(\frac{\nu_i}{q_i}\right). \] これを拡張して次の条件によって $\ell_h(a_h(n;k))$ を定義する: \[ \ell_h(a_h(n;k)) = \sum_{\nu=1}^n\ell_h(\nu) - \sum_{i=1}^r\sum_{\nu_i=1}^{k_i} \ell_h\left(\frac{\nu_i}{q_i}\right). \] このとき, 右辺の $\ell_h(x)=x^h/h-1/h$ の中の $-1/h$ の部分はキャンセルして消えるので, \begin{align*} \ell_h(a_h(n;k)) & =\frac{1}{h}\left( \sum_{\nu=1}^n \nu^h -\sum_{i=1}^r \sum_{\nu_i=1}^{k_i} \left(\frac{\nu_i}{q_i}\right)^h \right) =\frac{1}{h}\left( \sum_{\nu=1}^n \nu^h -\sum_{i=1}^r q_i^{-h} \sum_{\nu_i=1}^{k_i}\nu_i^h \right). \end{align*} %すなわち %\[ %a_h(n;k) %=\left( % 1 % +\sum_{\nu=1}^n \nu^h % -\sum_{i=1}^r q_i^{-h} \sum_{\nu_i=1}^{k_i}\nu_i^h %\right)^{1/h}. %\] $h>0$ ($\beta>1$) と仮定し, $n\to\infty$ で $k_i/n$ はほぼ一定 $k_i=n p_i + O(1)=n(p_i+O(1/n))$ という条件を仮定する. $n\to\infty$ のとき $\ell_h(a_h(n;k))$ がどのように振る舞うかを知りたい. $h>0$ と仮定したので, \[ \sum_{\nu=1}^r \nu^h = \frac{n^{h+1}}{h+1} + O(n^h) = \frac{n^\beta}{\beta} + O(n^{\beta-1}) \qquad (n\to\infty). \] さらに $k_i=np_i+O(1)$ と仮定したので, \[ \sum_{\nu_i=1}^{k_i}\nu_i^h = \frac{(np_i)^{h+1}}{h+1} + O(n^h) = \frac{n^\beta}{\beta}p_i^\beta+ O(n^{\beta-1}). \] ゆえに \begin{align*} \ell_h(a_h(n;k)) & =\frac{n^\beta}{\beta}\frac{1-\sum_{i=1}^r p_i^\beta q_i^{1-\beta}}{\beta-1} + O(n^{\beta-1}) =\frac{n^\beta}{\beta} T_\beta(p||q) + O(n^{\beta-1}) \qquad(n\to\infty). \end{align*} これが{\bf 目標としていた結果}である% \footnote{この結果(もしくはその拡張)を使えば 相対Tsallisエントロピーの場合に関する Sanovの定理の拡張を証明できるだろう. しかし, 2016年6月23日の時点で筆者はパラメーター $h=\beta-1$ による 多項分布の拡張 $a_h(n;k)$ が出て来る必然性を理解できていない.}. この結果は多項分布の漸近挙動 \[ \log a(n;k) = \log\left( \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \right) = n S(p||q) + O(\log n) \] の拡張になっている. %この結果は次のように書き直される: %\[ %a_h(n;k) %=e_h\left( \frac{n^\beta}{\beta} T_\beta(p||q) + O(n^{\beta-1}) \right) %=\left(1+(\beta-1)\frac{n^\beta}{\beta} T_\beta(p||q) + O(n^{\beta-1})\right)^{1/(\beta-1)}. %\] %この $h>0$ ($\beta>1$) の場合の結果は通常の $h=0$ ($\beta=1$) の場合の結果 %\[ %a(n;k)=\frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} %=\exp\left(n S(p||q) + O(\log n) \right) %\] %の拡張になっている. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{相対Tsallisエントロピーを漸近挙動に含む多項分布の拡張(2)} \label{sec:Tsallis-multinomial-2} Suyari-Scarfone \cite{Sutari-Scarfone} に\secref{sec:Tsallis-multinomial-2} とは異なる多項分布の拡張の仕方が書いてあったので以下で紹介することにする. \secref{sec:Tsallis-multinomial-2}の $a_h(n;k)$ 以外の記号を引き継ぐ. 文献 \cite{Sutari-Scarfone} の $q$ と \secref{sec:Tsallis-multinomial-2}の $h=\beta-1$ は $h=1-q$, $h+1=\beta=2-q$ によって対応している. 函数 $e_h(x)$ とその逆函数を $\ell_h(x)$ を \[ e_h(x)=(1+hx)^{1/h}>0 \quad \left(x>-\frac{1}{h}\right), \qquad \ell_h(x)=\frac{x^h-1}{h}>-\frac{1}{h} \quad (x>0) \] と定めると相対Tsallisエントロピーは \[ T_\beta(p||q) = \frac{1-\sum_{i=1}^r p_i^\beta q_i^{1-\beta}}{\beta-1} = \frac{1}{h}\left(1-\sum_{i=1}^r p_i^{h+1}q_i^{-h}\right) = - \sum_{i=1}^r p_i\ell_h\left(\frac{p_i}{q_i}\right) \] と表わせるのであった. 多項分布における確率は \[ a(n;k)=\frac{n!}{k_1\cdots k_r}q_1^{k_1}\cdots q_r^{k_r} \qquad \left(k=(k_1,\ldots,k_r),\ k_i\geqq 0,\ k_1+\cdots+k_r=n\right) \] であり, これの対数は次のように表わされる: \[ \log a(n;k) =\sum_{\nu=1}^n\log\nu -\sum_{i=1}^r \left( \sum_{\nu_i=1}^{k_i} \log\nu_i +k_i\log q_i^{-1} \right). \] この節ではこれを拡張して $\ell_h(a_h(n;k))$ を次のように定義する% \footnote{2016年7月6日現在, この定義の必然性を筆者は理解できていない.}: \[ \ell_h(a_h(n;k)) =\sum_{\nu=1}^n \ell_h(\nu) -\sum_{i=1}^r \left( \sum_{\nu_i=1}^{k_i} \ell_h(\nu_i) +\frac{k_i^{h+1}}{h+1}\ell_h(q_i^{-1}) \right). \] これは次のように書き直される: \[ \ell_h(a_h(n;k)) =\frac{1}{h}\left( \sum_{\nu=1}^n \nu^h -\sum_{i=1}^r\left( \sum_{\nu_i=1}^{k_i} \nu_i^h +\frac{k_i^{h+1}}{h+1}(q_i^{-h}-1) \right) \right). \] %すなわち %\[ %a_h(n;k) %=\left( % 1 % +\sum_{\nu=1}^n \nu^h % -\sum_{i=1}^r\left( % \sum_{\nu_i=1}^{k_i} \nu_i^h % +\frac{k_i^{h+1}}{h+1}(q_i^{-h}-1) % \right) %\right)^{1/h}. %\] $h>0$ ($\beta>1$) と仮定し, $n\to\infty$ で $k_i/n$ はほぼ一定 $k_i=n p_i + O(1)=n(p_i+O(1/n))$ という条件を仮定する. $n\to\infty$ のとき $\ell_h(a_h(n;k))$ がどのように振る舞うかを知りたい. $h>0$ と仮定したので, \[ \sum_{\nu=1}^r \nu^h = \frac{n^{h+1}}{h+1} + O(n^h) = \frac{n^\beta}{\beta} + O(n^{\beta-1}) \qquad (n\to\infty). \] さらに $k_i=np_i+O(1)$ と仮定したので, \begin{align*} & \sum_{\nu_i=1}^{k_i}\nu_i^h = \frac{(np_i)^{h+1}}{h+1} + O(n^h) = \frac{n^\beta}{\beta}p_i^\beta+ O(n^{\beta-1}), \\ & \frac{k_i^{h+1}}{h+1} = \frac{(np_i)^{h+1}}{h+1} + O(n^h) = \frac{n^\beta}{\beta}p_i^\beta+ O(n^{\beta-1}). \end{align*} そして $q_i^{-h}=q_i^{1-\beta}$ である. ゆえに, $n\to\infty$ において, \[ \ell_h(a(n;k)) =\frac{1}{h}\left( \frac{n^\beta}{\beta}-\sum_{i=1}^r \frac{n^\beta}{\beta}p_i^\beta q_i^{1-\beta} \right) + O(n^{\beta-1}) =\frac{n^\beta}{\beta}T_\beta(p||q) + O(n^{\beta-1}). \] これが{\bf 目標としていた結果}である. この結果は多項分布の漸近挙動 \[ \log a(n;k) = \log\left( \frac{n!}{k_1!\cdots k_r!}q_1^{k_1}\cdots q_r^{k_r} \right) = n S(p||q) + O(\log n) \] の拡張になっている. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Csisz\'arの $f$-divergence} \label{sec:f-divergence} 他にもたくさん文献があるのだが, Csisz\'ar \cite{Csiszar2008} に 詳しい参考文献欄がある. $f(x)$ は $0<x<\infty$ で下に凸な非負値函数であり, $f(1)=0$ (最小値)であると仮定する. 有限集合 $\{1,2,\ldots,r\}$ 上の確率分布 $p=(p_1,\ldots,p_r)$, $q=(q_1,\ldots,q_r)$ に対して, $q$ から $p$ への $f$-divergence $D_f(p||q)$ が \[ D_f(p||q)=\sum_{i=1}^r f\left(\frac{p_i}{q_i}\right)q_i \] と定義される. たとえば $f(x)=x\log x$ のとき, $f$-divergence は Kullback-Leibler divergence \[ D(p||q)=\sum_{i=1}^r p_i\log\left(\frac{p_i}{q_i}\right) \] に一致する. たとえば \[ f(x)=x\ell_h(x)=x\frac{x^h-1}{h}=\frac{x^\beta-x}{\beta-1}, \qquad h=\beta-1 \] のとき, $f$-divergence は \[ D_f(p||q) =\sum_{i=1}^r\frac{(p_i/q_i)^\beta-(p_i/q_i)}{\beta-1}q_i =\sum_{i=1}^r\frac{p_i^\beta q_i^{1-\beta}-p_i}{\beta-1} =\frac{\sum_{i=1}^r p_i^\beta q_i^{1-\beta}-1}{\beta-1} =-T_\beta(p||q) \] と Tsallis divergence (相対Tsallisエントロピーの $-1$ 倍)に一致する. 他の様々な相対情報量が $f$-divergence の特別な場合になっている. \paragraph{対数和不等式の一般化} $\{1,2,\ldots,r\}$ の部分集合 $A$ に対して, 確率分布 $p,q$ における $A$ の確率をそれぞれ \[ p(A) = \sum_{i\in A} p_i, \qquad q(A) = \sum_{i\in A} q_i \] と定義する. $A_1,\ldots,A_s$ は集合 $\{1,2,\ldots,r\}$ の分割であるとし, 集合 $\{A_1,A_2,\ldots,A_s\}$ 上の確率分布 $P=(P_1,\ldots,P_s)$, $Q=(Q_1,\ldots,Q_r)$ を $P_j=p(A_j)$, $Q_j=q(A_j)$ と定める. \secref{sec:log-sum}では対数和不等式からKullback-Leibler情報量 について \[ D(p||q)\geqq D(P||Q) \] という不等式が成立していることを示した. この不等式は{\bf 細部の情報を忘れると情報量は小さくなること}を意味している. $f$-divergence についても同様の不等式 \[ D_f(p||q)\geqq D_f(p||q) \] が成立していることを下に凸な函数 $f(x)$ に関するJensenの不等式を使って 示せる: \begin{align*} D_f(p||q) & =\sum_{j=1}^s\sum_{i\in A_j} f\left(\frac{p_i}{q_i}\right)q_i =\sum_{j=1}^s Q_j \sum_{i\in A_j} f\left(\frac{p_i}{q_i}\right)\frac{q_i}{Q_j} \\ & \geqq\sum_{j=1}^s Q_j f\left(\sum_{i\in A_j}\frac{p_i}{q_i}\frac{q_i}{Q_j}\right) =\sum_{j=1}^s f\left(\frac{P_j}{Q_j}\right)Q_j =D_f(P||Q). \end{align*} 特に $s=1$, $A_1=\{1,2,\ldots,r\}$ の場合を考えると $P_1=Q_1=1$, $f(1)=0$ より $D_f(P||Q)=0$ となるので \[ D_f(p||q)\geqq 0. \] 他にもKullback-Leibler情報量と同様の多くの性質を $f$-divergence が満たしている ことを示せる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{付録: 上極限と下極限に関する簡単な解説} \label{sec:limsup} 上極限 $\limsup$ と下極限 $\liminf$ は収束先として $\pm\infty$ を許せば 常に収束するので, 収束するかどうかわからない実数列の漸近挙動を調べるときにとても 便利である. 数学科の学生であれば上極限と下極限についても講義で習っていてよく知っているだろうが, 他学科の出身者は詳しく習ったことがないかもしれない. だから, この付録で上極限と下極限について簡単に解説しておくことにした. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{上極限と下極限の定義} $a_1,a_2,\ldots$ は実数列であるとする. $a_n,a_{n+1},a_{n+2},\ldots$ の上限 $\sup_{k\geqq n} a_k$ を \[ \sup_{k\geqq n} a_k =(\text{すべての $a_n,a_{n+1},a_{n+2},\ldots$ 以上の $\alpha$ の中で最小のもの}). \] ただし $\alpha$ は実数または $\infty$ であるとする% \footnote{上限の存在は実数の連続性によって保証される. 上限が常に存在することを実数の連続性そのものだと思ってもよい.}: \[ \sup_{k\geqq n} a_k =\min\{\,\alpha\in\R\cup\{\infty\}\mid a_k\leqq\alpha\ (k\geqq n)\,\}. \] 一般により小さな実数の集合の上限は小さくなるので $n$ に関する数列 $\sup_{k\geqq n} a_k$ は単調減少数列になる. したがって, 数列 $\sup_{k\geqq n} a_k$ は $n\to\infty$ で実数または $\pm\infty$ に収束する% \footnote{収束することも実数の連続性によって保証される.}. その収束先を実数列 $a_n$ の上極限(limit superior)と呼び, 次のように表わす: \[ \limsup_{n\to\infty} a_n = \lim_{n\to\infty}\sup_{k\geqq n} a_k. \] 同様に下極限(limit inferior)を次のように定義する: \begin{gather*} \inf_{k\geqq n} a_k =\max\{\,\alpha\in\R\cup\{-\infty\}\mid a_k\geqq\alpha\ (k\geqq n)\,\}, \\ \liminf_{n\to\infty} a_n = \lim_{n\to\infty}\inf_{k\geqq n} a_k. \end{gather*} 上限 $\sup$ は下限 $\inf$ 以上なので上極限と下極限は次の不等式を満たしている: \[ \liminf_{n\to\infty} a_n \leqq \limsup_{n\to\infty} a_n. \] 実数列 $a_n$ が収束するならば, $\sup_{k\geqq n} a_k$ と $\inf_{k\geqq n} a_k$ の差は $0$ に収束するので, \[ \liminf_{n\to\infty} a_n = \limsup_{n\to\infty} a_n = \lim_{n\to\infty} a_n \] が成立する. 逆に $\limsup_{n\to\infty} a_n$ と $\liminf_{n\to\infty} a_n$ が一致するならば 実数列 $a_n$ はそれらと同じ値に収束することもわかる. \begin{example}[上極限と下極限の例] 以下が成立していることを定義に基づいて確認してみよ: \begin{align*} & \limsup_{n\to\infty}(-1)^n = 1, \qquad \liminf_{n\to\infty}(-1)^n = -1, \\ & \limsup_{n\to\infty}\left( (-1)^n n \right)= \infty, \qquad \liminf_{n\to\infty}\left( (-1)^n n \right)= -\infty, \\ & \limsup_{n\to\infty}\left( (-1)^n\left(1+2^{-n}\right) \right)=1, \qquad \liminf_{n\to\infty}\left( (-1)^n\left(1+2^{-n}\right) \right)=-1. \end{align*} これらの上極限と下極限を図を描いて確認すれば 上極限と下極限の概念を直観的に理解できると思う. \qed \end{example} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{上極限と下極限の使い方} 上極限と下極限の典型的な使い方について説明しよう. 数列 $a_n$ の $n\to\infty$ での様子を知りたいとしよう. 数列 $a_n$ が $n\to\infty$ で収束する量 $B_n$, $C_n$ によって \[ B_n \leqq a_n \leqq C_n \] と評価されたとする(はさみうち!). このとき $n\to\infty$ で次が成立する: \[ \lim_{n\to\infty} B_n \leqq \liminf_{n\to\infty} a_n \leqq \limsup_{n\to\infty} a_n \leqq \lim_{n\to\infty} C_n. \] この評価は実数列 $a_n$ が収束していなくても成立する. もしも $B_n$ と $C_n$ が同じ値に収束するならば, この不等式より $a_n$ もそれらと同じ値に収束することがわかる. 以上の議論のパターンを知っていれば, $a_n$ が収束するとは限らない弱い条件のもとで上極限と下極限に関する不等式を示しておいて, 追加の強い条件のもとで $a_n$ が収束することを示せるようになる. Sanovの定理の定式化と証明に関する\secref{sec:Sanov}の議論は まさにそのようなタイプの議論の典型例になっている. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Mcmillanの不等式と平均符号長} \label{sec:Mcmillan} 以下の解説は連続ツイート \begin{center} \href {https://twitter.com/genkuroki/status/781366321665630209} {https://twitter.com/genkuroki/status/781366321665630209} \\ \href {https://twitter.com/genkuroki/status/781403859168002048} {https://twitter.com/genkuroki/status/781403859168002048} \end{center} の内容をまとめたものである. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Mcmillanの不等式} 集合 $A$ に対して $A$ の元を並べてできる語全体の集合を $A^*$ と書くことにする: \begin{align*} A^*=\{\, a_1a_2\ldots a_l \mid a_1,a_2,\ldots,a_l\in A,\; l=0,1,2,\ldots \,\}. \end{align*} $a=a_1a_2\cdots a_l$ の長さ $l$ を $\ell(a)=l$ と書くことにする. $A^*$ には語の連結で別の語を作る操作によって自然に積が定まる. $r$ は正の整数であるとし, $b$ は $2$ 以上の整数であるとする. 集合 $S$, $T$ はそれぞれ $r$ 個, $b$ 個の元からなる集合であるとする: $S=\{s_1,\ldots,s_r\}$, $T=\{t_1,\ldots,t_b\}$ と定める. 任意に与えられた長さが $1$ 以上の語 $w_1,\ldots,w_r\in T^*$ に対して, 写像 $C:S^*\to T^*$ を \begin{align*} C(s_{i_1}\cdots s_{i_m}) = w_{i_1}\cdots w_{i_m} \end{align*} によって定めることができる. この $C$ を $S$ の $b$ 文字による符号化と呼ぶ. 符号化 $C:S^*\to T^*$ が単射のとき, $C$ は{\bf 一意復号可能}であるという. \begin{theorem}[Mcmillanの不等式] \label{theorem:Mcmillan} $C$ は一意復号可能な $S$ の $b$ 文字による符号化であるとする. このとき $S$ の元 $s_i$ の符号化 $C(s_i)=w_i$ の長さを $l_i$ と書くと, \begin{align*} \sum_{i=1}^r b^{-l_i} \leqq 1 \end{align*} が成立している. \end{theorem} \begin{proof} $a=\sum_{i=1}^r b^{-l_i}$ とおく. $a\leqq 1$ を示せばよい. $l$ は $l_1,\ldots,l_r$ の最大値であるとし, $n$ は正の整数であるとする. このとき \begin{align*} a^n = \sum_{i_1,\ldots,i_n=1}^r b^{-(l_{i_1}+\cdots+l_{i_n})} = \sum_{k=1}^{nl} N_k b^{-k}. \end{align*} ここで $N_k$ は % \(%\begin{align*} l_{i_1}+\cdots+l_{i_n}=k \) %\end{align*} を満たす $s=s_{i_1}\cdots s_{i_n}$ 全体の個数である. そのとき $w=C(s)=w_{i_1}\cdots w_{i_n}$ は $b$ 種類の文字を $k$ 個並べて できる語になるので, そのような $w$ の個数は $b^k$ 個以下である. 仮定より $C:S^*\to T^*$ は単射なので, 上のような $s$ の個数も $b^k$ 個以下になる.　ゆえに \begin{align*} a^n = \sum_{k=1}^{nl} N_k b^{-k} \leqq \sum_{k=1}^{nl} b^k b^{-k} \leqq \sum_{k=1}^{nl} 1 = nl. \end{align*} したがって $n\to\infty$ で \begin{align*} a = (nl)^{1/n} = e^{(1/n)\log(nl)}\to e^0=1 \end{align*} となる. これで $a\leqq 1$ が示された. \qed \end{proof} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{平均符号長への応用} $p_i,q_i\geqq 0$, $\sum_{i=1}^r p_i=\sum_{i=1}^r q_i=1$ であるとする. Kullback-Leibler情報量は $0$ 以上になるのであった(Gibbsの情報不等式): \begin{align*} D(p||q)=\sum_{i=1}^r p_i\log\frac{p_i}{q_i}\geqq 0. \end{align*} この不等式は下に凸な函数 $f(x)=x\log x$ にJensenの不等式を適用すればただちに 証明される: \begin{align*} D(p||q) =\sum_{i=1}^r q_i f\left(\frac{p_i}{q_i}\right) \geqq f\left(\sum_{i=1}^r q_i\frac{p_i}{q_i}\right) =f(1)=0. \end{align*} $a_i\geqq 0$, $\sum_{i=1}^t a_i=a\leqq 1$ のとき, $q_i=a_i/a$ すなわち $a_i=a q_i$ とおいてこの不等式を使うと \begin{align*} \sum_{i=1}^r p_i\log\left(\frac{p_i}{a_i}\right) =\sum_{i=1}^r p_i\log\left(\frac{p_i}{a q_i}\right) %=D(p||q)-\sum_{i=1}^r p_i\log a =D(p||q)-\log a \geqq 0. \end{align*} この不等式は次のように書き直される: \begin{align*} a_i\geqq 0,\; \sum_{i=1}^t a_i\leqq 1 \implies -\sum_{i=1}^r p_i\log a_i \geqq -\sum_{i=1}^r p_i \log p_i. \tag{$*$} \end{align*} 両辺を $\log b$ で割れば対数の底を任意の $b>1$ にしても この不等式が成立していることがわかる. $C$ は $S=\{s_1,\ldots,s_r\}$ の $b$ 文字による符号化であり, 一意復号可能であると仮定し, $w_i=C(s_i)$ の長さを $l_i$ と書く. Mcmillanの不等式より \begin{align*} \sum_{i=1}^r b^{-l_i}\leqq 1 \end{align*} なので, $a_i=b^{-l_i}$ に対数の底が $b$ の場合の不等式($*$)を適用することによって, 不等式 \begin{align*} \sum_{i=1}^r p_i l_i \geqq -\sum_{i=1}^r p_i \log_b p_i \end{align*} が得られる. この不等式の左辺を $S$ 上の確率分布 $p_i$ に関する {\bf 平均符号長}と呼ぶ. 右辺は $S$ 上の確率分布 $p_i$ の(対数の底が $b$ の場合の)エントロピーである. すなわち, ``ソース'' $S$ 上の確率分布が $p_i$ のとき, 一意復号可能な符号化の平均符号長を``ソース'' $S$ 上の確率分布 $p_i$ の エントロピー未満にすることは不可能である. 一般に $S$ 上の分布 $a_i\geqq 0$, $\sum_{i=1}^r a_i\leqq 1$ に対して, $l_i=-\log_b a_i$ を事象 $s_i$ の{\bf 情報量}と呼ぶ. $b=2$ のとき事象 $s_i$ は $l_i$ bit の情報量を持つと言う. 情報量 $l_i=-\log_b a_i$ は $s_i$ を $b$ 種類の文字で表わしたときに 何文字必要であるかを意味していると解釈することができる. このとき, 対数の底が $b$ のKullback-Leibler情報量における確率分布 $q$ を確率分布とは限らない分布 $a$ に拡張したもの \[ D_b(p||a) =\sum_{i=1}^r p_i\log_b\left(\frac{p_i}{a_i}\right) =\sum_{i=1}^r p_i(-\log_b a_i) - \sum_{i=1}^r p_i(-\log_b p_i) \geqq 0 \] は分布 $a_i$ に対応する方法で(文字 $b_i$ を長さ $l_i=-\log a_i$ で) 一意複合化可能に符号化するときに% \footnote{そのときMcmillanの定理より, $\sum_{i=1}^r a_i\leqq 1$ となる.}, 「エントロピーよりも無駄に増えた平均符号長の大きさ」を意味していると解釈される. このようにKullback-Leibler情報量には「エントロピーからの平均符号長の増分」 という解釈が可能である. Kullback-Leibler情報量 $D(p||a)$ は 「平均符号長の長さで測ったソース $p$ そのもののエントロピーが 符号化 $a$ によってどれだけ増えるか」を意味しているとも考えられる. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\documentclass[a4paper,10pt]{article} \usepackage{graphicx,float,floatflt,pifont,epsfig,wrapfig} \usepackage{shadow,array} \usepackage[latin1]{inputenc} %\usepackage{aeguill} \usepackage[english,frenchb]{babel} \usepackage{url} \let\urlorig\url \renewcommand{\url}[1]{% \begin{otherlanguage}{english}\urlorig{#1}\end{otherlanguage}% } %% Mise en page \setlength{\headheight}{0cm} \setlength{\headsep}{0cm} \setlength{\topmargin}{-1.5cm} \newlength{\mymargin} \setlength{\mymargin}{1cm} \setlength{\oddsidemargin}{\mymargin} \addtolength{\oddsidemargin}{-1in} \setlength{\evensidemargin}{0cm} \setlength{\marginparwidth}{0cm} \setlength{\marginparsep}{0cm} \setlength{\marginparpush}{0cm} \setlength{\footskip}{0cm} \setlength{\textwidth}{21cm} \addtolength{\textwidth}{-2\mymargin} \setlength{\textheight}{280mm} \setlength{\parindent}{0cm} %% Style de titre de sections \newcommand{\titre}[1]{% \vfill% \noindent% \raisebox{0ex}[0mm][0mm]{{\Large \bf #1}}% \par% \vspace{0.1cm}% \hrule% % {\Large\bf #1\\} % \noindent\rule[4pt]{\linewidth}{2pt}% \vspace{0.2cm}% } %% Largeurs des colonnes par défaut \newlength{\leftcol} \setlength{\leftcol}{3cm} \newlength{\rightcol} \setlength{\rightcol}{14cm} \newcolumntype{P}[1]{>{\raggedleft\small\bf}p{#1}} %% Style de rubrique avec les dates à gauche et en gras \newenvironment{rubrique}[1]{% \titre{#1} \begin{tabular}{P{\leftcol}|p{\rightcol}}}% {\end{tabular}\vspace{0.75cm} } \usepackage{layout} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} %\layout \pagestyle{empty} %\titre{État civil} \begin{tabular}{>{\bf}p{2cm}p{10cm}} \multicolumn{2}{>{\Large\bf}p{12cm}} {Jean-Michel Rouet}\\ Adresse & 57 rue Madame, \\ & 75006 Paris\\ Téléphone & +(33) 1 74 30 60 73 \\ E-mail & Jean-Michel.Rouet@philips.com\\ État civil & Né le 14 Août 1974 à Fontenay-le-comte~(85). Marié, 2 enfants.\\ Nationalité & Française. \end{tabular}% \hfill% \begin{minipage}[bottom]{2.8cm}% %\raggedleft% \includegraphics[width=2.8cm]{photo}% \end{minipage} % \begin{tabular}{p{3.25cm}p{9cm}} % {\bf Situation militaire}& Réformé pour cause de chirurgie oculaire.\\ % \end{tabular} \vspace{0.4cm} \begin{center} \begin{tabular}{c} \hline\\ {\bf \Large Ingénieur en Télécommunications,} \\ {\bf \Large Docteur en Traitement du signal et télécommunications.}\\ \\ \hline \end{tabular} \end{center} %\flushleft \vspace {0.5cm} \begin{rubrique}{Projets et Expérience Professionnelle} Depuis Fév.~2000 & Ingénieur de recherche chez Philips France.\\ 1996--1999 & Thèse à l'ENST Bretagne et l'université de Rennes I en imagerie médicale sur le recalage élastique 3D multimodalités par optimisation génétique.\\ 1998--1999 & Élu trésorier de l'association des doctorants de l'ENST Bretagne, et élu suppléant au conseil de la recherche de la même école. Admnistration d'un réseau de machines unix (linux).\\ Mars--Août 1996 & Stage de fin d'études et de DEA à l'ENST Bretagne, traitant de recalage élastique 2D en imagerie médicale, par le biais d'algorithmes génétiques. \\ Juillet--Août 1995 & Stage à VOCALIS LTD près de Cambridge (Angleterre) sur un projet Européen de reconnaissance de la parole via une ligne téléphonique ; Programmation sous UNIX et création d'interface (Tcl/Tk). \\ Étés 1993-1994 & Stages au Crédit-Mutuel Océan à la Roche-sur-Yon~(85) au service Bourse, puis OPCVM.\\ \end{rubrique} \begin{rubrique}{Parcours Professionnel chez Philips France} 2000--2002 & Ingénieur de recherche dans la division Systèmes d'Imagerie Professionnelle de Philips France, à Limeil-Brevannes(94). Développement d'une librairie logicielle générique de segmentation (3DAO) à base de surfaces actives (maillages simplexes). Transfert et support de 3DAO pour une application d'analyse et de quantification du mouvement cardiaque en échographie 3D.\\ 2003--2005 & Ingénieur de recherche sénior au sein du groupe MedISys de Philips Recherche France, puis de Philips Medical Systems. Poursuite du développement et du support de 3DAO. Mise en application dans diverses applications médicales: Segmentation automatiques des principaux organes du thorax, Segmentation cardiaque en IRM 4D; Segmentation automatique d'images IRM de dépistage et de suivi du cancer du sein.\\ \end{rubrique} \begin{rubrique}{Formation} 1996--1999 & Thèse à l'{\sc ENST} Bretagne sur le \og\textit{Recalage 3D élastique en imagerie médicale}\fg, {\it soutenue le 8 décembre 1999}.\\ 1996 & Diplôme d'ingénieur de l'{\sc ENST} Bretagne. \\ & DEA STIR option Image mention bien.\\ 1995--1996 & Préparation du DEA STIR option Image (Université de Rennes 1).\\ 1993--1996 & Élève Ingénieur à l'École Nationale Supérieure des Télécommunications de Bretagne, option COmmunications, Formes et Images (COFI), voie d'approfondissement Image.\\ 1991--1993 & Classes Préparatoires au Lycée St-Joseph, La Roche-sur-Yon (85), spéciale M.\\ % Reçu à l'ENST Bretagne % (concours commun {\it Mines-Ponts}).\\ 1991 & Baccalauréat C, mention Assez Bien.\\ \end{rubrique} \begin{rubrique}{Compétences} Enseignement & Encadrement d'élèves ingénieurs de l'ENST Bretagne (traitement du signal, programmation et traitement d'images, recalage en imagerie médicale),\\ Images & Morphologie mathématique, segmentation, recalage, reconnaissance de formes,\\ Optimisation & Algorithmes génétiques,\\ Langages & C, C++, Ada, Perl, ...\\ Systèmes \mbox{\hspace{0.5cm}d'exploitation} & Unix (Solaris, HP-UX, Linux), MS-DOS, MS-Windows, et expérience en administration réseau sous Unix.\\ \end{rubrique} \pagebreak \vfill \begin{rubrique}{Langues Étrangères} Anglais & Courant, lu, parlé, écrit. Séjour en Grande Bretagne de deux mois. \\ & Présentations d'articles dans des conférences internationales. Contacts réguliers avec des clients aux Pays-bas et aux \'Etats-Unis.\\ Espagnol & Lu, parlé, écrit.\\ Italien & Notions. \end{rubrique} \begin{rubrique}{Centres d'Intérêt} Sports & Escalade, alpinisme, natation, volley-ball, randonnée. \\ Loisirs & Astronomie, voile, informatique, musique, encadrement de groupes d'enfants.\\ \end{rubrique} \vspace{0.5cm} \begin{rubrique}{Publications} Brevets & {\normalsize Auteur ou coauteur d'une quinzaine de brevets internationnaux portant sur des applications médicales (segmentation, visualisation, interaction, etc.)}\\[\baselineskip] %\vspace {0.5 cm} % \item S.~de~Putter, U.~Kose, M.~Breeuwer, R.~Hoogeveen, % H.~v.d.~Bosch, J.~Buth, J.-M.~Rouet, F.~v.d.~Vosse, F.~Gerritsen, % \og\textit{Automatic Segmentation and Tracking of Abdominal Aortic % Aneurysm from MR with 3D Active Objects}\fg, ???. [CARS'05] & S.~de~Putter, M.~Breeuwer, U.~Kose, F.~Laffargue, J.-M.~Rouet, R.~Hoogeveen, H.~v.d.~Bosch, J.~Buth, F.~v.d.~Vosse, F.A.~Gerritsen, \og\textit{Automatic Determination of the Dynamic Geometry of Abdominal Aortic Aneurysm from MR with Application to Wall Stress Simulations}\fg, CARS 2005, 22-25 Juin 2005, Berlin.\\[\baselineskip] [TMI'05] & Sílvia~D.~Olabarriaga, Jean-Michel~Rouet, Maxim~Fradkin, Marcel~Breeuwer et Wiro~J.~Niessen, \og\textit{Segmentation of thrombus in abdominal aortic aneurysms from CTA with nonparametric statistical grey level appearance modeling}\fg. IEEE Trans. on Medical Imaging, 24(4), pp.~477--485, Avril 2005.\\[\baselineskip] [CARS'04] & M.~Breeuwer, U.~Götte, R.~Hoogeveen, B.J.B.M.~Wolters, S.~de~Putter, H.~v.d.~Bosch, J.~Buth,~J.-M.~Rouet et F.~Laffargue, \og\textit{Assessment of the Rupture Risk of Abdominal Aortic Aneurysms by Patient-Specific Hemodynamic Modeling -- Initial Results}\fg, CARS 2004, Chicago.\\[\baselineskip] [ISMRM'04] & M.~Breeuwer, U.~Götte, K.~Visser, R.~Hoogeveen, F.~Laffargue, J.-M.~Rouet, B.~Wolters, S.~de~Putter, \og\textit{Assessment of the Rupture Risk of Abdominal Aortic Aneurysms by Patient-Specific Hemodynamic Modeling - Initial Results}\fg, Proceedings of the ISMRM 2004, Kyoto, Japan.\\[\baselineskip] [TMI'02] & Olivier~Gérard, Antoine~Collet-Billon, Jean-Michel~Rouet, Marie~Jacob, Maxim~Fradkin, et Cyril~Allouche, \og\textit{Efficient Model-Based Quantification of Left Ventricular Function in 3-D Echocardiography}\fg, IEEE Trans. on Medical Imaging, 21(9), pp.~1059--1068, Septembre 2002.\\[\baselineskip] [MICCAI'01] & Olivier~Gérard, Maxim~Fradkin, Antoine~Collet-Billon, Marie~Jacob, Jean-Michel~Rouet et Shérif~Makram-Ebeid, \textit{\og Automatic Analysis of the Left Ventricle in the Time Sequences of 3D Echo-Cardiographic Images}\fg. MICCAI 2001.\\[\baselineskip] [TITB'00] & Jean-Michel~Rouet, Jean-José~Jacq, Christian~Roux, \textit{\og Genetic algorithms for a robust 3-D MR-CT registration}\fg. IEEE Transactions on Information Technology in Biomedicine, 4(2), pp.~126--136, Juin 2000.\\[\baselineskip] [EMBS'98] & Jean-Michel Rouet, Jean-José Jacq, Christian Roux, \og\textit{3D Elastic Multimodality Image Registration through a Genetic Algorithm}\fg, IEEE EMBS, Hong-kong, Octobre 1998.\\[\baselineskip] [GBM'98] & Jean-Michel Rouet, Jean-José Jacq, Christian Roux, \og\textit{Recalage 3D élastique multimodalités par optimisation génétique}\fg, Forum Jeunes Chercheurs 98 en Génie Biologique et Médical, Brest, Mai 1998. (Premier prix poster de la conférence).\\[\baselineskip] [GRETSI'97] & Jean-Michel Rouet, Jean-José Jacq, Christian Roux, \og\textit{Recalage élastique 3D de surfaces numériques par optimisation génétique}\fg, GRETSI, Grenoble, Septembre 1997.\\[\baselineskip] \end{rubrique} \vfill \vspace{2.5cm} %\hspace{0pt} \end{document}

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\section{Data Analysis} \label{sec:analysis_overview} The Hall A physics data analysis model is straightforward. Raw data from the data acquisition (DAQ) are decoded and analyzed by an event-processing program. The event processor creates data summary files that contain raw and computed data, typically in ntuple and histogram format. Diagnostic information as well as final physics results are then extracted from the summary files with the help of interactive analysis tools such as PAW~\cite{paw} and ROOT~\cite{root}. This general scheme applies to both on-line and off-line analysis. For on-line analysis, experimenters have the option of analyzing either raw data stored in files on local disks of the DAQ computers or a random sample of the raw data stream that is distributed via network in real time. Network distribution is provided by the ET component of the CODA~\cite{coda} DAQ system. Raw data files are typically processed shortly after acquisition (quasi-offline analysis). This method is particularly suitable if the on-line data rate is relatively low (typically below 1k events/s) or while no data are being taken. At higher rates, simultaneous read and write access to the raw data storage may increase the DAQ computer deadtime. Such deadtime problems can be avoided by using the ET system; the main disadvantage of this system is that only a sample of the data, instead of the entire data set, can be analyzed. For off-line analysis, the raw data files are first retrieved from the JLab Mass Storage System (``tape silo'') to staging disks, from where they can be processed either interactively or as part of a batch job. For batch processing, the JLab Computer Center maintains a large PC farm, which at the time of this writing consists of 370 CPUs delivering approximately 11,500 SPECint95~\cite{jlabfarm}. The farm is shared among the various user groups from all three experimental halls performing data analysis. Interactive analysis is usually carried out on individual desktop computers or small PC clusters owned by individual groups. To date, virtually all farm and desktop systems run Linux. \subsection{General Features} \label{sec:espace} For the past several years, Hall A has been using the FORTRAN-based program ESPACE (\underline{E}vent \underline{S}canning \underline{P}rogram for Hall \underline{A} \underline{C}ollaboration \underline{E}xperiments)~\cite{espace} as the standard physics event-processing software. ESPACE was originally developed at Mainz and improved at MIT before being introduced in Hall A in 1995. It is written in FORTRAN 77 with the addition of many VMS-style (DEC Fortran) extensions such as structures and pointers. Common operations such as histogramming, graphics, and macro processing are implemented using various CERNLIB~\cite{cernlib} packages. ESPACE's capabilities include: \begin{itemize} \setlength{\parskip}{0ex} \item reading, decoding, and scaling (calibrating) raw event data, \item reconstruction of wire chamber tracks, computation of spectrometer focal-plane coordinates and target quantities, \item computation of basic physics quantities (e.g., angles, four-vectors, kinematics), \item dynamic definition of conditional tests (cuts) and selection of event data based on these tests, \item dynamic definition of histograms and ntuples and output of these in HBOOK~\cite{hbook} format, \item fitting of analysis parameters (e.g., timing and position offsets, spectrometer reconstruction matrix elements) to experimental data (``optimization''), \item display of single events in terms of detector hits in a graphics window, \item program control and analysis steering via the Kit for a User Interface Package (KUIP)~\cite{kuip}. \end{itemize} A dynamic definition of tests and histograms is implemented by the COOLHANDS package~\cite{coolhands}, which is accessible directly from KUIP. ESPACE has been used to date by almost all Hall A experiments for production data analysis. Its main advantages are the fact that it is relatively well debugged and has been adapted to the specific Hall A requirements. Its track reconstruction algorithm is sophisticated and provides high efficiency and resolution. The typical analysis speed is 100-200 events/s on a 500 MHz Linux PC. In the following, a detailed description of the tracking and reconstruction algorithm used in ESPACE is given. \subsection{Tracking \& Reconstruction Algorithm Overview} Tracking information is obtained from the two vertical drift chambers (VDCs) in each spectrometer. The lay-out of the VDCs is illustrated in Figure~\ref{fig:vdc_frame}. An important advantage of the two-chamber design is that it provides a long lever arm for the measurement of track angles, resulting in high angular tracking resolution. Global track angles are determined from the two track cross-over positions measured in the two VDCs. The cross-over positions can be reconstructed with very high precision and are insensitive to the details of the reconstruction algorithm. Knowledge of the {\it local\/} track angles in each wire plane is not necessary. The tracking analysis can be divided roughly into the following steps: \begin{enumerate} \item hit selection, \item cluster identification, \item TDC corrections, \item local cluster fitting, \item If multiple clusters are found in any plane: \begin{enumerate} \item path analysis, \item global cluster fitting, \item path selection, \item ``Golden Track'' selection. \end{enumerate} \item Focal-plane coordinate transformations. \item Reconstruction of target coordinates. \end{enumerate} We examine each step more closely in the following. \subsection{Hit detection and selection, and cluster identification} Figure \ref{fig:vdccluster} illustrates the passage of a charged particle through a VDC plane. Along its way, the particle ionizes the gas in the chamber. Ions and electrons generated in this process drift with nearly constant velocity along the lines of the electric field between the wires, which are grounded, and the cathode planes, which are held at a negative potential of about $-4$~kV. As the field intensifies in the region close to the wires, drifting electrons accelerate and cause further ionizations, resulting in an avalanche which induces an electrical signal (hit) on the wire. The signals are preamplified and sent to TDCs. The TDCs are capable of recording multiple hits per event and are operated in the common-stop mode. If multiple hits occur on a wire, the first hit corresponds to the largest TDC value. ESPACE uses only these first hits for further analysis, and all subsequent hits on a given channel are ignored. This approach is reasonable because multiple hits per wire are often associated with electronic ringing or track-induced noise, where only the leading edge of the signal is physically meaningful. A typical spectrum of the TDC values of the first hits is shown in the lower left panel of Fig.~\ref{vdc_online}. To eliminate noise further, hits that do not satisfy the condition $-0.5 D \leq t * \eta \leq 1.5 D$ are cut from the input data. Here, $D$ is the distance between the wire and the cathode planes (13.0~mm), $t$ the measured drift time, and $\eta$ the average electron drift velocity in the chamber (50~$\mu$m/ns). Once hits have been selected, clusters are identified. Clusters consist of hits with consecutive wire numbers. To allow for inefficiencies, clusters are allowed to have gaps of one wire without a hit. By design, good tracks cross the VDCs at an angle of approximately 45$^\circ$, corresponding to an angle of 55$^\circ$ with respect to the wire planes (cf., Eq.~(\ref{eq:thteq})). Thus, there are typically four to six hits in a cluster. \subsection{TDC corrections} In principle, tracks can be reconstructed using only the cluster center coordinates, which can be obtained from the known wire locations; however, the spatial resolution per plane available in this way is of order of the wire separation (4.2~mm), which is not sufficient to meet the precision requirements of the Hall A spectrometers. Better resolution can be obtained by analyzing the TDC timing information. The TDC data allow extraction of the projected drift distances $d_i$ within each wire cell $C_i$ (see Fig.~\ref{fig:vdccluster}). Once the distances $d_i$ are known, the cross-over point of the track in the wire plane can be determined with very high precision by a linear fit of drift distances vs.\ wire positions. The typical per-cluster position resolution obtained with the Hall A VDCs using this method is 225~$\mu$m FWHM~\cite{vdcNIM}. The TDCs directly measure the time between ionization and the arrival of the signal at the wire (the ``drift time''). The extraction of precise drift distances $d_i$ from the measured drift times requires a more detailed analysis. The raw TDC data must be corrected for a number of effects: \begin{enumerate} \item the time of flight between the cluster centroid and the first scintillator plane (S1); \item the dependence of the trigger scintillator timing on the amplitude of the scintillator signal (``timewalk''); and \item \label{item:tdd} the non-linear relationship between drift time and drift distance. \end{enumerate} While the first two corrections are relatively minor, the third one is important. The relationship between drift time and absolute drift distance is non-linear because of the non-uniform electric field within the cells; in particular, the mean drift velocity increases near the wires. The dependence of distance on time can be parameterized either analytically based on calculations or empirically based on data~\cite{vdcNIM,wechsler}. Three different parameterizations are implemented in ESPACE to linearize the drift times: \begin{enumerate} \item a fourth-order polynomial with fitted coefficients~\cite{wechsler}; \item a third-order polynomial with coefficients obtained from a GARFIELD~\cite{wechsler,garfield} simulation; and \item a two-dimensional lookup table generated from calibration data~\cite{vdcNIM}. \end{enumerate} In practice, the most stable results are usually obtained with the first method. Internally, ESPACE does not compute drift distances directly, but rather equivalent linearized drift times. Multiplication of these times with the average drift velocity $\eta$ yields drift distances. This approach allows a constant timing offset to be fitted along with the track parameters. This is important in the multi-cluster analysis (see section \ref{sec:multicluster}). The precision of the TDC corrections is not critically important for the precision of the final tracking results. Because of the symmetry of the cluster fit geometry, imprecise TDC data increase predominantly the error in the local track {\it angles\/}. The fitted cross-over positions are relatively insensitive to details of the corrections, with a highly symmetric cluster being the least sensitive. Eventually, only the local cross-over points, not the angles, are used to compute the track parameters (see Eqs.~(\ref{eq:alueq}) and (\ref{eq:alveq})). \subsection{Local cluster fitting} \label{sec:clusterfit} After determination of the TDC corrections, track positions and angles are extracted from the cluster data. If only one cluster is found per wire plane, a standard linear fit is performed on each cluster in each wire plane, and the analysis continues with the fitted local positions and slopes. Specifically, the fit is performed on the variables \begin{eqnarray} x_i &=& S_i \cdot \eta ( t_{\it off,i} - t_i + t_{corr,i} ) \\ y_i &=& w_i - w_0 \end{eqnarray} where $\eta$ is the average electron drift velocity, $t_{\it off,i}$ the TDC value for zero drift time (the ``TDC offset'') for the $i$-th wire, $t_i$ the measured TDC value for that wire, and $t_{corr,i}$ the sum of the TDC corrections explained above. The constants $w_i$ represent the position of the $i$-th wire. The relevant geometry is shown in Fig.~\ref{fig:vdccluster}. The quantity $S_i = \pm 1$ is the sign of the $i$-th drift distance. The sign $S_i$ is ambiguous because the TDC data contain no information as to whether a track passed below or above a wire and is determined in a separate step as explained below. The result of the fit are the intercept $u$ ($v$ for V planes), slope $\tau_u$ ($\tau_v$), their respective uncertainties, and $\chi^2$. Note that, with these definitions, the slope $\tau$ vanishes when the track is perpendicular to the wires. To resolve the ambiguity in the sign of the calculated drift distances, one observes that good tracks traverse the chamber at an angle of approximately 55$^\circ$ with respect to the $u$ ($v$) axis. Assuming a given track satisfies this criterion, all hits with smaller $u$ ($v$) coordinates than the cross-over point of the track in the wire plane can be assigned negative drift distances. The cross-over point can be taken to coincide with the wire that has the smallest drift distance (``pivot wire''). An ambiguity remains about the sign of the drift distance to be assigned to the pivot wire. It can be resolved by trial-and-error: two fits are performed, one with a positive and one with a negative value of the drift time of the pivot wire, and the fit with the smaller $\chi^2$ is assumed to be correct. The above method for resolving the sign ambiguity and determining the track parameters through a fit only works for clusters with three or more hits. For clusters with only two hits, it is usually possible to guess the signs of the two distances by requiring that the track slope be close to 55$^\circ$. Thus slope and intercept can be estimated, albeit with reduced precision and confidence. This procedure slightly improves the tracking efficiency at the expense of a lower resolution for some tracks. ``Clusters'' consisting of only one hit do not yield sufficient information and are discarded. At this point in the analysis, ESPACE distinguishes two cases: \begin{itemize} \item Exactly one cluster per plane. This is a ``single-cluster event''. The analysis continues as described in section \ref{sec:vdc_coords}. \item More than one cluster in at least one plane. This is considered a ``multi-cluster event'', even if only a single plane has multiple clusters. In this case, the analysis continues as described in the next section. \end{itemize} \subsection{Multi-Cluster Analysis} \label{sec:multicluster} Multiple clusters in a wire plane may occur for several reasons: \begin{itemize} \item Noise, which may originate, for example, from the electronics, cosmics, or radiation background. True noise clusters usually do not give reasonable fit results and thus are easy to remove. Cosmics coincident with an actual track are normally very rare due to the low cosmics rate. Cosmics and certain background noise may lead to valid tracks through the chamber, but can usually be eliminated easily because of unreasonable angles, reversed scintillator timing, and, eventually, failure to reconstruct to the target. \item Actual multiple tracks from the target. These may occur for essentially two reasons: (a) several tracks emitted from the same interaction in the target fall within the acceptance of the spectrometer; and (b) accidental coincidences of tracks from two separate interactions occur within the VDC timing window. The former case is rare because the Hall A spectrometers do not have a sufficiently large acceptance to be able to cover much of the phase space for multiparticle events. The latter case may occur rather frequently at sufficiently high singles rates, and thus it is the most likely cause of multi-track events. Usually, all tracks in true multi-track events can be reconstructed. \item Spurious tracks caused by delta rays, which are produced before or in the wire chamber by actual tracks. Such tracks often have unreasonable angles and/or do not make clusters in all wire planes (e.g., if they are generated inside the chamber); however, as they may occur close to actual tracks, they may cause overlapping clusters and thus corrupt valid tracking information. This may be a difficult situation to analyze, and actual tracks may not always be recoverable. An upper limit on the probability that spurious tracks occur in the chamber that disturb the regular tracking data is given by the abundance of clusters with high hit multiplicity. Typically, about $3 - 4\%$ of events in each spectrometer are found to have one or more clusters with eight or more hits. Such clusters cannot occur due to normal tracks alone and contain either spurious hits or are entirely due to tracks not originating from the target. \end{itemize} If multiple clusters occur in any plane, the association between clusters and tracks may become ambiguous. To determine the most probable track(s) through the chamber, an approach well known in wire chamber analysis is taken within ESPACE. All possible combinations of clusters from the four VDC planes are identified (each combination containing exactly one cluster from each plane), and each such combination is considered a possible path of the track through the chambers. A fit is then performed for each path, and the paths are ordered by the the fit's total $\chi^2$. The path(s) with the smallest $\chi^2$ represent(s) the best reconstructed track(s). In the following sections these steps are described in detail. As this algorithm is relatively involved and not guaranteed to yield improved tracking results, it is sometimes considered safer to disregard any events with multiple clusters per wire plane altogether at the expense of tracking efficiency and to consider only unambiguous single-cluster events. \subsubsection{Path analysis} \label{sec:pathanalysis} To identify paths through the chamber, ESPACE considers the wire planes in the order U1, U2, V1, and V2 (see Fig.~\ref{fig:vdc_frame}). This sequence is preferable over the actual physical sequence because hits from like wire planes (U or V) can be fitted together. For every cluster in plane U1, all combinations (``links'') with clusters in plane U2 are considered. The cluster in U1 is considered the ``start point'', and the cluster in U2, the ``end point'' of the link. There are $n_{u1} n_{u2}$ such links, where $n_{u1}$ and $n_{u2}$ are the numbers of clusters in U1 and U2, respectively. For each link, a fit is performed on the combined hits (typically $2\times 5 = 10$) of the clusters from both planes, U1 and U2. The fitting procedure used is described in the next section in more detail. The resulting $\chi^2$, cross-over position, timing offset $t_0$, and track slope are stored with the link. This procedure is repeated identically for the combination of planes V1 and V2. For the combination U1 and V1, it is not possible to perform a fit since the wire directions of the planes are orthogonal. Thus, only the possible links between these planes are stored. Next, a table is built of all connecting combinations of links. Two links connect if the end point of a link in one plane is the start point of a link in another plane. Thus, each combination contains exactly three links, one between each pair of wire planes in the sequence U1-U2, U2-V1, and V1-V2. There are $n_{u1} n_{u2} n_{v1} n_{v2}$ such combinations. Each is a possible path for the track. \subsubsection{Global cluster fitting} \label{sec:globalfit} In a multi-track situation or in the presence of noise, tracks other than the one that generated the event trigger will, in general, occur at times other than the trigger; a fit to the drift times must, therefore, allow for a timing offset, called $t_0$. Clusters belonging to the ``Golden Track'' (the track that generated the trigger) will have $t_0 \approx 0$, while clusters belonging to other tracks will, in general, have a non-zero fitted time offset. To accommodate $t_0$, ESPACE uses a three-parameter fit in the multi-track analysis. The fit routine used is derived from the {\tt curfit} algorithm of Bevington~\cite{bevington}. This is an iterative algorithm which is computationally relatively expensive. As in the single-track case, the ambiguity of the pivot-wire drift time must be resolved. This is again done by trial-and-error; however, since two clusters from two different wire planes are involved in the multi-cluster fit, {\it four\/} fits are performed on the same data, corresponding to the four possible sign combinations of the two pivot wires. The result with the smallest $\chi^2$ is chosen. (The number of fits is the same as in the case of single clusters, of course, although the single-cluster fit algorithm is simpler and fewer data are processed with each fit.) The computational requirements of this algorithm are relatively high. For instance, if two real tracks are present, generally there will be two clusters in each plane, and so $2^4 = 16$ paths to consider. Because a single path contains two pairs of wire planes (U1-U2 and V1-V2) that are fitted together, eight fits are performed for each path to resolve all ambiguities. As a result, $16\times 8 = 128$ iterative fits must be carried out to identify two tracks. \subsubsection{Path ordering and track identification} \label{sec:trackselect} Next in the analysis, paths are ordered according to a goodness-of-fit criterion, and the best-fit result(s) are selected. To order paths by their probability of describing a valid track, ESPACE uses the quantity \begin{equation} \chi^2_{tot} = \chi^2_{u1u2} + \chi^2_{v1v2} + \left(\frac{t_{0,v1v2} - t_{0,u1u2}}{\min(\sigma(t_{0,v1v2}), \sigma(t_{0,u1u2}))}\right)^2. \label{eq:chisqtot} \end{equation} Here, $\chi^2_{u1u2}$ and $\chi^2_{v1v2}$ are the $\chi^2$-values found in the U1-U2 and V1-V2 global cluster fits, respectively, $t_{0,u1u2}$ and $t_{0,v1v2}$ are the timing offsets obtained from these respective fits, and the $\sigma(t_0)$ are the uncertainties in those offsets. The minimum uncertainty of the two $t_0$ fits is used, rather than the combined uncertainty, in order to give smaller $\chi^2$ in situations where the two $t_0$ fits have comparable rather than dissimilar uncertainty. Using the difference of timing offsets as a goodness-of-fit criterion between the planes U2 and V1 is the best that can be done under the circumstances. Because the U and V coordinates are orthogonal, there is no good criterion for matching U and V clusters other than their timing. This is a design limitation of the Hall A VDCs. Different chamber designs include additional wire planes oriented in a third direction that allow easier correlation between clusters in different planes. Possible physical tracks are now selected from the ordered paths. This step relies on the assumption that each cluster belongs to at most one physical track, which is correct so long as clusters from different tracks do not overlap. ESPACE selects the maximum number of tracks from the available paths that do not have any clusters in common, starting from the path with smallest $\chi^2_{tot}$. Note that this means, for example, that in order to find two valid tracks, {\it every\/} VDC plane must have at least two clusters. Even if many possible paths were found in the preceding analysis, only a small number of tracks survive at this point. A typical histogram of the track multiplicity in a high-rate experiment is shown in Fig.~\ref{fig:trackmult}. In general, tracking results are only considered useful for physics analysis if a single track is found. Events with multiple tracks are typically discarded (see section~\ref{Limitations}). Using the single track criteria, the overall tracking efficiency varies between better than $95\%$ at low rate and $70 - 80\%$ at high rate. \subsubsection{Golden Track Selection} \label{sec:goldentrack} The final step in the multi-cluster analysis is to select the Golden Track from the set of tracks determined in the previous analysis. The timing offset $t_0$ obtained from the global cluster fits (section \ref{sec:globalfit}) can be used as a direct measure of the probability of a track to have generated the trigger. ESPACE uses the weighted average of the two timing offsets obtained, viz. \begin{equation} t_{0,av} = \frac{\frac{t_{0,u1u2}}{\sigma(t_{0,u1u2})^2} + \frac{t_{0,v1v2}}{\sigma(t_{0,v1v2})^2}} {\frac{1}{\sigma(t_{0,u1u2})^2} + \frac{1}{\sigma(t_{0,u1u2})^2}} \label{eq:t0av} \end{equation} to select the Golden Track. The quantities $t_0$ and $\sigma(t_0)$ in Eq.\ (\ref{eq:t0av}) are the same as in Eq.\ (\ref{eq:chisqtot}). The track with the smallest $t_{0,av}$ is chosen. Further analysis continues with this track only, and all other tracks found are subsequently ignored. \subsection{Coordinate Transformations and Target Reconstruction} \label{sec:vdc_coords} In the preceding analysis, the track through the VDC has been determined in terms of wire plane coordinates, $u$ and $v$. For further analysis, it is advantageous to convert the track coordinates to detector coordinates: $x_{det}$ and $y_{det}$, and their corresponding angular coordinates, $\theta_{det}$ and $\phi_{det}$. (By convention, $\theta_{det}$ and $\phi_{det}$ denote the tangents of the respective angles.) The relationship between the coordinate systems is shown in Fig.~\ref{fig:vdc_detcoord}. The coordinate transformation can be written as \begin{eqnarray} x_{det} &=& \frac{u\sin\gamma - v\sin\beta}{\sin(\gamma-\beta)} \label{eq:xeq} \\ y_{det} &=& \frac{u\cos\gamma - v\cos\beta}{\sin(\gamma-\beta)} \label{eq:yeq}\\ \theta_{det} &=& \frac{\sin\gamma\tan\alpha_u - \sin\beta\tan\alpha_v} {\sin(\gamma-\beta)} \label{eq:thteq} \\ \phi_{det} &=& \frac{\cos\gamma\tan\alpha_u - \cos\beta\tan\alpha_v} {\sin(\gamma-\beta)}. \label{eq:phieq} \end{eqnarray} Here, $\alpha_u$ and $\alpha_v$ are the global track angles in the $u$-$v$ coordinate system, i.e., the angles between the the $z$-axis and the projection of the track onto the $u$-$z$ and $v$-$z$ planes, respectively. In the single-cluster analysis, $\alpha_u$ and $\alpha_v$ are calculated using the fitted cross-over points $u_1$, $u_2$, $v_1$, and $v_2$ in the U1, U2, V1, and V2 planes, respectively, as follows: \begin{eqnarray} \tan\alpha_u &=& \frac{u_2 - u_1}{d_u} \label{eq:alueq}\\ \tan\alpha_v &=& \frac{v_2 - v_1}{d_v}, \label{eq:alveq} \end{eqnarray} where $d_u$ and $d_v$ are the separations of like planes, as illustrated in Fig.~\ref{fig:vdc_frame}. In general, $\tan \alpha_u$ and $\tan \alpha_v$ will be close to the local cluster slopes $\tau_u$ and $\tau_v$ (cf., Sect.~\ref{sec:clusterfit} and Fig.~\ref{fig:vdccluster}). In the multi-cluster analysis, $\alpha_u$ and $\alpha_v$ are determined directly in the global fit procedure (section \ref{sec:globalfit}) and are not calculated according to eqs.\ (\ref{eq:alueq}) and (\ref{eq:alveq}). The coordinates $u$ and $v$ in eqs.\ (\ref{eq:xeq}) and (\ref{eq:yeq}) are given by \begin{eqnarray} u &=& u_1 \\ v &=& v_1 - d_{uv1}\tan\alpha_v, \end{eqnarray} where $d_{uv1}$ is the separation between the U1 and V1 planes. If any VDC plane has no cluster at all, attempts are made to estimate the track parameters from available local data in another plane. For instance, if the U2 cluster is missing, then the global track angle $\alpha_u$ can be approximated by the available local angle in U1: \begin{equation} \tan \alpha_u = \tau_{u1} \end{equation} Similar replacements are made if other clusters are missing. In this way, up to one missing $u$ and one missing $v$ cluster can be tolerated at the expense of reconstruction precision. This missing cluster substitution occurs only if no plane has more than one hit --- it is not compatible with the multi-cluster analysis described above. Finally, ESPACE converts the VDC coordinates to focal-plane coordinates, which are suitable as input for the target reconstruction matrix multiplication. Focal-plane coordinates as well as the target reconstruction formalism are discussed in section~\ref{sec:approach}. \subsection{Limitations} \label{Limitations} The chief shortcomings of the ESPACE software are its lack of flexibility, maintainability, and to a lesser extent its lack of speed and heavy reliance on legacy components such as CERNLIB, KUIP, and HBOOK. The first two issues are of particular concern in view of planned detector upgrades and reconfigurations in Hall A. The addition of new detectors and the handling of multiple experimental configurations is not well supported by ESPACE and would require a significant effort to implement. The most significant limitation of the tracking algorithm is its inability to handle overlapping clusters of hits, even though sufficient information to analyze such clusters is in principle available due to the use of multi-hit TDCs. In the present implementation, ESPACE has no provision for handling this situation. Without special processing, overlapping clusters often corrupt the tracking information. Such events are not analyzable, resulting in a tracking inefficiency. The magnitude of this inefficiency is difficult to estimate, however, because ESPACE does not provide unambiguous information as to which events were not analyzable due to overlapping clusters or due to other reasons, nor are overlapping clusters even identified. This has prompted experiments that have taken high-rate data to discard multi-cluster events altogether in the analysis. The ratio of multi-cluster events to single-cluster events is well defined, and so the inefficiency due to omitting multi-cluster events can be readily calculated. \subsection{New Developments} To address many of the shortcomings of ESPACE, an effort is currently underway in Hall A to develop new analysis software using a flexible and highly maintainable object-oriented design implemented in C++~\cite{hallaroot}. The new analyzer is based on the ROOT system~\cite{root}, an object-oriented framework that has been under development at CERN since 1995 and has been adopted widely in the nuclear and particle physics community and elsewhere. The new analysis software is currently under active development and will be described in a future publication.

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\summary{2009}{9}{14} Agenda call: ??? Agenda announcement: \agoref{gentoo-council}{96c702e85f79b8f5e22472ae2c961534} \agendaitem{Update on LiveCD/DVD for Gentoo 10.0} \index{LiveDVD}\index{anniversary!10 year} \dev{solar} commmented that things were progressing fine. A new snapshot will be taken on September 20th and the cutoff date will be the 4th of October. \agendaitem{A Way to Modify the PMS such that it doesn't directly involve the EAPI Process} \index{PMS!modification} Reference: \bug{273261}, comment 18 \dev{tsunam} requested a decision on a process to modify PMS without involving the EAPI Process. There was discussion about whether PMS is a documenting simply documenting the ebuild API or if it is a broader document covering the entire tree. The agenda item was deferred until the next meeting to be discussed on mailing lists beforehand. \agendaitem{Discussion of the Need for a PMS/EAPI committee outside of the council} \index{PMS} \begin{enumerate} \item Either we form a new committee / working group for EAPI and PMS questions (more or less \dev{calchan}'s proposal). There should be one or two members from the council, plus someone from the PMS project, and a representative for each package manager. \item In principle also the PMS project could play this role, but with its current membership of only three developers it is too weak. So some relevant people (see above) would have to join. On the other hand, there is already a bugzilla alias (pms-bugs), a mailing list (gentoo-pms) and an IRC channel set up. \item Something (completely) different. \end{enumerate} Of the three proposals the council chose to do something complete different, and what will be done will be discussed on lists (in particular gentoo-pms) or at the next meeting.

https://ctan.altspu.ru/fonts/feyn/overheads.tex

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\documentclass{beamer} % Quick example of overheads, using the sample beamer description at % http://www.miwie.org/presentations/presentations.html#beamer \usepackage{feyn,url} \title{Feynman diagram font} \author{Norman Gray\\University of Glasgow} \date{v0.4.3, 2022 July 20} %\parindent0pt \begin{document} \frame{\titlepage} \section{A diagram} \frame { Here is a text diagram $\Feyn{fglf}$, and a displayed one: \[ \Diagram{\vertexlabel^a \\ fd \\ & g\vertexlabel_{\mu,c} \\ \vertexlabel_b fu\\} = \displaystyle ig\gamma_\mu (t^c)_{ab} \] This uses the `feyn' font for drawing diagrams: \url{https://purl.org/nxg/dist/feyn}. } \end{document}

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\input zb-basic \input zb-matheduc \iteman{ZMATH 1991h.03367} \itemau{Steinberg, G.} \itemti{Changes in calculus. Analysis im Mathematikunterricht des Gymnasiums: kommt Bewegung in festgefahrene Spuren.} \itemso{Contributions concerning mathematics teaching. Papers. Beitraege zum Mathematikunterricht. Vortraege. Steiner, H.G.; Cohors-Fresenborg, E.; Sorger, P. (and others) Bad Salzdetfurth: Franzbecker. 1991. p. 69-76 of 530 p. Conference: 25. Bundestagung fuer Didaktik der Mathematik, Osnabrueck (Germany), 4-8 Mar 1991 [ISBN 3-88120-204-8]} \itemcc{I10} \itemut{Calculus; Educational Objectives; Educational Analysis; ; Analysis; Bildungsziel; Didaktische Analyse} \itemli{} \end

https://spot.pcc.edu/math/clm/images/image-129.tex

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\documentclass[12pt]{article} \usepackage{amsmath,amssymb} \usepackage{pgfplots} \usepackage{xparse} \usepgfplotslibrary{patchplots} \usepackage{tkz-euclide} \usetkzobj{all} \usetikzlibrary{3d,calc} \usepackage{xltxtra} % curve, dot, and graph custom styles \pgfplotsset{pccplot/.style={color=red,mark=none,line width=1pt,<->,solid}} % primary style for curves \pgfplotsset{asymptote/.style={color=gray,mark=none,line width=1pt,<->,dashed}} \pgfplotsset{soldot/.style={color=red,only marks,mark=*}} \pgfplotsset{holdot/.style={color=red,fill=white,only marks,mark=*}} \pgfplotsset{blankgraph/.style={xmin=-10,xmax=10,ymin=-10,ymax=10,axis line style= {-, draw opacity=0 },axis lines=box,major tick length=0mm,xtick={-10,-9,...,10},ytick={-10,-9,...,10},grid=major,yticklabels={,,},xticklabels={,,},minor xtick=,minor ytick=,xlabel={},ylabel={},width=0.75\textwidth,grid style={solid,gray!40}}} % cycle list of plot styles for graphs with multiple plots \pgfplotscreateplotcyclelist{pccstylelist}{% pccplot\\% color=blue,mark=none,line width=1pt,<->,dashdotted\\% color=gray,mark=none,line width=1pt,<->,dashdotdotted\\% } \def\axisdefaultwidth{175pt} \def\axisdefaultheight{\axisdefaultwidth} \pgfplotsset{every axis/.append style={ axis x line=middle, % put the x axis in the middle axis y line=middle, % put the y axis in the middle axis line style={<->}, % arrows on the axis xlabel={$x$}, % default put x on x-axis ylabel={$y$}, % default put y on y-axis xmin = -7,xmax = 7, % most graphs have this window ymin = -7,ymax = 7, % most graphs have this window %xtick = {-6,-4,...,6}, % fix ticks %extra x ticks={-6, -4, -2}, %extra x tick labels={$-6\phantom{-}$, $-4\phantom{-}$, $-2\phantom{-}$}, %ytick = {-6,-4,...,6}, % fix ticks yticklabel style={inner sep=0.333ex}, minor xtick = {-7,-6,...,7}, % fix ticks minor ytick = {-7,-6,...,7}, % fix ticks scale only axis, % don't factor in axis and tick labels for width= and height= cycle list name=pccstylelist, tick label style={font=\footnotesize}, %label style={font=\scriptsize}, legend cell align=left, %legend style={font=\scriptsize}, %width = {ifthenelse(.85\linewidth>180pt,200pt,.85\linewidth)}, grid = minor, grid style = {solid,gray!40}, %every node near coord/.append style={ % font=\scriptsize %}, try min ticks=6, }} %\tikzset{axisnode/.style={font=\scriptsize,text=black}} % arrow style \tikzset{>=stealth} % framing the graphs \pgfplotsset{framed/.style={axis background/.style ={draw=gray}}} % next line is a bit more colorful %\pgfplotsset{framed/.style={axis background/.style ={draw=gray,fill=yellow!20,rounded corners=3ex}}} \ifdefined\tikzset \tikzset{ampersand replacement = \amp} \fi \newcommand{\Z}{\mathbb{Z}} \newcommand{\reals}{\mathbb{R}} \newcommand{\real}[1]{\mathbb{R}^{#1}} \newcommand{\fe}[2]{#1\mathopen{}\left(#2\right)\mathclose{}} \newcommand{\cinterval}[2]{\left[#1,#2\right]} \newcommand{\ointerval}[2]{\left(#1,#2\right)} \newcommand{\cointerval}[2]{\left[\left.#1,#2\right)\right.} \newcommand{\ocinterval}[2]{\left(\left.#1,#2\right]\right.} \newcommand{\point}[2]{\left(#1,#2\right)} \newcommand{\fd}[1]{#1'} \newcommand{\sd}[1]{#1''} \newcommand{\td}[1]{#1'''} \newcommand{\lz}[2]{\frac{d#1}{d#2}} \newcommand{\lzn}[3]{\frac{d^{#1}#2}{d#3^{#1}}} \newcommand{\lzo}[1]{\frac{d}{d#1}} \newcommand{\lzoo}[2]{{\frac{d}{d#1}}{\left(#2\right)}} \newcommand{\lzon}[2]{\frac{d^{#1}}{d#2^{#1}}} \newcommand{\lzoa}[3]{\left.{\frac{d#1}{d#2}}\right|_{#3}} \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\sech}{\operatorname{sech}} \newcommand{\csch}{\operatorname{csch}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \begin{document} \pagestyle{empty} \begin{tikzpicture} \begin{axis}[xtick={100},ytick={100},minor xtick={100}, minor ytick={100},title={$y=\fe{\cosh}{t}$},xlabel={$t$}] \addplot[pccplot,domain=-2.5:2.5]{(exp(x)+exp(-x))/2}; \end{axis} \end{tikzpicture} \end{document}

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\input zb-basic \input zb-matheduc \iteman{ZMATH 2011a.00961} \itemau{Blahut, Richard E.} \itemti{Modem theory. An introduction to telecommunications.} \itemso{Cambridge: Cambridge University Press (ISBN 978-0-521-78014-8/hbk). xiv, 497~p. (2010).} \itemab Digital communication theory (or {\it modem theory}) is that part of communication theory in which digital modulation and demodulation techniques play a prominent role in the communication process, either because the information to be transmitted is digital or because the information is temporarily represented in digital form for the purpose of transmission. The main task of communication theory is the design of efficient waveforms for the transmission of information over band-limited or power-limited channels. Digital communication systems are in widespread use and are now in the process of sweeping away even the time-honored analog communication systems, such as those used in radio, television, and telephony. This insightful book is ideal for senior undergraduate students studying digital communications and is also a useful reference for practising engineers. The general purpose of the book is to give a general introduction to the modulation waveforms and demodulation techniques that are central to the design of digital communication systems. The material in this book consists (for the most part) of selected chapters from {\it Digital Transmission of Information} (published in 1990), which have been rewritten and expanded to fit the needs of a course in modem theory and digital communications. The topics are confined to the modulation layer of communication theory. Waveforms and modulators are studied in Chapter 2 (for baseband channels) and in Chapter 5 (for passband channels). Basic demodulators are developed in Chapters 3 and 6 for baseband and passband channels, respectively. More advanced methods of demodulation for channels with dispersion are studied in Chapter 4. A stronger statement of optimality of the matched filter (introduced in Chapter 3) is deferred to Chapter 7, where it is shown to be part of the maximum-likelihood demodulator for both coherent and noncoherent demodulation in gaussian noise. These first seven chapters contain the central ideas of modulation and demodulation, which are at the core of the theory of modems. The final five chapters then go deeper into the subject by developing some of the other topics needed to round out the foundations of the theory of modems. Chapter 8 treats methods of synchronizing the transmitter and the receiver so that they have the same time reference. Next two chapters discuss methods of coding for communication channels to control errors. Chapter 9 discusses codes designed for an additive noise channel, Chapter 10 discusses codes designed for a discrete channel, usually binary. Finally, Chapters 11 and 12 advance the theory beyond the simple linear channel studied in most of this book. In the end of any chapter there are many exercises to test the reader. \itemrv{Zlatko Varbanov (Veliko Tarnovo)} \itemcc{M55 P25 R15} \itemut{modulation; demodulation; data transmission; synchronization; block codes; convolutional codes} \itemli{doi:10.1017/CBO9780511811401} \end

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\[W_{0,\nu}\left(2z\right)=\sqrt{\ifrac{2z}{\pi}}K_{\nu}\left(z\right),\]

https://cs.uwaterloo.ca/journals/JIS/VOL23/Nabawanda/naba5.tex

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\documentclass[12pt,reqno]{article} \usepackage[usenames]{color} \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsthm} \usepackage{amsfonts} \usepackage{amscd} \usepackage{graphicx} \usepackage[colorlinks=true, linkcolor=webgreen, filecolor=webbrown, citecolor=webgreen]{hyperref} \definecolor{webgreen}{rgb}{0,.5,0} \definecolor{webbrown}{rgb}{.6,0,0} \usepackage{color} \usepackage{fullpage} \usepackage{float} \usepackage{psfig} \usepackage{graphics} \usepackage{latexsym} \usepackage{epsf} \usepackage{breakurl} \usepackage{slashbox} \usepackage{enumerate,tikz,listings,array,longtable} \usetikzlibrary{shapes,arrows,chains} \usepackage{pgf} \DeclareMathOperator{\OCH}{OCH} \setlength{\textwidth}{6.5in} \setlength{\oddsidemargin}{.1in} \setlength{\evensidemargin}{.1in} \setlength{\topmargin}{-.1in} \setlength{\textheight}{8.4in} \newcommand{\seqnum}[1]{\href{https://oeis.org/#1}{\rm \underline{#1}}} \begin{document} \begin{center} \epsfxsize=4in \leavevmode\epsffile{logo129.eps} \end{center} \theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{conjecture}[theorem]{Conjecture} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \begin{center} \vskip 1cm{\LARGE\bf Run Distribution Over Flattened Partitions} \vskip 1cm \large Olivia Nabawanda\footnote{Corresponding author.}\\ Department of Mathematics\\Makerere University\\ P. O. Box 7062\\ Kampala \\ Uganda\\ \href{mailto:onabawanda@must.ac.ug}{\tt onabawanda@must.ac.ug}\\ \ \\ Fanja Rakotondrajao\\ D\'epartement de Math\'ematiques et Informatique\\ Universit\'e d'Antananarivo\\ Antananarivo \\ Madagascar\\ \href{mailto:frakoton@yahoo.fr}{\tt frakoton@yahoo.fr}\\ \ \\ Alex Samuel Bamunoba\\ Department of Mathematics\\Makerere University\\ P. O. Box 7062\\ Kampala \\ Uganda\\ \href{mailto:bamunoba@cns.mak.ac.ug}{\tt bamunoba@cns.mak.ac.ug} \end{center} \vskip .2 in \begin{abstract} The study of flattened partitions is an active area of current research. In this paper, our study unexpectedly leads us to the OEIS sequence \seqnum{A124324}. We provide a new combinatorial interpretation of these numbers. A combinatorial bijection between flattened partitions over $[n+1]$ and the partitions of $[n]$ is also given in a separate section. We introduce the numbers $f_{n, k}$ which count the number of flattened partitions over $[n]$ having $k$ runs. We give recurrence relations defining them, as well as their exponential generating function in differential form. It should be appreciated if its closed form is established. We extend the results to flattened partitions where the first $s$ integers belong to different runs. Combinatorial proofs are given. \end{abstract} \newcommand{\C}{\mathbb{C}} \newcommand{\PP}{\mathrm{P}} \newcommand{\B}{\mathbb{B}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\R}{\mathbb{R}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\fS}{\mathfrak{S}} \newcommand{\Id}{\mathrm{Id}} \newcommand{\cone}{\mathrm{cone}} \newcommand{\conv}{\mathrm{conv}} \newcommand{\height}{\mathrm{height}} \newcommand{\im}{\mathrm{im}} \newcommand{\HH}{\mathcal{H}} \newcommand{\fpa}{\mathrm{FPA}} \newcommand{\pn}{\mathrm{part}} \newcommand{\RP}{\mathrm{RelPrime}} \newcommand{\rp}{\mathrm{relprime}} \newcommand{\rpac}{\mathrm{rpac}} \newcommand{\relprime}{\mathrm{relprime}} \newcommand{\ptn}{\mathrm{part}} \newcommand{\Rpac}{\mathrm{Rpac}} \newcommand{\Relprime}{\mathrm{Relprime}} \newcommand{\Ptn}{\mathrm{Part}} \def\v{{\boldsymbol v}} \def\t{{\boldsymbol t}} \newcommand{\A}{\mathcal{V}} \newcommand{\m}{\mathfrak{m}} \section{Introduction and preliminaries}\label{sec:intro} The study of the different statistics of permutations such as descents, ascents, excedances and runs has a long history and has been an area of intensive research in the past years. A lot of work is available in the literature \cite{ehrenborg2000excedance, macmahon2001combinatory, mantaci2003exceedingly, sloane2008line, con1}. These statistics play an important role in combinatorics and mathematics as a whole. For a given positive integer $n$, we denote the set $\{1, 2, \ldots, n\}$ by $[n]$. A permutation $\sigma$ over $[n]$ is represented as a word $\sigma(1)\sigma(2)\cdots\sigma(n)$. We say that $\sigma$ has an {\it ascent (descent)} at position $i$ if $\sigma(i) < \sigma(i+1)\,(\sigma(i) > \sigma(i+1))$, where $i \in [n]$. A {\it run} in a permutation $\sigma$ is a subword $\sigma(i)\sigma(i+1)\cdots \sigma(i+p)\sigma(i+p+1)$ where $i, i+1, \ldots, i+p$ are consecutive ascents. In this case, $i-1$ (if it does exist) and $i+p+1$ are non ascents, where $i \in [n]$. For example, in $\sigma = 526134$, we have ascents at positions $2, 4$ and $5$. It also has descents at positions $1$ and $3$. The last element $4$ of $\sigma$ at position $6$ is neither an ascent nor a descent. A {\it right to left minimum} of a permutation $\sigma$ is an element $\sigma(i)$ such that $\sigma(i) < \sigma(j)$ for all $j > i$. For example, in $\sigma = 1246357$, the {\it right to left minima} are $\{1, 2, 3, 5, 7\}$. Counting permutations according to the number of runs has been studied from various perspectives in enumerative combinatorics. Canfield and Wilf \cite{canfield2008counting} considered a run as a subsequence of a permutation $\sigma$, whose values either increase on the interval (run up) or decrease on the interval (run down). More related work on permutation runs can also be found in articles \cite{bona2000combinatorial, ma2012explicit, ma2013enumeration, zhuang2016counting}. A permutation $\pi$ is said to be a {\it flattened partition} if it consists of runs arranged from left to right such that their first entries are in increasing order. It is clear that the first run always starts with $1$, and so all flattened partitions start with the integer $1$. For example, consider a permutation $\sigma = 139278456$. This is a flattened partition with three runs namely: $139, 278, 456$ whose first entries $1, 2, 4$ are in increasing order. However, the permutation $\sigma = 139456287$ is not a flattened partition since the first entries $1, 4, 2, 7$, of the runs $139, 456, 28, 7$ are not in increasing order. Given a non-empty finite subset $S$ of positive integers, a {\it set partition} $P$ of $S$ is a collection of disjoint non-empty subsets $B_{1},B_{2}, \ldots, B_{k}$ of $S$ (called blocks) such that $\displaystyle\cup_{i = 1}^{k}B_{i} = S$ \cite{mansour2012combinatoric, rota1964number}. We shall maintain the name and notion of ``flattened partition" introduced by Callan \cite{callan2009pattern}. Callan borrowed the notion ``{\it flatten}" from {\it Mathematica} programming language, where it acts by taking lists of sets arranged in increasing order, removes their parentheses, and writes them as a single list \cite{stephen1999mathematica}. Mansour et al.\ \cite{mansour2015counting} also used the same notion. To generate flattened partitions, the elements of each block are written as increasing subsequences, and blocks arranged from left to right in increasing order of their first entries. Carlitz \cite{carlitz1968generalized} also applied the notion ``{\it flatten}" to permutations expressed in cycle notation. We let $\mathcal{F}_{n}$ denote the set of all flattened partitions over $[n]$, $\mathcal{F}_{n, k}$ the set consisting of all flattened partitions over $[n]$ having $k$ runs, $f_{n, k}$ the cardinality of the set $\mathcal{F}_{n, k}$. In Table \ref{tab:t1}, we give the first few values of the numbers $f_{n, k}$. \begin{table}[H] \centering \footnotesize \begin{tabular}{|c| c c c c c|} \hline \backslashbox{$n$}{$k$} & $1$ & 2 & 3 & 4 & 5 \\ \hline $1$ & 1 & & & & \\ 2 & 1 & & & & \\ 3 & 1 & 1 & & & \\ 4 & 1 & 4 & 0 & & \\ 5 & 1 & 11 & 3 & 0 & \\ 6 & 1 & 26 & 25 & 0 & 0 \\ \hline \end{tabular} \caption{The numbers $f_{n, k}$} \label{tab:t1} \end{table} We notice that the terms in the column for $k = 2$ of Table \ref{tab:t1} correspond to the Eulerian numbers. Foata and Sch\"{u}tzenberger \cite{olivia} gave the fundamental work on these numbers. Mantaci and Rakotondrajao \cite{mantaci} gave a new combinatorial interpretation to the same. Many other references concerning Eulerian numbers can be found on the OEIS \seqnum{A000295}. In Section \ref{B}, we establish different recurrence relations of the numbers $f_{n, k}$ and give their combinatorial proofs. We also define the exponential generating function $F(x, u)$ of the numbers $f_{n, k}$ which is defined by \begin{equation*} F(x, u) = \sum_{n \geq 0}\sum_{k\geq 0} f_{n, k} x^{k}\frac{u^{n}}{n!} = \sum_{n \geq 0}\sum_{\sigma \in \mathcal{F}_{n}}x^{run(\sigma)}\frac{u^{n}}{n!}, \end{equation*} where $run(\sigma)$ is the number of runs in a flattened partition $\sigma$. In Section \ref{C}, we generalize the results in Section \ref{B} to flattened partitions over $[n]$ whose first $s$ integers belong to different runs . We let $f_{n, k}^{(s)}$ denote the number of flattened partitions over $[n]$ whose first $s$ integers belong to different runs, and $F^{[s]}(x, u)$ the exponential generating function for the numbers $f_{n, k}^{(s)}$. The first few values of $f_{n, k}^{(s)}$ for $s = 2$ and $s = 3$ are shown in Table \ref{tab:t3} and \ref{tab:t4}: \begin{table}[H] \begin{minipage}[b]{0.45\linewidth} \centering \footnotesize \begin{tabular}{|c| c c c c |} \hline \backslashbox{$n$}{$k$} & $2$ & 3 & 4 & 5 \\ \hline $2$ & 0 & & & \\ 3 & 1 & 0 & & \\ 4 & 3 & 0 & & \\ 5 & 7 & 3 & 0 & \\ 6 & 15 & 22 & 0 & \\ 7 & 31 & 105 & 15 & 0 \\ \hline \end{tabular} \caption{The numbers $f_{n, k}^{(2)}$} \label{tab:t3} \end{minipage} \begin{minipage}[b]{0.45\linewidth} \centering \footnotesize \begin{tabular}{|c| c c c |} \hline \backslashbox{$n$}{$k$} & $3$ & 4 & 5 \\ \hline 4 & 0 & & \\ 5 & 2 & 0 & \\ 6 & 12 & 0 & \\ 7 & 50 & 12 & 0 \\ 8 & 180 & 140 & 0 \\ \hline \end{tabular} \caption{The numbers $f_{n, k}^{(3)}$} \label{tab:t4} \end{minipage} \end{table} Mansour et al.\ \cite{mansour2015counting} gave a recursive formula for the number of flattened partitions over $[n]$, and also mention that the number of distinct permutations that can be obtained as flattened partitions over $[n]$ is the Bell number $B_{n-1}$. Let $\mathcal{P}_{n}$ denote the collection of partitions of $[n]$. Our study led us to the OEIS \seqnum{A124324} which counts the number of partitions of $[n]$ having $k$ blocks of size greater than $1$. The authors of the present paper were introduced to the OEIS \seqnum{A124324} by Heinz \cite{fhh} who gave a maple program for computing the terms of this sequence recursively. The first maple program which computes this sequence using the exponential generating function was given by Emeric Deutsch. A combinatorial bijection between elements of $\mathcal{P}_{n}$ having $(k-1)$ blocks of size greater than $1$ and $\mathcal{F}_{n+1, k}$ will be given in Section \ref{A}. \section{Flattened partitions and their behaviours on runs}\label{B} \subsection{Recurrence relations} We have $f_{n, 1} = 1$ for all $n \geq 1$ and $f_{n, k} = 0$ for all $k\geq n\geq 2$. It is not possible to have a flattened partition over $[n]$ whose number of runs $k$ is greater or equal to its length. \begin{theorem} \label{thm4} For all integers $n$ and $k$ such that $2 \leq k < n$, the numbers $f_{n, k}$ of flattened partitions over $[n]$ with $k$ runs satisfy the recurrence relation \begin{equation}\label{mum1} f_{n, k} = \sum_{m = 1}^{n-2}\left({n-1 \choose m} - 1\right)f_{m, k-1}. \end{equation} \end{theorem} \begin{proof} To construct a flattened partition $\pi$ over $[n]$ having $k$ runs, we consider a flattened partition $\tau$ over $[m]$ having $k-1$ runs, for an integer $m < n$. Since all flattened partitions start with element $1$, we insert the word of length $n-m$ starting with $1$, before a flattened partition $\tau$ to obtain $1\underbrace{\dots}_{n-m-1}\underbrace{\tau}_{m}$, and then re-order the elements of $\tau$ making sure the number of runs increase by one. The $n-m-1$ elements between $1$ and $\tau$ can be chosen from the set $\{2, 3, 4, \ldots, n\}$ of $(n-1)$ terms in $\displaystyle n-1 \choose n-m-1$ ways. In order to increase the number of runs by one, we avoid choosing the subset $\{2, 3, \ldots, n-m-1\}$ of consecutive elements. We thus have $\displaystyle \bigg({n-1 \choose n-m-1} - 1\bigg)$ possible subsets to be inserted after $1$. The minimum number of elements in the first run is $2$, implying that the maximum length of $\tau$ is $n-2$. Since $n \geq 3$, then the minimum length of $\tau$ is $1$. Thus we have that $1 \leq m \leq n-2$. Thus summing up over $1 \leq m \leq n-2$ gives the recurrence relation in Equation \eqref{mum1}. \end{proof} \begin{example} Let us construct flattened partitions over $[6]$ having $3$ runs from a flattened partition $\tau$ over $[3]$ having $2$ runs. We have $\tau = 132$. The favorable subsets of two terms from the set $\{2, 3, 4, 5, 6\}$ are: $\{2, 4\}, \{2, 5\}, \{2, 6\}, \{3, 4\}, \{3, 5\}, \{3, 6\}, \{4, 5\}, \{4, 6\}, \{5, 6\}$. Consider the pair $(\{3, 4\}, \tau)$, we get $\pi = 134265$. For the pair $(\{4, 6\}, \tau)$, we get $\pi = 146253$. \end{example} Let $a_{n}$ denote the maximum number of runs $k$ in a flattened partition of $[n]$. From Table \ref{tab:t1} above, we see that the maximum number of runs, $a_{n}$ results into a sequence $1, 1, 2, 2, 3, 3, 4, 4, 5, 5, \ldots,$ for $n \geq 1$. \begin{proposition}\label{pp} The maximal number $a_{n}$ of runs in a flattened partition over $[n]$ satisfies the relation \begin{equation*}\label{ks} a_{n} = a_{n-2} +1, \end{equation*} for all $n\geq 2$, with initial conditions $a_{0} = 0, a_{1} = 1$. \end{proposition} \begin{proof} Let $n$ be an integer such that $n \geq 2$. Consider a flattened partition $\tau$ over $[n-2]$ having maximal number of runs. Using the construction in Theorem \ref{thm4}, inserting two elements $1x$ where $x = \{3, 4, \ldots, n\}$ before $\tau$ and re-ordering the elements of $\tau$ can only add a maximum of $1$ run. Hence we have $a_{n} \geq a_{n-2} + 1$. On the other hand, inserting $n-2$ elements between $1$ and the identity $\tau = 1$ from the construction in the same theorem, we have $1\underbrace{\cdots}_{n-2}1$ and then re-ordering the elements of $\tau$. This means the subsets between $1$ and $\tau$ can be chosen from the set $\{3, 4, \ldots, n\}$ of $n-2$ elements whose maximum number of runs is $a_{n-2}$. Hence we have $a_{n} \leq a_{n-2}+1$. These two inequalities, together with $a_{0} = 0$ and $a_{1} = 1$, yield $a_{n} = a_{n-2}+1$. \end{proof} As an obvious conclusion, we have the following corollary: \begin{corollary} The maximal number of runs $a_{n}$ in a flattened partition over $[n]$ has the closed form $\displaystyle \dfrac{1}{4}\big(2n + (-1)^{n+1} +1\big)$ and its generating function $\displaystyle Y(x) = \sum_{n=0}^{\infty}a_{n}x^{n}$ is given by $\dfrac{x}{(1-x)^{2}(1+x)}$. \end{corollary} If $a$ is a starting point of a run in a flattened partition $\pi$ and $x$ is an integer such that $x < a$, then $\pi^{-1}(x) < \pi^{-1}(a)$. In other words, all integers smaller than $a$ are on its left. By contradiction, suppose there exists an $x < a$ on the right of $a$. Then $x$ is an element of another run. This makes the starting points of the runs of $\pi$ not to be in increasing order, which contradicts $\pi$ being a flattened partition. Hence $x$ should be on the left of $a$. Let $\mathcal{C}_{n, k}$ denote the set of flattened partitions over $[n]$ of the form {\it $1X2\cdots $}, having $k$ runs, where $X \in \{3, 4, 5, \ldots, n\}$. More precisely, each partition in $\mathcal{C}_{n, k}$ has only two elements in the first run. For example, we have $\mathcal{C}_{5, 2} = \{13245, 14235, 15234\}$. From the construction in Theorem \ref{thm4}, we have the following corollary: \begin{corollary}\label{sss} For all integers $n$ and $k$ such that $1 \leq k < n$, the cardinality of the set $\mathcal{C}_{n, k}$ is $(n-2)f_{n-2, k-1}$. \end{corollary} Let $\mathcal{K}_{n, k}$ denote the set of flattened partitions over $[n]$ having $k$ runs and containing either the subword $\mathbf{2n1}$ or the integer $\mathbf{n}$ at the end. In other words, deleting the integer $\textbf{n}$ does not affect the number of runs. Let $\mathcal{L}_{n, k}$ denote the set of flattened partitions over $[n]$ having $k$ runs and containing the subword $\mathbf{1n2}$, the set where deleting the integer $\textbf{n}$ reduces the number of runs by $1$. For example, we have $\mathcal{L}_{5, 2} = \{12354, 12534, 15234\}$ and $\mathcal{K}_{5, 2} = \{14523, 14235, 13524, 13452, 13425, 13245, 12453, 12435\}$. \begin{remark}\label{rmk} The sets $\mathcal{K}_{n, k}$ and $\mathcal{L}_{n, k}$ are mutually exclusive, i.e., $\mathcal{K}_{n, k} \cap \mathcal{L}_{n, k} = \emptyset$ and form a partition of the set $\mathcal{F}_{n, k}$, i.e., $\mathcal{F}_{n, k} = \mathcal{K}_{n, k} \cup \mathcal{L}_{n, k}$. \end{remark} For all integers $n$ and $k$ such that $1 \leq k <n$, the cardinalities of the sets $\mathcal{C}_{n, k}$ and $\mathcal{L}_{n, k}$ are equal. We use a variation of the bijection defined by Beyene and Mantaci \cite[p.\ 5]{fr} to construct a combinatorial bijection between the two sets. Let us consider the map $f : \mathcal{C}_{n, k} \rightarrow \mathcal{L}_{n, k}$ defined as follows: for each $\pi \in \mathcal{C}_{n, k}$, delete the subword $1X$ and let $\tau$ be the standardized form of the remaining elements. Insert the subword $n(X-1)$ after the smallest rightmost element to $(X-1)$ in $\tau$ and reorder to get $\sigma = f(\pi) \in \mathcal{L}_{n, k}$. \begin{example} Let us illustrate the map $f$ with $n = 5$ and $k = 2$. We have $C_{5, 2} = \{13245, 14235, 15234\}$. For $\pi = 13245$, then $\tau = 123$ and $\sigma = 15234$ i.e., $f(13245) = 15234$. Similarly, $f(14235) = 12534$, $f(15234) = 12354$. \end{example} \begin{proposition}\label{hhh} The map $f : \mathcal{C}_{n, k} \rightarrow \mathcal{L}_{n, k}$ is a bijection. \end{proposition} \begin{proof} We will prove that $f$ is surjective and injective. \begin{itemize} \item [(i)] \textbf{Surjectivity}. Let $g : \mathcal{L}_{n, k} \rightarrow \mathcal{C}_{n, k}$ be defined as follows: for each $\sigma \in \mathcal{L}_{n, k}$, delete the subword $nX$ and let $\tau$ be the standardized form of the remaining. Insert the subword $1(X+1)$ before $\tau$ and re-order to get $\pi \in \mathcal{C}_{n, k}$. It is obvious that $g$ is the inverse map of $f$. \item[(ii)] \textbf{Injectivity}. Let $\pi_{1}$ and $\pi_{2}$ be two elements in $\mathcal{C}_{n, k}$ such that $f(\pi_{1}) = f(\pi_{2})$. Necessarily, $\tau_{1} = \tau_{2}$ and hence $\pi_{1} = \pi_{2}$. \end{itemize} \end{proof} Let us illustrate the map $f^{-1}$ with $n = 5$ and $k = 2$. We have $\mathcal{L}_{n, k} = \{12354, 12534, 15234\}$. For $\sigma = 12354$, then $\tau = 123$ and $\pi = 15234$ i.e., $f^{-1}(12354) = 15234$. Similarly, $f^{-1}(12534) = 14235$, $f^{-1}(15234) = 13245$. \begin{theorem}\label{cvb} For all integers $n$ and $k$ such that $1 \leq k < n$, the cardinality of the set $\mathcal{K}_{n, k}$ is $kf_{n-1, k}$. \end{theorem} \begin{proof} Let us construct the elements of $\mathcal{K}_{n, k}$. Let $\pi \in \mathcal{F}_{n-1, k}$. Inserting $n$ at the end of a run of $\pi$ does not change the number of runs. There are $k$ possibilities of such insertions. This generates $k$ flattened partitions in the set $\mathcal{K}_{n, k}$. Thus $|\mathcal{K}_{n, k}| = kf_{n-1, k}$. \end{proof} \begin{theorem} For all integers $n$ and $k$ such that $1 \leq k < n$, $f_{n, k} = kf_{n-1, k} +(n-2)f_{n-2, k-1}$. \end{theorem} \begin{proof} From Remark \ref{rmk}, we have that $|\mathcal{F}_{n, k}| = |\mathcal{K}_{n, k}| + |\mathcal{L}_{n, k}|$. Using Theorem \ref{cvb}, Proposition \ref{hhh} and Corollary \ref{sss}, we then have that \begin{equation}\label{comp} f_{n, k} = kf_{n-1, k} +(n-2)f_{n-2, k-1}. \end{equation} \end{proof} \begin{corollary}\label{uu} For all integers $n$ and $k$ such that $1 \leq k < n$, we have \begin{equation*} kf_{n, k} = \sum_{m=1}^{n-2}\bigg(\binom{n}{m} - 1\bigg)f_{m, k-1}. \end{equation*} \end{corollary} \begin{proof} Considering Equation \eqref{mum1} and Equation \eqref{comp}, we deduce the result. \end{proof} We still do not have a direct combinatorial proof of Corollary \ref{uu}, and it remains an open problem worth investigating. \begin{theorem}\label{vv} For all integers $n$ and $k$ such that $1 \leq k \leq n$, the numbers $f_{n+2, k}$ of flattened partitions over $[n+2]$ having $k$ runs satisfy the recurrence relation \begin{equation}\label{oli} f_{n+2, k} = f_{n+1, k} + \sum_{i = 1}^{n}\binom{n}{i}f_{n+1-i, k-1}. \end{equation} \end{theorem} \begin{proof} To construct a flattened partition $\pi$ over $[n+2]$ for all $n \geq 0$ having $k$ runs, we use the property that the first two terms $1$ and $2$ of $\pi$ are either in the same run or in different runs. We consider these two possibilities to enumerate $f_{n+2, k}$. \begin{enumerate} \item If $1$ and $2$ are in the same run, by the construction in Theorem \ref{thm4}, $\pi$ is of the form $\pi = 1\underbrace{\tau}_{n+1}$, where $\tau$ is a subword of length $n+1$ whose starting integer is $2$. Deleting $1$ of $\pi$ and reducing each of the remaining terms by $1$ gives a flattened partition of length $n+1$, with the same number of runs $k$ i.e., $f_{n+1, k}$. \item If $1$ and $2$ are in different runs, suppose the first run has $(i+1)$ terms including the first term $1$. Using Theorem \ref{thm4}, the remaining $(i+1) - 1 = i$ terms in the first run can be chosen from the set $\{3, 4, \ldots, n+2\}$ of $(n+2)-2 = n$ terms. This is because the positions of $1$ and $2$ in $\pi$ are already known. There are $\displaystyle {n \choose i}$ ways to do this. The remaining $k-1$ runs have length $(n+2)-(i+1) = n+1-i$. Hence we have $f_{n+1-i, k-1}$ flattened partitions over $[n+1-i]$ with $k-1$ runs. Since the length of the first run including $1$ varies between $2$ and $n+1$, the number of flattened partitions over $[n+2]$ with $1$ and $2$ in different runs is given by $\displaystyle \sum_{i =1}^{n}{n \choose i}f_{n+1-i, k-1}$. \end{enumerate} Adding these two cases together gives \begin{equation*} f_{n+2, k} = f_{n+1, k} + \sum_{i = 1}^{n}{n \choose i}f_{n+1-i, k-1}. \end{equation*} \end{proof} \subsection{Generating function} \begin{theorem}\label{jk} The exponential generating function $F(x, u)$ of the run distribution over flattened partitions has the closed differential form \begin{equation}\label{gg} \frac{\partial F(x, u) }{\partial u} = x\exp(x(\exp(u) - 1)+ u(1-x)), \end{equation} with initial condition $\dfrac{\partial F(x, 0)}{\partial u} = x$. \end{theorem} \begin{proof} We have \begin{equation*} F(x, u) = \sum_{n \geq 1}\sum_{k\geq 1} f_{n, k} x^{k}\frac{u^{n}}{n!} = \sum_{n \geq 1}f_{n}(x)\frac{u^{n}}{n!} . \end{equation*} where $f_{n}(x)$ is the polynomial defined by $\displaystyle \sum_{k\geq 1} f_{n, k} x^{k} = f_{n}(x)$. From Equation \eqref{oli}, multiplying by $\displaystyle x^k \frac{u^n}{n!}$ and summing over $k$ and $n$ gives \begin{equation}\label{ooo} \sum_{n\geq 1}\sum_{k \geq 1}f_{n+2, k}x^k \frac{u^n}{n!} = \sum_{n\geq 1}\sum_{k \geq 1}\bigg(f_{n+1, k} + \sum_{i = 1}^{n}{n \choose i}f_{n+1-i, k-1}\bigg)x^k \frac{u^n}{n!}. \end{equation} Equation \eqref{ooo} can be rewritten as $A = B+C$, where \begin{equation*} A = \sum_{n\geq 1}\sum_{k \geq 1}f_{n+2, k}x^k \frac{u^n}{n!}, \end{equation*} \begin{equation*} B = \sum_{n\geq 1}\sum_{k \geq 1}f_{n+1, k}x^k \frac{u^n}{n!}, \end{equation*} and \begin{equation*} C = \sum_{n\geq 1}\sum_{k \geq 1}\bigg(\sum_{i = 1}^{n}{n \choose i}f_{n+1-i, k-1}x^k \frac{u^n}{n!}\bigg). \end{equation*} We have \begin{equation}A = \frac{\partial^2 F}{\partial u^2},\ B = \frac{\partial F}{\partial u}. \label{op} \end{equation} Fixing $i$ and summing over $k$ in $C$ gives \begin{equation}\label{no7} C = \sum_{n\geq 1}\sum_{i = 1}^{n}{n \choose i}\bigg( \sum_{k \geq 1}f_{n+1-i, k-1}x^k\bigg)\frac{u^{n}}{n!}. \end{equation} Equation \eqref{no7} can be re-written as \begin{equation}\label{no8} C = x\sum_{n\geq 1}\sum_{i = 1}^{n}{n \choose i}\bigg( \sum_{k \geq 1}f_{n+1-i, k-1}x^{k-1}\bigg)\frac{u^{n}}{n!}. \end{equation} Expanding the binomial coefficient $\displaystyle {n \choose i}$ in Equation \eqref{no8} and simplifying gives \begin{align*}\label{no9} C &= x\sum_{n\geq 1}\sum_{i = 1}^{n}\frac{u^i}{i!}\bigg( \sum_{k \geq 1}f_{(n-i)+1, k-1}x^{k-1}\frac{u^{(n-i)}}{(n-i)!}\bigg)\\ & = x\sum_{i = 1}^{\infty}\frac{u^i}{i!}\bigg(\sum_{n\geq i} \sum_{k \geq 1}f_{(n-i)+1, k-1}x^{k-1}\frac{u^{(n-i)}}{(n-i)!}\bigg)\\ & = x\sum_{i = 1}^{\infty}\frac{u^i}{i!}\bigg(\sum_{n \geq i} f_{(n-i)+1}(x)\frac{u^{n-i}}{(n-i)!}\bigg). \end{align*} We have \begin{align*} C &= x\sum_{i = 1}^{\infty}\frac{u^i}{i!}\frac{\partial F(x, u)}{\partial u}\\ & = x(\exp(u) - 1)\frac{\partial F(x, u)}{\partial u}. \end{align*} Substituting Equation \eqref{op} and $C = x(\exp(u) - 1)\dfrac{\partial F(x, u)}{\partial u}$ into Equation \eqref{ooo} gives \begin{equation}\label{o} \frac{\partial^2 F(x, u)}{\partial u^2} = \frac{\partial F(x, u)}{\partial u} + x(\exp(u) - 1)\frac{\partial F(x, u)}{\partial u}. \end{equation} Let $V = \dfrac{\partial F(x, u)}{\partial u}$. Then \begin{equation*} \frac{\partial V}{\partial u} = \frac{\partial^2 F(x, u)}{\partial u^2}. \end{equation*} Substituting $V$ into Equation \eqref{o} gives \begin{equation}\label{no11} \frac{\partial V}{\partial u} = V\big(x(\exp(u) - 1)+1\big) \end{equation} with initial condition $V(x, 0) = x$. Solving for $V$ in Equation \eqref{no11} gives \begin{equation*} V = \frac{\partial F(x, u)}{\partial u} = x \exp(-x)\exp({(x(\exp(u) - u)+u)}). \end{equation*} \end{proof} \section{Flattened partitions with the first \texorpdfstring{$s$}{Lg} terms in different runs}\label{C} We recall that $f_{n, k}^{(s)}$ and $F^{[s]}(x, u)$ are the number of flattened partitions over $[n]$ whose first $s$ integers belong to different runs and the exponential generating function for the numbers $f_{n, k}^{(s)}$ respectively. \begin{theorem} For all integers $s, k$ and $n$ such that $1 \leq s < k < n$, the numbers $f_{n+s+1, k}^{(s+1)}$ satisfy the relation \begin{equation}\label{ppp} f_{n+s+1, k}^{(s+1)} = \sum_{i_{1}, i_{2}, \ldots , i_{s} \geq 1}\binom{n}{i_{1}}\binom{n-i_{1}}{i_{2}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}} f_{n+1-\sum_{j=1}^{s}i_{j}, k-s}. \end{equation} \end{theorem} \begin{proof} Let $\pi$ be a flattened partition over $[n+s+1]$ having $k$ runs. Let $i_{1}+1, i_{2}+1, i_{3}+1, \ldots , i_{s}+1$ be the lengths of the $s$ first runs whose starting points are $1, 2, \ldots, s$ respectively. Since the first run, including $1$ has length $i_{1}+1$, we have $i_{1}$ terms to arrange out of the $(n+s+1)-s-1 = n$ terms. There are ${n \choose i_{1}}$ ways. For the second run, it remains to arrange $i_{2}$ terms out of $n-i_{1}$ terms. There are $\displaystyle {n-i_{1} \choose i_{2}}$ ways. Repeating the same process up to the $s^{th}$ run inductively gives $\displaystyle {n-i_{1} - i_{2}- \cdots - i_{s-1} \choose i_{s}} = {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}}$ possibilities. The remaining $k-s$ runs have length $(n+s+1)-((i_{1}+1) + (i_{2}+1) + \cdots (i_{s}+1)) = \displaystyle n+1- \sum_{j=1}^{s}i_{j}$. So we have $\displaystyle {n \choose i_{1}}{n-i_{1} \choose i_{2}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}}f_{n+1-\sum_{j=1}^{s}i_{j}, k-s}$. Summing over all possibilities of $i_{1}, i_{2}, \ldots , i_{s} \geq 1$ gives the result. \end{proof} \begin{theorem} The exponential generating function $F^{[s]}(x, u)$ for the numbers $f_{n+s, k}^{(s)}$ has the closed differential form \begin{equation}\label{ddw} \frac{\partial^{s+1} F^{[s+1]}(x, u)}{\partial u^{s+1}} = x^{s} (\displaystyle \exp(u) - 2)\displaystyle (\exp(u)-1)^{s-1} \frac{\partial F(x, u)}{\partial u}. \end{equation} \end{theorem} \begin{proof} We have \begin{equation*} \frac{\partial^{s+1}F^{[s+1]}(x, u)}{\partial u^{s+1}} = \sum_{n=1}^{\infty}\sum_{k\geq 1} f_{n+s+1, k}^{(s+1)} x^{k}\frac{u^{n}}{n!}. \end{equation*} From Equation \eqref{ppp}, multiplying by $\displaystyle x^k \frac{u^n}{n!}$ and summing over $k$ and $n$ gives \begin{equation}\label{nv} \sum_{n\geq 1}\sum_{k \geq s}f_{n+s+1, k}^{(s+1)}x^k \frac{u^n}{n!} = \sum_{n\geq 1}\sum_{k \geq s}\bigg(\sum_{i_{1}, i_{2}, \ldots , i_{s} \geq 1}{n \choose i_{1}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}} f_{n+1-\sum_{j=1}^{s}i_{j}, k-s}\bigg)x^k \frac{u^n}{n!} \end{equation} Let \begin{equation*} L = \sum_{n\geq 1}\sum_{k \geq s}f_{n+s+1, k}^{(s+1)}x^k \frac{u^n}{n!}, \end{equation*} and \begin{equation*} M = \sum_{n\geq 1}\sum_{k \geq s}\bigg(\sum_{i_{1}, i_{2}, \ldots , i_{s} \geq 1}{n \choose i_{1}}{n-i_{1} \choose i_{2}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}} f_{n+1-\sum_{j=1}^{s}i_{j}, k-s}\bigg)x^k \frac{u^n}{n!}. \end{equation*} We have \begin{equation}\label{hj}L = \dfrac{\partial^{s+1}F^{[s+1]}(x, u)}{\partial u^{s+1}}. \end{equation} Fixing $i$ and summing over $k$ gives \begin{align*} M &= \sum_{n \geq 1}\sum_{i_{1}, i_{2}, \ldots , i_{s} \geq 1}\bigg(\sum_{k} x^s {n \choose i_{1}}{n-i_{1} \choose i_{2}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}}f_{n+1-\sum_{j=1}^{s}i_{j}, k-s} x^{k-s} \bigg)\frac{u^n}{n!}\\ & = x^{s}\sum_{i_{1}, i_{2}, \ldots , i_{s} = 1}^{\infty}\sum_{n \geq i_{1}, i_{2}, \ldots , i_{s}}{n \choose i_{1}}{n-i_{1} \choose i_{2}}\cdots {n-\sum_{j=1}^{s-1}i_{j} \choose i_{s}}\bigg(\sum_{k \geq s}f_{n+1-\sum_{j =1}^{s}i_{j}, k-s}x^{k-s}\frac{u^n}{n!}\bigg)\\ & = x^s \sum_{i_{1}, i_{2}, \ldots , i_{s} = 1}^{\infty}\sum_{n \geq i_{1}, i_{2}, \ldots , i_{s}}\frac{n!}{(n-i_{1})! i_{1}!}\cdots \frac{(n-\sum_{j=1}^{s-1}i_{j})!}{ (n-\sum_{j=1}^{s}i_{j})!i_{s}!} \bigg(\sum_{k \geq s}f_{n+1-\sum_{j=1}^{s}i_{j}, k-s}x^{k-s}\frac{u^n}{n!}\bigg)\\ & = x^s \sum_{i_{1}, i_{2}, \ldots , i_{s} = 1}^{\infty}\frac{u^{i_{1}}}{i_{1}!}\frac{u^{i_{2}}}{i_{2}!}\cdots \frac{u^{i_{s}}}{i_{s}!}\bigg(\sum_{n \geq i_{1}, i_{2}, \ldots , i_{s}}\sum_{k \geq s}f_{n+1-\sum_{j =1}^{s}i_{j}, k-s}x^{k-s}\frac{u^{n-\sum_{j=1}^{s}i_{j}}}{(n-\sum_{j=1}^{s}i_{j})!}\bigg)\\ & = (x(\displaystyle \exp(u) - 1))^{s}\displaystyle \frac{\partial F(x, u)}{\partial u}. \end{align*} Substituting Equation \eqref{hj} and $(x(\displaystyle \exp(u) - 1))^{s}\displaystyle \frac{\partial F(x, u)}{\partial u}$ into Equation \eqref{nv} gives the result. \end{proof} \section{Bijection between flattened partitions over \texorpdfstring{$[n+1]$}{Lg} and partitions of \texorpdfstring{$[n]$}{Lg}}\label{A} Let $P \in \mathcal{P}_{n}$ be a partition of $[n]$, written as $P = B_{1}|B_{2}|\cdots|B_{k}$ where the elements in each block $B_{i}$ are written in increasing order. We write $P$ as $P'$ in such a way that in each block, the smallest element appears at the end but still maintaining the remaining elements. We construct a word $P_{+}$ from $P'$ by deleting the marks $``| "$ enclosing the different blocks of $P'$ and then increasing all the terms by $1$. Let $f : \mathcal{P}_{n} \rightarrow \mathcal{F}_{n+1}$ be a map which associates a partition $P$ of $[n]$ with a flattened partition defined by $f(P) = \sigma = 1P_{+}$. The map $f$ is well defined since if $P_{1}$ and $P_{2}$ are two set partitions over $[n]$ and assume that $P_{1} = P_{2}$, then $f(P_{1}) = 1P_{1+} = 1P_{2+} = f(P_{2})$. \begin{proposition} The map $f : \mathcal{P}_{n} \rightarrow \mathcal{F}_{n+1}$ is a bijection. \end{proposition} \begin{proof} Since both $\mathcal{P}_{n}$ and $\mathcal{F}_{n+1}$ are finite with the same size $B_{n}$, it suffices to prove that $f$ is injective. Let $P_{1}$ and $P_{2}$ be two partitions of $[n]$. Assume that $f(P_{1}) = f(P_{2})$. Then by definition, $1P_{1+} = 1P_{2+}$. Since the map $f$ is well defined, the strings $P_{1+}$ and $P_{2+}$ are equal after deleting $1$ from the front. Thus $P_{1} = P_{2}$. \end{proof} \begin{example}\label{far} Consider a partition $P = 12|3|45$ of $[5]$. Re-ordering $P$ such that in each block, the smallest entry appears at the end of the partition gives $P' = 21|3|54$. Then $P_{+} = 32465$. And thus $\sigma = 1P_{+} = 132465$. \end{example} Let $\sigma \in \mathcal{F}_{n+1}$ having $k$ runs. Let us define $P= f^{-1}(\sigma)$ as follows: Insert the mark $``|"$ at the end of each right to left minimum of $\sigma$. Delete element $1$. Re-order to get the blocks of the partition $P$. \begin{example}\label{nol1} Consider a flattened partition $\sigma = 132465$ over $[6]$. Inserting the mark $``|"$ at the end of each right to left minimum $1|32|4|65|$. Deleting $1$ and re-ordering the remaining gives the partition $P = 12|3|45$. \end{example} We now give a property of our bijection. This bijection preserves the number of blocks of size greater than $1$ in a partition and the number of runs of its corresponding flattened partition. \begin{theorem} For any integer $n \geq 0$, if $P$ is a partition over $[n]$ and $\sigma$ its corresponding flattened partition over $[n+1]$, then the following assertions are equivalent: \begin{enumerate} \item [(i)] the number of blocks of size greater than $1$ of the partition $P$ is $k-1$, \item [(ii)] the number of runs of the flattened partition $\sigma$ is equal to $k$. \end{enumerate} \end{theorem} \begin{proof} For $n = 0$, $1$ is the only flattened partition corresponding to the empty set. Consider a partition $P$ of $[n]$ having $(k-1)$ blocks of size greater than $1$. Using the construction of the map $f$, we write each of the blocks in such a way that the smallest elements of each block appear at the end. Thus the smallest elements become the starting points for a run in a flattened partition $\sigma = f(P)$ if the block has at least two elements as well as integer $1$. The element of singleton blocks becomes a right to left minimum in $\sigma$ and is not a starting point of a run. So $\sigma$ has $k$ runs. Conversely, consider a flattened partition $\sigma$ having $k$ runs. Placing a mark $``|"$ after the right to left minima forms a partition of $[n+1]$. Since a starting point of a run is preceded by a greater element, except the integer $1$, the blocks with two or more elements consist of those containing a starting point. Deleting the integer $1$ and re-ordering the remaining blocks gives $(k-1)$ blocks of size greater than $1$. \end{proof} In Example \ref{far}, the partition $P$ has $2$ blocks of size greater than $1$ and the corresponding flattened partition, $\sigma$ has $3$ runs. \section{Acknowledgment} We would like to thank the editor and the anonymous referee for their comments and useful suggestions. This work was financially supported by the Swedish Sida bilateral program with Makerere University, 2015-2020, project 316 ``Capacity building in Mathematics and its applications". The first author would like to thank in a special way Prof.\ Paul Vaderlind (Stockholm University), Prof.\ Roberto Mantaci (University Paris Diderot 7) and the D\'epartement de Math\'ematiques et Informatique, Universit\'e d'Antananarivo for hosting her during research visits. \begin{thebibliography}{99} \bibitem{fr} F. Beyene and R. Mantaci, Exhaustive generation algorithm for flattened set partitions, preprint, 2020. Available at \url{https://cutt.ly/xorkr2M}. \bibitem{bona2000combinatorial} M. B{\'o}na and R. Ehrenborg, A combinatorial proof of the log-concavity of the number of permutations with $k$ runs, {\it J. Combin. Theory Ser. A} {\bf 90} (2000), 293--303. \bibitem{callan2009pattern} D. Callan, Pattern avoidance in ``flattened" partitions, {\it Discrete Math.} {\bf 309} (2009), 4187--4191. \bibitem{canfield2008counting} E. R. Canfield and H.S. Wilf, Counting permutations by their alternating runs, {\it J. Combin. Theory Ser. A} {\bf 115} (2008), 213--225. \bibitem{carlitz1968generalized} L. Carlitz, Generalized Stirling numbers, {\it Combinatorial Analysis Notes, Duke University} (1968), 8--15. \bibitem{ehrenborg2000excedance} R. Ehrenborg and E. Steingrimsson, The excedance set of a permutation, {\it Adv. Appl. Math.} {\bf 24} (2000), 284--299. \bibitem{olivia} D. Foata and M. P. Sch\"{u}tzenberger, {\it Th\'eorie G\'eom\'etrique des Polyn\^omes Eul\'eriens}, Springer, 2006. \bibitem{fhh} A. Heinz, Personal communication to the second author. \bibitem{ma2012explicit} S. Ma, An explicit formula for the number of permutations with a given number of alternating runs, {\it J. Combin. Theory Ser. A} {\bf 119} (2012), 1660--1664. \bibitem{ma2013enumeration} S. Ma, Enumeration of permutations by number of alternating runs, {\it Discrete Math.} {\bf 313} (2013), 1816--1822. \bibitem{macmahon2001combinatory} P. A. MacMahon, {\it Combinatorial Analysis}, Academic Press, 1960. \bibitem{mansour2012combinatoric} T. Mansour, {\it Combinatorics of Set Partitions}, CRC Press, 2012. \bibitem{mansour2015counting} T. Mansour, M. Shattuck, and S. Wagner, Counting subwords in flattened partitions of sets, {\it Discrete Math.} {\bf 338} (2015), 1989--2005. \bibitem{mantaci2003exceedingly} R. Mantaci and F. Rakotondrajao, Exceedingly deranging!, {\it Adv. Appl. Math.} {\bf 30} (2003), 177--188. \bibitem{mantaci} R. Mantaci and F. Rakotondrajao, A permutation representation that knows what Eulerian means, {\it Discrete Math. Theor. Comput. Sci.} {\bf 4} (2001), 101--108. \bibitem{rota1964number} G. Rota, The number of partitions of a set, {\it Amer. Math. Monthly} {\bf 71} (1964), 498--504. \bibitem{sloane2008line} N. J. A. Sloane et al., The on-line encyclopedia of integer sequences, Available at \url{https://oeis.org}, 2019. \bibitem{con1} J. Steinhardt, Permutations with ascending and descending blocks, {\it Electron. J. Combin.} {\bf 17} (2010), \#R14. \bibitem{stephen1999mathematica} S. Wolfram, {\it The Mathematica Book}, Cambridge University Press, 2000. \bibitem{zhuang2016counting} Y. Zhuang, Counting permutations by runs, {\it J. Combin. Theory Ser. A} {\bf 142} (2016), 147--176. \end{thebibliography} \bigskip \hrule \bigskip \noindent 2010 {\it Mathematics Subject Classification}: Primary 05A05; Secondary 05A10, 05A15, 05A18. \noindent \emph{Keywords:} flattened partition, generating function, recurrence relation, run, set partition. \bigskip \hrule \bigskip \noindent (Concerned with sequence \seqnum{A000295} and \seqnum{A124324}.) \bigskip \hrule \bigskip \vspace*{+.1in} \noindent Received February 10 2020; revised versions received July 1 2020; August 5 2020; October 15 2020. Published in {\it Journal of Integer Sequences}, October 15 2020. \bigskip \hrule \bigskip \noindent Return to \htmladdnormallink{Journal of Integer Sequences home page}{https://cs.uwaterloo.ca/journals/JIS/}. \vskip .1in \end{document}

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\documentclass[DIV=9,% BCOR=0mm,% headinclude=false,% footinclude=false,open=any,% fontsize=11pt,% oneside,% paper=a4]% {scrbook} \usepackage{fontspec} \usepackage{polyglossia} \setmainfont{Linux Libertine O} % these are not used but prevents XeTeX to barf \setsansfont[Scale=MatchLowercase]{CMU Sans Serif} \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text} \setmainlanguage{italian} % global style \pagestyle{plain} \usepackage{microtype} % you need an *updated* texlive 2012, but harmless \usepackage{graphicx} \usepackage{alltt} \usepackage{verbatim} % http://tex.stackexchange.com/questions/3033/forcing-linebreaks-in-url \PassOptionsToPackage{hyphens}{url}\usepackage[hyperfootnotes=false,hidelinks,breaklinks=true]{hyperref} \usepackage{bookmark} % footnote handling \usepackage[fragile]{bigfoot} \usepackage{perpage} \DeclareNewFootnote{default} \DeclareNewFootnote{B} \MakeSorted{footnoteB} \renewcommand*\thefootnoteB{(\arabic{footnoteB})} \deffootnote[3em]{0em}{4em}{\textsuperscript{\thefootnotemark}~} % continuous numbering across the document. 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Doesn't looks so \DeclareRobustCommand{\sout}[1]{\texorpdfstring{\hsout{#1}}{#1}} \usepackage{wrapfig} \usepackage{indentfirst} % remove the numbering \setcounter{secnumdepth}{-2} % remove labels from the captions \renewcommand*{\captionformat}{} \renewcommand*{\figureformat}{} \renewcommand*{\tableformat}{} \KOMAoption{captions}{belowfigure,nooneline} \addtokomafont{caption}{\centering} % avoid breakage on multiple <br><br> and avoid the next [] to be eaten \newcommand*{\forcelinebreak}{\strut\\*{}} \newcommand*{\hairline}{% \bigskip% \noindent \hrulefill% \bigskip% } % reverse indentation for biblio and play \newenvironment*{amusebiblio}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newenvironment*{amuseplay}{ \leftskip=\parindent \parindent=-\parindent \smallskip \indent }{\smallskip} \newcommand*{\Slash}{\slash\hspace{0pt}} \addtokomafont{disposition}{\rmfamily} \addtokomafont{descriptionlabel}{\rmfamily} % forbid widows/orphans \frenchspacing \sloppy \clubpenalty=10000 \widowpenalty=10000 % http://tex.stackexchange.com/questions/304802/how-not-to-hyphenate-the-last-word-of-a-paragraph \finalhyphendemerits=10000 % given that we said footinclude=false, this should be safe \setlength{\footskip}{2\baselineskip} \title{Colpo su colpo} \date{1977} \author{Émile Henry} \subtitle{} % https://groups.google.com/d/topic/comp.text.tex/6fYmcVMbSbQ/discussion \hypersetup{% pdfencoding=auto, pdftitle={Colpo su colpo},% pdfauthor={Henry, Émile},% pdfsubject={},% pdfkeywords={opuscoli}% } \begin{document} \begin{titlepage} \strut\vskip 2em \begin{center} {\usekomafont{title}{\huge Colpo su colpo\par}}% \vskip 1em \vskip 2em {\usekomafont{author}{Émile Henry\par}}% \vskip 1.5em \vskip 3em \includegraphics[keepaspectratio=true,height=0.5\textheight,width=1\textwidth]{e-h-emile-henry-colpo-su-colpo-x-cover.jpg} \vfill {\usekomafont{date}{1977\par}}% \end{center} \end{titlepage} \cleardoublepage \tableofcontents % start a new right-handed page \cleardoublepage \chapter{Nota introduttiva} Chi alza la mano contro i dominatori e contro i loro servi paga con la vita. Ecco l’insegnamento che si trae dalla lettura di questo libro dedicato alla vicenda di Émile Henry, l’anarchico che decise, sul finire dell’Ottocento, di attaccare con le bombe il nemico di classe. Lo tengano presente i compagni che si illudono di mettere paura. Chi gestisce il dominio non si impaurisce facilmente. Serra i ranghi e va avanti. Anzi, non appena si accende qualche fuocherello, qui e là, immediatamente invoca leggi speciali e provvedimenti esemplari. Normale amministrazione. Spetta a noi decidere che fare. Stare a guardare, aspettando che tutto vada a soqquadro per scendere dal marciapiede su cui siamo fermi, oppure attaccare per primi. Anche a costo di trovare schierati contro – chi poteva immaginarselo – una buona parte dei nostri stessi compagni. Malatesta, a suo tempo, altri ai giorni nostri. Questo libretto, uscito la prima volta per le edizioni Vulcano nel 1978, e subito da me recensito su “Anarchismo” dette vita a una polemica ben più astiosa e indigesta delle righe sopratono ma, in fondo, genericamente bonarie, di Malatesta (qui riportate in \emph{Appendice}). Chi volesse leggerla la troverà nel mio libro: Gianfranco Bertoli e Alfredo M. Bonanno, \emph{Carteggio 1998-2000}, Trieste 2003, pp. 450-480. Qui di seguito mi limito a riportare la mia recensione che dette origine a tanto squallore. E riprendo questo mio scritto perché lo ritengo tutt’ora valido per chiarire i motivi dell’attacco di Henry, i quali rimangono sempre l’obiettivo primario di ogni anarchico che vuole guardarsi la mattina allo specchio senza ridersi in faccia vedendo riflessa la maschera di un buffone. Con buona pace di tutti i distinguo filosofici. \bigskip Trieste, 30 ottobre 2011 \begin{flushright} Alfredo M. Bonanno \end{flushright} \clearpage Una raccolta contenente una biografia di Henry, due sue lettere, il resoconto del processo, alcuni aforismi, e un’appendice con una interessante lettera di Malatesta. Il volumetto, occorre dirlo subito, presenta un problema che supera di gran lunga lo stupido barcamenarsi degli storici, anche degli storici dell’anarchismo: il gesto di Henry fu qualcosa di spaventoso, qualcosa che scosse non soltanto la cosiddetta “opinione pubblica”, ma anche i compagni. E la lettera di Malatesta, inserita nell’appendice, è un esempio di queste perplessità, colte dall’anarchico italiano e giustificate in un certo modo, mettendo avanti la solita cautela, quella stessa cautela che pochi anni prima aveva fatto gridare al “provocatore” nei confronti di Ravachol a gente come Grave e come Kropotkin. Ma, andiamo con ordine. Non è per nulla vero che il gesto di Henry si inserisce nella catena di attentati e di attacchi che gli anarchici “fine secolo” realizzarono contro le istituzioni e i loro rappresentanti. Il gesto di Henry opera un “salto di qualità” che venne colto, seppure nebulosamente, anche dai compagni che in quel momento si trovavano a lottare contro la repressione. Questo giovane, colto e intelligente, opera con freddezza una decisione che altri avevano maturato e compreso, ma non realizzato: attacca la borghesia, non questo o quel rappresentante dell’istituzione Stato, questo o quel poliziotto, magistrato, carnefice, aguzzino, spia o traditore, no: tutta la borghesia. Egli colpisce nel mucchio, senza discriminazioni. Sceglie con cura uno dei posti che questa classe frequenta, vi si reca con il suo ordigno infernale, accende la miccia, lancia la bomba e se ne va. Di più, cerca anche di sfuggire alla cattura. Non è un martire, è un guerrigliero, non vuole sacrificarsi, vuole continuare nella sua lotta, vuole continuare a colpire nel mucchio. Per far questo fugge, cerca di coprirsi la ritirata, spara per difendersi, finché non cade prigioniero nelle mani del nemico. E qui, una volta preso, non chiede pietà, non si chiude in un mutismo del resto anche giustificabile: fa del processo una tribuna per spiegare e illustrare il suo gesto contro tutti (compagni compresi) e contro tutto. Non cerca attenuanti, non parla di “errori”, ma dice chiaramente che ha inteso colpire proprio nel mucchio, senza preventiva discriminazione, perché proprio nel mucchio si annidano quei colpevoli dello sfruttamento che sono meno individuabili, i rappresentanti di quella classe bottegaia, perbenista, codina, sanfedista, pronta ad accorrere nelle piazze dove si ghigliottina, pronta a battere le mani a qualsiasi sottoprodotto napoleonico, pronta a mettere il proprio sostegno sotto i piedi del dittatore di turno. Nel gesto di Henry è inclusa un’analisi del concetto di classe. Non tanto nelle sue lettere o nello stesso dibattito processuale, ma proprio nel gesto in se stesso. Il comportamento collettivo della classe borghese comprende, in forme ben delineate, in quanto classe al potere (o diretta sostenitrice del potere) una coscienza di classe ben adeguata alle reazioni specifiche dei rapporti di forza (ideologici ed economici). La classe borghese sa quello che vuole, e la frangia bottegaia lo sa anche meglio della media e alta borghesia. E questa coscienza di sé la estrinseca anche nel passatempo, nel divertimento, nello scegliere un caffè, un ristorante, un bordello, una crociera, un luogo di vacanza. La selezione che si opera in questi posti non è solo determinata dal prezzo dei prodotti, dei servizi e di quello che occorre avere con sé per recarvisi, ma è determinata dalla stessa aria che vi si respira, dall’atmosfera che vi è stata creata “apposta”, dalla scelta delle bardature, dei ninnoli, dei quadri, degli specchi, dei bicchieri e della moquette. Un proletario – anche oggi, con tutto l’inquinamento che è stato causato dal consumismo imperante – raramente metterebbe piede al Caffè Greco a Roma, e se per errore vi capitasse dentro ne fuggirebbe ben presto, non tanto perché spaventato dai prezzi che vi si praticano, quanto perché estraniato da quell’atmosfera che vi è stata creata e che si sente come qualcosa di solido, un’atmosfera che solo con una valutazione superficiale può essere riportata alla necessità del capitale di “vendere”. Qui non si tratta di quei luoghi di massa dove si sacrifica al dio “merce”, si tratta di altri luoghi, più intimi e raccolti, dove il sacrificio alla religione della “merce” è fatto in forma più raffinata, in forma accessibile solo a pochi, in forma che opera una selezione automatica e che trova riscontro – quasi perfetto – nell’adeguarsi della coscienza di classe borghese alla situazione dei rapporti di forza oggi in campo. Non si venga a dire che la situazione storica di fine Ottocento era diversa della presente e che allora questi posti erano ben più precisamente “isolati” di quanto non accada oggi, proprio perché la borghesia ancora all’apice dello sfruttamento coloniale si sentiva sicura di sé e voleva autogratificarsi anche con bordelli e caffè oltre che con chiese e monumenti alla vittoria. Anche oggi, in fase di profonde trasformazioni sociali, la borghesia mantiene una certa coscienza di sé, almeno quelle fasce che non sono state risucchiate irrimediabilmente nel baratro della criminalizzazione a seguito delle difficoltà, per il capitale, di mantenere un livello sufficientemente sicuro di occupazione. Ma quelle altre fasce, quelle garantite, quelle che si sono anche ingrossate con l’accesso di altri gruppi – prima proletari – oggi sono il nucleo reazionario più coerente e più difficile a smuovere. E questo nucleo, questo coacervo d’interessi e di squallore, di linguaggio gergale e di stucchevoli imitazioni di passati splendori, questo nucleo si ritrova ancora negli stessi posti, negli stessi caffè, negli stessi bordelli. Ecco. La cosa più umoristica (e tragica, nello stesso tempo) è che questo nucleo reazionario ha assunto gli atteggiamenti del progressismo parolaio della cosiddetta sinistra, e per meglio solidificare la coscienza del proprio status sociale ha rigettato le vesti sorpassate di una reazione che si vestiva di nero (e che oggi farebbe ridere) per indossare le vesti di una reazione che si veste di rosso e che non fa più ridere ma mette paura. Ecco. Colpire nel mucchio, oggi, a tanto tempo dal gesto di Henry, non solo sarebbe un gesto valido ma sarebbe anche un contributo teorico al movimento, ancora una volta, un salto qualitativo. Malatesta scriveva: “Una cosa è comprendere e perdonare, un’altra è rivendicare. Questi non sono atti che possiamo accettare, incoraggiare, imitare. Noi dobbiamo essere risoluti ed energici, ma dobbiamo cercare di non oltrepassare mai il limite segnato dalla necessità. Noi dobbiamo fare come il chirurgo che taglia quando è necessario, ma evita di infliggere inutili sofferenze: in una parola, dobbiamo essere ispirati dal sentimento dell’amore degli uomini, di tutti gli uomini”. Amore o odio. L’alternativa è errata. Nello scontro di classe non si può sentire amore per il proprio nemico, i sentimenti che possono stimolare questo amore sono quelli della reazione comune agli stessi stimoli della classe, cioè il sentirsi non solo partecipi della stessa classe del nemico ma il sentirsi interessati alle stesse cose e agli stessi ideali, in caso contrario, quando il nemico si vede come tale – come nemico di classe – e i suoi interessi e i suoi ideali non si condividono, ma anzi suscitano disgusto e sdegno, il risultato può essere uno solo: l’odio. Ed Henry rispondeva: “È vero che gli uomini non sono che il prodotto delle istituzioni; ma queste istituzioni sono cose astratte che esistono solo fintanto che ci sono uomini in carne ed ossa per rappresentarle. Non c’è quindi che un modo per colpire le istituzioni; cioè colpire gli uomini; ed accogliamo con felicità tutti gli atti energici di rivolta contro la società borghese, perché non perdiamo di vista il fatto che la Rivoluzione non sarà che la risultante di tutte queste Rivolte particolari”. \bigskip [Recensione a E. Henry, \emph{Colpo su colpo}, Edizioni Vulcano, Bergamo 1978, pagine 174, pubblicata su “Anarchismo” n. 23-24, 1978] \chapter{“La Java des bon enfants”} \begin{verse} Dans la rue des Bons-Enfants,\forcelinebreak On vend tout au plus offrant.\forcelinebreak Y avait un commissariat,\forcelinebreak Et maintenant il n’est plus là. Une explosion fantastique,\forcelinebreak N’en a pas laissé une brique,\forcelinebreak On crut qu’c’était Fantômas,\forcelinebreak Mais c’était la lutte des classes! Un poulet zélé vint vite,\forcelinebreak Qui portait une marmite,\forcelinebreak Qu’était à renversement,\forcelinebreak Il la retourne imprudemment. Le brigadier, le commissaire,\forcelinebreak Mêlés au poulet vulgaire,\forcelinebreak Partent en morceaux épars,\forcelinebreak Qu’on ramasse sur un buvard. Contrairement à ce qu’on croyait,\forcelinebreak Y’en avait qui en avait,\forcelinebreak L’étonnement est profond:\forcelinebreak On peut les voir jusqu’au plafond. Voilà bien ce qu’il fallait,\forcelinebreak Pour faire la guerre au palais,\forcelinebreak Sache que ta meilleure amie,\forcelinebreak Prolétaire, c’est la chimie. Les socialos n’ont rien fait,\forcelinebreak Pour abréger les méfaits,\forcelinebreak De l’infamie capitaliste,\forcelinebreak Heureusement vient l’anarchiste. Il n’a pas de préjugés,\forcelinebreak Les curés seront mangés,\forcelinebreak Plus de patrie, plus de colonie,\forcelinebreak Et tout le pouvoir il le nie. Encore quelques beaux efforts,\forcelinebreak Et disons qu’on se fait fort,\forcelinebreak De régler radicalement,\forcelinebreak Le problème social en suspend. Dans la rue des Bons-Enfants,\forcelinebreak Viande à vendre au plus offrant,\forcelinebreak L’avenir radieux prend place,\forcelinebreak Et le vieux monde est à la casse. \end{verse} \chapter{“La Giava des bon enfants”} \begin{verse} In Rue des Bons Enfants,\forcelinebreak Si vende tutto al miglior offerente.\forcelinebreak Una volta c’era un commissariato\forcelinebreak E adesso non c’è più. Un’esplosione fantastica\forcelinebreak Non c’è rimasto un mattone\forcelinebreak Si è pensato fosse stato Fantômas,\forcelinebreak Ma era la lotta di classe! Un pollo zelante arrivò subito\forcelinebreak Portando una pentola\forcelinebreak Che era girata sottosopra\forcelinebreak E che lui rigirò imprudentemente. Il brigadiere, il commissario,\forcelinebreak Mischiati a dei volgari polli\forcelinebreak Si sparsero dappertutto in pezzi\forcelinebreak Che poi vennero ramazzati via. Contrariamente a quel che si crede,\forcelinebreak Hanno avuto quel che si meritavano\forcelinebreak La sorpresa è profonda,\forcelinebreak La si può vedere fino alle fondamenta. Questo è ciò che serviva\forcelinebreak Per far la guerra ai palazzi,\forcelinebreak Sappiate che il vostro migliore amico\forcelinebreak Proletari, è la chimica. I socialisti non hanno fatto niente,\forcelinebreak Per ridurre il danno\forcelinebreak Del capitalista infame\forcelinebreak Fortunatamente arriva l’anarchico. Non ha pregiudizi,\forcelinebreak I preti verranno mangiati,\forcelinebreak Niente più patria, e nemmeno colonie,\forcelinebreak E qualsiasi potere, lui lo nega. Ancora un piccolo sforzo,\forcelinebreak E potremo dire che saprà\forcelinebreak Liquidare radicalmente\forcelinebreak Il problema sociale in sospeso. In Rue des Bons Enfants,\forcelinebreak Si vendono bistecche al miglior offerente,\forcelinebreak Si vede un avvenire radioso\forcelinebreak E il vecchio mondo s’è rotto. \end{verse} [Sul disco della prima registrazione (1973, \emph{Pour en finir avec le travail}. \emph{Chansons du prolétariat révolutionnarie}, con musiche di Francis Lemonnier e la voce di Jacques Marchais) questa canzone è stata attribuita a Raymond Callemin, detto Raymond la Science (un membro della “Banda Bonnot”), 1912. In verità il brano fu scritto negli anni Sessanta da Guy Debord] \chapter{Biografia} \section{1872-1887} Nasce a Saint-Martin Provensals (Spagna), il 26 settembre 1872, di Constant, Joseph, Émile, Félix Henry, secondo figlio di Rose Caubet-Lasale e di Fortuné Henry Mausel, condannato a morte in contumacia per la sua partecipazione attiva alla Comune. La famiglia Henry è originaria di Nîmes, dove il nonno di Émile era pellicciaio. Fortuné Henry era stato redattore capo del “Panurge”, giornale pubblicato a Carcassonne verso il 1860: “In seguito ad articoli di una violenza straordinaria, ebbe a sostenere numerosi processi che portarono alla morte del suo giornale”. (“Le Petit Journal”, 17 febbraio 1894). Colonnello durante la Comune, esercitò in seguito le professioni di capomastro di cave, poi di ingegnere. Dopo l’amnistia, va a Parigi con la sua famiglia (1882). Suo padre muore poco dopo per le conseguenze di un avvelenamento da vapore di Mercurio. Émile Henry studia alla scuola municipale Jean-Baptiste Say dove è allievo brillante ed ottimo compagno (anno scolastico 1884-1885: 2° premio; 1885-1886: 1° premio; 1886-1887: 2° premio; 1887-1888 – anno preparatorio alla École Polytechnique: 5° attestato). Uno dei suoi professori dirà più tardi di lui: “Era un ragazzo perfetto, il più onesto che si possa incontrare”. Durante l’anno scolastico 1884-1885, fa parte della terza compagnia del battaglione scolastico e ottiene a fine anno l’ottavo attestato di merito. Al momento del processo, quando lo si accuserà di aver rifiutato il servizio militare, dichiarerà: “Avevo fatto tre anni di battaglione scolastico ed è tutto quello che potevo fare come militare”. Gli anni 1884-1887 vedono lo sviluppo dalla propaganda anarchica: oratori come Tortelier o Fortuné Henry,\footnote{Joseph Jean-Marie Tortelier, 1854-1925. Uno dei creatori della Lega degli Antipatrioti (agosto 1886). Partecipa nel 1887 alla manifestazione del 9 marzo all’Esplanade des Invalides a fianco di Louise Michel e di Émile Pouget, il che gli vale tre mesi di carcere. Partigiano dell’azione diretta, è uno dei primi a diffondere in Francia l’idea dello sciopero generale rivoluzionario. Partecipa al Congresso di Londra (1896). Si unisce alle posizioni di Pouget durante l’affare Dreyfus. Tortelier non ha lasciato nessuno scritto. Jean Charles Fortuné Henry, nato a Limeil-Brévannes il 3 agosto 1869. La sua azione rivoluzionaria gli vale la condanna a vari anni di prigione (tredici anni in tutto). Nel 1903 fonda una colonia anarchica a Aiglemont (Ardenne), l’”Essai”, che animerà fino al 1908. Con Georges Yvetot, E. Janvion, Girault, Francis Jourdain, Miguel Almereyda (pseudonimo di Eugène Vigo) e Delalé, rappresenta gli antimilitaristi francesi al Congresso di Amsterdam (1904). Ha scritto tra l’altro: \emph{Ravachol anarchiste}? \emph{Parfaitement} (1892), \emph{L’Essai} (1903), \emph{Communisme expérimental} (1905), \emph{Lettres de pioupious} (1906), \emph{Grève et sabotage} (1908).} fratello di Émile, intervengono in riunioni pubbliche. Nel settembre 1886, Charles Malato di ritorno da Numea dove aveva accompagnato il padre, comunardo deportato, partecipa alla rinascita della stampa anarchica: con Léon Ortiz, Schiroky, Gérendal e Pausader\footnote{Pausader, detto Jacques Prolo, collaboratore di alcuni giornali anarchici, de “L’Eveil” (con Georges Yvetot e A. Salmon), finirà come redattore capo del “Bollettino municipale” della città di Parigi. Ha pubblicato \emph{Le communisme devant le parti ouvrier} (\emph{VIII Congres}) (1887) e \emph{Les Anarchistes} tomo X della \emph{Histoire des partis socialistes en France}, pubblicato sotto la direzione di A. Zevaès (1912).} – che Émile Henry incontrerà qualche anno più tardi – fonda “La révolution cosmopolite”, “giornale rivoluzionario socialista indipendente”. 12 gennaio 1887. “Clément Duval\footnote{Clément Duval, 1850-1935. Uno dei fondatori, nel 1882, del gruppo anarchico “La Panthère des Batignolles”, frequentato da Joseph Tortelier, di cui divenne amico. Condannato una prima volta a un anno di prigione per furto, è condannato a morte l’11 gennaio 1887 per l’incendio e il saccheggio dell’albergo Lemaire. Poco dopo, la sua pena sarà commutata ai lavori forzati a vita. Nel 1901, evade dalla Guyana con alcuni compagni e arriva a New York dove, nel 1929, appaiono le sue \emph{Memorie autobiografiche} (Biblioteca de l’Adunata dei Refrattari, Newark-New Jersey; ora in 4 voll. per le edizioni dell’Arkiviu-Bibrioteka “T. Serra”, Guasila 1996-2002).} è condannato a morte per aver espropriato il palazzo di una riccastra e aver fatto qualche asola nella pellaccia dello sbirro Rossignol. Non osando accorciarlo, la governanza lo spedisce alla Guyana”. (“Almanach du Père Peinard”, 1894). \section{1888-1891} Émile Pouget, Ricard e Constant Martin fondano un quindicinale anarchico, il “Ça ira” (maggio 1888). Ammesso alla École Polytechnique lo stesso anno, Émile Henry rinuncia agli studi. “Per non essere militare e non essere costretto a tirare sulla gente come a Fourmies”, dichiarò al suo processo, riferendosi al 1° maggio 1891 quando la truppa sparò sulla folla, uccidendo dieci persone tra cui due ragazzi di 11 e 13 anni. Lascia la scuola Jean-Baptiste Say nel novembre 1890 ed entra, il mese seguente, nella ditta di un parente, il signor Bordenave, che accompagna a Venezia per cooperare ai lavori pubblici di cui quest’ultimo è incaricato. Dopo qualche mese lascia questa occupazione, in seguito ad un malinteso (Émile Henry credeva che ci si aspettasse da lui una “sorveglianza occulta” del personale). 24 febbraio 1889. Primo numero de “Le Père Peinard” di É. Pouget. Tornato a Parigi, Émile Henry rimane tre mesi senza lavoro, poi trova un impiego poco remunerato in una ditta di commercio. “La guerra agli uffici di collocamento sta prendendo un andamento pratico: la baracca di un collocatore della rue Chénier viene fatta saltare con la dinamite, i danni si limitano ad un pezzo di muro buttato giù, ma la paura degli sfruttatori diventa enorme”. (“Almanach du Père Peinard”, 1894). Qualche settimana più tardi, il 10 novembre 1888, “saltano in aria due covi di collocatori, in rue Boucher e rue Française”. (\emph{Ibidem}). 8 aprile 1890. “A Roubaix, un proletario, Vanhausen cacciato dalla galera Vanoutryve, buca la pancia del direttore e dopo si suicida”. (\emph{Ibidem}). 1° maggio 1891. L’esercito spara sulla folla a Fourmies (Nord): 10 morti. A Clichy, violenti scontri tra anarchici e polizia. Decamps e Dardare, due compagni arrestati, vengono selvaggiamente picchiati condannati a cinque e tre anni di carcere. Il presidente Benoît, che dirigeva il dibattimento, ed il sostituto Bulot, che aveva richiesto la pena di morte, saranno i primi bersagli di Ravachol, l’anno dopo. Il 5 maggio Zo d’Axa\footnote{Zo d’Axa, pseudonimo di Galland, 1864-1930. “L’Endehors” ebbe numerosi collaboratori: P.N. Roinard, Félix Fénéon, Tabarant, C. Meunier, Georges Darien, Octave Mirbeau, L. Descaves, Louise Michel, S. Faure, Émile Henry, Errico Malatesta, Malato, ecc. Ricercato per istigazione all’omicidio, Zo d’Axa, “ventisette anni accusato di associazione di malfattori” fu incarcerato a Mazas e messo in segreta come Pouget e Grave. Posto in libertà provvisoria, lasciò subito la Francia (cfr. il suo libro \emph{De Mazas à Jérusalem}, Chamuel éditeur, 1895, disegni di Lucien Pissaro, Steinlen, Félix Valloton; tr. it. Gratis, Firenze 2006). Visita l’Inghilterra, l’Italia, la Turchia, la Palestina. Estradato, viene riportato a Parigi dove è incarcerato a Sainte-Pélaigie con i detenuti politici. Tra il 1897 e il 1899, pubblica “La Feuille”, giornale dreyfusardo illustrato da Willette, Luce, Steinlen, Léandre, Hermann-Paul, Couturier e Anquetin. Poi, parte per l’America da cui porta le \emph{Note di viaggio} che usciranno su “L’Ennemi du Peuple”. Muore a Marsiglia nel 1930.} pubblica il primo numero de “L’Endehors”. È questa l’epoca in cui, secondo le proprie affermazioni, Émile Henry si lancia nel movimento rivoluzionario. Nello stesso anno, fa la conoscenza della signora Gauthey, moglie di un amico di suo fratello, alla quale egli scrive il 14 settembre : “Io che ho tanto bisogno di affetto, di consolazione, di carezze, di amore, mi vedo solo e isolato, perso in questo ampio turbine dgli egoismi umani; e talvolta la vita mi sembra orribile e vorrei scomparire, annullarmi per sfuggire alle angosce perpetue che stringono e spezzano il cuore e il pensiero! Amarvi e non essere riamato!”. (Questa lettera fu pubblicata su “Le Journal”, 17 maggio 1894). \section{1892} All’inizio dell’anno Sébastien Faure lancia una campagna contro il Primo Maggio e i “tre otto”, rivendicazione giudicata riformista e antirivoluzionaria. Pouget, Malato, Prolo, Martin, Tortelier, Brunet, Schiroky e Émile Henry, di cui ha usato i nomi senza averli consultati, esprimono il loro disaccordo in una dichiarazione comune: “I compagni sottoscritti protestano contro l’uso del loro nome fatto senza il loro consenso, e dichiarano di essere invece contrari ad una campagna contro il Primo Maggio per le seguenti ragioni: “1. Ogni volta che il popola abbandona l’officina per scendere in piazza, l’interesse di tutti gli anarchici, qualunque siano le tendenze del movimento, deve essere di partecipare, per cercare di farlo deviare in favore della rivoluzione sociale. “2. Gli anarchici non sono un partito di cospiratori, che cerca di fare una rivoluzione di sorpresa, non contano più sul Primo Maggio che su un’altra data; ma poiché il popolo in quella data ha delle tendenze di rivolta, sarebbe assurdo, anzi meschino, consigliarli di rimanere a riposo in quel giorno. “3. Il congresso della rue Rochechouart, fissando il Primo Maggio come data di una manifestazione, aveva in prospettiva unicamente fini politici. Sperava di far manovrare a perfezione le masse irreggimentate dai suoi amici. Ma, come sempre, il popolo è andato oltre quello che i suoi pretesi rappresentanti avrebbero voluto. “Invece di essere una sfilata internazionale dell’esercito socialista elettorale, è successo che, grazie all’intervento degli anarchici, i proletari hanno agito\dots{} “4. Il timore da parte di qualche compagno che le manifestazioni periodiche impediscano all’azione di prodursi all’infuori delle date fissate non ha fondamento\dots{}”. Il 10 febbraio, “garottamento a Xeres di quattro persone arrestate, venti giorni prima, nell’insurrezione anarchica dei contadini che avevano preso d’assedio la città”. (“Almanach du Père Peinard”, 1894). Primi attentati anarchici: esplosione al ristorante Véry (2 morti) il 25 aprile, che segue quelle del boulevard Saint-Germain (11 marzo), della caserma Lobau (15 marzo) e della rue de Clichy (27 marzo). Nel corso di un meeting di solidarietà a Ravachol, tenuto nel quartiere del Temple, Fortuné Henry prende la parola ed estrae dalla tasca un oggetto che degli informatori prendono per una pistola. Arrestato l’indomani, viene imprigionato. Viene arrestato anche Émile Henry. “Aveva già una notorietà nel partito, era conosciuto dalla famiglia Reclus e amico di Sébastien Faure”. (“Le Petit Journal”, 16 febbraio 1894). Fortuné, giudicato, viene assolto. Qualche mese più tardi sarà condannato dalla Corte d’Assise di Bourges, per incitamento all’omicidio, a tre anni di carcere. Non essendoci alcuna prova seria contro Émile, viene rilasciato. Tuttavia il suo padrone, un commerciante della rue du Sentier, che non apprezza la propaganda che egli svolge con i suoi compagni, lo licenzia. Egli scopre, nell’ufficio che Émile Henry occupava, dei manoscritti relativi alla fabbricazione di esplosivi. Eppure, a sentire Malato, Émile Henry, sarebbe stato ostile, in quell’epoca, agli atti di Ravachol; dopo aver condannato l’assassino dell’eremita di Chambles ed il profanatore della tomba (“Dovremmo finirla con questa gente che disonora il nostro partito; vogliono sfruttare gli altri e vivere confortevolmente nello stile borghese, non pensano a sacrificare la loro vita per delle idee”, frase attribuita a Émile Henry da Malato, cfr. “The Fortnightly Review”, 1° settembre 1894), si sarebbe opposto anche alla dinamite: “Tali atti (\dots{}) ci fanno un gran male\dots{} Un vero anarchico (\dots{}) abbatte il suo nemico; non fa saltare case in cui ci sono donne, bambini, lavoratori e domestici”. (\emph{Ibidem}). Dichiarazioni sorprendenti se nell’agosto dello stesso anno, rispondendo ad un articolo di Errico Malatesta (“Un peu de théorie”, “L’Endehors” n. 68, 21 agosto 1892. Vedi \emph{Appendice}) scrive: “I futuri Ravachol, prima di rischiare la loro testa nella lotta, dovranno forse sottomettere i loro progetti al beneplacito dei Malatesta, eretti a Grande Tribunale, che giudicheranno l’opportunità delle azioni?”. (“L’Endehors” n. 69, 28 agosto 1892). Henry deporrà la sua prima bomba meno di tre mesi dopo. Per un periodo fu amministratore de “L’Endehors”: “Émile Henry, la cui costante preoccupazione fu di lavorare per l’idea, s’incaricava, senza alcun profitto, del noioso lavoro di amministrazione, della corrispondenza con i distributori de ‘L’Endehors’. Per quanto il lavoro fosse modesto, riservato, egli ci teneva a collaborare al lavoro comune. E lo faceva, benché esistessero delle divergenze fra noi: ma l’anarchia non è forse parente prossima della mia concezione individualistica, affermatrice dell’orgoglio di essere, fuori dalle regole restrittive, fuori dalle tenaglie delle leggi? “Lo sento ancora, quasi un bambino, ma già serio. Deciso, settario perfino come lo diventano obbligatoriamente coloro ai quali nessun dubbio turba la fede, coloro che vedono – ipnotizzati, potrei dire – il fine, e, allora, ragionano, giudicano e sentenziano con una matematica implacabile. Credeva fermamente nell’avvento di una società futura, costruita logicamente, armoniosa e bella”. (Zo d’Axa, \emph{Da Mazas a Gerusalemme}). E Zo d’Axa aggiungeva più avanti: “Si stupiva che avendo compreso la bassezza di un’epoca, ci si potesse ancora trovare qualche gioia”. 11 luglio. Esecuzione di Ravachol. Émile Henry è segnalato alla polizia “perché si dedica a studi di chimica sospetti” (secondo uno degli atti di accusa letti dal cancelliere Wilmès al processo di Henry). In agosto, i minatori di Carmaux scendono in sciopero e occupano gli uffici e gli edifici della miniera. Malgrado il rapido intervento dei socialisti, che presto controllano il movimento e organizzano delle sottoscrizioni, il lavoro riprenderà solo il 3 novembre. Incorporato nel 148° Reggimento di linea, Émile Henry si sottrae alla chiamata del servizio militare. In settembre, cerca lavoro presso un orologiaio, poi entra, dietro raccomandazione di Léon Ortiz che vi ha lavorato per tre anni, come impiegato presso Dupuy, scultore-decoratore in rue Rocroi. Abita al 31 di rue Véeron, non lontano dalla rue Lepic dove sta Ortiz. Ai primi del mese di novembre, Émile Henry si procura un astuccio di metallo, tre chili di clorato di potassio e un flacone di sodio. Possiede anche venti cartucce di dinamite. Con l’aiuto di un detonatore e di una marmitta acquistata in rue Lepic, fabbrica una bomba a rovesciamento. L’8 novembre, lascia il suo ufficio verso le 10 per fare due commissioni per Dupuy. Prima si reca da un liquidatore giudiziario di rue Tronchet, in vettura, poi in place Blanch. Da qui, raggiunge rue Véron, prende dall’armadio la bomba già pronta e si fa condurre con un’altra vettura in avenue de l’Opéra. Depone l’ordigno all’interno del numero 11 che ospita gli uffici della miniera di Carmaux, e va subito da un architetto di boulevard de Courcelles, sempre in vettura. Fatta la seconda commissione, torna a piedi in rue Rocroi. Intanto, la bomba è stata scoperta da Simon Garnier, portinaio della casa, e da un fattorino della compagnia di nome Garin. Trasportata al commissariato di polizia di rue des Bons-Enfants, non appena posata, esplode, uccidendo cinque persone: il vigile Réaux, il sotto-brigadiere Formorin, il fattorino Garin, il segretario del commissariato Pousset – che stava per essere nominato commissario – e l’ispettore Troutot. D’altronde Henry aveva previsto la possibilità che la bomba fosse scoperta prima di esplodere: “Secondo i miei esperimenti, supponevo che la marmitta sarebbe scoppiata cinque o sei minuti dopo essere stata posta davanti agli uffici della compagnia di Carmaux, ma non ignoravo che se si fosse presa la marmitta prima dell’esplosione, sarebbe stata portata al commissariato di polizia del quartiere, di modo che, nel caso in cui i ricchi dell’avenue de l’Opéra fossero sfuggiti alla sorte che destinavo loro, ero certo di colpire i poliziotti, ugualmente miei nemici”. Loubet, allora ministro dell’Interno, Quesnay de Beaurepaire, procuratore generale, e Goron, capo della Pubblica Sicurezza, accorrono sul posto. Mentre visitano il commissariato distrutto, il sotto-brigadiere Henrion, che torna dalla Prefettura, cade morto stecchito di fronte allo spettacolo: “La porta d’ingresso era stata completamente strappata e proiettata a pezzi per le scale. L’ingresso era cosparso di detriti di legno, vetro e carta. La porta, che dall’ingresso si apriva sull’ufficio degli ispettori, non esisteva più; ma sulla soglia per traverso un cadavere sdraiato sul ventre”. Era quello del vigile Réaux. “Le due gambe erano tagliate all’altezza dei ginocchio. Il busto rimaneva coperto da brandelli di vestiti mezzo bruciati e stracciati, mentre le cosce erano completamente nude. La faccia era appoggiata contro il suolo. Il pavimento della stanza era un mucchio di detriti di tutti i tipi, legno, gesso, carta, pezzi di carne e di vestiti, il muro che divideva l’ufficio degli ispettori da quello del segretario era stato completamente portato via e proiettato contro il muro, di fronte alla porta d’ingresso. Nell’angolo dell’ufficio, entrando a destra, giaceva un tronco totalmente carbonizzato, ricoperto di detriti: era quello che rimaneva del signor Garin, l’impiegato della compagnia delle miniere di Carmaux. Vicino a lui, contro il muro, di fronte alle finestre, si trovava un altro cadavere, sdraiato sulla schiena, le gambe tagliate e coperto anch’esso di detriti. La mano destra, in un gesto istintivo, era stata portata davanti al viso. Era il sotto-brigadiere Formorin. Infine, dove si trovava il muro divisorio, giaceva, in uno stato orribile, quasi una poltiglia, il corpo del signor Pousset, segretario del commissario di polizia. L’ispettore Troutot, che si trovava anche lui negli uffici al momento dell’esplosione, era stato portato via ancora in vita. Fu prelevato da una vettura delle Ambulanze urbane e portato all’ospedale. Dopo aver subito l’amputazione di una gamba, spirò verso le cinque di sera, tra spaventose sofferenze”. (“Le Petit Journal”, 20 novembre 1892). La casa sarebbe interamente crollata se, sopra il commissariato, non si fosse stato il deposito della libreria Dentu, quattrocentomila volumi, il cui peso (80 tonnellate) fece resistenza. Secondo alcune testimonianze, Henry era accompagnato da una donna quando posò la sua bomba: “La sua complice, ‘la donna della mantella’ dell’avenue dell’Opéra, è stata fermata nei giorni scorsi in un albergo di rue de la Seine. Si chiama Adrienne Chailley, età ventotto anni, conosciuta nel quartiere latino, di cui frequentava alcune birrerie. Appartiene ad un’eccellente famiglia ed ha ricevuto una certa istruzione. Ha fatto spesso delle conferenze sull’emancipazione della donna. È una donna bruna, dal viso largo e corto, il naso camuso, gli occhi tondi a fior di testa. I capelli sono tagliati corti: tipo volgare dell’ubriaca. Il signor Espinas, giudice istruttore (\dots{}) ha interrogato a lungo l’imputata in questi ultimi giorni. Non vuole rispondere alle domande del giudice e non si lascia estorcere che generiche affermazioni”. (“Le Petit Journal”, 23 febbraio 1894; cfr. anche J. Maitron, \emph{Le Mouvement anarchiste en France}, Parigi 1975, tomo I, nota p. 243). Sembra più verosimile che si fosse egli stesso travestito (cfr. A. L. Zevaès, “Sous le signe de la dynamite. E. Henry”, “Vendémiaire”, 30 dicembre 1936 – 6 gennaio 1937; per Jean Paulhan, sarebbe stato Félix Fénéon a dare a Henry un vestito di sua madre, cfr. “La Quinzaine Littéraire”, luglio-agosto 1966). 10 novembre: Émile Henry lascia il suo padrone alle quattro e dichiara di recarsi dalla madre a Brévannes. In effetti va in Inghilterra. La madre di Émile Henry aveva ereditato questa casa da una cognata la cui influenza sui fratelli Henry, al loro ritorno dalla Spagna, è presentata in questi termini da “Le Petit Journal” del 16 febbraio 1894: “Li viziava quanto poteva, mentre discuteva con loro della necessità di riformare la società massacrando una parte di coloro che la compongono”. La signora Henry gestiva con il figlio più giovane un negozio di vini con l’insegna “Alla Speranza!”, frequentato principalmente da operai scavatori. Fa allora pervenire al suo padrone la lettera seguente: “Parigi, 11 novembre 1892 “Signor Dupuy, “La signora Dupuy le ha senz’altro fatto sapere che, leggermente indisposto, avevo lasciato l’ufficio alle quattro. “La notte che ho trascorso, essendo stata molto cattiva, mi ha fatto decidere di passare un giorno o due da mia madre in campagna. “Mi dispiace lasciarla solo in questo momento, in cui avrebbe bisogno dei miei servizi, ma la prego di considerare che sono stato già molto malato qualche mese fa e mi preoccupo di una grave ricaduta. “Non passo in ufficio questa mattina, perché mi reco direttamente da casa mia a casa di mia madre. “Suo devotissimo “Émile Henry”. Due ore più tardi, il signor Dupuy riceveva una seconda lettera: “Signor Dupuy, “In primo luogo, la prego di scusarmi se le ho nascosto la verità quando, giovedì sera, ho lasciato il suo ufficio col pretesto di un’indisposizione. “In realtà temevo le conseguenze delle investigazioni poliziesche che non dovevano mancare di provocare gli ultimi avvenimenti anarchici. È confessarle che O\dots{} non è l’unico anarchico che abbia avuto il piacere di prestare il proprio lavoro ad un padrone quale è lei. “Ho già avuto a che fare con la polizia. Arrestato il 30 maggio, senza alcun pretesto, ho avuto l’insigne onore di dormire al fresco e di abitare una cella graziosamente messa a mia disposizione al grande carcere. Rilasciato qualche tempo dopo (e senza nessun altro motivo), fin dall’indomani mi sono visto congedato dal mio padrone, il signor Vanoutryve, 32 rue du Sentier, con l’unico pretesto che avevo delle idee sovversive. “Infine, dopo numerosi tentativi infruttuosi per ritrovare un posto che mi permettesse più o meno di vivere, il mio amico O\dots{} mi ha proposto di entrare da lei, e lei mi ha assunto come impiegato. “Se racconto tutti questi dettagli, che possono anche non interessarla, è per mostrarle che avevo ben qualche motivo di temere la polizia, che colpirà a tutta forza i rivoluzionari che conosce, attivi o no. “Non ho intenzione di fare settimane, forse mesi di carcere preventivo, prima dell’arresto dei veri autori dell’esplosione dell’8 novembre. (L’esempio di Bricou e di sua moglie, incarcerati dal mese di maggio, non è rassicurante). “Creda al mio più sincero dispiacere. “Émile Henry”. Tra i detriti viene trovato un frammento di giornale in cui si parla dei fratelli Henry. Fortuné può dimostrare che il giorno dell’esplosione era a Bourges. Per quanto riguarda Émile, una perquisizione al suo domicilio, ordinata da Cavard, capo delle Brigate di ricerca, non dà nessun risultato e l’inchiesta abbandona questa pista, tanto più che la polizia, dopo aver verificato il suo orario, giudica impossibile che Émile abbia potuto deporre l’ordigno ed effettuare le commissioni affidategli quel giorno. Intorno al 20 dicembre, in seguito ad una lettera del suo ex padrone indirizzata ad Ortiz (al domicilio londinese di Matha), Émile Henry si presenta da Dupuy per incassare una somma che gli era ancora dovuta al momento della partenza. \section{1893} Émile Henry viaggia: soggiorna in Inghilterra, in Belgio (cfr. “Le Petit Journal” del 16 febbraio 1894: “\dots{} un agente della polizia belga lo avrebbe riconosciuto sotto il nome di Meurin”), forse in Germania (in marzo, sua madre riceve una lettera di Émile Henry imbucata a Berlino). In maggio è nuovamente a Parigi e si installa al n. 10 del boulevard Morland, con il nome di Louis Dubois. Lavora come apprendista – non salariato – da un fabbro, impiego che manterrà fino alla fine del mese di giugno. L’8 luglio, lascia boulevard Morland. Sembra che in quel periodo sia in relazione con Ortiz e “la sua banda di ladri” (la formula è di Maitron). Al processo dei Trenta (agosto 1894), Léon Ortiz sarà accusato di aver partecipato con tre complici, tra cui Émile Henry, ad un furto commesso a Ficquefleur (Orne) nel 1893. In assenza di prove formali, l’accusa si ridurrà a supposizioni. Tuttavia Ortiz sarà condannato a quindici anni di lavori forzati. Senza preoccuparsi dei dinieghi di Ortiz e di Émile Henry, Jean Grave, con la sua proverbiale scorrettezza scrive in \emph{Le Mouvement Libertaire sous la III République} (Parigi 1930, p. 133): “Tra i testimoni sfilarono i notabili di Ficquefleur, dove Émile Henry ed i suoi complici avevano fatto un così bel colpo”. 13 novembre. Un calzolaio anarchico, Léon-Jules Léauthier, che ha deciso di “bucare un borghese” (“Se avessi avuto la dinamite, avrei potuto fare meglio”), si reca in un ristorante dell’avenue de l’Opéra e colpisce col suo trincetto il signor Georgewitch, ministro della Serbia. Qualche giorno dopo, l’agente Colson trova la morte nel corso dell’arresto di un altro anarchico, Marpeaux, ricercato per furto e ricettazione. Marpeaux sarà condannato ai lavori forzati a vita malgrado si proclami innocente. 9 dicembre. Vaillant getta la sua bomba al Palais-Bourbon. 20 dicembre. Émile Henry si reca a Belleville e affitta una camera, al 48 di villa Faucheur (rue des Envierges), sempre col nome di Louis Dubois. 18 gennaio. La Prefettura di polizia è avvisata dell’arrivo a Parigi di quattro anarchici, tra cui Émile Henry. Cinque giorni dopo, questi eludono la sorveglianza degli ispettori incaricati di pedinarli (cfr. “Le Petit Journal”, 15 febbraio 1894). \section{1894} 5 febbraio. Esecuzione di Vaillant. Matha,\footnote{Armand Matha, detto Louis, 1860-1930. Ex garzone di parrucchiere di Casteljaloux (Loire-et-Garonne) venuto a Parigi nel 1891. Amico di Émile Henry da diversi anni, collaboratore del “Falot Cherbourgeois”, del “Libertaire” e de “L’Endehors”, di cui fu il gestore. Uno degli accusati del processo dei Trenta: “Quando mi vedo in presenza di un anarchico come Matha, che era sparito da diciotto mesi e torna tutt’a un tratto; quando ritrovo da Fénéon i detonatori e il flacone di mercurio di Émile Henry, ho il diritto di dire a Matha: ‘Se non riuscite a provare di essere venuto in Francia per fare qualcosa di confessabile, vi riterremo l’emissario della banda di Londra, di questa associazione di malfattori che noi ricerchiamo’”. (Requisitoria dell’avvocato generale Bulot, udienza dell’8 agosto 1894). Libertad e “L’Anarchie” prenderanno le sue difese, nel 1907, quando sarà compromesso in un affare di valuta falsa montato della polizia (vedi Albert Libertad, \emph{Le culte de la charogne}, Paris 1976, p. 38; tr. it. Edizioni Anarchismo, Catania 1987, testo non presente nell’edizione italiana).} che si trovava a Londra per sfuggire a diverse condanne, è tornato anch’egli a Parigi. Sa che Émile Henry prepara un attentato e cerca di dissuaderlo. L’11 febbraio, Émile Henry gli dichiara: “La tua amicizia m’importuna”. Tuttavia prende appuntamento con lui per l’indomani. Di ritorno a Belleville, confeziona una bomba munita di una miccia da minatore la cui lunghezza è calcolata per bruciare quindici secondi. 12 febbraio. Émile Henry avverte il custode della villa Faucheur che non tornerà per qualche giorno. Lascia nella sua camera tre chili e mezzo di acido picrico, materiale per fabbricare ancora una quindicina di bombe, e si porta via quella che aveva preparato. Con una pistola carica, di cui aveva morsicato le pallottole – “Per fare più male”, dirà in seguito – e con un pugnale di cui ha avvelenato la lama, si dirige dapprima verso l’avenue de l’Opéra, poi va alla Gare Saint-Lazare. Sono le otto e mezza quando si siede all’interno del Café Terminus. Alle nove, avvicina il suo sigaro acceso alla miccia, si alza, fa qualche passo in direzione della porta, e, prima di fuggire, lancia la sua bomba verso un palco dove suonano dei musicisti. “Ci si lanciò subito all’inseguimento, e si riuscì a raggiungerlo. Allora, si voltò, tirò fuori dalla tasca una pistola e fece fuoco. Due inseguitori, il signor Maurice, garzone di parrucchiere, e il signor Etienne, impiegato alla gare de l’Ouest, furono colpiti. In quel momento, arrivarono di corsa delle guardie. Una di loro, di nome Poisson, raggiunse il fuggitivo e gli gridò: ‘Ferma!’. Il criminale fece nuovamente fuoco, e tre pallottole colpirono la sventurata guardia. Ma, benché gravemente ferito, egli ebbe la forza di prendere il suo assassino e di tenerlo fino all’arrivo dei suoi colleghi; poi, mentre si tratteneva il fuggitivo, cadde al suolo, in preda ad orribili sofferenze. Era accorsa la folla. Si voleva mettere a morte il criminale. Fu con grande fatica che le guardie riuscirono a proteggerlo conducendolo al commissariato di polizia”. (“Le Petit Parisien”, 25 febbraio 1894). La polizia sospetterà più tardi Ortiz, Matha e Chericotti di avergli dato aiuto al momento del suo arresto. L’esplosione ferisce una ventina di persone (una sola morirà). Octave Mirbeau, che vede nell’atto di Henry una “provocazione poliziesca”, dichiara: “Un nemico mortale dell’anarchia non avrebbe agito meglio di quell’Émile Henry, quando lanciò la sua inspiegabile bomba, in mezzo a tranquille e anonime persone, venute in un caffè, per bervi un bicchiere prima di andare a dormire\dots{} È di moda, oggi, fra questi criminali, il dichiararsi (anarchici), quando hanno fatto un bel colpo\dots{} Ogni partito ha i suoi criminali ed i suoi pazzi, perché ogni partito ha i suoi uomini”. E, da Londra, Malato aggiunge: “Condivido pienamente il giudizio di Octave Mirbeau: l’atto di Émile Henry, che pure è un anarchico di grande intelligenza e grande coraggio, ha colpito soprattutto l’anarchia\dots{} Approvo la violenza che mira all’ostacolo, che colpisce il nemico, non quella che colpisce ciecamente”. Per vari giorni, Émile Henry cerca di ingannare la polizia sulla sua persona e sul suo domicilio, il che permette a tre compagni – Matha, Ortiz e Millet — di “traslocare” il suo materiale: nella mattinata del 14 febbraio, il guardiano della villa Faucheur constata il furto, ma il commissario di polizia chiamato sul posto scopre solo una miccia Bickford, due palle di piombo e delle ceneri. 17 febbraio. Perquisizione a casa della signora Henry, a Brévannes. Roulier, procuratore della Repubblica, e un giudice istruttore di Corbeil, sequestrano lettere e documenti appartenenti ai fratelli Henry. Tra questi documenti, una foto di gruppo in cui compaiono Émile e Fortuné. “Uno dei personaggi tiene una bandiera nera sulla quale si distinguono queste parole: ‘Morte ai borghesi’. Questa fotografia è stata scattata a Dijon, il 9 aprile 1892”. (“Le Petit Journal”, 19 febbraio 1894). 19 febbraio. Numerose perquisizioni ai domicili degli anarchici conosciuti dalla polizia. Arresto di Sébastien Faure. Un’operazione dello stesso genere era stata condotta il 1° gennaio. 20 febbraio. Due nuove esplosioni in rue Saint-Jacques e faubourg Saint-Martin. Entrambe sembrano essere state opera dell’anarchico Amedeo Pauwels, detto Rabardy, conciatore, nato il 29 gennaio 1864 in Belgio. Amico di Paul Reclus, era stato arrestato ed espulso in seguito ai violenti scontri del 1° maggio 1891 a Clichy. Rifugiatosi in Lussemburgo, poi in Spagna, Pauwels morirà il 15 marzo 1894 nella chiesa della Maddalena, ucciso dall’esplosione della bomba che vi aveva appena deposto: “Era facile prevedere che gli anarchici se la sarebbero presa un giorno con la Chiesa. L’attentato di questa settimana allontanerà ancora di più da questi assassini coloro le cui idee si avvicinano maggiormente alle loro, i socialisti. Il portavoce di questi ultimi, Jaurès, in un eloquente appello, ha rimproverato al partito di governo di aver eliminato la preghiera, questa vecchia canzone che cullava la miseria umana”. (“Le Petit Journal”, supplemento illustrato, 26 marzo 1894). Da Londra, dove si è rifugiato poco prima del processo dei Trenta, Émile Pouget dirà di Pauwels che era “spinto dall’idea di smentire una porcheria, raccontata dai giornali borghesi, quella secondo cui gli anarchici sarebbero pagati dai preti”. (“Le Père Peinard”, serie londinese, n. 1, settembre 1894). 23 febbraio. Diverse persone, sospettate di essere gli autori dell’esplosione della rue des Bons-Enfants sono messe a confronto con Émile Henry. Egli allora rivendica l’attentato. Oltre ad Adrienne Chailley, tre persone almeno erano accusate di aver partecipato all’attentato: “Innanzitutto un tale Bonnard, di trentadue anni, calzolaio, amico di Émile Henry, che abitava a Grenelle. Sarebbe stato lui ad aiutare il giovane anarchico a confezionare la bomba. È stato arrestato nel mese di dicembre, qualche giorno dopo l’attentato di Vaillant al Palais-Bourbon. Aveva tre anni di galera da scontare. Touny, il commissario di divisione, fece una perquisizione nella sua camera e vi scoprì diverse marmitte a cui erano stati levati i manici e vari oggetti che dimostravano che si occupava della costruzione di bombe. (\dots{}) Un altro complice è pure sotto chiave. È Auguste Crétaud, di ventun’anni, operaio lattoniere. Avrebbe aiutato i suoi complici nella confezione della bomba. L’anarchico Joseph Mérigeaut, recentemente condannato per detenzione di materie esplosive, è anche compromesso in questo delitto. (\dots{}) Alla Procura si spera di far presto completa luce su questo spaventoso attentato”. (“Le Petit Journal”, 23 febbraio 1894). 24 febbraio. La signora Henry, convocata dal giudice istruttore Meyer, incontra suo figlio. Dupuy, ex-padrone di Émile Henry, assiste all’incontro. Secondo “Le Petit Journal” del 26 febbraio 1894, Émile Henry avrebbe dichiarato a Dupuy: “Signore, ho appreso che mi avevate reso giustizia. Malgrado la corrente dell’opinione pubblica, avete osato dire forte la mia probità; ve ne ringrazio. Se, dal vostro punto di vista, ho commesso dei crimini, la mia coscienza mi assolve: è tutto quello che mi importa”. Il signor Dupuy rispose: “Il mio compito era semplice: dire la verità”. – “Non tutti hanno questo coraggio, e, ancora una volta, vi ringrazio di averlo avuto”. Mentre l’inchiesta prosegue, per tutta la Francia si moltiplicano le perquisizioni e gli arresti di anarchici. 26 febbraio. Émile Henry viene condotto al suo vecchio domicilio di rue Véron da Espinas, giudice, e Clément, commissario di polizia alle delegazioni giudiziarie. Lo sorvegliano diversi ispettori: “\dots{} il prigioniero indicò in quale armadio era venuto, l’8 novembre 1892, a prendere la sua macchina infernale. Poi, aprendo le tende, disse ai magistrati: ‘Che panorama avevo da qui, eh! E nemmeno caro, 170 franchi all’anno’”. (“Le Petit Journal”, 28 febbraio 1894). 27 febbraio. Émile Henry scrive al direttore della Conciergerie, dove è incarcerato. Nella sua cella, annota le opere di Jean-Jacques Rousseau. “Gli arresti di anarchici continuano senza soste a Parigi. Ogni mattina, al sorgere del sole, un certo numero di commissari di polizia, accompagnati da agenti della brigata di ricerca, si presentano al domicilio dei compagni e, dopo la perquisizione fatta alle loro abitazioni, li mandano in galera con l’accusa di affiliazione ad una associazione di malfattori”. (“Le Petit Journal”, 1 marzo 1894). Ogni giorno, la maggior parte dei giornali non manca di comunicare ai suoi lettori nomi ed indirizzi dei “compagni” arrestati. 28 febbraio. Émile Henry viene condotto “da numerosi agenti delle brigate di ricerca” alla sede della compagnia delle miniere di Carmaux per una ricostruzione dell’attentato dell’8 novembre 1892. 12 marzo. Ernest Borde, ferito durante l’attentato al Café Terminus, muore in seguito alle ferite riportate. 18 marzo. Arresto a Parigi di L. Ortiz, “presunto complice di Émile Henry”. “In tasca, aveva una pistola bulldog che non ha fatto in tempo ad usare”. (“Le Petit Journal”, 20 marzo 1894). Lo stesso giorno, durante una processione religiosa a La Coruña (Spagna), José Vasquez tira due colpi di fucile sull’immagine del Cristo gridando: “Viva l’anarchia!”. 4 aprile. Bomba al ristorante Foyot. Diversi feriti, tra cui Laurent Tailhade che perderà un occhio in seguito alle ferite. Poco dopo viene arrestato Matha: non si può dimostrare la sua colpevolezza e ci si accontenterà di farlo comparire al Processo dei Trenta, quattro mesi dopo. Meunier, al quale la polizia attribuisce l’esplosione al ristorante Véry, e che era stato condannato a morte in contumacia dalla corte d’Assise della Seine, viene arrestato a Londra. 18 aprile. L’avvocato Hornbostel, difensore di Émile Henry, scrive al ministro della giustizia per chiedergli di accordare a Émile Henry, detenuto a Clairvaux, un permesso di tre giorni per presentarsi alle Assise e prendere la difesa di suo fratello. 27 aprile. Émile Henry compare alla corte di Assise della Seine. Il ruolo di Pubblico Ministero è coperto dal procuratore generale Bulot, “a cui Ravachol, prendendosela con lui al boulevard Saint-Germain, e mancandolo, aveva assicurato la carriera”. (A. Salomon, \emph{La Terreur noire}. \emph{Chronique du mouvement libertaire}, Paris 1959). Gran parte dei dibattimenti, presieduti dal consigliere Pelletier, viene dedicata all’attentato contro la compagnia delle miniere di Carmaux. Malgrado le lezioni di dizione prese per l’occasione presso l’attore tragico Silvain della Comédie-Française, l’avvocato Hornbostel si rende ridicolo e non riesce ad evitare a Henry la pena di morte. Dopo il verdetto, Émile Henry viene ricondotto alla Conciergerie dove, malgrado le istanze del suo avvocato, rifiuta di firmare il suo ricorso in Cassazione. Vestito con la camicia di forza, viene messo nella cella n. 11. L’indomani, viene trasferito alla Grande-Roquette, cella dei condannati a morte. Legge (Herzen, Cervantes\dots{}) e scrive aforismi. 2 maggio. Nuovo rifiuto di Henry di firmare il ricorso. “Émile Henry attese la morte tranquillamente; rifiutò di firmare la domanda di grazia; il presidente Carnot – che un soprannome popolare indicava come il papà Ammazza Sempre – aveva giudicato di ‘lasciare che la giustizia seguisse il suo corso’. Henry fu ghigliottinato il 21 maggio 1894”. (S. Faure, “Le Libertaire” n. 50, 24-30 ottobre 1896). “Come per Ravachol, condotto al supplizio con i genitali legati alle braccia incrociate dietro la schiena, Henry fu legato dagli stessi esecutori nell’identico modo. Le caviglie si toccavano, impedendogli di avanzare: ‘Per Dio! queste corde sono troppo strette, non si può camminare, gridò, dopo aver lanciato lo stesso grido urlato in Corte di Assise: ‘Compagni, coraggio. Viva l’anarchia!’. Tutti gli spettatori erano stupefatti del modo in cui quelle corde lo stringevano: Henry rotolava più che camminare, tanto erano strette”. (E. Lephay, “Un précurseur”, in “Le Libertaire” n. 28, 23-29 maggio 1896). Lo stesso giorno, sei anarchici sono fucilati a Montjuich (Spagna) per l’attentato contro il maresciallo Martinez Campos. 24 maggio. Dopo una falsa inumazione nel cimitero di Ivry, i resti di Émile Henry sono inumati a Brévannes. “Nel momento in cui la bara stava per essere posta nella fossa, Michaut, commissario di polizia di Gentilly, incaricato della constatazione legale, si era avvicinato e pronunciò le parole: ‘Poiché nessuno vi si oppone, il corpo sarà donato alla Facoltà di Medicina’. L’autopsia fatta dai medici della Facoltà ha dato luogo ad osservazioni che sono state comunicate alla stampa”. (“Le Petit Parisien” 3 giugno 1894). Conviene qui citare quell’avvoltoio di Henri de Rothschild che, sotto il prudente pseudonimo di André Pascal, ha fornito la spiegazione di questa storia: “(\dots{}) Paul Poirier era stato nominato professore di anatomia alla Facoltà di Medicina, quando un’altra sventura, di tipo criminale, apportò qualche scossa nel laboratorio del maestro (\dots{}). Era nel 1894. Era stato trasportato alla Facoltà di Medicina il corpo di un anarchico, Émile Henry, emulo del celebre Ravachol, ghigliottinato la mattina stessa sulla piazza della Roquette. Il professor Poirier lo richiese per il suo laboratorio, come si era prenotato quello di Pranzini, qualche anno prima. Immediatamente, insieme a tre miei compagni, fui incaricato di prelevare sul cadavere dei frammenti anatomici di ogni tipo, destinati a dissezioni e preparazioni, che dovevano arricchire il museo della Facoltà. Già da due buone ore, eravamo occupati ad un lavoro abbastanza singolare, quando una comunicazione venne a disturbare il ‘Capo’. La prefettura di polizia lo informava che la famiglia del ghigliottinato aveva richiesto il suo corpo e che occorreva rinviarlo immediatamente all’obitorio, dove lo si doveva mettere nella bara. Poirier si era precipitato nel laboratorio dove stavamo lavorando: ‘Alt, ragazzi!’ disse col suo tono di comando, ‘dobbiamo restituire Henry alla sua famiglia!’ e ci diede l’ordine di aggiustare tutti i danni che avevamo fatto, procurandoci su altri cadaveri quello che mancava già al corpo dell’anarchico. Per due ore, dovemmo dedicarci ad un vero lavoro di rammendo per fare scomparire il saccheggio commesso con i nostri scalpelli. Fu così che restituimmo alla sua famiglia il corpo di Henry, aggiustato in modo così brillante che nessuno poté immaginarsi gli oltraggi che aveva subito. Sic itur ad astra!”. (A. Pascal [Henri de Rothschild], \emph{Pranzini}: \emph{le crime de la rue Montaigne}, Paris 1933). Aggiungiamo che questo Poirier, che organizzava per la Scuola Pratica di Anatomia un museo, in particolare una collezione di tatuaggi prelevati sui cadaveri destinati all’insegnamento, aveva pensato, nel 1887, “di resecare trenta o quaranta centimetri quadri della pelle della schiena di Pranzini, per trasformare questo cuoio umano in portafoglio”. (\emph{Ibidem}). Meno di un mese dopo l’esecuzione di Henry, il 18 giugno, il prefetto di Lione riceve dal Ministero dell’Interno un telegramma confidenziale: “Si apprende che è stata ora conclusa una tacita intesa tra anarchici e socialisti per fare una contro-manifestazione al momento del passaggio del presidente della Repubblica a Lione. Si tratterebbe anche di accogliere il presidente con le grida di ‘Viva Henry’ e il canto della Carmagnola”. Sei giorni dopo, a Lione, “Carnot l’Assassino” o “l’iningrassabile pecari dell’Eliseo” (“La Revue Libertaire”) è liquidato da Caserio. Un manifesto pubblicato all’indomani dell’esecuzione Valliant si intitolava appunto “A Carnot l’Assassino”: “Questo manifesto contiene le ingiurie più volgari nei confronti del presidente della Repubblica”. (“Le Petit Journal”, 20 febbraio 1894). \chapter{Lettera ai compagni de “L’Endehors”} Compagni de “L’Endehors”, Leggo nel vostro ultimo numero un articolo del compagno Malatesta, intitolato “Un po’ di teoria”. [Vedi \emph{Appendice}]. Vi prego di voler inserire queste poche righe di riflessioni personali in merito. Il compagno Malatesta, dopo aver sviluppato l’imminenza e la necessità di una rivoluzione violenta, e considerato che il ruolo degli anarchici è di contribuire alla sua prossima venuta, dice che “ogni atto di propaganda o di realizzazione, con la parola o con il fatto, individuale o collettivo, è bene quando serve ad avvicinare e facilitare la Rivoluzione\dots{}”. Parlando poi di atti di rivolta ispirati dall’odio risultante da lunghe sofferenze subite dal proletariato, Malatesta aggiunge che comprende e perdona questi atti, ma che: “Una cosa è comprendere e perdonare, un’altra rivendicare. Questi non sono atti che possiamo accettare, incoraggiare, imitare. Dobbiamo essere risoluti ed energici, ma dobbiamo cercare di non oltrepassare mai il limite imposto dalla necessità. Dobbiamo fare come il chirurgo che taglia quando è necessario, ma evita di infliggere inutili sofferenze\dots{}”. Farò osservare al compagno Malatesta che questa parte del suo articolo è per lo meno strana per la penna di un anarchico. In effetti, cosa vogliono gli anarchici? L’autonomia dell’individuo, lo sviluppo della libera iniziativa, che, sole, potranno assicurargli la felicità; se diventa comunista, è per semplice ragionamento, perché comprende che solo attraverso la felicità di tutti, liberi e autonomi, come lui, troverà la sua propria. E tuttavia, cosa vuole Malatesta? Restringere questa iniziativa, intaccare questa autonomia, dichiarando che gli atti di un uomo – per quanto sincero e convinto egli sia – non sono da accettare, né rivendicare, quando superano il limite imposto dalla necessità. Ma chi dunque può giudicare quando il limite è stato superato? Chi può garantire che tale atto è utile alla Rivoluzione, mentre tale altro le nuoce? Dovranno forse i futuri Ravachol, prima di rischiare la propria testa nella lotta, sottomettere i loro progetti all’accettazione dei Malatesta eretti a Gran Tribunale, che giudicheranno l’opportunità o l’inopportunità degli atti? Diciamo al contrario questo: Quando un uomo, nella società attuale, diventa un ribelle cosciente del suo atto, – e tale era Ravachol – è perché il suo cervello ha fatto un lavoro di deduzione che abbraccia tutta la sua vita, analizzando le cause delle sue sofferenze; lui solo può giudicare se ha ragione o torto di provare odio, di essere selvaggio, “e perfino feroce”. Noi stimiamo, per quanto ci riguarda, che gli atti di rivolta brutale come quelli che si sono verificati, e che sono all’origine della polemica esistente tra “anarchici” e “terroristi” – stile Merlino – stimiamo, dicevo, che questi atti sono giusti, perché risvegliano la massa, la scuotono come una violenta frustata, e le mostrano il lato vulnerabile della Borghesia, ancora tutta tremante al momento in cui il Ribelle cammina verso il patibolo\dots{} Capiamo perfettamente che tutti gli anarchici non abbiano il temperamento di un Ravachol. Ognuno di noi ha una fisionomia e delle attitudini speciali che lo differenziano dai suoi compagni di lotta. Perciò non ci stupiamo di vedere dei rivoluzionari fare ogni sforzo su un punto preciso per esempio, come i compagni Merlino e Malatesta, sul raggruppamento dei proletari in associazioni bene organizzate. Ma non riconosciamo loro il diritto di dire: “Solo la nostra propaganda è quella buona; fuori da essa non vi è salvezza”. È un vecchio rimasuglio di autoritarismo che non vogliamo sopportare, e faremmo presto a dividere la nostra causa da quella dei pontificatori o aspiranti tali. Inoltre, il compagno Malatesta ci dice che l’odio non genera l’amore. Noi gli rispondiamo che è l’amore che genera l’odio. Più amiamo la libertà e l’eguaglianza, più dobbiamo odiare tutto ciò che si oppone al fatto che gli uomini siano liberi ed eguali. Sicché, senza perderci nel misticismo, poniamo il problema nel campo della realtà e diciamo: È vero che gli uomini non sono che il prodotto delle istituzioni; ma queste istituzioni sono cose astratte che esistono solo fintanto che ci sono uomini in carne ed ossa per rappresentarle. Non c’è quindi che un modo per colpire le istituzioni; cioè colpire gli uomini; ed accogliamo con felicità tutti gli atti energici di rivolta contro la società borghese, perché non perdiamo di vista il fatto che la Rivoluzione non sarà che la risultante di tutte queste Rivolte particolari. Compagni, l’argomento comporterebbe lunghi sviluppi, ma spero che queste poche righe basteranno per far riflettere i compagni capaci di farsi influenzare da un nome conosciuto come quello di Malatesta. A voi e all’Anarchia! \begin{flushright} Émile Henry \end{flushright} [Pubblicato su “L’Endehors” n. 69, 28 agosto 1892] \chapter{Lettera al direttore della Concergerie} Signor Direttore, Nel corso della visita che avete fatto nella mia cella domenica 18 corrente, avete avuto con me una discussione, d’altronde molto amichevole, sulle idee anarchiche. Vi siete molto stupito; mi avete detto, di conoscere le nostre teorie sotto un aspetto nuovo per voi, e mi avete chiesto di riassumervi per iscritto la nostra conversazione, al fine di ben conoscere ciò che vogliono i compagni anarchici. Vi sarà facile comprendere, Signore, che in poche pagine non si può sviluppare una teoria che analizza tutte le manifestazioni della vita sociale attuale, le studia come un medico ausculta un corpo malato, le condanna perché sono contrarie alla felicita dell’umanità e, al loro posto, costruisce una vita tutta nuova, basata su princìpi completamente antagonisti di quelli sui quali è costruita la vecchia società. D’altronde, altri hanno già fatto ciò che mi chiedete di fare. I Kropotkin, i Reclus, i Sébastien Faure, [una riga illeggibile] le loro idee, e hanno portato avanti il loro sviluppo il più lontano possibile. Leggete \emph{Evoluzione e rivoluzione} di Reclus [Libreria Editrice Sociale, Milano s.d.]; \emph{La morale anarchica} [La Fiaccola, Ragusa 1994], \emph{Parole di un ribelle} [Edizioni Anarchismo, Trieste 2012], \emph{La conquista del pane} [Edizioni Anarchismo, Trieste 2008] di Pëtr Kropotkin; \emph{Autorità e libertà}, \emph{Il macchinismo e le sue conseguenze} di Sébastien Faure; \emph{La società morente e l’anarchia} di Grave [F. Serantoni Editore, Firenze-Roma 1907]; \emph{Fra contadini} di Malatesta [La Fiaccola, Ragusa 1972]; leggete ancora quei numerosi opuscoli, quegli innumerevoli manifesti che, da quindici anni, sono apparsi volta per volta, ognuno sviluppando idee nuove, secondo quanto lo studio o le circostanze suggerivano ai loro autori. Leggete tutto ciò, e allora potrete farvi un giudizio più o meno valido sull’Anarchia. E tuttavia, guardatevi bene dal credere che l’Anarchia sia un dogma, una dottrina inattaccabile, indiscutibile, venerata dai suoi adepti come il Corano dai musulmani. No, la libertà assoluta che noi rivendichiamo, sviluppa incessantemente le nostre idee, le eleva verso orizzonti nuovi (secondo i cervelli dei vari individui) e le getta fuori dai quadri stretti di ogni regolamentazione e di ogni codificazione. Noi non siamo dei “credenti”, noi non ci inchiniamo né davanti a Reclus, né davanti a Kropotkin, noi discutiamo le loro idee, noi le accettiamo quando sviluppano nei nostri cervelli delle impressioni positive, ma le respingiamo quando non fanno vibrare niente in noi. Noi siamo lungi dal possedere la fede cieca dei collettivisti [All’epoca, venivano chiamati “collettivisti” i socialisti parlamentari, ndr], che credono in una cosa, perché Guesde ha detto che dovevano crederci, e che hanno un catechismo di cui sarebbe sacrilegio discutere i paragrafi. Avendo ben stabilito questo, cercherò di svilupparvi, brevemente e rapidamente, ciò che intendo, io, per Anarchia, senza per questo impegnare altri compagni che, su certi punti, possono avere opinioni diverse dalle mie. Voi non contesterete il fatto che oggi il sistema sociale è cattivo, e la prova è che ognuno ne soffre. Dallo sventurato vagabondo senza pane, e senza casa, che conosce la fame in modo costante, fino al miliardario, che teme sempre una rivolta di morti-di-fame che turbi la sua digestione, tutta l’umanità prova l’angoscia. Ebbene! su quali basi riposa la società borghese? Fatta astrazione dai princìpi di famiglia, di patria e di religione, che ne sono solo dei corollari, possiamo affermare che le due pietre di volta, i due princìpi fondamentali dello stato attuale sono l’Autorita e la Proprietà. Non voglio dilungarmi maggiormente su questo argomento. Mi sarebbe facile dimostrare che tutti i mali di cui soffriamo derivano dalla proprietà e dall’autorità. La miseria, il furto, il crimine, la prostituzione, le guerre, le rivoluzioni, altro non sono che le risultanti di questi due princìpi. Quindi, essendo cattive le due basi della Società, non c’è da esitare. Non bisogna cercare un mucchio di palliativi (vedi socialismo) che non servono ad altro che a spostare il male; occorre distruggere i due germi viziosi, ed estirparli dalla vita sociale. È per questo che noi, anarchici, vogliamo sostituire la proprietà individuale col Comunismo, e l’autorità con la Libertà. Quindi, non più titoli di possesso né titoli di dominazione: eguaglianza assoluta. Quando diciamo eguaglianza assoluta, non pretendiamo che tutti gli uomini debbano avere uno stesso cervello, stessa organizzazione fisica; noi sappiamo benissimo che vi sarà tra gli uomini sempre la più grande diversità di attitudini cerebrali e corporali. È proprio questa varietà di capacità che realizzerà la produzione di tutto ciò che è necessario all’umanità, e contiamo anche su questa per mantenere lo spirito d’iniziativa in una società anarchica. Ci saranno ingegneri e manovali, è evidente, ma senza che l’uno abbia una qualunque superiorità sull’altro; perché il lavoro dell’ingegnere non servirebbe a niente senza il concorso del manovale, e viceversa. Essendo ognuno libero di scegliere il mestiere che farà, non ci saranno altro che esseri che obbediranno senza costrizioni alle inclinazioni che la natura ha posto in loro (garanzia di buona produzione). Qui si pone una questione. E i pigri? Ognuno vorrà lavorare? Noi rispondiamo: sì, ognuno vorrà lavorare, ed ecco perché: Oggi, la media della giornata di lavoro è di 10 ore. Molti operai sono occupati in lavori assolutamente inutili alla Società, in particolare agli armamenti militari di terra e di mare. Molti sono anche colpiti dalla disoccupazione. Aggiungete a questo un numero considerevole di uomini validi che non producono nulla: soldati, preti, poliziotti, magistrati, funzionari, ecc. Si può quindi affermare, senza essere tacciati di esagerazione, che su cento individui capaci di produrre un lavoro qualunque, cinquanta solamente forniscono uno sforzo veramente utile alla Società. Sono questi cinquanta che producono tutta la ricchezza sociale. Da qui la deduzione che se tutti lavorassero, la giornata di lavoro, invece di essere di 10 ore, scenderebbe a 5 solamente. Consideriamo inoltre che, allo stato attuale, il totale dei prodotti manufatti è di quattro volte più alto, e il totale dei prodotti agricoli tre volte più considerevole della quantità necessaria ai bisogni dell’umanità; cioè un’umanità tre volte più numerosa sarebbe vestita, alloggiata, riscaldata, nutrita, in poche parole avrebbe soddisfatti tutti i suoi bisogni, se lo spreco e altre molteplici cause non venissero a distruggere questa sovrapproduzione. (Troverete questa statistica dei prodotti nel piccolo opuscolo: \emph{I prodotti della Terra e i prodotti dell’Industria}). Da quanto precede possiamo quindi dedurre la seguente conclusione: Una società in cui ognuno collaborasse al lavoro comune, e che si accontentasse di una produzione che non superasse enormemente i suoi consumi (l’eccesso del primo sulla seconda dovrebbe costituire una piccola riserva), dovrebbe chiedere ad ognuno dei suoi membri validi uno sforzo di sole due o tre ore, forse anche meno. Chi allora rifiuterebbe di dare una cosi piccola quantità di lavoro? Chi vorrebbe vivere con la vergogna di essere disprezzato da tutti e considerato un parassita? La proprietà e l’autorità, che vanno sempre insieme, si sostengono una con l’altra, per tenere schiava l’umanità! Che cos’è il diritto di proprietà? È un diritto naturale? È legittimo che uno mangi mentre l’altro digiuni? No, la Natura creandoci, ci fece degli organismi simili, e uno stomaco di manovale esige le stesse soddisfazioni di uno stomaco di finanziere. E tuttavia, oggi, una classe ha accaparrato tutto, rubando all’altra classe non solo il pane del corpo, ma ancora il pane dello spirito. Sì, in un secolo che viene chiamato di progresso e di scienza, non è doloroso pensare che milioni di intelligenze, avide di sapere, si trovino nell’impossibilità di sbocciare? Quanti figli del popolo, che sarebbero forse diventati uomini di alto valore, utili all’umanità, non sapranno mai null’altro che le poche nozioni indispensabili inculcate loro dalla scuola elementare! La proprietà, ecco il nemico della felicità umana perché crea la diseguaglianza e, perciò, l’odio, l’invidia la rivolta cruenta. L’autorità, dal canto suo, non è che la sanzione della proprietà. Essa viene a mettere la forza al servizio della spoliazione. Ebbene! essendo il lavoro un bisogno naturale, convenite con me, Signore, che nessuno sfuggirà alla domanda di uno sforzo tanto minimo come quello di cui abbiamo parlato più sopra. (Il lavoro è un bisogno così naturale che la Storia ci mostra uomini di Stato che si tolgono con felicità dalle preoccupazioni della politica per lavorare come semplici operai. Per citare solo due esempi ben noti: Luigi XVI faceva il fabbro; ai nostri giorni, Gladstone, “the great old man”, approfitta delle sue vacanze per abbattere egli stesso alcune querce delle sue foreste, come un semplice boscaiolo). Vedete dunque bene, Signore, che non sarà necessario ricorrere ad una legge per evitare la pigrizia. Se, per un caso straordinario, qualcuno volesse tuttavia rifiutare l’aiuto ai suoi fratelli, sarebbe sempre meno costoso nutrire quello sventurato, che mantenere legislatori, magistrati, poliziotti e guardiani per domarlo. Molte altre questioni si pongono, ma sono di ordine secondario; l’importante era stabilire che la soppressione della proprietà, la “presa nel mucchio”, non porterebbe ad un arresto della produzione in seguito ad uno sviluppo della pigrizia, e che la Società anarchica saprebbe nutrirsi e soddisfare tutti i suoi bisogni. Tutte le altre obiezioni che si potrebbero sollevare saranno facilmente confutate ispirandosi a questa idea: un ambiente anarchico svilupperà in ognuno dei suoi membri la solidarietà e l’amore dei suoi simili, perché l’uomo saprà che lavorando per gli altri lavorerà contemporaneamente per sé. Un’obiezione che pare più fondata è questa: Se nessuna autorità esiste più, se non c’è la paura del gendarme per arrestare il braccio dei criminali, non rischiamo di vedere i delitti ed i crimini moltiplicarsi in proporzione spaventosa? La risposta è facile: Possiamo classificare i crimini commessi oggi in due categorie principali: i crimini per interesse e i crimini passionali. I primi scompariranno da sé, perché non ci sarà più motivo per questi delitti, legati alla proprietà, in una società che ha soppresso la proprietà. In quanto ai secondi, nessuna legislazione può impedirli. Lungi da questo, la legge attuale, che assolve il marito che assassina sua moglie colpevole di adulterio, non fa che favorire la frequenza di questi crimini. Al contrario, una società anarchica eleverà il livello morale dell’Umanità. L’uomo comprenderà che non ha nessun diritto su una donna che si dà ad un altro, poiché questa donna non fa che obbedire alla propria natura. Di conseguenza i crimini, nella futura società, diventeranno sempre più rari, fino a che scompariranno completamente. Vi riassumo, Signore, il mio ideale di una società anarchica. – Non più autorità, molto più contraria alla felicità dell’umanità di qualche eccesso che si potrebbe produrre agli inizi di una società libera. Al posto dell’organizzazione attuale, raggruppamenti di individui per simpatia ed affinità, senza leggi e senza capi. – Non più proprietà individuale; messa in comune dei prodotti; lavoro di ognuno secondo i suoi bisogni, consumo di ognuno secondo i suoi bisogni, cioè, secondo volontà. – Non più famiglia, egoista e borghese, che rende l’uomo proprietà della donna, e la donna proprietà dell’uomo; che esige da due esseri che si sono amati un momento, di essere legati l’uno all’altro fino alla fine dei loro giorni. La Natura è capricciosa, chiede sempre nuove sensazioni. Vuole l’amore libero. Ecco perché vogliamo l’unione libera. – Non odio tra fratelli, non più patrie, che gettano gli uni sugli altri degli uomini che non si sono nemmeno mai visti. Sostituzione dell’attaccamento gretto e meschino dello sciovinista alla sua patria, con l’amore ampio e fecondo dell’Umanità intera, senza distinzione di razza né di colore. – Non più religioni, forgiate dai preti per degradare le masse e dar loro la speranza di una vita migliore, mentre essi stessi godono della vita terrestre. Al contrario, sviluppo continuo delle scienze, messe alla portata di ogni essere che si sentirà attratto verso il loro studio, portando a poco a poco tutti gli uomini ad una coscienza del materialismo. Studio particolare dei fenomeni ipnotici che la scienza comincia ora a constatare, al fine di smascherare i ciarlatani che presentano agli ignoranti, sotto una luce meravigliosa e soprannaturale, dei fatti di ordine puramente fisico [“Egli (Fortuné Henry, fratello di Émile) ci raccontò che lui e suo fratello erano stati spiritisti prima di diventare anarchici”. (J. Grave, \emph{Le Mouvement libertaire sous la III République}, Paris 1930)]. – In un parola, niente più intralci al libero sviluppo della natura umana. Libero sviluppo di tutte le facoltà fisiche, cerebrali e mentali. Che una Società con tali basi arrivi subito all’armonia perfetta, non sono abbastanza ottimista per sperarlo. Ma ho la profonda convinzione che due o tre generazioni basteranno per strappare l’uomo all’influenza della civiltà artificiale che subisce oggi, e per riportarlo allo stato di natura, che è lo stato di bontà e di amore. Ma per fare trionfare questo ideale, per creare una società anarchica su basi solide, occorre incominciare col lavoro di distruzione. Occorre gettare a terra il vecchio edificio tarlato. È quello che facciamo. La borghesia sostiene che non arriveremo mai al nostro scopo. L’avvenire, un avvenire ben vicino, glielo dimostrerà. Viva l’Anarchia! \bigskip (27 febbraio 1894) \begin{flushright} Émile Henry \end{flushright} \chapter{Il processo} Giustizia Criminale – Corte di Assisi della Senna Presidenza del signor Potier, consigliere \bigskip Attentati dell’Hotel Terminus e della rue des Bons-Enfants Assassinii – Distruzione di edificio con l’aiuto di materie esplosive \section{Udienza del 27 aprile} Le misure di ordine, abituali per i grandi processi criminali, sono state prese sia all’interno che all’esterno del Palazzo di giustizia. Numerosi agenti stazionano nelle piazze circostanti l’edificio; altri si tengono vicino ad ogni porta, ispezionano con cura ogni persona che entra. Il fatto che il collegio dei giurati della Senna è chiamato oggi ad ascoltare presenta una gravità eccezionale. I crimini imputati all’accusato hanno provocato la più legittima e la più profonda emozione. Forse più di tutte le altre imprese dello stesso tipo, sottoposte precedentemente ai tribunali di repressione, queste costituiscono ciò che si chiama l’attentato anarchico, cioè la violenza odiosa quanto terribile ispirata dall’odio cieco della società, perpetuata senza discernimento né ragione, portando ferite e morte a caso, tra una folla di gente sconosciuta, di donne e di bambini, con l’aiuto di strumenti di distruzione di una potenza inaudita. Questa volta l’accusato non è un uomo volgare, la cui educazione elementare sia stata trascurata. È intelligente, istruito. Fin dalla sua infanzia si è visto circondato della benevolenza di tutti: borsista alla scuola J.-B. Say, ammesso all’École Polytechnique. Ci si domanda quale deplorevole miraggio lo abbia fatto rinunciare all’avvenire assicurato che si apriva davanti a lui, per farne un adepto delle detestabili dottrine che disonorano la nostra epoca. Alle undici e mezzo, il settore dell’aula d’assise riservato al pubblico è invaso da un pubblico elegante, nel quale vi sono molte signore. I testimoni, i membri del foro e i giornalisti occupano i posti a loro destinati. Dietro la corte sta un gran numero di magistrati. L’aula offre un aspetto insolito. Il tavolo riservato ai corpi di reato è carico di pacchetti di vestiti e biancheria macchiati di sangue che sono appartenuti sia all’accusato Émile Henry che alle vittime delle esplosioni. Dei tovaglioli annodati contengono dei detriti provenienti dai rivestimenti di legno e dai pavimenti del Café Terminus. Si notano anche diverse marmitte in ghisa simili a quella deposta presso la sede amministrativa delle miniere di Carmeaux, avenue de l’Opéra. Intorno al tavolo vi sono delle sedie, dei tavoli in marmo spaccati al momento dell’esplosione del Café Terminus. Una piccola scatola contiene dei pezzi di ghisa estratti dalla ferita del signor van Herrenweghen, una delle persone colpite al Café Terminus. A mezzogiorno meno un quarto, la Corte entra in seduta. Su richiesta dell’avvocato generale signor Bulot, ordina l’aggiunta di un consigliere assessore e di due giurati supplementari. Dopo una breve sospensione dedicata al sorteggio dei giurati, l’udienza si apre a mezzogiorno. Le guardie portano l’accusato. È un giovane di ventidue anni, dalla fisionomia fine e dolce, dal colorito pallido e smunto. I capelli castani sono tagliati a spazzola. Una leggera barba bionda orna il mento. Seduto al banco degli accusati, la schiena appoggiata contro la balaustra, ostenta un sorriso indifferente. È vestito di nero. L’avvocato generale signor Bulot occupa il posto del pubblico ministero. L’avvocato Hornbostel è seduto al banco della difesa. Alle domande d’uso, che gli sono poste dal presidente, l’accusato dichiara di chiamarsi Henry (Émile-Joseph-Félix), nato il 26 settembre 1877 a Saint-Marin presso Barcellona (Spagna), impiegato, domiciliato alla Conciergerie. Per i due crimini distinti addebitati a Émile Henry, sono stati redatti due atti di accusa. Il cancelliere signor Wilmès ne dà lettura. Questi documenti sono cosi formulati: \section{Il Café Terminus} L’accusato è nato in Spagna, dove suo padre si era rifugiato dopo gli avvenimenti del 1871, ai quali aveva partecipato attivamente. Nel 1882, dopo l’amnistia, i suoi genitori tornarono in Francia. Ricevette un’educazione completa, si presentò agli esami dell’École Polytechnique ma non riuscì nella seconda parte della prova. Entrò allora nella ditta di un ingegnere-costruttore che lo inviò a Venezia per cooperare a dei lavori pubblici di cui era imprenditore. Dopo soli tre mesi, lasciò una posizione che poteva assicurare la sua carriera. Tornato a Parigi, trovò in una ditta di commercio un impiego a 125 franchi al mese. In quel periodo divenne, secondo la sua espressione, un anarchico deciso. La superiorità della sua istruzione gli fece acquisire in poco tempo una certa notorietà tra i “compagni”. Il 30 maggio 1892, in seguito ai primi attentati anarchici, fu arrestato, ma non tardò ad essere rimesso in libertà. Poco tempo dopo, il suo padrone, che lo vedeva fare propaganda tra i suoi colleghi, decise di licenziarlo. Dopo la sua partenza, scoprì nel suo ufficio dei manoscritti relativi alla fabbricazione degli esplosivi e una specie di manuale intitolato: \emph{Anarchia pratica}, che iniziava con questa parole: “Preghiamo i compagni di esercitarsi in queste fabbricazioni”. Dopo aver collaborato per qualche tempo all’amministrazione del giornale “L’Endehors”, l’accusato entra come impiegato alle scritture presso il signor Dupuy, scultore-decoratore. All’indomani dell’esplosione della rue des Bons-Enfants, scomparve. Malgrado questa coincidenza stupefacente, nega di aver partecipato a questo attentato. “È partito quindi, disse, per l’Inghilterra, temendo di essere nuovamente arrestato”. Si perdono le sue tracce da quel periodo fino al 20 dicembre scorso. A questa data, si presentò alla Villa Faucheur, rue des Envierges, e affittò una stanza sotto il nome di Louis Dubois. Là si procurò le sostanze necessarie alla fabbricazione di ordigni esplosivi, in particolare dell’acido picrico, e si occupò a preparare una bomba. In una piccola marmitta di metallo, a cui tolse il manico e il bottone che sormontava il coperchio, introdusse un involucro cilindrico di zinco. Tra questo involucro e le pareti svasate della marmitta pose, come dichiarò, 120 palle. Nel cilindro di zinco, ne dispose un altro sensibilmente più piccolo, e riempì di una sostanza esplosiva lo spazio che li separava. Infine, nel più piccolo, mise una cartuccia di dinamite con un innesco al fulminato di mercurio. A questo innesco arrivava una miccia da minatore la cui lunghezza calcolata per bruciare in quindici secondi. Il 12 febbraio, lasciò la sua stanza, dopo aver avvertito il guardiano della villa che non sarebbe rientrato per qualche giorno. Vi lasciava, secondo la sua dichiarazione, tre chili e mezzo di acido picrico. Portava con sé la bomba, secondo l’esempio di Vaillant, nella cintura dei pantaloni. Era munito di un revolver carico di cui aveva masticato le pallottole, al fine, disse, di fare più male, e di un pugnale, di cui aveva cercato di avvelenare la lama. Così armato, si diresse verso l’avenue de l’Opéra, gettò un’occhiata al ristorante Bignon, poi al Café Americano, poi al Café de la Paix, ma in nessuno di questi locali trovò un numero sufficiente di vittime, e continuò la sua strada. Al Café Terminus, dove arrivò verso le otto e mezzo, la folla era particolarmente stretta intorno ad un palco dove l’orchestra suonava. Entrò, si sedette davanti ad un tavolino posto molto vicino alla porta e chiese una birra che pagò in anticipo. Se ne fece servire presto una seconda con un sigaro che pagò ugualmente appena gli furono portati. Attendeva che il pubblico fosse ancora più numeroso. Alle nove, avvicinò il suo sigaro acceso all’estremità della miccia, poi si alzò e raggiunse la porta da cui una piccolissima distanza lo divideva. Allora si girò e lanciò la bomba in direzione dell’orchestra. L’ordigno incontrò il lampadario, ruppe uno dei tulipani di cristallo, e cadde a terra spandendo un fumo spesso e acre. Qualche secondo dopo, scoppiò con una detonazione sorda, sfondando il pavimento e ferendo diciassette persone. L’assassino prese la fuga gridando: “Ah! Il miserabile, dov’è?”. Fu immediatamente rincorso dal cameriere Tissier e da due consumatori che lo avevano visto lanciare l’ordigno. Il vigile urbano Poisson, che era di servizio al rifugio posto di fronte al caffè, si lanciò anch’egli dietro di lui. All’angolo della rue du Havre e della rue d’Isly, un impiegato della Compagnia dell’Ovest, il signor Etienne, lo raggiunse e gli mise la mano sulla spalla dicendogli: “Ti tengo, canaglia!”. “Non ancora!”, rispose l’accusato, che gli tirò un colpo di pistola in pieno petto. La pallottola fortunatamente si schiacciò su un bottone e non penetrò, ma Etienne cadde, svenuto. Il signor Maurice, parrucchiere, lo prese a sua volta, un po’ più lontano. Un secondo colpo di pistola lo gettò a terra, procurandogli una ferita delle più serie. In quel momento arrivava il vigile urbano Poisson. L’accusato lo prese di mira ma lo mancò e continuò la sua corsa. Poisson tirò fuori la sciabola e riprese l’inseguimento. Guadagnava terreno, quando un colpo d’arma da fuoco lo raggiunse al petto. Rimasto in piedi, alzò il braccio per colpire, ma l’accusato scaricò su di lui gli ultimi due colpi della sua pistola. Una delle pallottole colpì il fianco destro; l’altra si perse nel portafogli dell’agente. Questi si precipitò sull’accusato e cadde con lui. Altri agenti sopraggiunsero nel momento in cui Poisson perdeva conoscenza. Si impadronirono di Henry, che dovettero proteggere contro il furore dei presenti. Nel corso dell’interrogatorio, Henry, che aveva prima preso il falso nome di Breton, non ha manifestato nessun pentimento per questa serie di atti criminali. Egli ha, al contrario, espresso davanti ad una delle sue vittime, il signor Etienne, il rimpianto di aver fatto uso di un revolver difettoso e di aver diminuito la forza della sua bomba chiudendo male il coperchio della marmitta. L’esperto incaricato dal giudice istruttore ha dichiarato che l’ordigno progettato da Henry era “combinato e costruito in modo tale da dare la morte cadendo in mezzo alla folla, e da distruggere parzialmente l’edificio nel quale sarebbe stato lanciato”. Come tutti gli anarchici, afferma di aver agito sotto la spinta di una decisione puramente personale. Tuttavia, nonostante l’atto istruttorio non stabilisca alcuna complicità legalmente caratterizzata, risulta che altri anarchici conoscevano i suoi progetti. Infatti, nella mattinata del 14 febbraio, il guardiano della Villa Faucheur constatò che la porta della stanza di Henry era stata aperta con scasso. Il commissario di polizia, chiamato sul posto, scoprì una miccia da minatore, delle pallottole di piombo e una piccola quantità di polvere verde. Nella stufa si trovavano ceneri di carte bruciate. Ora, secondo le dichiarazioni di Henry stesso, aveva lasciato nel suo alloggio tre chili e mezzo di acido picrico che gli dovevano servire per fabbricare dodici o quindici altre bombe, se, come egli contava, sfuggiva alla giustizia, dopo la prima esplosione. È perciò evidente che gli autori dello scasso avevano lo scopo di portar via il resto delle sostanze esplosive che avevano preparato. \section{La rue des Bons-Enfants} Gli uffici della Compagnia delle miniere di Carmaux occupavano l’ammezzato di una casa al n. 11 dell’avenue de l’Opéra. Una seconda porta dà sulla rue d’Argenteuil. L’8 novembre 1892, tra le undici e le undici e mezzo del mattino, il signor Bernick, volendo parlare al capo della contabilità, il signor Bellois, salì le scale senza incontrare nessuno. Nell’angolo a sinistra del pianerottolo, contro la porta, vide un oggetto abbastanza voluminoso che dovette scavalcare per entrare. Qualche istante più tardi, il signor Bellois, che lo riaccompagnava, notò lo stesso pacchetto, constatò che era molto pesante e chiamò il signor Augenard, cassiere, e il fattorino Garin. Si strappò il giornale che lo avvolgeva e che era tenuto da uno spago, e si vide una marmitta di ghisa il cui coperchio capovolto era fissato con una striscia di latta o reggetta attaccata ai due manici. Era posta sul coperchio, col fondo per aria. Il custode Gamier e il fattorino la portarono con precauzione nella rue d’Argenteuil e la deposero sul marciapiede. Un assembramento abbastanza numeroso si formò intorno all’ordigno e varie persone notarono una polvere bianca di cui una parte, molto fine, era sfuggita dagli interstizi del coperchio. Il fattorino chiamò il vigile urbano Cartier, che era incaricato di far attraversare l’avenue de l’Opéra ai bambini che uscivano dalla scuola della rue d’Argenteuil. Cartier, trattenuto dal suo servizio, non poté egli stesso portare via la marmitta, ma in quel momento arrivarono il sotto-brigadiere Formorin e l’agente Réaux, e li mise a conoscenza di quanto avveniva. Il custode diede una borsa, l’ordigno vi fu posto, e Garin, accompagnato da Formorin e Réaux, lo portò verso il commissariato del quartiere del Palazzo Reale. La casa in cui era installato il commissariato è situata in rue des Bons-Enfants. Si compone di un cortile, questo si apre sulla via con un portone. Gli uffici erano al primo piano dell’ala sinistra Erano esattamente le 11,35 quando il sotto-brigadiere, il vigile urbano e Garin entrarono nel cortile. Attraversandolo Garin disse a Réaux: “È pesante, non faresti male a darmi una mano!”. L’agente venne in suo aiuto e tutti e tre presero le scale. Erano passati appena due minuti quando risuonò una detonazione formidabile. Quando si penetrò nel commissariato, ci si trovò davanti ad uno spettacolo di un orrore inesprimibile. Nell’ingresso un cadavere giaceva in mezzo ai detriti, faccia contro terra; i vestiti erano quasi completamente scomparsi; le carni avevano preso un colore grigiastro. Era il vigile Réaux, con le due gambe staccate sotto le ginocchia, le cosce stritolate, il viso e le mani come carbonizzati. Nella sala del pubblico, che seguiva l’ingresso, la distruzione era completa. Là era scoppiato l’ordigno. Il pavimento era sfondato. Era un mucchio di detriti tritati, di pezzi di legno dilaniati, di vestiti e pezzi di carne. Da un lampione a gas fissato al soffitto pendeva un pacco di budella. I muri erano schizzati di sangue. Vicino alla finestra, si camminava letteralmente sui brandelli di carne, di fegato e di polmone. L’esplosione aveva fatto in quella sala quattro vittime: il sotto-brigadiere Formorin, il fattorino Garin, il segretario del commissariato Pousset, il cui corpo aveva appena conservato una forma umana, e l’ispettore Troutot che, malgrado le sue orribili ferite, agonizzava ancora. Morì nel corso della giornata. I primi elementi per l’indagine furono forniti dal giornale che avviluppava l’ordigno. Era il numero del “Temps” del 1° giugno 1892. Si poteva supporre che l’assassino non l’avesse conservato senza motivo, forse conteneva qualche informazione che poteva avere per lui un interesse speciale. Ora, questo numero riportava l’arresto dei fratelli Henry, arresto che aveva avuto luogo il 30 maggio e che era stato mantenuto. L’istruzione stabilì presto che di questi due anarchici uno, Fortuné, era a Bourges, l’8 novembre. I sospetti si fermarono perciò su Émile Henry. Nel mese di luglio, era stato segnalato come dedito a studi di chimica sospetti. L’8 novembre, era uscito dalla casa del suo padrone, il signor Dupuy, verso le dieci e un quarto del mattino, e non vi era tornato che a mezzogiorno. Secondo la signora Dupuy, aveva mostrato un violenta emozione quando il suo padrone era tornato, portando un giornale che rendeva conto della catastrofe. All’indomani, si era detto ammalato, e, il 10 novembre, alle quattro, lasciava l’ufficio col pretesto di andare a farsi curare da sua madre. Invece di andare a Brévannes, partiva per Londra, da dove incaricava due o tre giorni dopo di imbucare, a Orléans, una lettera destinata al signor Dupuy. In questa lettera dichiarava che, benché estraneo al crimine della rue des Bons-Enfants, “non aveva affatto intenzione di fare mesi di detenzione preventiva prima dell’arresto dei veri autori dell’esplosione”. Malgrado tutte queste circostanze sospette, non esistevano contro di lui indizi positivi. E anche le prime verifiche, alle quali si era proceduto sul suo orario durante la mattinata dell’8 novembre potevano essergli favorevoli. Partito verso le dieci dalla rue de Rocroi, vi era di ritorno verso mezzogiorno, dopo aver fatto le commissioni di cui era stato incaricato, in rue Tronchet e boulevard de Courcelles; le distanze sono notevoli e, a meno di una rapidità del tutto eccezionale, si poteva pensare che, in questo intervallo di due ore, gli sarebbe mancato il tempo per portare la bomba in avenue de l’Opéra. Arrestato dopo il delitto del Café Terminus, invocò questo alibi e persistette nei suoi dinieghi fino al 23 febbraio. Ma in quella data, messo a confronto con altri anarchici sospettati di aver partecipato all’attentato dell’8 novembre, rinunciò a questo sistema e dichiarò di essere il solo colpevole. Diede in seguito delle spiegazioni dettagliate sulla progettazione ed il compimento del suo delitto. Aveva deciso di provare ai minatori di Carmaux, sfruttati da ambiziosi, che solo gli anarchici erano capaci di dedizione. Una sera, si recò al n. 11 dell’avenue de l’Opéra e si assicurò, leggendo l’iscrizione incisa su una targa, che la Compagnia aveva lì i suoi uffici. La porta era chiusa e non poté entrare nell’edificio per studiarne la disposizione. Poco dopo, vi ritornò in pieno giorno e salì fino ai piani superiori. Così informato, si occupò della costruzione dell’ordigno. Possedeva venti cartucce di dinamite di cui rifiuta di far conoscere la provenienza e decide di fabbricare una bomba a rovesciamento. Per fare il detonatore, si procurò dalla signora Colin, cartaia, 107, rue La Fayette, un astuccio di metallo del prezzo di 1,50 F. Il 4 novembre, alle sette di sera, comprò nella ditta di prodotti chimici Billaut, place de la Sorbonne, 4 chili di clorato di potassio a 4 F. il chilo. Otteneva uno sconto del 10 per cento dicendosi assistente in una scuola di Saint-Denis, e pagò solo 14,40 F. Aveva chiesto contemporaneamente 100 grammi di sodio, ma per quest’ultimo prodotto non potendo essere maneggiato alla luce, lo si pregò di tornare all’indomani. Il 5 novembre a mezzogiorno, venne a prendere il flacone che pagò 2,65 F. Fabbricò il detonatore secondo un sistema conosciuto. Il rovesciamento dell’ordigno metteva dell’acqua in contatto con il sodio il quale, prendendo fuoco, doveva a sua volta far detonare tre inneschi al fulminato di mercurio. Fatto ciò, comprò dal signor Comte, chincagliere in rue Lepic, una marmitta da 3,30 F. Nel centro, mise il detonatore che circondò con venti cartucce di dinamite, poi riempì lo spazio vuoto con 4 chili di clorato di potassio, mischiati a una eguale quantità di zucchero in polvere. Adattò il coperchio con una reggetta, avendo cura di girarlo. Grazie alla concavità del coperchio, poteva passare la mano sotto la striscia di latta che formava così un manico. L’8 novembre, lasciò il suo ufficio poco dopo le dieci e prese una vettura, per andare in rue Tronchet, dove arrivò verso le dieci e un quarto. Fece in un momento la commissione di cui era incaricato; prese, una seconda vettura e si fece condurre in place Blanche. Erano allora le dieci e mezzo. Raggiunse rapidamente la rue Véron a piedi, prese in un armadio la bomba già pronta, tornò in place Blanche, salì su una terza vettura e si fece condurre in avenue de l’Opéra. Scese ad una certa distanza dal n. 11, ma, siccome era ancora accaldato per la corsa, si fermò davanti ad una boutique dopo aver deposto la bomba sul marciapiede. Dopo un momento, credendosi notato da un custode e avendo fretta di finire, la riprese ed entrò nel vestibolo del n. 11. Incrociò due persone che non gli fecero caso, salì le scale e ridiscese quasi subito dopo aver piazzato l’ordigno all’ingresso degli uffici, il coperchio sotto. Uscito dalla casa, prese una quarta vettura, andò in boulevard de Courcelles, dove arrivò verso le undici e mezzo e, fatta la sua commissione, tornò a piedi in rue de Rocroi. Aveva previsto il caso in cui l’ordigno fosse stato tolto dalla polizia: “Secondo i miei esperimenti, disse nel corso del suo interrogatorio del 24 febbraio, supponevo che la marmitta sarebbe scoppiata cinque o sei minuti dopo essere stata deposta davanti alla porta degli uffici della compagnia di Carmaux, ma non ignoravo che se si fosse presa la marmitta prima dell’esplosione, sarebbe stata portata al commissariato di polizia del quartiere, di modo che, nel caso in cui i ricchi dell’avenue de l’Opéra fossero sfuggiti alla sorte che destinavo loro, ero certo di colpire i poliziotti, ugualmente miei nemici”. Certo è che Henry conosceva la disposizione interna della casa. L’ha descritta molto esattamente e, condotto sui luoghi, si è diretto senza esitazione verso il punto in cui la bomba è stata trovata. La descrizione minuziosa che ha dato dell’ordigno concorda esattamente con l’analisi degli esperti, i signori Vieille e Girard. Non è riconosciuto dal personale della chincaglieria Comte, ma tutte le indicazioni che ha fornito sul negozio, sulla marmitta che ha comperato e sul prezzo sono conformi alla realtà. Lo stesso vale per l’acquisto dell’astuccio di metallo. In quanto ai suoi acquisti fatti in place de la Sorbonne, è provato che alla data e all’ora indicate da lui, la ditta Billaut ha ricevuto un pagamento di 14,40 F. Infine, è dimostrato che l’itinerario seguito da Henry, l’8 novembre, può facilmente essere percorso nelle condizioni che ha precisato. La prova della sua colpevolezza si trova così nettamente stabilita. Essa esce con evidenza dalle constatazioni dell’indagine, che confermano in tutti i punti le dichiarazioni dell’accusato. Il Presidente Potier procede all’interrogatorio dell’accusato. \bigskip Presidente: Accusato, alzatevi. Come vi chiamate? Henry: Émile, ho ventun anni e mezzo. P. Il vostro domicilio? H. Alle Carceri della Conciergerie. P. Il 12 febbraio scorso verso le otto siete andato al Café Terminus? H. Sì, alle otto, non alle otto e mezzo come dice l’atto d’accusa. P. Nascondevate una bomba nella cinta dei calzoni\dots{} H. No. Nella tasca del mio soprabito. Volevate che mi sbottonassi i calzoni in pieno caffè? P. Perché avete scelto il Café Terminus? H. Perché è un caffè frequentato dalla borghesia. La mia prima intenzione era di buttare la bomba in altro ritrovo, sono stato da Bignon e al Café de la Paix, ma non v’era che poco pubblico; l’ora dell’aperitivo di questi signori era già passata. P. Avevate detto all’istruttoria che ne volevate ammazzare il più gran numero possibile. H. E lo confermo anche qui. P. Al Terminus vi siete seduto ordinando una Bock e avete aspettato: quanto, all’incirca? H. Un’ora buona. P. Perché aspettavate? H. Perche vi fossero più avventori. P. E poi? H. Ma lo sapete bene; non ve l’ha anche pochi minuti or sono rammentato l’atto d’accusa quel che è avvenuto di poi? P. Ai giurati voi dovete dirlo perché essi vi giudicheranno. Crollando il capo, quasi a dire che la commedia l’annoia, Henry comincia con aria svogliata: Ho preso dalla tasca la mia bomba e me la sono collocata sulle ginocchia togliendone il giornale che l’avviluppava. Ho acceso al sigaro la miccia e quando ho constatato che prendeva mi sono diretto verso la porta e ho lanciato la bomba nel mezzo della sala. P. Voi, che avete tanto disprezzo della vita degli altri\dots{} H. Dei borghesi soltanto, se vi piace\dots{} P. Avete tutto calcolato per salvar la vostra e metterla al sicuro\dots{} H. È naturalissimo; come avrei potuto coltivare la speranza di ricominciare e di fare magari più vaste applicazioni, se alla prima mi fossi lasciato cogliere? P. Avevate dunque calcolato, meditato ogni circostanza per sfuggire alle conseguenze del vostro attentato? H. E seriamente. Ero nel vano della porta d’entrata quando scagliai la bomba nel bel mezzo della sala. Di lì, a girare inosservato nelle gallerie della stazione di Saint Lazare, montare alla sala d’aspetto, prendere un biglietto qualunque, perdermi tra la folla dei viaggiatori e scendere in rue d’Amsterdam tranquillo, sicuro di poter ricominciare più gagliardamente, non mi pareva né impossibile né difficile. Farla franca per ricominciare subito, non avevo altra preoccupazione. P. I vostri calcoli non sono tornati. Alla porta un cameriere vi ha veduto, e voi slanciandovi innanzi gridando: “Il miserabile, eccolo lì!”, come se voleste dell’attentato inseguire un autore immaginario, avete indarno cercato di ingannarlo. H. Non so che importanza possa avere nel vostro piano d’accusa questo dettaglio, so però che è assolutamente fantastico. P. Vedremo dopo: certo voi fuggivate. Girato l’omnibus che passava vi siete lanciato per la rue du Havre attingendo la rue d’Isly, mentre alle vostre calcagna montava inseguendovi la folla. Un cittadino coraggioso, un impiegato della Compagnia dell’Ovest, vi afferra, vi mette la mano sulle spalle gridandovi: “Ti tengo alla perfine, canaglia!”. H. Un eroe insomma\dots{} P. “Non ancora!”, avete risposto voi\dots{} H. Niente, niente. Nulla di vero nella risposta che mi prestate. P. Gli avete tirato un colpo di rivoltella. Fortunatamente il proiettile s’è schiacciato su di un bottone della giacca, e allora il barbiere Meurice\dots{} H. Secondo cittadino eroe\dots{} P. Meurice cerca di arrestarvi a sua volta e voi\dots{} H. Gli tiro un secondo colpo di rivoltella. P. Erano l’uno e l’altro lavoratori, questi due\dots{} H. Me ne dispiace, ma la colpa è tutta loro. Che c’entravano essi? Perché venivano ad immischiarsi in cose che non li riguardavano? P. Avete detto in istruttoria che se la vostra rivoltella fosse stata migliore li avreste spacciati. H. Ma sicuramente. P. In fondo alla rue d’Isly aveste un po’ d’esitazione. H. Non ho esitato affatto. Ero chiuso in un cerchio, mi sono fermato e quando il poliziotto Poisson, la daga sguainata, mi si è lanciato addosso ho sparato le mie cartucce fino all’ultima. P. Non dico certo che abbiate esitato nell’assassinio. Soltanto nella fuga vi siete indugiato, e l’agente che v’inseguiva dal Terminus vi ha potuto raggiungere. Avete scaricato la rivoltella, ma gli agenti erano diventati moltitudine e hanno coordinato ogni loro sforzo a proteggervi contro l’indignazione della folla. H. Già, già, contro l’indignazione della folla che ignorava il mio attentato. Quando si dice! P. Vi hanno trovato addosso un “pugno americano” e una scatola di cartucce col proiettile scanalato. Con che scopo? H. Tò! Per fare il più gran male possibile. P. Difatti è un pregiudizio antico dei soldati d’Africa. H. Scusate, ma è un’altra cantonata. Non sono mai stato soldato. P. Ne riparleremo tra poco. Avevate anche indosso un pugnale che si credette avvelenato. H. Lo era. L’avevo avvelenato l’anno scorso per colpire un agente provocatore, un sedicente anarchico che aveva denunciato alla polizia e fatto mandare in galera un bravo compagno. Le circostanze non mi hanno favorito, ma dopo dieci o dodici mesi non è da meravigliarsi che il veleno se ne sia andato. P. Se vi fosse riuscito avreste colpito Poisson? All’istruttoria avete deplorato che il colpo vi sia mancato. H. Ho deplorato semplicemente di non aver potuto opporre resistenza più energica. P. Se le circostanze ve lo avessero consentito vi sareste servito del pugnale? H. Senza uno scrupolo né un indugio. P. Veniamo ora all’attentato, Henry; vi sono dettagli che è bene siano precisati. Voi avete lanciato la bomba mirando al centro dell’orchestra. H. Ma l’ho buttata troppo alta e l’ho mandata contro il lampadario facendola cadere in tal modo troppo vicino, dove c’era meno pubblico. P. È vero, più in là avrebbe fatto un maggior numero di vittime, ma venti persone sono state attinte. H. Non ne avete fin qui contate che diciassette nel vostro atto d’accusa. P. Venti, di cui alcune gravemente, una, il signor Borde, rimasta uccisa. H. E vada per venti. P. Avete voluto uccidere? H. Certamente. P. Avete difatti allestito la vostra bomba con cura meticolosa. Vaillant aveva dichiarato che se si fosse proposto d’uccidere non avrebbe caricato di chiodi ma di proiettili la sua macchina infernale. Voi nella vostra avevate caricato centoventi palle. H. È che io non volevo ferire, volevo uccidere. P. Al commissariato di polizia avete detto dapprima di chiamarvi Breton negando di essere l’autore dell’attentato, ma avete soggiunto subito di essere anarchico: “Di borghesi più ne creperà, meglio sarà” avete cinicamente commentato. Davanti al giudice istruttore l’indomani, nelle carceri della Conciergerie avete confessato il delitto, avete descritto minutamente la vostra bomba, ne disegnaste i particolari da vero artista. H. Troppo buono, signor Presidente, non valgo davvero le vostre felicitazioni, perché l’apparecchio era riuscito manchevole, il coperchio non chiudeva bene. P. L’esito non v’ha appagato? Che cosa volevate di più? H. Contavo su una ventina di morti ed una trentina di feriti. La lezione voleva essere severa. Passa un brivido nel pubblico, mentre il Presidente spiega come scoperto il domicilio di Henry la polizia recatasi a perquisirlo l’abbia trovato svaligiato. I compagni dovevano esser passati ben avanti agli sbirri ed aver asportato gli esplosivi rimastivi. P. Molti ne avevate in camera vostra? H. Da confezionare una dozzina di bombe uguali, per lo meno. P. E non avete idea degli amici che sono andati a sottrarli? H. La domanda è indiscreta. Cercateli, quando li avrete scovati e li porterete qui, vi dirò se li conosco. P. Si sta cercando, e si troveranno, forse si è già trovato\dots{} H. Con tutto il rispetto che vi debbo mi permetto di dubitarne. P. Voi siete un cinico. H. Non è cinismo, è convinzione. P. Quanto a convinzione voi siete convinto\dots{} d’aver perpetrato dei delitti. H. Come spirito non c’è male, ma non potete chiamare cinismo quello che è convinzione. P. Al nodo: avete voluto assassinare Etienne che v’inseguiva? H. Sì. P. Avete voluto assassinare Meurice e Poisson che si sforzavano d’arrestarvi? H. Sì. P. Avete voluto uccidere i consumatori al Café Terminus? H. Sì. P. Avete voluto distruggere il Terminus? H. Veramente, la vecchia baracca non mi interessava. P. Ebbene, le cinque domande a cui avete risposto comportano cinque volte la pena capitale. H. Lo so, lo so. E ne basta una, vero? P. Basterebbe, anche se il vostro nome, le vostre generalità rimanessero ignorate e voi non foste che “l’X di Pechino”, come vi siete qualificato al commissario di polizia. Ma è gloria della nostra giustizia rispettare le forme di rito anche sotto l’impeto travolgente della pubblica indignazione, anche in cospetto del criminale più perverso. E la preliminare di queste forme impone la ricerca dell’identità dell’accusato, e la Corte dirà chi sia l’assassino di tanti innocenti. H. Di tanti borghesi, e badate bene, di borghesi innocenti non ve ne sono, comunque vi piaccia qualificarli. P. Era gente in ogni caso quella del Café Terminus verso la quale non avevate personalmente ragione di rancore, voi deplorate soltanto di non averne potuto accopparne di più. Il presidente rintraccia e mette in luce i precedenti di Henry e ad un certo punto gli domanda: ‘Che cosa faceva vostro padre?’ H. Non vi riguarda e non ve lo dirò. P. Era proprietario di cave a Brevanne. Trascinato nella rivoluzione comunalista del 1871 e condannato a morte, emigrò in Spagna donde tornò nel 1881, dopo l’amnistia. Morì l’anno di poi, nel 1882, lasciando vedova vostra madre con tre bambini. È esatto? H. Non vi riguarda. II presidente ricorda che Émile Henry alla scuola Jean-Baptiste Say vinse nel 1888 una borsa di studio che lo ammetteva al Politecnico. P. Non avevate che diciotto anni\dots{} H. Oh, per questo, non ne avevo che sedici e mezzo; ma è un dettaglio senza importanza. P. Non avete persistito: la carriera militare non si confaceva alle vostre aspirazioni\dots{} H. Potete dire che le urtava, intollerabilmente. P. Avete rinunciato alla brillante carriera\dots{} H. Brillante prospettiva davvero: un giorno o l’altro m’avrebbero ordinato di mitragliare un branco di affamati come al tenente Chapu i poveri lavoratori di Fourmies. Grazie tante, preferisco ancora essere qui. Il presidente passa in rassegna diversi impieghi tenuti da Henry. Uno dei suoi zii, il signor Bordenave, lo vuole nella grande industria che egli dirige e lo manda rappresentante della Casa a Venezia con un primo stipendio di milleduecento franchi. P. Avevate dinnanzi a voi un magnifico avvenire nella Casa e la speranza di guadagnare la vita lavorando. H. Cosa in sé così onorevole, quanto sono spregevoli i vostri onestissimi borghesi che la vita vivono magari con tutte le lussurie, ma di lavorare non vogliono sapere, anzi! hanno di chi fatica orrore e disprezzo. P. Lasciaste il posto in seguito ad un attrito senza importanza, e tornato a Parigi avete potuto collocarvi presso un grande mercante di panni di Roubaix a cui vi avevano raccomandato parecchi vostri condiscepoli della Jean-Baptiste Say. E la raccomandazione doveva essere autorevole, se per farvi posto si è creato per voi un impiego speciale. H. Onore insigne davvero, ottocento franchi all’anno per un diciottenne licenziato dalla scuola Jean-Baptiste Say! P. Ve ne sono molti a Parigi che un posto simile 1’invidierebbero\dots{} H. Questa è la disgrazia! P. Gli è piuttosto che a quel tempo incominciavate a subire l’influenza del vostro fratello maggiore Fortuné, che è anarchico. Avevate con lui assistito già ad un meeting convocato in onore di Ravachol nel corso del quale vostro fratello parlò così violentemente che fu arrestato; anzi foste arrestato anche voi. H. Già, cercavano mio fratello ed hanno arrestato me che di propositi violenti non avevo avuto altra colpa che di ascoltarne; ma si sono mai trovate d’accordo la decenza, il buon senso e la polizia? P. Qualche ragione dell’arresto potrebbe trovarsi, Henry. Il vostro padrone Veilleux dopo d’avervi congedato ha rinvenuto nel vostro scrittoio un manuale d’anarchia pratica. Trovò pure la traduzione da voi iniziata di un foglio italiano dal titolo: “Viva il furto!” il quale concludeva con l’utilità pratica delle bombe a rovesciamento con cui si possono mandare all’aria i poliziotti che le sequestrano. Vi siete di poi impiegato presso un orologiaio con l’intento di impratichirvi nell’applicazione dei movimenti d’orologeria alle vostre bombe. H. Ma è inarrivabile, signor Presidente, la fantasia audace delle vostre deduzioni. P. Alla fine siete entrato a far parte del giornale “L’Endehors” del quale era gerente il compagno vostro Matha, di cui vi si è trovata indosso al momento dell’arresto la fotografia. Sapete che è arrestato anche lui? H. So che ne sono stati arrestati tanti, che sarebbe più facile numerare quelli rimasti fuori che non quelli razziati dai vostri mammalucchi in queste ultime settimane. P. Non avete voluto esser soldato, vero? Dal momento, del resto, che vi eravate ricusato ad esser ufficiale era ingenuo sperare che vi sareste acconciato ad essere un fantaccino. H. No. Ho fatto tre anni di battaglione scolastico, e come dose di militarismo è tutto quello che potevo sopportare. P. Ed eccovi così renitente. Ma è cosa legittimamente dovuta codesta imposta del sangue\dots{} H. \dots{}che voi non l’avete pagata. P. Che la vostra stessa famiglia vi biasima, quantunque al biasimo rispondiate che l’affare non la riguarda. H. Infatti del dovere mio sono il solo giudice. P. Vostra madre stessa\dots{} H. Oh lasciatela un po’ stare, che la vostra intrusione è villana! Mia madre soffriva di vedermi espatriare, e soltanto ad ovviare a questa sventura convergeva le sue preghiere che furono sul punto di farmi arrendere ai suoi voleri. Ma sono innanzi tutto anarchico, e per me il sentimento dell’anarchia è superiore ad ogni altra considerazione. P. Vostro ultimo padrone è stato lo scultore Dupuy. Non fu Ortiz, l’anarchico ladro, che vi trovò questo posto? H. Sta bene, ma poiché siete così meticoloso anche nei dettagli più minuti, perché non dite pure che a quell’epoca Ortiz era anarchico e non era ladro, anche se, dopo, l’aver osato l’espropriazione non gli toglie come anarchico proprio nulla? La verità che è ingrata, che vi mortifica, non la volete a questo banco, e non trova eco nei vostri interrogatori irosi, decisamente! Si arriva cosi alla sparizione di Henry due giorni dopo l’esplosione della rue des Bons-Enfants. P. È un delitto che avete personalmente confessato in istruttoria, volete dirne ai giurati le ragioni? H. I motivi li dirò domani, i fatti subito e volentieri. E con una lucidezza, con una precisione matematica in uno stile fermo e breve – dice un cronista giudiziario che la deposizione raccolse – Henry fa la storia delle peregrinazioni sue di quel giorno, la corsa alla rue Veron per cercarvi la bomba, quella più lunga all’avenue de l’Opéra per deporvela, e l’ultima, forsennata, per rientrare in ufficio senza che Dupuy, il suo padrone, avesse a giudicar soverchiamente prolungata la sua assenza per le poche commissioni sbrigate. H. V’assicuro che non ho perduto il mio tempo pur prendendo in due ore quattro vetture. Ero in missione, come un buon borghese, e non ho camminato a piedi. Il presidente, a completare i dettagli dell’attentato, ricorda come la bomba trasportata dagli uffici della Compagnia di Carmaux al Commissariato di polizia della rue des Bons-Enfants scoppiasse nell’ufficio del commissario facendovi la strage orrenda che è nota. Quando alla detonazione la folla invase gli uffici della rue des Bons-Enfants l’orrore dello spettacolo la fece allibire. Erano dappertutto grumi di sangue e di cervello, lembi di carne e di intestini. Al becco del gas, che al soffitto scende nel centro della sala, era un gomitolo di budella. Intorno Garin, Formorin, Réaux, il comissario, i vice-commissari erano cadaveri disfatti; mutilato orrendamente il segretario Pousset, agonizzante in un angolo ancora un ispettore di polizia, Grouteau. La polizia, la magistratura hanno sempre sospettato di Henry, debbo dirlo, ma Henry era scomparso. Poi rivolgendosi ad Henry subitamente, gli chiede: Ma con voi era un complice, non è vero? H. No, ero solo – ribatte vivamente. La fretta e l’energia con cui Henry respinge l’ipotesi di un complice nell’attentato della rue des Bons-Enfants confermano, in luogo di eliminare, nella Corte e nel pubblico il sospetto che un complice egli lo abbia avuto. Certo Henry aveva allestito la marmitta: era manifesta la diligenza e la accuratezza di un tecnico nella preparazione; certo Henry era stato sui luoghi che aveva esplorato con cura dal momento che al giudice istruttore aveva potuto disegnarne, da artista, la pianta topografica. Ma aveva da solo potuto trasportare la pesantissima marmitta dalla rue Veron all’avenue de l’Opéra? E nel breve tempo di due ore aveva potuto andare, tornare, e far nel contempo le commissioni del suo padrone Dupuy? L’ipotesi di un complice non è temeraria, ma chi è, dov’è questo collaboratore misterioso che tutte le indagini della polizia non sono riuscite a identificare? né trarre dalle tenebre tutte le ricerche sagaci dell’istruttoria? Il complice? Per quante indagini abbia fatto la polizia giudiziaria e per quanto se ne sia arrovellata l’istruttoria non sono riusciti a identificarlo. Non potrebbe chiarire il mistero che Henry, ma il Presidente che contro la decisa e irremovibile fermezza dell’imputato si è indarno urtato durante il tormentoso interrogatorio rinuncia disperato all’impresa. Alcuni testimoni hanno ben deposto di aver veduto, nell’ora in cui Henry doveva trovarsi alla rue Veron per prendervi la bomba, uscire di casa una donna con un paniere sotto il braccio. Henry stesso aveva dichiarato al giudice che, scendendo dalle scale, codesta donna aveva egli pure veduto, ma quando il giudice convinto che quella donna misteriosa avesse accompagnato Henry fino agli uffici della Compagnia Carmaux all’avenue de l’Opéra, ha chiesto all’imputato qualche ragguaglio sulla fisionomia, sulla figura, l’età probabile, l’acconciatura della donna sospetta, non gli ha cavato più una parola. La polizia, il giudice istruttore, il presidente vorrebbero ora concordemente rifarsi di questo mutismo di Henry buttandogli addosso una badilata di letame e vituperi. Col pretesto di ricercare come e dove Henry sia vissuto durante il tempo che intercorre tra l’attentato alla Compagnia di Carmaux e quello al Terminus, essi si sforzeranno di dimostrare che egli è vissuto di scrocchi, alle spalle di Ortiz che, come vedremo a suo tempo, è stato al famoso “Processo dei Trenta” convinto di non aver soverchio rispetto per quello che i comandamenti di santa madre chiesa e del codice penale chiamano la roba degli altri. Non sarebbe una rivincita per poter gabbare al pubblico come un ladruncolo o un manutengolo codesto giovane che sulle soglie della prima giovinezza ha la fierezza irriducibile e sdegnosa di uno stoico maturo? E il Presidente vi si butta a corpo morto, ma non resta a lui l’ultima parola. Henry lo mette a segno con una scudisciata sanguinosa che lo guarisce repentinamente dalla fregola dei sospetti e delle insinuazioni. P. Siamo ormai alla fine, Henry; non ho più che una domanda da farvi e voi sapete qual è, dal momento che alla Conciergerie mi sono sforzato di mettervene in rilievo la gravità. Scomparso il 10 novembre del 1892 dall’ufficio del vostro padrone, il signor Dupuy, non vi ritroviamo che nel dicembre del 1893, alla rue des Envierges, sotto il nome di Dubois. Che cosa avete fatto durante questi tredici mesi di intervallo? H. Potrei rispondervi che sono affari miei, in cui non avete nulla a vedere; ma ho detto in istruttoria che nell’aprile ho fatto un viaggio in Belgio. Potete accertarvene domandando se a Bruxelles non ho durante due mesi abitato al 10 Boulevard Morland donde uscivo alle sette del mattino vestito da lavoro e non rientravo dall’officina meccanica in cui ero impiegato che ogni sera verso le sei. P. Verificheremo, quantunque è la prima volta che voi ci parliate del vostro soggiorno a Bruxelles. H. Vuol dire semplicemente che la vostra domanda era indiscreta e la mia risposta sarebbe stata inopportuna. P. Converrete però che a magra risposta dar conto di due mesi su tredici. Come avete vissuto durante il resto del tempo? H. Come sempre: del mio lavoro. P. La vostra prima bomba avrete potuto prepararla con lo stipendio che guadagnavate presso il Dupuy, ma la seconda che deve esservi costata abbastanza come avete potuto prepararla, come ve ne siete potuto procurare i mezzi? H. Lavorando. P. Dove e come? H. Siete curioso! P. E debbo esserlo. H. E allora cercate; debbo farvi io stesso le spese della curiosità? P. E di tacere avete torto, tutto facendo credere che durante questo tempo siate vissuto con l’Ortiz o sovvenuto dall’Ortiz, vostro compagno antico divenuto un complice mariuolo. H. Tutto, induce? Ma non v’è l’ombra di un’apparenza che vi autorizzi a codesta insinuazione, a meno che vi illudiate che i sottovoce della sbirraglia irresponsabile si possano francamente gabellare per atti di fede. P. Vi hanno confrontato con Ortiz e avete dichiarato che non lo conoscevate. H. Perché io non sono né poliziotto né spia. P. Una donna arrestata insieme con Ortiz ha dichiarato di avervi veduto con lui in un bar a Londra. H. In un bar avrebbero potuto vedermi anche al fianco vostro. Quanta gente e quanto diversa s’accomuna dinanzi al banco di un liquorista? P. Un altro testimone dichiara di avervi veduto a Parigi nel 1893 e che le vostre mani candidissime gli erano parse quelle di un uomo che non lavora, e noi ci domandiamo se voi non siete un po’ come Ortiz, l’amico vostro, un ladro come molti altri anarchici. Vaillant ha dichiarato che per preparare la sua bomba ha ricevuto cento franchi da un ladro. È il ladro Ortiz che ha fatto le spese della bomba per l’attentato del Café Terminus? Siate cauto! H. Ho poche cautele da prendere, perché dalla Corte uscirò soltanto per passare nelle mani del boia, e non me ne dimentico. P. Non alludo a questo, alludo a una confessione che torna amara alla vostra fierezza: fino ad essere un assassino voi convenite senza sforzo; ma non volete dire che a un ladro voi avete teso le mani che si sono inzuppate di tanto sangue. H. Non parlate del sangue di cui si sono macchiate le mie mani perché il pubblico non veda quello in cui avete tuffato avidamente, recidivamente le vostre e di cui avete tinto in rosso la vostra toga di consigliere? L’udienza sospesa alle due e mezzo, è ripresa alle tre e un quarto. Vengono interrogati i testimoni. \bigskip Agelon, ventisette anni, cameriere al Café Terminus: Verso le otto meno dieci, un cliente si è seduto vicino alla porta, mi ha chiesto una birra e mi ha pagato; alle nove, mi ha chiesto un’altra birra e un sigaro. Un attimo dopo, avviene l’esplosione. Presidente: Il consumatore, era l’accusato? Agelon: Sì, signore. P. Siete stato ferito? A. Sì, alla gamba. \bigskip Paquet, cameriere al Café Terminus: Verso le nove camminavo nel caffè quando ho visto l’accusato fare un movimento; un globo mi a caduto in testa. Presidente: Siete stato ferito? Paquet: Sì. Pr. Avete visto il movimento del braccio? Pa. Sì, la bomba doveva, secondo il movimento del braccio, cadere vicino al palco. Pr. C’era più gente da quella parte? Pa. Sì, signore. \bigskip Lousteau, ventiquattro anni, cameriere al Café Terminus: Ho notato l’accusato, che si è seduto, ha chiesto una birra, poi un’altra birra e un sigaro, che ha pagato subito. L’ho perfettamente riconosciuto. Presidente: Siete stato ferito? Lousteau: Sì, alla caviglia. \bigskip Frugier, ventun’anni, cameriere al Café Terminus: Ero sulla terrazza e sentii un rumore, quello del lampadario che si rompeva; sono stato urtato da Henry che diceva: “Il miserabile, dov’è?”. Sono entrato nel caffè. Henry: È falso. Frugier: Confermo la mia dichiarazione. \bigskip Tissier (Louis): Ho sentito il rumore di un lampadario che si spezza ed ho visto fuggire un uomo: venne preso. È partito un colpo d’arma da fuoco. \bigskip Etienne (Gustave), ventotto anni, impiegato alla compagnia dell’Ovest: Verso le nove di sera, arrivando in rue d’Isly, mi sono precipitato su di lui, dicendogli: “Ti tengo canaglia”. – “Non ancora”, ha risposto. Mi ha sparato a bruciapelo. Sono svenuto e non so niente altro. Henry: Riconosco l’atto, ma le parole non le ho pronunciate. \bigskip Maurice (Léon), parrucchiere: Verso le nove, ho sentito uno sparo, poi ho visto un giovane che correva. Una folla lo seguiva; l’ho inseguito, e mi ha sparato a bruciapelo con la pistola; sono caduto soffocato dal sangue. Presidente: A che distanza ha sparato? Maurice: A bruciapelo. P. Quali sono le conseguenze? M. Non ci vedo più bene e non sento più; e tutti i giorni sputo sangue e soffro terribilmente. \bigskip Poisson, brigadiere dei vigili. Presidente: Siete stato decorato recentemente e tutti salutano con rispetto questa onorificenza. Poisson: Ho inseguito l’accusato; mi ha sparato tre volte in successione; alla quarta, quando lo minacciavo con la mia sciabola, si è fermato, sono stato colpito e ho perso conoscenza: avevo una pallottola nel petto. \bigskip Contet (Jules), vigile: Il 12 febbraio, stavo finendo il servizio quando ho sentito un colpo di arma da fuoco e Poisson che inseguiva Henry, l’ho fermato mentre tentava di estrarre il suo pugnale. \bigskip Lenoir, vigile: Il 12 febbraio, stavo finendo il servizio quando sento una detonazione; mi precipito e vedo un individuo che fugge. Gli corro dietro e, in rue d’Isly, sento due detonazioni; in fondo alla via sento vari colpi di pistola e vedo Henry sparare tre volte su Poisson. \bigskip Petit, quarantaquattro anni: Ero al caffè, nella rue de Rome, verso le nove; il cameriere mi dice che c’è battaglia in rue d’Isly. Ho visto Henry sparare gli ultimi due colpi sull’agente Poisson. Ci siamo precipitati per fermarlo e ho ricevuto un colpo di bastone sulla testa; non so da chi venisse, ho supposto che vi fosse un complice, è una semplice impressione. Van Herreweghen, quarant’anni, disegnatore (il testimone avanza zoppicando faticosamente): alle otto e mezzo, ero con il mio amico signor Borde; parlavamo di disegni; stavo andando via e mi ero fermato al Café Terminus. Quasi subito siamo saltati in aria. Presidente: Il signor Borde era vostro amico? Van Herreweghen: Amico intimo; era disegnatore. P. Quali sono le conseguenze delle vostre ferite? Van H. Ora, cammino meglio; l’arteria è stata recisa. Ho avuto diciassette ferite nella gamba. \bigskip Signora Emmanuel: Ero al caffè e attendevo degli amici quando ho notato Henry; ho creduto che lanciasse la sua birra per aria. Ho visto presto che era una bomba. Sono stata ferita così come mio marito. \bigskip Signora Leblanc: Ho visto lanciare un oggetto in aria; ho creduto che fosse il bicchiere lanciato da un consumatore. Sono stata ferita alla mano e alla gamba; sono stata a letto diciotto giorni. \bigskip Beck (Albert-Jules), architetto, piazza Vintimille: Ero al Café Terminus, al momento dell’esplosione; sono stato ferito alla mano da una scheggia di metallo; ho avuto, inoltre, cinque ferite. \bigskip Michel, funzionario delle poste: Sono stato ferito, al Café Terminus, e sono rimasto circa due mesi senza poter far nulla; sono stato venti giorni senza dormire. \bigskip Signora Kingsbourg, un’altra vittima ancora troppo sofferente, non si presenta. \bigskip Garnier (Eugène): Sono stato ferito in quattro punti; ho ricevuto quattro centimetri di scatola di sardine nel tallone e una pallottola nel polpaccio. (All’accusato): Sembrate indifferente a questa sfilata. Henry: Sono completamente indifferente, come voi lo siete delle miserie che ho conosciuto e visto da vicino. \bigskip Villevaleix (Pierre), ex-ministro di Haiti a Parigi: Ero al Café Terminus quando sento un rumore secco causato dal rumore del lampadario. Mi alzai, avvenne l’esplosione e fui ferito alla gamba. Sono completamente guarito. \bigskip Baronessa di Eichstedt: Sono stata ferita al Café Terminus, il 12 febbraio, al fianco sinistro. Presidente: La signora è ancora in preda a gravi disturbi nervosi. \bigskip Signora Hadamla: Sono stata ferita al piede sinistro e molto impressionata dall’esplosione. \bigskip Descaves, perito-architetto, rue de Miromesnil: Nel caffè, il lampadario era rotto. L’ordigno è caduto sotto un tavolo e ha rotto il piede di ghisa. C’erano ventotto fori di pallottole sotto il tavolo e un buon numero sul soffitto. Gli specchi erano a pezzi. Se l’ordigno fosse stato lanciato più dritto, avrebbe colpito l’orchestra. Alcuni frammenti di uno specchio sono stati proiettati fino a dieci metri. \bigskip Girard, capo del laboratorio municipale: Il 12 febbraio, sono stato chiamato al Terminus; ho constatato soprattutto l’odore acre del fumo; ai piedi di un tavolo il pavimento era sfondato e macchiato di una sostanza gialla, è acido picrico. Il pavimento e il bitume erano polverizzati. I tavoli di marmo sono stati perforati dai proiettili. Gli specchi che dividevano il caffè dal ristorante erano crivellati di fori rotondi e regolari. Nei detriti ho trovato dei pezzi dell’ordigno di latta e di zinco. Era una piccola marmitta nella quale si trovava dell’acido picrico, della dinamite e una miccia Bickford. A villa Faucher, ho trovato il manico della marmitta che deve essere servita per l’esplosione. C’erano dei giubbetti di flanella impregnati di acido picrico e della sabbia che serviva a fondere l’acido picrico. C’era anche dell’amianto e delle pallottole deformate, simili a quelle che abbiamo ritrovato al Terminus. Abbiamo esaminato un pugnale, ma non era avvelenato. L’ordigno aveva un piccolo difetto\dots{} Henry: Abbiamo discusso, il signor Girard ed io e siamo rimasti d’accordo su questo difetto. Girard: È esatto. Avvocato Hornbostel: Henry correva qualche pericolo? G.: Trasportandolo, no; ma dandogli fuoco, rischiava la morte. \bigskip Descout, dottore in medicina, perito: Ho visitato i signori Etienne, Poisson e Maurice. Poisson aveva una contusione al petto e tracce di ferite alle mani e al torace. Il signor Maurice era più gravemente colpito. Il signor Etienne è stato colpito, ma ha riportato una semplice contusione. Ho visitato vari feriti: il signor Villevaleix era stato colpito con tre proiettili alle gambe; il signor Garnier ha ricevuto tre ferite alle gambe; si sono cicatrizzate in una ventina di giorni; la signora Kingsbourg a stata ferita nello stesso modo; questa signora, molto anemica, è ancora molto sofferente. \bigskip Vibert, dottore in medicina: Ho fatto l’autopsia del signor Borde. Le ferite, molto numerose, hanno prodotto dei focolai di suppurazione che hanno portato la morte. Si è dovuto amputare la gamba, ma questa operazione non ha salvato il paziente. La baronessa di Eichstedt e sua sorella, la signora Hadamla, erano molto doloranti, e soprattutto sotto shock per l’incidente. Il signor Van Herreweghen è stato colpito molto gravemente; può appena camminare. \bigskip Socquet, dottore in medicina: Ho esaminato diciassette persone; nessuna è stata colpita gravemente e non ho constatato nessuna infermità permanente o temporanea. \bigskip Peigné, custode della villa Faucher: Il 20 dicembre, Henry ha affittato una camera sotto il nome di Louis Dubois. L’ha lasciata, al momento del suo arresto. Aveva dichiarato di assentarsi per qualche giorno. La seconda notte dopo il suo arresto, ho constatato che la sua camera era stata svaligiata. \bigskip Signora Petit, villa Faucheur: Nella notte tra martedì e mercoledì, dal 14 al 15, è stata svaligiata la camera di Dubois. Presidente: Lo riconoscete? Petit: Perfettamente. Avvocato Hornbostel: Henry riceveva visite? Petit: No, nessuna. \bigskip Presidente (all’accusato): In un’altra istruzione dite di aver abitato in boulevard Morland n. 10. Il custode della casa lo dichiara infatti; e dice che lavoravate in rue de Turenne, da un fabbro. Ma nessuno dei fabbri di rue de Turenne vi conosce. Henry: Ero impiegato dal signor Durand, 155 rue du Temple; rivolgetevi a lui. Ho imparato il mestiere di fabbro e potevo con quel mestiere guadagnarmi da vivere. P. Farò verificare la cosa. \bigskip Le Fraper, studente di diritto: Posso affermare di aver visto, in avenue de l’Opéra, una donna che portava una borsa nella quale si trovava un oggetto ricoperto da un giornale. Erano circa le undici di mattina, e lasciavo la Società delle Miniere di Carmaux. Henry: Non ho visto il testimone. Ci vorrebbe una borsa enorme per portare un simile ordigno. \bigskip Bernick, dentista: Sono andato, alle undici, alla Società di Carmaux, ho notato l’ora in place de Théâtre-Français. Ho visto un oggetto avvolto nella carta. Il signor Bellois, che ho avvertito, ha sollevato l’oggetto. È stato portato via subito. \bigskip Bellois: Ho notato, davanti alla porta della società di Carmaux, un pacchetto che ho constatato essere molto pesante; ho tolto la carta che lo avvolgeva; ho visto allora un oggetto di forma sferica; ho fatto avvertire il signor Augenard, poi il custode. Il fattorino Garin ha portato via la marmitta. L’oggetto mi è parso semisferico e bluastro; credo che fosse qualcosa simile a queste marmitte qui sul tavolo dei corpi del reato. \bigskip Augenard, impiegato della società di Carmaux: Sono uscito col signor Le Fraper, verso le undici, e non c’era nulla all’ingresso. Poco dopo, il signor Bellois mi ha chiamato e mi ha mostrato un oggetto. Ho creduto fosse un pacco deposto da una lavandaia. Ha strappato il giornale e abbiamo visto uno strumento estremamente pericoloso, del tutto diverso da quanto vedo sul tavolo dei corpi di reato. Era un ordigno di ferro battuto, con viti di rame, fatto con molta cura. Avvocato Hornbostel: L’ordigno era più leggero o pesante di quello che è qui? Augenard: Era meno alto di questa marmitta e più largo. \bigskip Garnier, custode, avenue de l’Opéra 11: Sono stato chiamato da Garin per vedere quello che c’era all’ingresso: ho visto l’oggetto e l’ho portato via. Sulla marmitta c’era un’etichetta grattata e una cifra scritta col gesso; l’ho portata giù, sul marciapiede della rue d’Argenteuil, poi, Garin ed io abbiamo messo l’oggetto in un tovagliolo. Era una marmitta di ghisa, una pentola, come quelle che sono qui. Sono stato io ad aprirla. Presidente: Siete custode; sapete bene che cos’è una marmitta? Garnier: Certamente. Avvocato Hornbostel: Il custode ha visto entrare Henry? G. No, l’abitacolo è in una rientranza. \bigskip Signora Garnier, custode, avenue de l’Opéra 11: Ho visto una marmitta di ghisa come quella che è qui. Avvocato Hornbostel: La custode ha visto Henry? Signora Garnier: No; c’è un gran movimento di persone nella casa, e ci sono due ingressi. \bigskip Cartier, ex-vigile urbano: Ho visto, quando ero vigile urbano, in rue d’Argenteuil, la bomba dell’avenue de l’Opéra. C’erano alcune persone. L’ordigno somigliava ad una pentola; una marmitta di ghisa, ben fatta e molto ben confezionata; c’era un’etichetta grattata. \bigskip Gung’l (Nicolas), segretario del giornale “Le Matin”: L’8 novembre vidi, in rue d’Argenteuil, un assembramento di persone e scorsi una marmitta di ghisa. L’indomani pubblicai su “Le Matin” la descrizione dell’ordigno che avevo visto. Mi è stata presentata una marmitta su un tavolo, dal signor Espinas, subito non l’ho riconosciuta: mi è sembrata più alta. Poi è stata posta per terra ed ho riconosciuto, nell’oggetto che mi veniva presentato, l’ordigno che avevo visto in rue d’Argenteuil. \bigskip Denis (Léon), custode, rue des Bons-Enfants: Ho visto arrivare, verso mezzogiorno e mezzo, tre persone che portavano una marmitta; Garin ha chiesto all’agente Réaux di aiutarlo. Lo spettacolo dell’esplosione era orribile; ho camminato, senza rendermene conto, sul corpo del segretario del commissario di polizia, ridotto in briciole e mescolato ai detriti. \bigskip Sauvage, vigile urbano: Il 12 novembre, ho sentito una detonazione in rue des Bons-Enfants. Entrando nel commissariato, ho visto quattro persone morte e una sul punto di spirare\dots{} Gli abbiamo prestato soccorso. \bigskip Cacheux, vigile urbano: Sono entrato in rue des Bons-Enfants dopo l’incidente; era uno spettacolo orribile; ho aiutato a trasportare una persona morente. \bigskip Le Louvrier: Ho visto l’esplosione, sono arrivato ed ho scorto, nel commissariato, dei cadaveri, una melma sanguinante. Una delle vittime viveva ancora; ho dato un aiuto a trasportarlo. \bigskip L’udienza è tolta alle sei e rinviata al giorno dopo per continuare le deposizioni, i dibattimenti, e formulare la sentenza. \bigskip \bigskip \section{Udienza del 28 aprile} \bigskip Il pubblico è numeroso quanto ieri e le misure di ordine pubblico hanno lo stesso vigore. L’udienza viene aperta a mezzogiorno. L’accusato Émile Henry conserva la sua aria indifferente. Mentre continuano le deposizioni dei testimoni, rimane appoggiato alla balaustra, e gira verso la folla il suo volto sul quale si nota un sorriso forzato. Presidente (all’accusato): Vi ricordo che ieri avete dichiarato che, durante l’anno 1893, abitavate a Parigi. Avete dato indicazioni nuove a questo riguardo. Abbiamo fatto verificare queste informazioni. Il capo della polizia ci fa sapere che il fatto si trovava descritto in un altro incartamento. L’abbiamo trovato, infatti; ho fatto cercare il fabbro di cui ci avete parlato. Per approfondire più completamente il dibattimento, farò ascoltare, in virtù del nostro potere discrezionale, il signor Henri Meyer, giudice istruttore presso Tribunale della Senna, che deporrà su quanto concerne le ricerche alle quali si è proceduto a vostro riguardo. (Al giudice Meyer): Siete stato incaricato dell’istruttoria sull’esplosione al Café Terminus, e dal signor Espinas di quella sull’attentato della rue des Bons-Enfants? Meyer: Sì. P. Henry sostiene di aver abitato in boulevard Morland e di avervi dichiarato\dots{} Vogliate dirci se, all’infuori dei due procedimenti di cui si sta trattando, avete avuto occasione di occuparvi dei domicili di Henry. M. Ho istruito diverse azioni giudiziarie dirette contro duecentottanta anarchici, credo; ho cercato i vari domicili di Henry. È andato via il 22 novembre 1892; disse di recarsi in Germania e poi in Inghilterra. Dal maggio al luglio 1893, ha abitato in boulevard Morland e avrebbe lavorato presso un fabbro, in rue de Turenne; non è esatto. Mi sono occupato di lui in occasione di un furto commesso a Ficquefleur, a danno di una signora: quattro malfattori mascherati sona entrati a casa sua; l’hanno terrorizzata e anche cloroformizzata. L’hanno costretta con le minacce a indicare dove erano i suoi valori. Ma hanno trovato solo le ricevute. Ora, la descrizione dei ladri somiglia molto a quella di quattro persone scese a Ficquefleur; uno di loro diceva di essere ingegnere al servizio di un ricco inglese. Sono stato colpito dalla somiglianza delle descrizioni di queste persone con quelle di Ortiz e di Henry. L’altro ieri, ho fatto un confronto tra questi individui e il sindaco del comune di La Riviére-Saint-Sauveur; mi ha detto che quello che diceva di essere il figlio del ricco inglese era Henry. Quest’ultimo ha protestato. Henry: Protesto energicamente: non so di che cosa si tratta. M. Il sindaco ha affermato con fermezza di riconoscere Henry. Gli stranieri dissero che dovevano impiantare una fabbrica nella zona. Il sindaco li ha ricevuti a casa sua, hanno preso il tè. È un commerciante importante di Le Havre. H. Nego assolutamente. Avvocato Hornbostel: Il signor giudice istruttore si occupato di Henry e dell’attentato di Barcellona? M. Assolutamente no. Avvocato H. Non si è forse accusato Henry di un furto di un milione, e di aver fermato delle diligenze sulle strade? M. Non ho mai sentito parlare di questo. \bigskip Weber, quarantanove anni, negoziante: Mi ero istallato al numero 13 di avenue de l’Opéra, e vendevo vaselina e prodotti di profumeria. L’etichettatura e la presentazione dei flaconi somigliavano a quelli di una farmacia. Avvocato Hornbostel: Il testimone ha visto l’accusato? W. No. Dupuy (Alphonse), trentacinque anni, scultore: Ho dato lavoro a Henry fino al 10 novembre 1892. Ero molto contento di lui e gli ho aumentato lo stipendio. Poi, l’11, è andato via; l’ho rivisto in dicembre. È venuto a prendersi l’ultimo mese, che gli dovevo. Avevo ricevuto una lettera di Ortiz, da Londra, che non mi dava il suo indirizzo esatto; gli scrissi che avrei dato alla persona che sarebbe venuta in nome di Henry la somma che gli dovevo. Dopo questa lettera, è venuto Henry stesso. Henry: Non è la lettera che mi ha fatto venire; è la perquisizione fatta a casa mia; sono venuto a sentir notizie dal signor Dupuy. D. Nella mattinata, Henry doveva ricopiare un conto molto lungo dove c’erano degli errori; ho dovuto farlo ricominciare. Verso le dieci e mezzo sono partito, mi ha accompagnato. Poi, è ritornato un momento a mezzogiorno. Mi ha chiesto i soldi dell’omnibus. Ora, è stato dimostrato che non si potevano fare in omnibus, né tanto meno a piedi, le commissioni, e fare l’attentato. Avvocato Hornbostel: Quale era l’atteggiamento di Henry quel giorno? D. Si è occupato in modo continuo di lavori di scrittura; ho qui questi lavori. Il Presidente, dopo aver preso visione dei registri portati dal signor Dupuy, li fa presentare all’accusato, poi passare sotto gli occhi dei signori giurati. Sono copie di lettere, scritte dopo l’attentato da Émile Henry, prima che si conoscesse il delitto della rue des Bons-Enfants. Il signor Presidente ordina il sequestro di questi testi e la loro aggiunta ai corpi del reato. Avvocato H. Come ha accolto Henry la notizia dell’attentato? D. Si è dimostrato estremamente scosso e in modo sincero. Avvocato H. Il testimone crede, in sua fede e coscienza, che Henry ne sia l’autore? Presidente: Non porrei la domanda. Il signor Dupuy non è un giurato. \bigskip Bernard, commissario di polizia: Il 27 febbraio, ho fatto il percorso che Henry dichiara di aver fatto. Ho proceduto esattamente secondo le indicazioni di Henry; ed ero, alle dieci e cinquantasette, sulle scale della casa dell’avenue de l’Opéra. Avevo preso come lui quattro vetture. Il percorso che indicava poteva essere fatto, al limite; io l’ho fatto. Presidente: Signori giurati, ho appena ricevuto le informazioni del signor Durand. (All’accusato): Il signor Durand dichiara che vi siete presentato da lui per imparare a limare, allo scopo di essere ammesso nelle compagnie degli operai militari; non pretendevate alcun salario. Henry: Vivevo miseramente. P. Ma insomma vivevate. H. Vivevo meno bene di voi, è evidente. P. Da dove venivano le vostre risorse? Ve lo chiedo ancora una volta. H. Ripeto che non voglio dirvi niente. \bigskip Signora Colin: Hanno comperato un astuccio di vetro per mettere i portapenne. Ne ho venduti fino al 1893; poi ho cambiato modello. Avvocato Hornbostel: La testimone riconosce l’accusato? Signora Colin: Non riconosco l’accusato. \bigskip Comte, chincagliere: Non ricordo di aver venduto una marmitta all’accusato; ma egli ha descritto con precisione il negozio; anche il prezzo è esatto: era segnato col gesso. Avvocato Hornbostel: Il testimone riconosce l’accusato? Comte: Tutti possono entrare. Henry certamente vi è entrato. \bigskip Guyot, commerciante di prodotti chimici: Abbiamo venduto, nella nostra ditta, del clorato di potassio all’accusato che aveva dichiarato di essere assistente in uno stabilimento di Saint-Denis. La vendita è stata fatta di sera; ultima della giornata. \bigskip Vieille (Paul), ingegnere delle polveri e salnitri: Ho verificato i residui della bomba della rue des Bons-Enfants; ho ritrovato dei pezzi di ghisa corrispondenti a quelli di una marmitta; sopra si distinguono le nervature di queste marmitte; inoltre, ho ritrovato dei pezzi di ferro a reggetta. Questi pezzi provengono dalla chiusura. Nel 1892, avevamo trovato che si trattava di una marmitta di ghisa con una reggetta. Abbiamo notato che ci doveva essere della dinamite o un detonante analogo. Abbiamo pensato che non ci fosse miccia. Doveva essere un innesco meccanico, un congegno ad orologeria, o un innesco chimico. Si trattava di quest’ultimo, l’altro avrebbe lasciato delle tracce, come le spire di molle, che non abbiamo ritrovato. Il testimone indica la composizione della miscela detonante ed il processo di innesco. Dichiara che le indicazioni date da Henry sono molto plausibili e molto esatte. Presidente: Le vostre ricerche concordano con le dichiarazioni di Henry? Vieille: Completamente. Avvocato Hornbostel: quali erano le proporzioni della miscela? P. Le proporzioni indicate da Henry possono dare un’esplosione? V. Incontestabilmente: le si adopera generalmente per gli inneschi. P. Un urto poteva far scoppiare l’ordigno? V. Se il detonatore avesse fallito, l’apparecchio non avrebbe funzionato. Ma può darsi che un tale ordigno posto violentemente su un tavolo scoppi per il semplice urto; o il movimento può far funzionare il detonatore o far avvenire un’esplosione. Poiché è stato posato poco tempo prima dell’esplosione, abbiamo supposto che il fatto di essere stato posato abbia potuto provocare l’esplosione. \bigskip Girard, capo del laboratorio municipale: Sono stato chiamato il giorno dell’esplosione della rue des Bons- Enfants. Era orribile; camminavo letteralmente su resti di carne umana. Tra le rovine, abbiamo trovato dei pezzi di ghisa che avevano delle forme particolari: quelle di una marmitta casalinga. Il 12 novembre abbiamo comprato varie marmitte. Abbiamo constatato che la marmitta doveva essere chiusa con una reggetta. Quando ho visto Henry, gli ho detto se la marmitta era chiusa con del filo di ferro; subito ha risposto: “No, con una reggetta”. Ho portato una marmitta nella sua cella, con un tubo e il necessario per chiudere la marmitta. Ha fatto l’operazione; ma ha rifiutato di piazzare il tubo. Ho considerato che aveva contribuito a fare l’ordigno, ma ho la convinzione che non fu solo nel momento di chiuderlo. Le reggette erano dure. Ha fatto fatica a torcerle e a passarle nei manici. Il signor Girard prende una delle marmitte simile a quella dell’ordigno e spiega la sua conformazione. Girard: Henry ha dichiarato di aver messo otto chili di polvere di clorato; aveva un volume troppo grande; ma mi ha anche dichiarato di aver mischiato più intimamente i prodotti; così ha potuto inserire tutto; era esatto. Sono certo che egli ha collaborato alla confezione dell’ordigno; ma non ha potuto farlo da solo. Inoltre, aveva messo venti cartucce di dinamite. Dove le aveva prese? Henry (vivamente): Vengono da una fabbrica borghese. Avvocato Hornbostel: I due ordigni, quello del Terminus e quello della rue des Bons-Enfants, erano simili? G. No. Avvocato H. Quale era il più pericoloso dei due per Henry? G. Tutti e due; uno accendendolo, l’altro confezionandolo H. Un fabbro ha dichiarato che un uomo solo poteva chiuderlo. G. Sì, quando l’ordigno non è carico! Ma quando lo è, è un’altra cosa. Il sostituto procuratore generale: La fabbricazione dell’ordigno poteva lasciare delle tracce nell’appartamento? G. No; poteva benissimo non lasciare alcuna traccia. Bordenave (Jean), ingegnere edile: Non ho mai conosciuto Henry padre. La madre di Émile mi ha chiesto di facilitarle la riacquisizione del suo immobile di Brévannes. Henry è entrato da me nel 1889. Prima veniva a casa mia. Lavorava molto bene. Lo portai a Venezia per fargli vedere dei lavori. Volevo portarlo con me e assicurargli un avvenire. A Venezia, incontrò cattive compagnie e mi lasciò bruscamente col pretesto che non voleva fare la sorveglianza degli operai; sorveglianza necessaria, ma che non doveva per niente essere fatta in modo occulto. Avvocato Hornbostel: Nel corso dell’istruttoria il signor Bordenave ha abbracciato l’accusato? B. Dal giudice istruttore si è gettato al mio collo e mi ha abbracciato. Henry: Desidero dire una parola. Presidente: Fate una domanda. H. Voglio dire qualcosa. P. Dite. L’accusato (vivamente): Non voglio più; me lo avete rifiutato. \bigskip Vielleur, negoziante: Henry è stato portato da me da una persona di tutta fiducia. Non avendo nessun impiego da offrirgli, stava andando via, quando sulle sue istanze, e constatando la sua intelligenza, gli ho creato un impiego. Sono stato estremamente soddisfatto di lui. Solo due mesi dopo il suo licenziamento ho saputo che era anarchico. A fine maggio, è stato arrestato, come suo fratello, ed ho dovuto licenziarlo. Gli pagai il mese per permettergli di vivere. Mi sono informato, e ho appreso che scriveva molto, ho trovato delle note relative all’anarchia: erano dei consigli agli anarchici. Avvocato Hornbostel: È stato l’arresto a causare il licenziamento? Vielleur: Certamente. \bigskip Descaves, perito architetto: Sono stato incaricato di esaminare una pianta, tracciata a mano e a memoria da Henry, della scala della casa del n. 11 dell’avenue de l’Opéra. Era esatta, tranne un piccolo particolare. \bigskip Il presidente dà lettura di un processo verbale di accertamento che riguardava la riproduzione esatta della scena della deposizione della marmitta. Henry è stato lasciato libero di seguire la strada che voleva. È arrivato senza esitazione e senza nessuna ricerca. Si sentono poi i testimoni della difesa. \bigskip Brémant, capo d’istituto a Fontenay-sous-Blois: Émile Henry è stato mio allievo; era un modello. Aveva maturità straordinaria, una grande dolcezza. Mi ha lasciato a dodici anni, ed ho conservato eccellenti rapporti con lui. Una volta mi ha anche dedicato un componimento in versi. \bigskip Le Fermous: Sono stato collega di Émile Henry alla scuola J.-B. Say. Era un ottimo compagno, un amico molto indulgente; avevo molto affetto per lui. \bigskip Boutin (Charles), studente: Ho conosciuto Henry alla scuola J.-B. Say. Era un allievo brillante, e un ottimo compagno. Da allora l’ho rivisto, ma solo per un momento. \bigskip Philippe, istitutore alla Scuola Politecnica: Sono stato professore di Henry alla scuola J.-B. Say; era un ragazzo perfetto, il più onesto che si potesse incontrare; prima di presentarsi all’École Polytechnique, mi ha chiesto quel che doveva fare; gli ho risposto che lo ritenevo perfettamente capace di accedervi. Presidente: Avrebbe potuto, con le sue conoscenze, crearsi un’esistenza onorata e agiata presso un costruttore che si fosse interessato di lui? Philippe: Avrebbe potuto crearsi un’ottima esistenza sotto la direzione del suo parente. Conosceva poco la vita, meno dei ragazzi della sua età. \bigskip Brajus, sessantacinque anni: Ho conosciuto molto il padre, la madre, i figli Henry. Si sono sempre comportati bene, e la mia casa a stata sempre aperta per loro. Ho sempre seguito Émile. Nel 1893, è venuto a trovarmi due o tre volte. Avvocato Hornbostel: Il testimone ha dato del denaro ad Henry? Brajus: Sua madre mi ha chiesto qualche volta di anticiparle del denaro che mi ha restituito. \bigskip Gauthey (Jules-François), operaio battilastra: Ho conosciuto Henry nel 1891, veniva a trovarmi. Presidente: L’avete visto nel 1893? Gauthey: L’ho visto una volta; ma è venuto in mia assenza più di una volta, vestito da operaio. P. Aveva le mani bianche? G. Mia moglie l’ha visto e mi ha detto che era fabbro. Nel 1891, stimavo Henry. Amava molto i bambini. \bigskip Presidente (rivolgendosi al testimone per fargli prestare giuramento): Alzate la mano destra. Goupil, dottore in medicina, pone la mano destra dietro la schiena. Presidente: Alzate la mano destra. Goupil: Rifiuto di prestare giuramento per rispetto alla vostra religione che non ho la gioia di praticare né di conoscere. Non essendo la citazione data dal testimone notificata alla Procura, il Procuratore generale si oppone al giuramento del dottor Goupil, per permettere che possa essere sentito a titolo di informazione. G. Ho conosciuto Henry padre. L’ho anche avuto come mio segretario. L’ho curato alla fine della sua vita. Émile ha avuto una gioventù eccellente; è un giovanotto molto nervoso; l’ho già detto davanti a molti di voi, signori giurati, parlo di coloro che hanno voluto ricevermi. Henry: Non sono pazzo. G. Ho raccolto delle note che ho rimesso al difensore, e che indicano lo stato mentale dell’accusato. H. Vi ringrazio; ma sono cosciente di ciò che ho fatto; non sono pazzo. I risultati che ho ottenuto in collegio, li ho conseguiti dopo il tifo. Mio padre è morto in seguito ad un avvelenamento da vapori di mercurio. Ancora una volta vi ringrazio; ma non sono un pazzo; sono responsabile dei miei atti. \bigskip Ogier d’Ivry (conte): Sono parente acquisito di Émile Henry. L’ho conosciuto giovane, ottimo allievo, sognatore, squilibrato. Aveva come patrono, come genio protettore, san Luigi; poi seguì le orme di suo padre. C’è negli uomini un sentimento di rivolta straordinario; viene dagli antichi camisardi, il padre era nella Comune. Questi saranno più anarchici dell’anarchia o più monarchici del re sotto la monarchia. Sempre all’opposizione e nella rivolta. L’avevo spinto a entrare all’École Polytechnique. \bigskip Presidente: Signori giurati, prima di far ascoltare l’ultimo testimone, tengo a domandare all’accusato e al suo difensore se non rinunciano a sentirlo. Avvocato Hornbostel: No. P. Tengo allora a spiegare in quali condizioni questo testimone è stato citato. Ho ricevuto da Henry la seguente lettera: “Signor Presidente, “Mia madre ha manifestato il desiderio di assistere al mio processo; ho cercato invano di dissuaderla. Temendo a giusta ragione che le emozioni di due giorni di udienza le riescano troppo penose, ho l’onore di pregarla, signor presidente, di rifiutare qualunque autorizzazione che potrebbe chiederle per assistervi. “Vogliate accettare, signor presidente, i miei sinceri saluti. Émile Henry. “25 aprile 1894. Conciergerie”. Questa lettera mi è stata trasmessa dal difensore. Del resto, era apparsa nei giornali prima di essergli trasmessa. L’avvocato mi ha chiesto il permesso di far entrare la madre dell’accusato all’udienza. Mi sono rifiutato energicamente, dichiarando che non avrei mai permesso ad una madre di venire qui e sentire il Procuratore generale chiedere la pena capitale per suo figlio. Ho aggiunto che c’era un solo modo di farla entrare, cioè citarla come teste. Se questo testimone viene chiamato, la legge mi obbliga a sentirlo. Henry: Ignoravo che mia madre fosse citata\dots{} Non voglio qui vedere il suo dolore. P. È precisamente quello che avevo voluto evitarvi. Rinunciate a sentire il testimone? H. Vi rinuncio assolutamente. Avvocato H. Anch’io vi rinuncio. \bigskip Essendo esaurito l’elenco dei testimoni, l’udienza è sospesa alle due e mezzo; viene ripresa alle tre. Il Procuratore generale Bulot pronuncia la sua requisitoria. Si esprime in questi termini: Signori, questo caso, secondo i dibattimenti, non comporta né una lunga esposizione, né una lunga discussione dei fatti. Intendo esaminare molto rapidamente le accuse contro Émile Henry. Esaminare i fatti nell’ordine in cui sono stati considerati dall’accusa. Il 12 febbraio scorso, un giovanotto percorreva con lo sguardo (e quale sguardo!) i caffè e i ristoranti; va prima sul boulevard, poi in un caffè, dove va molta gente, vicino alla gare Saint-Lazare. Là, entrava e si sedeva. Un’orchestra suonava. Essendo poca la clientela attendeva per circa un’ora. Alle nove, il caffè era gremito soprattutto intorno all’orchestra. C’erano dei borghesi, ma ancor più degli artigiani, che vivono del prodotto del loro lavoro, abitanti del quartiere; venivano a passare la serata o ad aspettare un treno. II giovanotto tira fuori dalla sua tasca la bomba, una piccola marmitta; avvicina il suo sigaro alla miccia, si assicura che il fuoco abbia preso, si avvicina alla porta che dà sulla strada e getta l’ordigno nella parte più gremita di gente, vicino all’orchestra. Era stato notato. I signori Emmanuel e il signor Leblanc credettero che un consumatore scostumato lanciasse un bicchiere contro il lampadario. Anche i camerieri lo avevano visto. Fugge, urta un cameriere che rientrava; e allora, per ingannare, grida: “Ah! il miserabile; dov’è?”. Ciò turba il suo orgoglio e lo nega. Henry: Non mi turba affatto. Presidente: Non interrompete. Procuratore generale: Prendo solo, di quanto dice Henry, quello che è dimostrato. Non deve pensare di intimorire nessuno qui. Viene inseguito; il cameriere Tissier si ferma; prende la rue du Havre e la rue d’Isly. Coraggiosamente, inseguendolo, il signor Etienne si precipita su di lui, lo afferra e riceve un colpo di pistola in pieno petto: un bottone para il colpo. Un parrucchiere, il signor Maurice, accorre; e una pallottola lo raggiunge; cade e la caduta è ancora più grave della ferita. L’agente Poisson arriva alla testa degli inseguitori. Riceve colpo su colpo altre tre pallottole e cade sull’accusato. Quest’ultimo viene arrestato, con l’aiuto del signor Petit, un coraggiosissimo cittadino; viene condotto al Café Terminus. Questa scena si è svolta ad una velocità inaudita. Egli ha ferito, con sei colpi di pistola, due persone. Rimpiange solo di non aver ucciso le sue vittime, e di non aver potuto adoperare il suo pugnale. Questi delitti sono gia sufficienti per comminare la pena capitale. Al Café Terminus, la bomba era scoppiata, rompendo il pavimento, spezzando gli specchi, i tavoli, i rivestimenti e riempiendo la sala di fumo. Si sentivano le urla delle vittime. Conoscete la composizione dell’ordigno, la sua forza; ve ne è stato parlato sufficientemente. Tuttavia, ricordate che c’era nella bomba dell’acido picrico e centoventi pallottole che dovevano, secondo l’intenzione stessa dell’accusato, fare un gran numero di vittime. Henry prima nega tutto; questo è il primo impulso di tutti i criminali. Anche lui ci tiene alla vita, lo ha detto; ha detto perché: per fare altre vittime! Altri ci tengono per venire in aiuto alla loro famiglia, ai loro figli, a una madre\dots{} Henry: Non occupatevi di mia madre; ve lo proibisco. Procuratore generale: Sono felice di vedere l’accusato uscire dalla sua impassibilità. Rispetto vostra madre e la compiango; ma voi non rispettate abbastanza le vittime che, anche loro, hanno una madre. Ne riparleremo; vuole salvarsi per ricominciare nuovi attentati. Cinque testimoni lo avevano visto; non poteva negare a lungo; allora, assume quell’atteggiamento arrogante che non ha più abbandonato. In quel momento, alla villa Faucheur, veniva svaligiata una camera; si scoprì che era la camera di Henry; quanto a lui, confessò di avere a casa sua di che confezionare quindici bombe; ma la maggior parte era scomparsa. Appena fu arrestato Émile Henry, fu interrogato sull’attentato della rue des Bons-Enfants. Per dieci giorni ha negato; questo non fermava l’istruttoria. Erano state arrestate diverse persone con le quali fu posto a confronto. Allora confessa. Fa delle rivelazioni di cui accetto solo la parte che è dimostrata, il resto non l’accetto. Avendo meditato a lungo su quanto avrebbe detto, con un’apparente sincerità, dichiarò di essere l’autore dell’attentato della ditta delle miniere di Carmaux. Spiegò l’istallazione degli uffici della Société de Carmaux. Lo ha fatto con una precisione estrema, ha segnalato a quindici mesi di distanza che una targa sulla strada portava il nome della Compagnia e sotto le parole “nell’ammezzato”, dettaglio che gli impiegati della compagnia non avevano notato. Ha fatto inoltre uno schizzo delle scale, provando così di averle salite. Ha dichiarato di aver visitato il fabbricato, che c’erano delle modiste. Fatte tutte queste constatazioni, ha inoltre indicato come ha fatto il suo ordigno. Sappiamo che cos’è un ordigno: la stampa ce ne ha descritti molti, ma era necessario indicare quale era esattamente l’ordigno che era servito al delitto. Era una marmitta speciale, che portava un’etichetta, un prezzo segnato; e ha indicato dove ha acquistato la marmitta, esponendo la topografia del negozio e il posto occupato dalle marmitte. I testimoni hanno confermato queste dichiarazioni. È stato trovato il tubo destinato a servire da detonatore, o, per lo meno, un tubo identico, dalla signora Colin. Ha comprato del clorato di potassio alla ditta Fontaine. Henry sostiene di aver portato da solo l’ordigno in avenue de l’Opéra. Qui non sono d’accordo con lui, credo che non abbia potuto fabbricare da solo il suo ordigno, soprattutto per mettere le reggette. Ci volevano almeno due persone, una per mantenerlo, l’altra per mettere la reggetta. E così, sono stati in due a portarlo; ha confezionato il suo ordigno aiutato da Lambert; perché, se Lambert fosse un ragazzo onesto, si sarebbe presentato da quando si parla di lui. Per portare l’ordigno, ha trovato una “compagna” (credo si dica cosi nell’ambiente). Ammetto che ha fatto tutte le commissioni che ha detto; ma per quello che riguarda avenue de l’Opéra, non siamo più d’accordo. Era pericoloso per un uomo trasportare quell’enorme pacco. Arrivato al n. 13, davanti al negozio del signor Weber, ha messo la marmitta nella borsa della donna che attendeva alla porta, là, ha incontrato il signor Le Fraper. Henry: Dite il nome. Presidente: Vi avverto che posso farvi espellere dall’aula; ascoltate il Procuratore generale; ascolteremo il vostro avvocato. Procuratore generale: Il signor Le Fraper aveva visto una donna portare l’ordigno, Henry lo sapeva e risponde “sì, ho incontrato una donna e un uomo giovane che ho salutato col cappello e che mi hanno ricambiato il saluto”, e allora tutto si spiegava. Ma il signor Le Fraper ha visto la donna, ma non il giovane che portava la marmitta. L’accusato ha voluto dimostrare troppo e non dimostra niente. Quando ha visto che era stata ricostruita la forma della marmitta e che era stato ritrovato il numero del giornale “Le Temps” che la avvolgeva, giornale conservato per cinque mesi, ha supposto che fosse prudente evitare ricerche lunghe e serie. Allora ha deciso di confessare, per salvare i suoi complici, affinché possano circolare liberamente; sono quelli che hanno preso le quindici bombe della villa Faucheur e di cui numerose sono forse già servite da allora. La Stampa, che ha pubblicato tante lettere, credo senza il consenso di Henry, ma non senza quello del suo difensore, pubblica oggi una lettera di un compagno di Londra che parla della compagna, dei complici, e della generosità di Henry per essersi assunto tutte le responsabilità. Con questi mezzi di difesa portati da noi, che non mi preoccupano affatto, sono state chieste delle attenuanti, da tutti i punti di vista. Si è detto del problema, occorre che io ne discuta. Henry dichiara di non essere pazzo, ma il dottor Goupil attribuisce la debolezza del suo cervello al troppo lavoro; l’intelligenza che egli ha dimostrato da allora ne conferma il contrario. Il padre era morto per una congestione cerebrale. Ma Henry ve l’ha detto: è un caso. Aveva il tifo: “Si può morire, dicono, o rimanere idioti”. Ma da allora ha dato prove della sua intelligenza. Se avessi il minimo dubbio, non verrei mai a chiedere la pena capitale. Il dottor Goupil ne vede la traccia nella stessa atrocità del crimine, ma questo non ci potrebbe fermare, perché è l’anarchia. Abbiamo avuto anarchici gloriosi, particolarmente Ravachol; Vaillant, invece, cavillava sulle sue intenzioni; non era un glorioso. Abbiamo avuto Willis, povero vecchio pazzo, condannato a qualche anno di galera. Abbiamo avuto Léauthier; e dopo aver letto le sue memorie, ho sentito la sua debolezza, e sono stato preso da un senso di pietà. Abbiamo avuto Gross e, in una notevole arringa, l’avvocato Saint-Auban ci diceva: “Lasciate che il pensiero umano si sviluppi, l’attentato non riflette il libro”. Qui l’attentato riflette il giornale. Il suo attentato, quello della rue des Bons-Enfants, riflette bene le indicazioni del giornale. Questo giornale indica il tempo necessario affinché il liquido attraversi il tampone; nel frattempo il compagno può procurarsi un alibi. Il giornale dichiara che occorre far saltare i borghesi nel loro palazzo, pensando che la bomba può sempre scoppiare tra le mani dei poliziotti. Henry è la prova vivente del pericolo della propaganda con lo scritto, altrettanto pericolosa di quella del fatto. L’uomo che ha compiuto questi fatti non è un pazzo. Li ha preparati a lungo ed eseguiti freddamente. Ora, come è diventato anarchico questo giovane borghese? Qui siamo in presenza non di Ravachol, Léauthier e altri, ma in presenza di un borghese. Suo padre era proprietario; è una nota singolare per un anarchico; era imprenditore di cave, poi ingegnere; e la sfortuna lo ha colpito facendolo ammalare. Come è stato educato l’accusato? Ai nostri tempi, ci si è molto impietositi per certi anarchici, per una ragazzina, dimenticando gli orfani che gli attentati avevano potuto fare. Ci si è impietositi anche per la sorte di Émile Henry; ha avuto una borsa di studio, si è diplomato, è stato ammesso all’École Polytechnique, era un piccolo borghese. Entrò dal signor Bordenave, a sedici anni e mezzo gli dà un posto e vuol costruirgli il suo avvenire. Inizia con 75 franchi al mese; non potevano bastare al suo orgoglio, era insufficiente, avrebbe voluto iniziare dove gli altri finiscono. È orgoglioso e crudele. Dopo l’affare Terminus, dichiara di chiamarsi Breton, di arrivare da Marsiglia o da Pechino, come volete. Vedete quanto è freddo e ironico. Aggiunge che rimpiange di non aver ucciso più persone e di non aver fatto uso del suo pugnale: “Ho ucciso troppa poca gente! Altri verranno dopo di me, e riusciranno meglio”. Ecco quello che dichiara. Avete visto il suo atteggiamento, ieri, in presenza delle vittime. Quando il signor van Herreweghen deponeva, mostrava la sua indifferenza di fronte a questa vittima ancora impotente che piangeva la morte del suo amico. Dopo l’attentato della rue des Bons-Enfants di cosa ha vissuto? Dichiara di aver lavorato da un fabbro, lavorava ma senza essere pagato. L’anarchia pura non predica solo la violenza, ma anche il furto. È legato ad Ortiz, che è un ladro, e a molti altri. Si fanno ricerche, e quarantotto ore fa, lo si confronta con una persona che non è un testimone qualunque, che ha ricevuto a casa sua la visita di due individui spariti dal paese dopo aver commesso un furto abominevole da una vecchia donna, dove non hanno potuto trovare niente. Questo testimone riconosce Henry e non si sbaglia. Se non potete far conoscere le vostre fonti di sussistenza, tutti i sospetti sono permessi. Vi devo parlare delle vittime: sono pieno di pietà per la signora Henry, e il suo lutto non comincerà col vostro verdetto; il suo lutto è iniziato il giorno del delitto: la signora Henry, vostra madre, è la vostra prima e più dolorosa vittima. Cinque vittime sono morte in rue des Bons-Enfants; la sesta, poco tempo fa, è spirata dopo orribili sofferenze. I feriti: il signor van Herreweghen, ancora inabile; il signor Maurice, parrucchiere; queste signore atterrite che si nascondono nel loro terrore, e molti altri. Henry sghignazza davanti a queste vittime! Garin, il fattorino della Société de Carmaux, lascia una vedova incinta e due figlioletti; vive con una piccola pensione. Réaux aveva ventotto anni; lascia una vedova e una bambina. Formorin lascia una vedova e un bambino. Troutot lascia una vedova e tre figli. Pousset lascia due figli e una vedova. Ecco il bilancio dell’anarchia: Pousset era figlio di un ufficiale; allievo a La Flèche, era andato a Saint-Cyr, era diventato ufficiale; amava una donna senza dote, l’ha sposata e ha dovuto spezzare la sua carriera; ha fatto un poco di tutti i mestieri; ha studiato diritto, si è laureato in legge, segretario del commissario di polizia, e doveva presto diventare commissario di polizia. L’assurda bomba della rue des Bons-Enfants ha spezzato tutto ciò. Ecco quello che ha fatto. È la soluzione della questione sociale alla maniera degli anarchici. I delitti di Henry sono delitti atroci; l’opinione pubblica ha per loro solo odio e vendetta. Stava per essere fatto a pezzi dalla folla. La giustizia è più fredda, calma; quello che la folla avrebbe fatto sotto l’impulso della collera, fatelo col sangue freddo necessario alla giustizia. Pensate che solo la pena capitale può eguagliare i suoi crimini. In caso contrario, evaderebbe in qualunque condizione, la vita di una guardia carceraria non lo fermerebbe. Ed è la morte di molte persone che voi pronuncereste colla vostra indulgenza. La vostra debolezza sarebbe senza scuse. Per quanto riguarda delitti ordinari, ho già richiesto la pena capitale; anche per i delitti anarchici ho dovuto già richiederla. Nel 1891 ho chiesto, in questa sala, una condanna capitale per un anarchico. I vostri predecessori si sono mostrati indulgenti; è stato condannato a cinque anni di carcere. Da quel giorno sono cominciati gli attentati anarchici. È per vendicare quest’uomo che Ravachol ha commesso i suoi crimini. Chi vuole vendicare quest’ultimo? È Vaillant; è l’attentato da Foyot; è ogni giorno un attentato nuovo. Le attenuanti costituirebbero un atto di debolezza. Vi conosco abbastanza per non temerlo. L’udienza sospesa alle cinque meno un quarto è ripresa alle cinque e dieci minuti. Émile Henry chiede la parola, che gli viene accordata. Si alza e voltandosi verso i signori giurati, si esprime in questi termini: Signori giurati, [Questa versione della dichiarazione di Émile Henry a stata ripresa integralmente da: L. Galleani, \emph{Il processo di Emilio Henry}, Genova 1956, Collana Anteo. La versione della “Gazette des Tribunaux” e la “Declarations d’Émile Henry”, “Documents d’histoire”, Aiglemont 1907, a cura di Fortuné Henry già discordanti tra di loro, si differenziano per alcuni passaggi da questa che abbiamo adottato]. Voi conoscete i fatti di cui sono accusato: dell’esplosione della rue des Bons-Enfants che ha ucciso cinque persone e cagionato la morte d’una sesta; dell’esplosione del Café Terminus che ha ucciso una persona e cagionato la morte di una seconda e ferito un certo numero di altre, e finalmente di sei colpi di rivoltella tirati da me contro coloro che mi inseguivano dopo quest’ultimo attentato. Il corso del processo vi ha dimostrato come io mi riconosca l’autore responsabile di questi atti. Non presento dunque la mia difesa, poiché in nessun modo io cerco di sfuggire alle rappresaglie della società che ho attaccato. Del resto, io non riconosco che un solo tribunale, me stesso; il verdetto di ogni altro mi lascia indifferente. Io voglio semplicemente darvi la spiegazione dei miei atti e dirvi in qual modo io sono stato condotto a compierli. Da non molto tempo io sono anarchico. Non è che verso la metà dell’anno 1891 che sono entrato nel movimento rivoluzionario. Prima io vi aveva vissuto in ambienti completamente imbevuti della morale odierna. Ero stato abituato a rispettare e anche ad amare i princìpi di patria, di famiglia, di autorità e di proprietà. Ma gli educatori della generazione attuale, scordano troppo spesso una cosa, ed è che la vita, colle sue lotte e colle sue discussioni, colle sue ingiustizie e colle sue iniquità, s’incarica bene, l’indiscreta, di aprir gli occhi agli ignoranti, e di aprirli alla realtà. Ed è ciò che accade a me, come accade a tutti. Mi avevano detto che la vita era facile e largamente aperta alle intelligenze e alle energie, e l’esperienza mi dimostra che solo i cinici e gli arruffoni possono trovare un buon posto al banchetto della vita. Mi avevano detto che le istituzioni sociali erano basate sulla giustizia e sull’eguaglianza, ed io non constatai invece intorno a me che menzogne e furberie. Ogni giorno che passava, mi toglieva un’illusione. Dovunque andassi, ero testimone degli stessi dolori presso gli uni, degli stessi godimenti presso gli altri; e non tardai a comprendere che le grandi parole le quali mi avevano insegnato a venerare – onore, abnegazione, dovere – non erano che un maschera buttata sulle più vergognose turpitudini. L’usuraio [Nella “Gazette des tribunaux” e nella “Declarations d’Émile Henry” vi è usinier (industriale)] che accumula una fortuna colossale alle spese del lavoro degli operai i quali, invece, mancano di tutto, è un signore onesto. Il deputato, il ministro, le cui mani sono sempre aperte alle offerte di corruzione, sono gente devota al bene pubblico. L’ufficiale che esperimenta il futile nuovo modello su dei fanciulli di sette anni compie il suo dovere, e in pieno Parlamento, riceve le felicitazioni del Presidente del Consiglio. Tutto questo che vidi mi nauseò, e il mio spirito si diede a criticare l’organizzazione sociale. Questa critica è stata fatta troppo spesso perché io la ricominci. Mi basterà dire che divenni il nemico di una società che giudicai criminale. Attirato per un momento dal socialismo non tardai ad allontanarmi da questo partito. Avevo troppo amore per la libertà, troppo rispetto per l’iniziativa individuale, troppa ripugnanza per l’irreggimentazione per diventare un numero nell’esercito matricolato del Quarto Stato. Del resto, mi avvidi che in fondo il socialismo non cambia nulla all’ordine attuale. Esso mantiene il principio autoritario, e questo principio, malgrado ciò che ne possano dire taluni pretesi liberi pensatori, non è che un vecchio residuo della fede in una potenza superiore. Degli studi scientifici mi avevano gradualmente iniziato al gioco delle forze naturali. Ora, io era materialista e ateo; avevo compreso che l’ipotesi Dio era scartata dalla scienza moderna, la quale non ne aveva più bisogno. La morale religiosa e autoritaria basata sul falso, doveva dunque sparire. Qual era allora la nuova morale in armonia con le leggi della natura che doveva rigenerare il vecchio mondo e creare l’umanità felice? Fu a tal momento che entrai in relazione con alcuni compagni anarchici, i quali io considero ancora oggi come i migliori che abbia mai conosciuto. Il carattere di questi uomini mi sedusse di primo tratto. Apprezzai in loro una grande sincerità, un’assoluta franchezza, un disprezzo profondo di tutti i pregiudizi, e io volli conoscere l’idea che rendeva questi uomini così differenti da tutti coloro che avevo visto sino allora. Questa idea trovò nel mio spirito un terreno reso adattissimo a riceverla da osservazioni e riflessioni personali. Essa non fece che precisare ciò che era in me di vago e indeciso. Divenni a mia volta anarchico. Non mi spetta sviluppare qui la dottrina dell’Anarchia. Solo voglio accennare al suo lato rivoluzionario, al suo lato distruttore e negativo per il quale io compaio innanzi a voi. In questo momento di lotta acuta tra la borghesia e i suoi nemici, io sono quasi tentato di dire col Souvarine del \emph{Germinal}: “Tutti i ragionamenti sull’avvenire sono delittuosi, perché impediscono la distruzione pura e semplice e ostacolano il cammino della rivoluzione”. Dacché un’idea è matura e ha trovato una formula, bisogna senza più tardare cercarne la realizzazione. Io ero convinto che l’organizzazione attuale è cattiva e ho voluto lottare contro di essa per affrettarne la sparizione. Io ho portato nella lotta un odio profondo, ogni giorno ravvivato dallo spettacolo nauseante di questa società in cui tutto è basso, [tutto è losco, tutto è brutto – unicamente nella versione di L. Galleani], in cui tutto è di ostacolo all’espansione delle passioni umane, alle tendenze generose del cuore, al libero slancio del pensiero. Io ho voluto colpire tanto fortemente e tanto giustamente quanto ho potuto. Passiamo dunque al primo attentato che ho commesso, all’esplosione della rue des Bons-Enfants. Avevo seguito con attenzione gli avvenimenti di Carmaux. Le prime notizie dello sciopero mi avevano colmato di gioia: i minatori parevano disposti a rinunciare finalmente agli scioperi pacifici e inutili, nei quali il lavoratore attende pazientemente che i suoi pochi soldi trionfino dei milioni delle compagnie. Essi parevano entrati in una via di violenza che si affermò risolutamente il 15 agosto 1892. Gli uffici e gli edifici della miniera furono invasi da una folla stanca di soffrire senza vendicarsi: giustizia stava per essere fatta dell’ingegnere così odiato dagli operai, quando le solite persone s’interposero. Chi erano costoro? Gli stessi che fanno abortire tutti i movimenti rivoluzionari, perché temono che, una volta slanciato, il popolo non obbedisca più alla loro voce; gli stessi che spingono migliaia di uomini a soffrire privazioni per mesi interi, allo scopo di crearsi una popolarità alle spese delle loro sofferenze e così ottenere una candidatura – voglio dire i capi socialisti [voglio dire i\dots{} non appare nella “Déclarations d’Émile Henry”]. Questi uomini infatti presero la direzione del movimento. Si vide d’un tratto precipitarsi sul paese una nuvolaglia di signori, bravi chiacchieroni, i quali si misero a disposizione intera dello sciopero, organizzarono sottoscrizioni, fecero conferenze, rivolsero per ogni parte appelli di fondi. I minatori abdicarono ogni loro iniziativa nelle loro mani. Ciò che accadde lo si sa. Lo sciopero si prolungò eternamente, i minatori fecero una più intima conoscenza con la fame, loro abituale compagna; esaurirono il piccolo fondo di riserva del loro sindacato e quello delle corporazioni che vennero loro in aiuto; poi, in capo a due mesi, con le orecchie basse, tornarono alla loro galera più miserabili di prima. E pur sarebbe stato così semplice, dal principio, attaccare la Compagnia nel suo solo lato sensibile, nel denaro; bruciare il deposito del carbone, spezzare le macchine di estrazione, demolire le pompe di prosciugamento. Certo, la Compagnia avrebbe capitolato rapidamente. Ma i grandi pontefici del socialismo non ammettono questi sistemi che sono sistemi anarchici. A questo gioco si rischia la prigione e, chi sa? forse una di quelle palle che fecero meraviglie a Fourmies. Né c’è da guadagnare alcun mandato legislativo. In breve, l’ordine per un istante turbato regnò di nuovo a Carmaux. La Compagnia continuò più potente che mai il suo sfruttamento e i signori azionisti si felicitarono del risultato dello sciopero. Via, i dividendi sarebbero ancora buoni da riscuotere. Fu allora che mi decisi a mescolare a questo concerto di accenti felici, una voce che i borghesi avevano già intesa, ma che essi credevano morta con Ravachol: la voce della dinamite. Ho voluto dimostrare alla borghesia che ormai non vi sarebbero più per essa gioie complete, che i suoi trionfi insolenti sarebbero turbati, che il vitello d’oro tremerebbe sulla sua base, sino alla scossa definitiva che lo getterà giù nel sangue. Nello stesso tempo ho voluto far comprendere ai minatori come non vi sia che una sola categoria di uomini, gli anarchici, i quali sentono sinceramente le loro sofferenze e sono pronti a vendicarle. Questi uomini non siedono al Parlamento come i signori Guesde e compagnia, ma vanno alla ghigliottina. Preparai dunque la mia bomba. Per un momento mi ritornò alla mente l’accusa che era stata lanciata a Ravachol. E le vittime innocenti? Ma io risolsi presto la questione. La casa in cui si trovano gli uffici della compagnia di Carmaux non era abitata che da borghesi; non vi sarebbero state dunque vittime innocenti. La borghesia tutta quanta vive dello sfruttamento dei disgraziati; essa deve tutta quanta espiare i suoi delitti. Con questa certezza assoluta della legittimità del mio atto, io deposi la mia bomba innanzi alle porte dell’ufficio della Società. Nel corso del dibattimento ho spiegato in qual modo io sperassi, nel caso che la mia macchina fosse stata scoperta, che essa scoppiasse all’ufficio di polizia, colpendo sempre così i miei nemici. Ecco dunque i moventi che mi hanno fatto commettere il primo attentato che mi si rimprovera. Passiamo al secondo, quello del Café Terminus. Io ero venuto a Parigi all’epoca dell’attentato di Vaillant. Avevo assistito alla repressione formidabile che succedette a quell’attentato. Fui testimone delle misure draconiane adottate dal governo contro gli anarchici. Da tutte le parti si esercitava lo spionaggio, si facevano perquisizioni e arresti. In quelle razzie operate a casaccio una quantità di individui erano arrestati e gettati in prigione. Che avveniva delle mogli e dei figli di questi compagni durante il loro incarceramento? Nessuno se ne preoccupava. L’anarchico non era più un uomo, era una bestia feroce cacciata da tutte le parti e di cui la stampa borghese, questa vile schiava della forza, domandava su tutti i toni lo sterminio. Nello stesso tempo, i giornali e gli opuscoli libertari venivano sequestrati, il diritto di riunione proibito. Peggio ancora: quando la polizia voleva sbarazzarsi di un compagno, una spia deponeva una qualche sera nella camera di lui un pacco contenente tannino, cosi egli diceva; il giorno seguente aveva luogo una perquisizione, in forza di un ordine datato due giorni prima, e si trovava invece una scatola riempita di polvere sospetta. Così il compagno veniva processato e gli si affibbiavano tre anni di galera. Chiedete se ciò non è vero al miserabile denunciatore che si introdusse presso il compagno Mérigeaut [Joseph Mérigeaut, condannato nel 1894 per detenzione di materie esplosive. Per un periodo era stato sospettato di aver partecipato all’attentato della rue des Bons-Enfants]. E, come coronamento a questa crociata, non fu udito il signor Raynal, ministro dell’interno, dichiarare alla Camera che le misure prese dal governo avevano ottenuto un buon risultato, in quanto avevano gettato il terrore nel campo anarchico? Ma non se ne aveva ancora abbastanza. Si era condannato a morte un uomo che non aveva ucciso nessuno. Bisognava dar prova di coraggio sino all’ultimo: un bel mattino lo ghigliottinarono. Ma, signori borghesi, voi avevate un poco troppo contato senza il vostro ospite. Voi avevate arrestato centinaia d’individui, avevate violato numerosi domicili; ma eranvi ancora degli uomini da voi ignorati, rimasti nell’ombra, che assistevano alla vostra caccia all’anarchico e che non aspettavano che il momento favorevole per dare a loro volta la caccia ai cacciatori. Le parole del signor Raynal erano una sfida gettata agli anarchici; il guanto fu raccolto. La bomba al Café Terminus è la risposta a tutte le vostre violazioni della libertà, a tutti i vostri arresti e perquisizioni in massa contro gli stranieri, alle vostre condanne, alla vostra ghigliottina. Ma perché, direte voi, prendersela con pacifici consumatori che stanno ad ascoltar la musica e che, forse, non sono né magistrati né deputati né funzionari? Perché? La cosa è semplice. La borghesia non ha fatto che un mucchio degli anarchici. Un uomo solo, Vaillant, aveva lanciato una bomba; i nove decimi dei compagni non lo conoscevano neppure. Ma ciò non valse a nulla. Le persecuzioni infierirono in massa. Fu data la caccia a tutti coloro che avevano relazione con anarchici. Ebbene, giacché voi rendete così un partito [Questa parola, usata all’epoca, assumeva un significato simile a movimento. Non stava ad indicare l’organizzazione politica strutturata in modo gerarchico, che invece l’attuale termine partito indica (ndr).] tutto quanto responsabile degli atti di un sol uomo e colpito in massa, anche noi colpiamo in massa! Dobbiamo noi prendercela soltanto coi deputati che fanno le leggi ai nostri danni, coi magistrati che le applicano, coi poliziotti che ci arrestano? Io non lo credo. Tutti questi uomini non sono che strumenti i quali non agiscono in loro proprio nome, essendo state le loro funzioni istituite dalla borghesia in sua difesa; essi non sono dunque più colpevoli degli altri. I buoni borghesi i quali, senza pur essere rivestiti di nessuna funzione, riscuotono le rendite dei loro titoli, i buoni borghesi che vivono oziosi dei benefici del lavoro degli operai, debbono avere anch’essi la loro parte di rappresaglie. E non soltanto essi, ma tutti coloro che sono soddisfatti dell’ordine attuale, coloro che applaudono agli atti del governo e si fanno suoi complici, questi impiegati da 300 a 500 franchi al mese che odiano il popolo più ancora dei grossi borghesi, questa massa stupida e pretenziosa che si schiera sempre dal lato del più forte, e forma la clientela abituale del Café Terminus e degli altri grandi caffè. Ecco perché io ho colpito nel mucchio senza scegliere le mie vittime. Bisogna che la borghesia comprenda che coloro i quali hanno sofferto sono finalmente stanchi delle loro sofferenze, e mostrano i denti e colpiscono tanto più brutalmente quanto maggiore brutalità si è usata con loro. Essi non hanno alcun rispetto della vita umana, perché i borghesi stessi non se ne occupano. Non spetta agli assassini della Settimana Sanguinosa e di Fourmies di trattare gli altri da assassini. Se i ribelli non risparmiano né le donne né i fanciulli borghesi, è perché neppure vengono risparmiate le donne e i fanciulli di coloro che essi amano. Non sono forse vittime innocenti quei fanciulli che, nei sobborghi, muoiono lentamente di anemia, perché il pane è scarso in casa; quelle donne che nei vostri laboratori impallidiscono e sfioriscono per guadagnare quaranta soldi al giorno, felici pur anco quando la miseria non le costringe a prostituirsi; quei vecchi di cui avete fatto macchine da produzione per tutta la vita e che gettate sul lastrico e all’ospedale quando le loro forze sono esaurite? Abbiate almeno il coraggio dei vostri delitti, o signori borghesi, e convenite che le nostre rappresaglie sono grandemente legittime. Certo, non m’illudo. Io so che i miei atti non saranno ancora ben compresi dalle folle insufficientemente preparate. Anche fra gli operai, per i quali ho lottato, molti, traviati dai vostri giornali, mi credono loro nemico. Ma questo poco importa. Io non mi preoccupo del giudizio di nessuno. Non ignoro nemmeno che vi sono individui sedicenti anarchici, i quali si affrettano a rinnegare ogni solidarietà coi propagandisti del fatto. Essi tentano di stabilire una distinzione sottile fra teorici e terroristi. Troppo vili per rischiare la loro vita, rinnegano coloro che agiscono; ma l’influenza che essi pretendono di avere sul movimento rivoluzionario è nulla. Oggi il campo appartiene all’azione, senza piegare né indietreggiare. Alexander Herzen, il rivoluzionario, ha detto: “O l’una cosa o l’altra: o levarsi a giustiziere e camminare innanzi, o far grazia e vacillare a mezza strada”. Noi non vogliamo far grazia né vacillare, e procederemo sempre innanzi finché la rivoluzione, scopo degli sforzi nostri, venga finalmente a coronare l’opera nostra, rendendo il mondo libero. In questa guerra senza pietà che abbiamo dichiarata alla borghesia, noi non domandiamo alcuna pietà. Noi diamo la morte, noi sapremo subirla. Così attendo con indifferenza il vostro verdetto. So che la mia testa non sarà l’ultima che mozzerete; altre ne cadranno ancora, perché i morti di fame cominciano a conoscere la strada dei vostri caffè e dei vostri grandi ristoranti Terminus e Foyot. Altri nomi voi aggiungerete alla lista dei nostri morti. Voi avete impiccato a Chicago, decapitato in Germania, garrotato a Xeres, fucilato a Barcellona, ghigliottinato a Montbrison e a Parigi, ma ciò che non potrete mai distruggere è l’Anarchia. Le sue radici sono troppo profonde; essa è nata nel seno stesso di una società putrida che si sfascia; essa è una reazione violenta contro l’ordine stabilito. Essa rappresenta le aspirazioni egualitarie e libertarie che battono in breccia l’autorità odierna; essa è dappertutto e ciò che la rende inafferrabile finirà coll’uccidervi. Ecco, o signori giurati, ciò che dovevo dirvi. Ascolterete ora il mio avvocato. Siccome le vostre leggi impongono un difensore, la mia famiglia ha scelto il signor Hornbostel. Ma, qualunque cosa egli possa dirvi, non modifica in nulla ciò che io ho detto. Le mie dichiarazioni sono 1’espressione esatta del mio pensiero. Ad esse mi attengo integralmente. \bigskip Dopo questa dichiarazione, l’avvocato Hornbostel presenta la difesa dell’accusato: Non è senza una certa emozione che sono in questa sede, nuova per me, per presentare la difesa del mio giovane e sventurato cliente. Esponendovi come sia arrivato all’anarchismo, egli ha svolto metà del mio compito. Mi ha permesso di evitare fastidiose apologie non condividendo altro che la sua compassione per certe miserie. Oggi l’emozione è passata, l’eccitazione è spenta e questi dibattimenti si svolgono in mezzo all’apatia generale. Oggi si manifesta per lui un sentimento di misericordia; uno dei suoi carcerieri, sottoposto all’attrazione ch’egli esercita intorno a sé, si è fatto destituire per la sua indulgenza. Avete sentito le deposizioni di questi testimoni, di queste persone onorate. Ed io, che cosa sono qui, se non un altro testimone che la legge gli impone? Non possiamo renderci conto qui del suo delitto; lui che va così, in un luogo sconosciuto per colpire degli sconosciuti. Non è un volgare ambizioso: ha creduto di essere predestinato, di essere il propagatore di una idea che doveva presto germinare e svilupparsi. Vi è stato incitato dagli atti del padre, non si segue forse sempre la carriera del proprio padre? Io, figlio di avvocato, mi sono dato all’avvocatura; figlio di insorto, è diventato un ribelle. Suo padre, massone militante al momento della guerra del 1870, ha fatto di tutto per evitare spargimenti di sangue e mettere in opera uno dei più bei princìpi della massoneria. Vi ricorderete di questi fatti quando dovrete deliberare la sentenza. Non credete che i sentimenti del padre possano passare nell’animo del figlio? Henry è stato concepito durante quelle orribili notti della Comune, in mezzo al sangue della lotta, delle esplosioni, mentre il padre stesso partecipava ardentemente a questa insurrezione. Questo è il segreto del suo stato d’animo, l’unica causa del suo delitto. Chi ci dice che l’anarchia non è l’aurora di qualche nuova religione? Il giudaismo, l’islamismo sono stati fondati così. Sono i precursori di Émile Henry: l’anarchia si fonderà sul sangue degli anarchici, non su quello di coloro che essi faranno versare; come quello del maresciallo Ney e di Baudin che fecero sorgere nuove ere. Avete visto i pellegrinaggi sulla tomba di Vaillant; che cosa si farà per Henry, di quale aureola sarà circondata la sua fronte e di quale culto sarà avvolta la sua memoria? Forse i suoi compagni della Scuola Say andranno ad inchinarsi devotamente sulla sua tomba e i passanti si chiederanno quale Dio viene così onorato! Volete fare questo nuovo martire, dare all’anarchia questa nuova forza? Henry disprezza, come me, coloro che vendono le proprie idee; disprezza coloro che sognano l’opposizione al governo; opposizione simile a quella tanto poco fruttuosa che fu fatta sotto l’Impero. Si dà interamente e senza ripensamenti alla difesa delle sua idee. La borghesia si è commossa ed è pietà ciò che oggi tutti sentiamo per questo giovane sognatore. Il procuratore generale vi chiede di salvare la società; essa ha i suoi difensori naturali: le corti marziali. Voi, siete dei giurati incaricati di giudicare secondo la vostra coscienza. Si istituiscano corti marziali ma non si venga a sottomettere a pacifici cittadini dei delitti di questa natura e vecchi di tre mesi! Potete condannare Henry alla pena di morte come un Anastay, un Pranzini, un Prado? Henry non è né un Prado, né un Gamahut [L’avvocato Hornbostel evoca qui degli “affari criminali” dell’epoca: François Louis Anastay, ufficiale condannato a morte nel 1892 per l’assassinio, il 4 dicembre 1891, della baronessa Dellard; Henri Pranzini, condannato a morte nel 1887 per un triplice omicidio commesso nello stesso anno, ecc.]; il suo atto differisce dal crimine, come un delitto di stampa differisce dal furto. Qui si tratta di un ragazzo onesto che è stato spinto solo dalla passione politica. Farete questa differenza. Durante le poche ore in cui è stato innanzi a voi, avete potuto giudicare Henry solo in modo imperfetto. È una intelligenza giovane e brillante; piena di illusioni. Questa è la prima di tutte le attenuanti. Voi conoscete la sua famiglia, sua madre, i suoi parenti. Debbo parlarvi di sua madre? Quando si ha una madre e ci si lascia difendere per poterla abbracciare ancora una volta, non c’è rigore che possa resistere! È un ribelle, non un criminale incallito. Nessuno dei sui conoscenti più intimi si è vergognato di lui o dei suoi atti. Sarebbero arrossiti se avesse compiuto un furto. Henry era un asceta e viveva di pane e acqua; l’atto che ha compiuto era completamente disinteressato. È il Gavroche che sale sulle barricate per ridere degli assalitori. Qual era l’interesse di Henry? Nessuno: non poteva credere all’esito immediato dell’anarchia e non poteva sperare niente da un prossimo successo. Questo atto si allinea tra i delitti passionali, e mai avete visto ergersi il patibolo per tali delitti. Il fanatismo, ecco la sua passione! Non voglio fare qui il processo al fanatismo. È stato il fanatismo a prenderlo come una piovra, come un virus rabico e lo ha preso interamente. Henry, che amava il popolo, odiava la folla, questa caricatura del popolo; ed è ciò che lo ha guidato al Café Terminus. Il fanatismo ha guidato Émile Henry; è il vandeano che si nasconde per uccidere il soldato del re. È il bersagliere che colpisce il nemico. Henry poteva essere solo un criminale politico o un pazzo; merita la pietà, come un bambino trascinato in questo terribile ingranaggio del fanatismo politico. Vi è stata una quantità di crimini politici i cui autori sono oggi liberi; ciò che crea il delitto politico è l’antagonismo politico e la sconfitta. Quanti uomini, un tempo ribelli, membri della Comune, sono oggi nelle cariche più elevate! Henry ha seguito un’idea politica che presenta una certa grandezza, gente come lui vi si dedica fino alla morte. Se Henry è innocente per il delitto della rue des Bons-Enfants, se confessa un delitto di cui è innocente, per discolpare gli altri, questo dà un esempio della virtù di cui i più grandi non possono che contestarne l’elevazione. Non vorrete che una condanna capitale venga a dare all’anarchia una nuova rinascita. Essa si spegne, scompare, si incomincia a riderne, viene presa in giro; non fatela rivivere facendo un martire. Non si colpisce il colpevole con la pena capitale alla sua prima infrazione ai regolamenti sociali. Non si ghigliottina un ragazzo che ha una madre e che ha compiuto un atto fatale. Pensate che concedendo le attenuanti a Henry, colpite forse mortalmente l’anarchia. L’udienza, sospesa alle sei e trentacinque, viene ripresa alle sette e mezzo. La giuria si accorda per un verdetto affermativo su tutte le questioni e muto sulle attenuanti. Su domanda del Presidente, se non abbia qualcosa da aggiungere in sua difesa, Henry risponde di no: “Accetto, aggiunge, la condanna qualunque essa sia”. La Corte condanna Henry alla pena di morte. Uscendo, Henry grida: “Compagni, coraggio! Viva 1’anarchia!”. L’udienza è tolta alle otto meno un quarto. Poco dopo, quando la folla si fu dispersa e il Palazzo rimase vuoto, tre donne vestite a lutto uscivano dalla porta della Place Dauphine: una di loro singhiozzando, avanzava faticosamente appoggiata alle altre due. Era la madre di Émile Henry. \bigskip (Vedi la “Gazette des Tribunaux” 28 e 29 aprile 1894) \chapter{Aforismi} \begin{quote} Una volta, il chiostro si apriva per le anime stanche o disgustate dagli spettacoli del mondo, oggi noi non abbiamo altro rifugio che negli ospedali e nelle carceri. Cosa vogliono gli anarchici? L’autonomia dell’individuo, lo sviluppo della sua libera iniziativa che, soli, potranno assicurargli tutta la felicità possibile. Se l’anarchico ammette il comunismo come concezione sociale, è per semplice deduzione, perché comprende che è solo nella felicità di tutti, liberi e autonomi come lui, che troverà la sua stessa felicità. Quando un uomo, nella società attuale, diventa un ribelle cosciente della propria azione – e tale era Ravachol – è perché ha fatto nel suo cervello un lavoro di analisi doloroso le cui conclusioni sono imperative e non possono essere eluse se non per vigliaccheria. Lui solo tiene la bilancia, lui solo è giudice della ragione o del torto di odiare e di essere selvaggio, “persino feroce”. Ritengo che gli atti di brutale rivolta siano giusti, perché svegliano la massa, la scuotono come una violenta frustata e le mostrano il lato vulnerabile della Borghesia ancora tutta tremante al momento in cui il Ribelle sale al patibolo. Ognuno di noi ha una fisionomia e delle attitudini speciali che lo differenziano dai suoi compagni di lotta. Così, non siamo stupiti dal vedere i rivoluzionari tanto divisi nella direzione dei lori sforzi. Ci si domanda quale sia la buona tattica: essa è ovunque proporzionale alla somma di energia che si apporta all’azione. Ma non riconosciamo a nessuno il diritto di dire: “Solo la nostra propaganda è quella buona; fuori di essa non v’è salvezza”. È un vecchio residuo di autoritarismo nato dalla vera o falsa ragione che i libertari non devono tollerare. Fa’ ciò che credi sia meglio e fallo con amore. A coloro che dicono: “L’odio non genera l’amore”, rispondete che è l’amore, vivo, che spesso genera l’odio. L’odio che non poggia su una bassa invidia, ma su un sentimento generoso, è una passione sana e potentemente vitale. Più amiamo il nostro sogno di libertà, di forza e di bellezza, più dobbiamo odiare ciò che si oppone al suo avvenire. Nella storia del progresso umano c’è un solo partito, è il partito del movimento. I socialisti non vogliono capire che la libertà dell’individuo è necessaria alla vera libertà del popolo. Nella dedica del suo libro, \emph{Dall’altra sponda}, Alexandre Herzen precisa un atteggiamento veramente rivoluzionario ed efficace quando dice: “Noi non costruiamo, noi demoliamo; noi non annunciamo affatto delle nuove rivelazioni, noi sopprimiamo la vecchia menzogna”. Questo libro di Herzen è pieno di sprazzi e di rivelazioni, ma non vi mancano nemmeno le osservazioni mordaci: è un buon libro per il carcere; e lontano dalla strada mi piace prenderlo come un’eco: “I Francesi non possono liberarsi dall’idea dell’organizzazione monarchica; hanno la passione della polizia e dell’autorità; ogni francese è nel suo animo un commissario di polizia; egli ama l’allineamento e la disciplina; tutto ciò che è indipendente, individuale, lo irrita; comprende l’uguaglianza solamente come livellamento e si sottomette volentieri all’arbitrio della polizia purché tutti vi si sottomettano. Mettete un gallone sul cappello di un francese ed egli diventa un oppressore, comincia ad opprimere chiunque non porti quel grado; egli esige il rispetto nei confronti dell’autorità.” Vi è un diritto che prevale su tutti gli altri, è il diritto all’insurrezione. L’uomo libero è colui agli occhi del quale i filosofi sono superstiziosi, e i rivoluzionari conservatori. I liberali sono in politica della stessa odiosa razza dei protestanti. La società moderna è come una vecchia nave che affonderà nella tempesta per non aver voluto sbarazzarsi del suo carico accumulato durante il viaggio nel corso dei secoli; vi sono delle cose preziose, ma che pesano troppo. Tutti i partiti politici sono logori, ecco perché noi appariamo. L’operaio che si ubriaca almeno una volta a settimana non fa cosa diversa da chi cerca illusioni. Se io fossi un filosofo scriverei qualcosa sulla necessità di ubriacarsi per addormentare la volontà che ci fa soffrire. Quanti esseri hanno attraversato la vita senza mai svegliarsi! E quanti altri si sono accorti che stavano vivendo solo per il monotono tic-tac degli orologi! Tra la beatitudine dell’incoscienza e l’infelicità di sapere, io ho scelto. Finora i popoli hanno inteso la fratellanza solo come hanno fatto Caino ed Abele. Che dire di quei rivoluzionari che sono solo dei vili ragionatori e che riflettono quando invece bisogna colpire? La sfera delle idee generali ha rimpiazzato in loro il mondo della contemplazione. C’è un’asserzione di Proudhon che, al suo tempo, è stata ritenuta immorale e che oggi sarebbe criminale. Vale a dire che la Repubblica è fatta per gli uomini e non gli individui per la Repubblica. L’uomo ha bisogno talvolta di credere alla potenza della propria volontà; è allora che entra nella lotta. Tra gli economi di se stessi e i prodighi di se stessi, credo che i prodighi siano i migliori calcolatori. Più amiamo la libertà e l’uguaglianza, più dobbiamo odiare quanto si oppone alla libertà e all’uguaglianza degli uomini. Così, senza perderci nel misticismo, poniamo il problema sul terreno della realtà, e diciamo: È vero che gli uomini sono solo il prodotto delle istituzioni; ma queste istituzioni sono cose astratte che esistono solo in quanto vi sono uomini in carne ed ossa per rappresentarle. C’è quindi un solo mezzo per colpire le istituzioni: colpire gli uomini. Una volontà che si spinge fino al suicidio può generare atti di dedizione definitivi e senza speranza. Uno dei primi insegnamenti dell’anarchia è questo: “Sviluppa la tua vita in tutte le direzioni, opponi alla ricchezza fittizia dei capitalisti, la ricchezza reale degli individui possessori di intelligenza ed energia”. Amo tutti gli uomini nella loro umanità e per quello che dovrebbero essere, ma li disprezzo per quello che sono. Inoltre, ho ben il diritto di uscire dal teatro quando la recita mi diventa odiosa, ed anche di sbattere la porta uscendo, pur col rischio di turbare la tranquillità di quelli che ne sono soddisfatti. \end{quote} Grande Roquette, maggio 1894 \bigskip [Questi “aforismi postumi” sono stati pubblicati la prima volta col titolo di “Pensées” su “Le Libertarie” n. 28, 23-29 maggio 1896. Sono poi apparsi nel n. 7 dei “Documents d’histoire” (febbraio 1907) che Fortuné Henry pubblicava a Aiglemont (Ardenne)] \chapter{Appendice. Errico Malatesta: “Un po’ di teoria”} La rivolta minaccia ovunque; qui è l’espressione di un’idea, là il risultato di un bisogno; più spesso, la conseguenza dell’intrecciarsi dei bisogni e delle idee che si generano e si rafforzano reciprocamente. Essa attacca le cause del male o colpisce di fianco, è cosciente o istintiva, umana o brutale, generosa o strettamente egoista, ma cresce e si estende sempre più. È la storia che cammina; inutile attardarsi per lamentarsi delle vie che sceglie, poiché queste vie sono state tracciate da tutta l’evoluzione anteriore. Ma la storia è fatta dagli uomini; e poiché noi non vogliamo rimanere spettatori indifferenti e passivi della tragedia storica, poiché vogliamo concorrere con tutte le nostre forze a determinare gli avvenimenti che ci sembrano più favorevoli alla nostra causa, ci occorre un criterio per guidarci nella valutazione dei fatti che si producono, e soprattutto per scegliere il posto che vogliamo occupare nella lotta. Il fine giustifica i mezzi. Si è molto sparlato di questa massima. In realtà, essa è la guida universale del comportamento. Si potrebbe dire meglio: ogni fine comporta il suo mezzo. La morale occorre cercarla nello scopo; il mezzo è fatale. Dato lo scopo che ci si prefigge, per volontà o per necessità, il grande problema della vita è trovare il mezzo che, secondo le circostanze, conduce il più sicuramente e con il minimo spreco di energie possibile allo scopo desiderato. Dal modo in cui si risolve questo problema dipende, per quanto ciò possa dipendere dalla volontà umana, il raggiungimento, per un uomo o un partito, del suo scopo, utile alla sua causa e che non serva, senza volerlo, la causa nemica. Aver trovato il mezzo buono: ecco il segreto dei grandi uomini e dei grandi partiti, che hanno lasciato le loro tracce nella storia. Lo scopo dei gesuiti è, per quelli mistici, la gloria di Dio; per gli altri, la potenza della compagnia. Essi devono quindi cercare di rimbecillire le masse, di terrorizzarle, di sottometterle. Lo scopo dei giacobini e di tutti i partiti autoritari, i quali credono di essere in possesso della verità assoluta, è di imporre le loro idee alla massa dei profani. Essi devono per questo tentare di impadronirsi del potere, di assoggettare le masse e fissare l’umanità sul letto di Procuste delle loro concezioni. Per quanto ci riguarda, vogliamo un’altra cosa: ben diverso è il nostro scopo, quindi ben diversi debbono essere i nostri mezzi. Noi non lottiamo per prendere il posto degli sfruttatori e degli oppressori di oggi, e non lottiamo nemmeno per il trionfo di un’astrazione. Noi non siamo come quel patriota italiano che diceva: “Che importa se tutti gli Italiani muoiono di fame, purché l’Italia sia grande e gloriosa!”. E nemmeno, come quel compagno che confessava che gli sarebbe indifferente massacrare i tre quarti degli uomini, purché l’Umanità fosse libera e felice. Noi vogliamo la felicità degli uomini, di tutti gli uomini, senza eccezione. Noi vogliamo che ogni essere umano possa svilupparsi e vivere nel modo più felice possibile. E noi crediamo che questa libertà e questa felicità non possono essere date agli uomini da un uomo o da un partito, ma che tutti gli uomini devono scoprirne da sé le condizioni e conquistarle. Noi crediamo che solo l’applicazione più completa del principio di solidarietà può distruggere la lotta, l’oppressione e lo sfruttamento; che la solidarietà non può essere che il risultato del libero accordo, l’armonizzazione spontanea e voluta degli interessi. Per noi, tutto ciò che tenta di distruggere l’oppressione economica e politica; tutto ciò che serve ad elevare il livello morale ed intellettuale degli uomini, a dar loro la coscienza dei loro diritti e delle loro forze e a persuaderli a prendere le loro cose in mano essi stessi; tutto ciò che provoca l’odio contro l’oppressione e l’amore fra gli uomini, ci avvicina al nostro scopo e quindi è bene: soggetto solamente ad un calcolo quantitativo per ottenere con un dato sforzo il massimo risultato utile. Ed è al contrario male, perché in contraddizione con lo scopo, tutto quanto tende a conservare lo stato attuale, tutto quanto tende a sacrificare un uomo, contro la sua volontà, al trionfo di un principio. Noi vogliamo il trionfo della libertà e dell’amore. Ma rinunciamo per questo all’impiego di mezzi violenti? Niente affatto. I nostri mezzi sono quelli che le circostanze ci permettono e ci impongono. Certo non vorremmo strappare un capello a nessuno; noi vorremmo asciugare tutte le lacrime e non farne versare alcuna. Ma è pur necessario lottare in questo mondo per non rimanere sterili sognatori. Verrà il giorno, e noi lo crediamo fermamente, in cui sarà possibile fare il bene degli uomini senza far del male né a se stessi né agli altri. Oggi questo non è possibile. Anche il più puro ed il più dolce dei martiri, colui che si farebbe trascinare al patibolo per il trionfo del bene, senza resistenza, benedicendo i suoi persecutori come il Cristo della leggenda, costui ancora farebbe molto male. Oltre al male che farebbe a se stesso, che pure è importante, farebbe spandere lacrime amare a tutti coloro che lo amano. Si tratta dunque, sempre, in tutti gli atti della vita, di scegliere il minor male, di cercare di fare il meno male per la più grande somma di bene possibile. L’umanità si trascina stentatamente sotto il peso dell’oppressione politica ed economica; è abbruttita, degradata, uccisa (e non sempre lentamente) dalla miseria, dalla schiavitù, dall’ignoranza e dalle loro conseguenze. Per la difesa di questo stato di cose esistono potenti organizzazioni militari e poliziesche, che rispondono con la galera, il patibolo, il massacro ad ogni serio tentativo di cambiamento. Non ci sono mezzi pacifici, legali, per uscire da questa situazione; ed è naturale, poiché la legge è fatta appositamente dai privilegiati per difendere i privilegi. Contro la forza fisica che ci sbarra il cammino, c’è solo l’appello alla forza fisica, solo la rivoluzione violenta. Evidentemente la rivoluzione produrrà tanta infelicità e tante sofferenze; ma se ne producesse cento volte di più, sarebbe ancora una benedizione in confronto a quanto si patisce oggi. Si sa che in una sola grande battaglia si uccide più gente che nella più sanguinosa delle rivoluzioni; si sa che milioni di bambini in tenera età muoiono ogni anno per mancanza di cure; si sa che milioni di proletari muoiono prematuramente del male della miseria; si conosce la vita stentata, senza gioia e senza speranza, che l’immensa maggioranza degli uomini conduce; si sa che anche i più ricchi e i più potenti sono molto meno felici di quel che potrebbero essere in una società di eguali; e si sa che questo stato di cose dura da un tempo immemorabile, durerebbe per un tempo indefinito senza la rivoluzione – ma una sola rivoluzione, che attaccasse risolutamente le cause del male, potrebbe mettere per sempre l’umanità sulla via della felicità. Venga dunque la rivoluzione; ogni giorno che tarda è una quantità enorme di sofferenze inflitte agli uomini. Lavoriamo affinché venga presto e sia tale da liquidare ogni oppressione ed ogni sfruttamento. È per amore degli uomini che siamo rivoluzionari: non è colpa nostra se la storia ci ha costretti a questa dolorosa necessità. Quindi, per noi anarchici, o per lo meno (poiché in fondo le parole sono solo convenzioni) per coloro tra gli anarchici che vedono le cose come noi, ogni atto di propaganda o di costruzione, con la parola o con il fatto, individuale o collettivo, è bene quando serve ad avvicinare e facilitare la rivoluzione, quando serve ad assicurare alla rivoluzione il concorso cosciente delle masse e a darle questo carattere di liberazione universale, senza il quale si potrebbe sì avere una rivoluzione, ma non la rivoluzione che noi desideriamo. Ed è soprattutto in fatto di rivoluzione che occorre tener conto del principio del mezzo più economico, perché qui la spesa si calcola in vite umane. Noi conosciamo abbastanza le orribili condizioni materiali e morali nelle quali si trova il proletariato, per non spiegarci gli atti di odio, di vendetta, perfino anche di ferocia che si potranno produrre. Noi comprendiamo che ci sono degli oppressi i quali, essendo sempre stati trattati dai borghesi con la più ignobile durezza, avendo sempre visto che tutto era permesso al più forte, un giorno, quando si troveranno per un momento i più forti, si diranno: “Facciamo, anche noi, come i borghesi”. Noi comprendiamo che possa succedere che nella febbre della battaglia, delle nature originariamente generose, ma non preparate da una lunga ginnastica morale, molto difficile nelle condizioni presenti, perdano di vista l’obiettivo da raggiungere, prendano la violenza come fine a se stessa e si lascino andare a impeti selvaggi. Ma una cosa è comprendere e perdonare, un’altra rivendicare. Questi non sono atti che possiamo accettare, incoraggiare, imitare. Noi dobbiamo essere risoluti ed energici, ma dobbiamo cercare di non oltrepassare mai il limite segnato dalla necessità. Noi dobbiamo fare come il chirurgo che taglia quando è necessario, ma evita di infliggere inutili sofferenze: in una parola, dobbiamo essere ispirati dal sentimento dell’amore degli uomini, di tutti gli uomini. Ci pare che questo sentimento di amore sia il fondo morale, l’anima del nostro programma: a noi pare che solo concependo la rivoluzione come il grande giubileo umano, come la liberazione e la fraternizzazione di tutti gli uomini, a qualunque classe o partito essi abbiano appartenuto, il nostro ideale si potrà realizzare. La rivolta brutale si produrrà certamente, ed essa potrà anche servire a dare una grande spinta che deve scuotere il sistema attuale; ma se essa non trovasse il contrappeso dei rivoluzionari che agiscono per un ideale, si divorerebbe da sé. L’odio non produce amore; con l’odio non si rinnova il mondo. E la rivoluzione dell’odio, o fallirebbe completamente, oppure porterebbe ad una nuova oppressione, che potrebbe anche chiamarsi anarchica, come si chiamano liberali i governi attuali, ma sarebbe ugualmente un’oppressione e non mancherebbe di produrre gli effetti che ogni oppressione produce. \bigskip [Pubblicato su “L’Endehors” n. 68, 21 agosto 1892] % begin final page \clearpage % new page for the colophon \thispagestyle{empty} \begin{center} \bigskip \includegraphics[width=0.25\textwidth]{anarchismologo.pdf} \bigskip \end{center} \strut \vfill \begin{center} Émile Henry Colpo su colpo 1977 \bigskip \emph{Coup pour coup}. Textes établis par Roger Langlais, Ed. Plasma, Paris 1977\forcelinebreak Prima edizione italiana: Casa editrice Vulcano, Bergamo 1978\forcelinebreak Traduzione di Isabella de Caria\forcelinebreak seconda edizione: novembre 2013\forcelinebreak Opuscoli provvisori n. 36 \bigskip \textbf{www.edizionianarchismo.net} \end{center} % end final page with colophon \end{document}

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\centerline{\bf\TeX\ as a Feminist Issue} \medskip\noindent I work in the Polytechnic of Central London's Computer Centre as an Applications Programmer and I've been wrestling with \TeX\ since early 1986, long enough to have been taken over by the \TeX\ world, to have become unhealthily obsessed. For me, working in computing is a feminist issue. Not only is computing dominated by men but it's seen as a {\it science} and so a male preserve in all senses. But that is not why I believe \TeX\ is a feminist issue. \TeX\ seems capable of changing the world in a way that particularly affects women. Look about at the academic \TeX\ community. At first glance it appears that \TeX\ is by men and for men. How many women do you notice contributing to the distribution lists? I am on \hax\ and {\sc uk}\TeX\ and I do find myself scanning for female names amongst the Peters, Grahams, Michaels and Phils, not to mention Malcolms. Barbara Beeton is of course a heroine but apart from her I seem to remember about four women on \hax\ and one on {\sc uk}\TeX. This is not to say that women are not reading the lists. List contributions often seem to be a particularly macho affair; try not to mail a question without pointing out why you think the question should never have arisen and what you would do to fix it. I know this is an exaggeration but the tone of many of the contributions shows me that they are most unlikely to have been written by women. Count the women on the \TeX\ Users Group Steering Committee and Site Coordinators list. There are only three (or possibly two if Rilla is a male name) out of the total of twenty eight. Sebastian Rahtz commented in the last issue of \TeX line that at the Seattle TUG Meeting men discussed {\tt dvi} driver standards and women discussed standards of macros. I was surprised and pleased to hear that women dominated any of the discussions, (and not at all surprised by which standards they were interested in). Installing \TeX\ in 1986 was a tricky business. The distribution tape that I got assumed that you knew not only what \TeX\ was but also {\IniTeX, \WEB, \Tangle, {\sc Vir\TeX} and so on. Pointers were given to where files were without any description of why you might need them. At one point, having decided I wanted to know a little about \TeX\ before I rushed out and bought a laser printer, I tried to get Andrew Trevorrow's \DVItoVDU program going. I kept notes on the problems I encountered. These started: \item{1}What, which, where pixel files? \item{2}Looks like I need \MF\ to create them (from reading {\tt pxl.inf} file). \item{3}No documents on \MF, try {\sc TUGboat}. \item{4}Cannot find \MF\ program in source or executable. \item{5}Seem to have some documentation in \TeX\ format, but can't preview it because no pixel files \dots \noindent All this seems laughable now, but I really was going spare then. If I hadn't gone and spoken to William Black at Oxford I don't think I'd have got anywhere. That combined with my programming abilities of course and knowledge of the VMS operating system. My initial problems may seem irrelevant to feminism but if the only way to get a system running is through programming ability and contacts in the \TeX\ world women are going to be at a disadvantage. There are less of them and certainly far less qualified in Computer Science. Where \TeX\ really becomes a feminist issue is over the problem of who uses \TeX\ and how. \TeX\ exists to format text. Traditionally the people who enter text onto computers and the people who type text out on word-processors and typewriters are {\it women}. Hundreds of women in offices all over the world sitting over keyboards using their hard-won typing and layout skills to produce mountains of paper. Now what has happened? Suddenly a tool exists (and this applies to all sorts of desktop publishing software as well) that not only is esoteric and needs skill to use, but also allows far greater control over and quality in the output, and {\it men} start to enter their own text! Male research students typing their own theses instead of paying typists, male lecturers typing their own notes, male writers typing their own books. And of course they are most likely to be male because we're talking about {\it scientific} typesetting here. My first reaction to this is great joy. It's about time the boring job of copy-typing disappeared. A work's author is likely to take more care over its appearance and correctness than anyone else. Why should tasks be subdivided into interesting and boring parts, and the majority of the boring parts handed to women? But this being a male dominated society we live in, things are not so simple. What will happen to the displaced typists? Surely they too should have the opportunity to use \TeX? And of course once the novelty of \TeX\ has worn off the boring bits are handed back to the women. We get highly paid programmers and designers to write the macros and build up the style sheets and then the typists get to use them without a proper explanation of how \TeX\ works or what they can do to manipulate the results themselves. In our Computer Centre our head's first reaction to \TeX\ was very enthusiastic. Having seen a demonstration that I gave and printed out a letter for himself using the standard letter macro, he decided that we should offer a `typesetting service' on a small scale to the rest of the Poly. We would undertake to produce pretty laser printed output from people's rough drafts. The person to do all the work was a woman who is employed here as a data-entry clerk. She duly started to learn \TeX\ and was enjoying it. Picking the different typefaces and learning tricks of layout are far more satisfying (and I'm sure less bad for the health) than typing in files of meaningless numbers. She has never done any programming and the approach was new and intriguing for her. But when it became clear to our head that even after a week she could not produce fancy ruled tables he decided not to pursue the matter. I did suggest that she be sent on a \TeX\ training course, but it would have cost more than we get for our whole Applications Programming team annual training budget. I give this story as an example of the problems lying in the way of any individual woman trying to use \TeX\ to her advantage rather than letting \TeX\ lead to a decrease in demand for her skills. It is difficult. Even those women who can get to a training course may find it inappropriate. The Advanced \TeX\ course that I went on last year was addressed to programmers. The opening remarks were about structured programming and the format of dvi files, neither of which are extremely relevant to a very skilled technical typist. What I would like to see happen is \TeX\ being made more accessible to everyone. By this I mean the whole of \TeX{}. I don't think people necessarily need protecting from complexity, that often make things less flexible and less interesting. I would like recognition to be given to the skills of typists, they often know far more about what makes good layout than we programmers, and can type a lot better. Electronic publishing is recognised as taking skills out of the hands of printers and I would like to see those skills given to a wide range of people, not just concentrated in the hands of a few men once again. Care should be taken by those responsible for introducing new technologies to make sure that their effects are beneficial, it doesn't do to just let things loose on the world and see what happens. Things are not equal. Practical steps to be taken are: \item{$\bullet$}make the distribution tapes self explanatory, \item{$\bullet$}carry on with the work on standardisation which can only make things easier for newcomers, \item{$\bullet$}design training courses both with and for non-computer people, \item{$\bullet$}watch out around you for who is being taught what, and try to stop obvious injustices, \item{$\bullet$}have a feminist revolution. \smallskip \noindent Meanwhile; is anyone else interested in this issue? I would be very interested in hearing from women using \TeX\ to know what you think about the way that \TeX\ is presented and taught. \smallskip \rightline{\sl Maria Tuck}

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\input texinfo @c -*-texinfo-*- @c %**start of header @setfilename xboard.info @settitle XBoard @c %**end of header @include version.texi @ifinfo @format INFO-DIR-SECTION Games START-INFO-DIR-ENTRY * xboard: (xboard). An X Window System graphical chessboard. END-INFO-DIR-ENTRY @end format @end ifinfo @titlepage @title XBoard @page @vskip 0pt plus 1filll @include copyright.texi @end titlepage @ifset man .TH xboard 6 "$Date: " "GNU" .SH NAME .PP xboard @- X graphical user interface for chess .SH SYNOPSIS .PP .B xboard [options] .br .B xboard -ics -icshost hostname [options] .br .B xboard -ncp [options] .br .B |pxboard .br .B cmail [options] @end ifset @node Top @top Introduction @cindex introduction @ifset man .SH DESCRIPTION @end ifset XBoard is a graphical chessboard that can serve as a user interface to chess engines (such as GNU Chess), the Internet Chess Servers, electronic mail correspondence chess, or your own collection of saved games. This manual documents version @value{VERSION} of XBoard. @menu * Major modes:: The main things XBoard can do. * Basic operation:: Mouse and keyboard functions. * Menus:: Menus, buttons, and keys. * Options:: Command options supported by XBoard. * Chess Servers:: Using XBoard with an Internet Chess Server (ICS). * Firewalls:: Connecting to a chess server through a firewall. * Environment:: Environment variables. * Limitations:: Known limitations and/or bugs. * Problems:: How and where to report any problems you run into. * Contributors:: People who have helped developing XBoard. * CMail:: Using XBoard for electronic correspondence chess. * Other programs:: Other programs you can use with XBoard. @ifnottex * Copyright:: Copyright notice for this manual. @end ifnottex * Copying:: The GNU General Public License. * Index:: Index of concepts and symbol names. @end menu @node Major modes @chapter Major modes @cindex Major modes XBoard always runs in one of four major modes. You select the major mode from the command line when you start up XBoard. @table @asis @item xboard [options] As an interface to GNU Chess or another chess engine running on your machine, XBoard lets you play a game against the machine, set up arbitrary positions, force variations, watch a game between two chess engines, interactively analyze your stored games or set up and analyze arbitrary positions. To run engines that use the UCI standard XBoard will draw upon the Polyglot adapter fully transparently, but you will need to have the polyglot package installed for this tio work. @item xboard -ics -icshost hostname [options] As Internet Chess Server (ICS) interface, XBoard lets you play against other ICS users, observe games they are playing, or review games that have recently finished. Most of the ICS "wild" chess variants are supported, including bughouse. @item xboard -ncp [options] XBoard can also be used simply as an electronic chessboard to play through games. It will read and write game files and allow you to play through variations manually. You can use it to browse games off the net or review games you have saved. These features are also available in the other modes. @item |pxboard If you want to pipe games into XBoard, use the supplied shell script @file{pxboard}. For example, from the news reader @file{xrn}, find a message with one or more games in it, click the Save button, and type @samp{|pxboard} as the file name. @item cmail [options] As an interface to electronic mail correspondence chess, XBoard works with the cmail program. See @ref{CMail} below for instructions. @end table @node Basic operation @chapter Basic operation @cindex Basic operation To move a piece, you can drag it with the left mouse button, or you can click the left mouse button once on the piece, then once more on the destination square. To under-promote a Pawn you can drag it backwards until it morphs into the piece you want to promote to, after which you drag that forward to the promotion square. Or after selecting the pawn with a first click you can then click the promotion square and move the mouse while keeping the button down until the piece that you want appears in the promotion square. To castle you move the King to its destination or, in Chess960, on top of the Rook you want to castle with. In crazyhouse, bughouse or shogi you can drag and drop pieces to the board from the holdings squares displayed next to the board. Old behavior, where right-clicking a square brings up a menu where you can select what piece to drop on it can still be selected through the @samp{Drop Menu} option. Only in Edit Position mode right and middle clicking a square is still used to put a piece on it, and the piece to drop is selected by sweeping the mouse vertically with the button held down. The default function of the right mouse button in other modes is to display the position the chess program thinks it will end up in. While moving the mouse vertically with this button pressed XBoard will step through the principal variation to show how this position will be reached. Lines of play displayed in the engine-output window, or PGN variations in the comment window can similarly be played out on the board, by right-clicking on them. Only in Analysis mode, when you walk along a PV, releasing the mouse button might forward the game upto that point, like you entered all previous PV moves. As the display of the PV in that case starts after the first move a simple right-click will play the move the engine indicates. In Analysis mode you can also make a move by grabbing the piece with a double-click of the left mouse button (or while keeping the @kbd{Ctrl} key pressed). In this case the move you enter will not be played, but will be excluded from the analysis of the current position. (Or included if it was already excluded; it is a toggle.) This only works for engines that support this feature. When connected to an ICS, it is possible to call up a graphical representation of players seeking a game in stead of the chess board, when the latter is not in use (i.e. when you are not playing or observing). Left-clicking the display area will switch between this 'seek graph' and the chess board. Hovering the mouse pointer over a dot will show the details of the seek ad in the message field above the board. Left-clicking the dot will challenge that player. Right-clicking a dot will 'push it to the back', to reveal any dots that were hidden behind it. Right-clicking off dots will refresh the graph. Most other XBoard commands are available from the menu bar. The most frequently used commands also have shortcut keys or on-screen buttons. These shortcut keystrokes are mostly non-printable characters. Typing a letter or digit while the board window has focus will bring up a type-in box with the typed letter already in it. You can use that to type a move in siuations where it is your turn to enter a move, type a move number to call up the position after that move in the display, or, in Edit Position mode, type a FEN. Some rarely used parameters can only be set through options on the command line used to invoke XBoard. XBoard uses a settings file, in which it can remember any changes to the settings that are made through menus or command-line options, so they will still apply when you restart XBoard for another session. The settings can be saved into this file automatically when XBoard exits, or on explicit request of the user. Note that the board window can be sized by the user, but that this will not affect the size of the clocks above it, and won't be remembered in the settings file. To persistently change the size of the clocks, use the @code{size} command-line option when starting XBoard. The default name for the settings file is /etc/xboard/xboard.conf, but in a standard install this file is only used as a master settings file that determines the system-wide default settings, and defers reading and writing of user settings to a user-specific file like ~/.xboardrc in the user's home directory. When XBoard is iconized, its graphical icon is a white knight if it is White's turn to move, a black knight if it is Black's turn. @node Menus @chapter Menus, buttons, and keys @cindex Menus @menu * File Menu:: Accessing external games and positions. * Edit Menu:: Altering games, positions, PGN tags or comments. * View Menu:: Controlling XBoard's shape and looks. * Mode Menu:: Selecting XBoard's mode. * Action Menu:: Talking to the chess engine or ICS opponents. * Engine Menu:: Controlling settings and actions of the engine(s). * Options Menu:: User preferences. * Help Menu:: Getting help. * Keys:: Other shortcut keys. @end menu @node File Menu @section File Menu @cindex File Menu @cindex Menu, File @table @asis @item New Game @cindex New Game, Menu Item Resets XBoard and the chess engine to the beginning of a new chess game. The @kbd{Ctrl-N} key is a keyboard equivalent. In Internet Chess Server mode, clears the current state of XBoard, then resynchronizes with the ICS by sending a refresh command. If you want to stop playing, observing, or examining an ICS game, use an appropriate command from the Action menu, not @samp{New Game}. @xref{Action Menu}. @item New Shuffle Game @cindex New Shuffle Game, Menu Item Similar to @samp{New Game}, but allows you to specify a particular initial position (according to a standardized numbering system) in chess variants which use randomized opening positions (e.g. Chess960). You can also press the @samp{Pick Fixed} button to let XBoard generate a random number for you. The thus selected opening position will then persistently be chosen on any following New Game command until you use this menu to select another. Selecting position number -1 (or pushing the @samp{Randomize} button) will produce a newly randomized position on any new game. Using this menu item in variants that normally do not shuffle their opening position does cause these variants to become shuffle variants until you use the @samp{New Shuffle Game} menu to explicitly switch the randomization off, or select a new variant. @item New Variant @cindex New variant, Menu Item Allows you to select a new chess variant in non-ICS mode. (In ICS play, the ICS is responsible for deciding which variant will be played, and XBoard adapts automatically.) The shifted @kbd{Alt+V} key is a keyboard equivalent. If you play with an engine, the engine must be able to play the selected variant, or the corresponding choice will be disabled. XBoard supports all major variants, such as xiangqi, shogi, chess, chess960, makruk, Capablanca Chess, shatranj, crazyhouse, bughouse. But not every board size has built-in bitmaps for un-orthodox pieces! Only sizes bulky (72) and middling (49) have all pieces, while size petite (33) has most. These sizes would have to be set at startup through the @code{size} command-line option when you start up XBoard for such variants to be playable. You can overrule the default board format of the selected variant, (e.g. to play suicide chess on a 6 x 6 board), in this dialog, but normally you would not do that, and leave them at '-1', which means 'default' for the chosen variant. @item Load Game @cindex Load Game, Menu Item Plays a game from a record file. The @kbd{Ctrl-O} key is a keyboard equivalent. A pop-up dialog prompts you for the file name. If the file contains more than one game, a second pop-up dialog displays a list of games (with information drawn from their PGN tags, if any), and you can select the one you want. Alternatively, you can load the Nth game in the file directly, by typing the number @kbd{N} after the file name, separated by a space. The game-file parser will accept PGN (portable game notation), or in fact almost any file that contains moves in algebraic notation. Notation of the form @samp{P@@f7} is accepted for piece-drops in bughouse games; this is a nonstandard extension to PGN. If the file includes a PGN position (FEN tag), or an old-style XBoard position diagram bracketed by @samp{[--} and @samp{--]} before the first move, the game starts from that position. Text enclosed in parentheses, square brackets, or curly braces is assumed to be commentary and is displayed in a pop-up window. Any other text in the file is ignored. PGN variations (enclosed in parentheses) also are treated as comments; however, if you rights-click them in the comment window, XBoard will shelve the current line, and load the the selected variation, so you can step through it. You can later revert to the previous line with the @samp{Revert} command. This way you can walk quite complex varation trees with XBoard. The nonstandard PGN tag [Variant "varname"] functions similarly to the -variant command-line option (see below), allowing games in certain chess variants to be loaded. Note that it must appear before any FEN tag for XBoard to recognize variant FENs appropriately. There is also a heuristic to recognize chess variants from the Event tag, by looking for the strings that the Internet Chess Servers put there when saving variant ("wild") games. @item Load Position @cindex Load Position, Menu Item Sets up a position from a position file. A pop-up dialog prompts you for the file name. The shifted @kbd{Ctrl-O} key is a keyboard equivalent. If the file contains more than one saved position, and you want to load the Nth one, type the number N after the file name, separated by a space. Position files must be in FEN (Forsythe-Edwards notation), or in the format that the Save Position command writes when oldSaveStyle is turned on. @item Load Next Position @cindex Load Next Position, Menu Item Loads the next position from the last position file you loaded. The shifted @kbd{PgDn} key is a keyboard equivalent. @item Load Previous Position @cindex Load Previous Position, Menu Item Loads the previous position from the last position file you loaded. The shifted @kbd{PgUp} key is a keyboard equivalent. Not available if the last position was loaded from a pipe. @item Save Game @cindex Save Game, Menu Item Appends a record of the current game to a file. The @kbd{Ctrl-S} key is a keyboard equivalent. A pop-up dialog prompts you for the file name. If the game did not begin with the standard starting position, the game file includes the starting position used. Games are saved in the PGN (portable game notation) format, unless the oldSaveStyle option is true, in which case they are saved in an older format that is specific to XBoard. Both formats are human-readable, and both can be read back by the @samp{Load Game} command. Notation of the form @samp{P@@f7} is accepted for piece-drops in bughouse games; this is a nonstandard extension to PGN. @item Save Position @cindex Save Position, Menu Item Appends a diagram of the current position to a file. The shifted @kbd{Ctrl+S} key is a keyboard equivalent. A pop-up dialog prompts you for the file name. Positions are saved in FEN (Forsythe-Edwards notation) format unless the @code{oldSaveStyle} option is true, in which case they are saved in an older, human-readable format that is specific to XBoard. Both formats can be read back by the @samp{Load Position} command. @item Save Selected Games @cindex Save Selected Games Will cause all games selected for display in the current Game List to be appended to a file of the user's choice. @item Save Games as Book @cindex Save Games as Book, Menu Item Creates an opening book from the currently loaded game file, incorporating only the games currently selected in the Game List. The book will be saved on the file specified in the @samp{Common Engine} options dialog. The value of @samp{Book Depth} specified in that same dialog will be used to determine how many moves of each game will be added to the internal book buffer. This command can take a long time to process, and the size of the buffer is currently limited. At the end the buffer will be saved as a Polyglot book, but the buffer will not be cleared, so that you can continue adding games from other game files. @item Mail Move @itemx Reload CMail Message @cindex Mail Move, Menu Item @cindex Reload CMail Message, Menu Item See @ref{CMail}. @item Exit @cindex Exit, Menu Item Exits from XBoard. The @kbd{Ctrl-Q} key is a keyboard equivalent. @end table @node Edit Menu @section Edit Menu @cindex Menu, Edit @cindex Edit Menu @table @asis @item Copy Game @cindex Copy Game, Menu Item Copies a record of the current game to an internal clipboard in PGN format and sets the X selection to the game text. The @kbd{Ctrl-C} key is a keyboard equivalent. The game can be pasted to another application (such as a text editor or another copy of XBoard) using that application's paste command. In many X applications, such as xterm and emacs, the middle mouse button can be used for pasting; in XBoard, you must use the Paste Game command. @item Copy Position @cindex Copy Position, Menu Item Copies the current position to an internal clipboard in FEN format and sets the X selection to the position text. The shifted @kbd{Ctrl-C} key is a keyboard equivalent. The position can be pasted to another application (such as a text editor or another copy of XBoard) using that application's paste command. In many X applications, such as xterm and emacs, the middle mouse button can be used for pasting; in XBoard, you must use the Paste Position command. @item Copy Game List @cindex Copy Game List, Menu Item Copies the current game list to the clipboard, and sets the X selection to this text. A format of comma-separated double-quoted strings is used, including all tags, so it can be easily imported into spread-sheet programs. @item Paste Game @cindex Paste Game, Menu Item Interprets the current X selection as a game record and loads it, as with Load Game. The @kbd{Ctrl-V} key is a keyboard equivalent. @item Paste Position @cindex Paste Position, Menu Item Interprets the current X selection as a FEN position and loads it, as with Load Position. The shifted @kbd{Ctrl-V} key is a keyboard equivalent. @item Edit Game @cindex Edit Game, Menu Item Allows you to make moves for both Black and White, and to change moves after backing up with the @samp{Backward} command. The clocks do not run. The @kbd{Ctrl-E} key is a keyboard equivalent. In chess engine mode, the chess engine continues to check moves for legality but does not participate in the game. You can bring the chess engine into the game by selecting @samp{Machine White}, @samp{Machine Black}, or @samp{Two Machines}. In ICS mode, the moves are not sent to the ICS: @samp{Edit Game} takes XBoard out of ICS Client mode and lets you edit games locally. If you want to edit games on ICS in a way that other ICS users can see, use the ICS @kbd{examine} command or start an ICS match against yourself. @item Edit Position @cindex Edit Position, Menu Item Lets you set up an arbitrary board position. The shifted @kbd{Ctrl-E} key is a keyboard equivalent. Use mouse button 1 to drag pieces to new squares, or to delete a piece by dragging it off the board or dragging an empty square on top of it. When you do this keeping the @kbd{Ctrl} key pressed, or start dragging with a double-click, you will move a copy of the piece, leaving the piece itself where it was. In variants where pieces can promote (such as Shogi), left-clicking an already selected piece promotes or demotes it. To drop a new piece on a square, press mouse button 2 or 3 over the square. This puts a white or black pawn in the square, respectively, but you can change that to any other piece type by dragging the mouse down before you release the button. You will then see the piece on the originally clicked square cycle through the available pieces (including those of opposite color), and can release the button when you see the piece you want. (Note you can swap the function of button 2 and 3 by pressing the shift key, and that there is an option @code{monoMouse} to combine al functions in one button, which then acts as button 3 over an empty square, and as button 1 over a piece.) To alter the side to move, you can click the clock (the words White and Black above the board) of the side you want to give the move to. To clear the board you can click the clock of the side that already has the move (which is highlighted in black). If you repeat this the board will cycle from empty to a 'pallette board' containing every piece once to the initial position to the one before clearing. The quickest way to set up a position is usually to start with the pallette board, and move the pieces to were you want them, duplicating them where necessary by using the @kbd{Ctrl} key, dragging those you don't want off board, and use static button 2 or 3 clicks to place the Pawns. The old behavior with a piece menu can still be configured with the aid of the @code{pieceMenu} option. Dragging empty squares off board can create boards with 'holes' (inaccessible black squares) in them. Selecting @samp{Edit Position} causes XBoard to discard all remembered moves in the current game. In ICS mode, changes made to the position by @samp{Edit Position} are not sent to the ICS: @samp{Edit Position} takes XBoard out of @samp{ICS Client} mode and lets you edit positions locally. If you want to edit positions on ICS in a way that other ICS users can see, use the ICS @kbd{examine} command, or start an ICS match against yourself. (See also the ICS Client topic above.) @item Edit Tags @cindex Edit Tags, Menu Item Lets you edit the PGN (portable game notation) tags for the current game. After editing, the tags must still conform to the PGN tag syntax: @example <tag-section> ::= <tag-pair> <tag-section> <empty> <tag-pair> ::= [ <tag-name> <tag-value> ] <tag-name> ::= <identifier> <tag-value> ::= <string> @end example @noindent See the PGN Standard for full details. Here is an example: @example [Event "Portoroz Interzonal"] [Site "Portoroz, Yugoslavia"] [Date "1958.08.16"] [Round "8"] [White "Robert J. Fischer"] [Black "Bent Larsen"] [Result "1-0"] @end example @noindent Any characters that do not match this syntax are silently ignored. Note that the PGN standard requires all games to have at least the seven tags shown above. Any that you omit will be filled in by XBoard with @samp{?} (unknown value), or @samp{-} (inapplicable value). @item Edit Comment @cindex Edit Comment, Menu Item Adds or modifies a comment on the current position. Comments are saved by @samp{Save Game} and are displayed by @samp{Load Game}, PGN variations will also be printed in this window, and can be promoted to main line by right-clicking them. @samp{Forward}, and @samp{Backward}. @item Edit Book @cindex Edit Book, Menu Item Pops up a window listing the moves available in the GUI book (specified in the @samp{Common Engine Settings} dialog) from the currently displayed position, together with their weights and (optionally in braces) learn info. You can then edit this list, and the new list will be stored back into the book when you press 'save changes'. When you press the button 'add next move', and play a move on the board, ithat move will be added to the list with weight 1. Note that the listed percentages are neither used, nor updated when you change the weights; they are just there as an optical aid. When you right-click a move in the list it will be played. @item Revert @itemx Annotate @cindex Revert, Menu Item @cindex Annotate, Menu Item If you are examining an ICS game and Pause mode is off, Revert issues the ICS command @samp{revert}. In local mode, when you were editing or analyzing a game, and the @code{-variations} command-line option is switched on, you can start a new variation by holding the Shift key down while entering a move not at the end of the game. Variations can also become the currently displayed line by clicking a PGN variation displayed in the Comment window. This can be applied recursively, so that you can analyze variations on variations; each time you create a new variation by entering an alternative move with Shift pressed, or select a new one from the Comment window, the current variation will be shelved. @samp{Revert} allows you to return to the most recently shelved variation. The difference between @samp{Revert} and @samp{Annotate} is that with the latter, the variation you are now abandoning will be added as a comment (in PGN variation syntax, i.e. between parentheses) to the original move where you deviated, for later recalling. The @kbd{Home} key is a keyboard equivalent to @samp{Revert}. @item Truncate Game @cindex Truncate Game, Menu Item Discards all remembered moves of the game beyond the current position. Puts XBoard into @samp{Edit Game} mode if it was not there already. The @kbd{End} key is a keyboard equivalent. @item Backward @cindex Backward, Menu Item @cindex <, Button Steps backward through a series of remembered moves. The @samp{[<]} button and the @kbd{Alt+LeftArrow} key are equivalents, as is turning the mouse wheel towards you. In addition, pressing the ??? key steps back one move, and releasing it steps forward again. In most modes, @samp{Backward} only lets you look back at old positions; it does not retract moves. This is the case if you are playing against a chess engine, playing or observing a game on an ICS, or loading a game. If you select @samp{Backward} in any of these situations, you will not be allowed to make a different move. Use @samp{Retract Move} or @samp{Edit Game} if you want to change past moves. If you are examining an ICS game, the behavior of @samp{Backward} depends on whether XBoard is in Pause mode. If Pause mode is off, @samp{Backward} issues the ICS backward command, which backs up everyone's view of the game and allows you to make a different move. If Pause mode is on, @samp{Backward} only backs up your local view. @item Forward @cindex Forward, Menu Item @cindex >, Button Steps forward through a series of remembered moves (undoing the effect of @samp{Backward}) or forward through a game file. The @samp{[>]} button and the @kbd{Alt+RightArrow} key are equivalents, as is turning the mouse wheel away from you. If you are examining an ICS game, the behavior of Forward depends on whether XBoard is in Pause mode. If Pause mode is off, @samp{Forward} issues the ICS forward command, which moves everyone's view of the game forward along the current line. If Pause mode is on, @samp{Forward} only moves your local view forward, and it will not go past the position that the game was in when you paused. @item Back to Start @cindex Back to Start, Menu Item @cindex <<, Button Jumps backward to the first remembered position in the game. The @samp{[<<]} button and the @kbd{Alt+Home} key are equivalents. In most modes, Back to Start only lets you look back at old positions; it does not retract moves. This is the case if you are playing against a local chess engine, playing or observing a game on a chess server, or loading a game. If you select @samp{Back to Start} in any of these situations, you will not be allowed to make different moves. Use @samp{Retract Move} or @samp{Edit Game} if you want to change past moves; or use Reset to start a new game. If you are examining an ICS game, the behavior of @samp{Back to Start} depends on whether XBoard is in Pause mode. If Pause mode is off, @samp{Back to Start} issues the ICS @samp{backward 999999} command, which backs up everyone's view of the game to the start and allows you to make different moves. If Pause mode is on, @samp{Back to Start} only backs up your local view. @item Forward to End @cindex Forward to End, Menu Item @cindex >>, Button Jumps forward to the last remembered position in the game. The @samp{[>>]} button and the @kbd{Alt+End} key are equivalents. If you are examining an ICS game, the behavior of @samp{Forward to End} depends on whether XBoard is in Pause mode. If Pause mode is off, @samp{Forward to End} issues the ICS @samp{forward 999999} command, which moves everyone's view of the game forward to the end of the current line. If Pause mode is on, @samp{Forward to End} only moves your local view forward, and it will not go past the position that the game was in when you paused. @end table @node View Menu @section View Menu @cindex Menu, View @cindex View Menu @table @asis @item Flip View @cindex Flip View, Menu Item Inverts your view of the chess board for the duration of the current game. Starting a new game returns the board to normal. The @kbd{F2} key is a keyboard equivalent. @item Show Engine Output @cindex Show Engine Output, Menu Item Shows or hides a window in which the thinking output of any loaded engines is displayed. The shifted @kbd{Alt+O} key is a keyboard equivalent. XBoard will display lines of thinking output of the same depth ordered by score, (highest score on top), rather than in the order the engine produced them. Usually this amounts to the same, as a normal engine search will only find new PV (and emit it as thinking output) when it searches a move with a higher score than the previous variation. But when the engine is in multi-variation mode this needs not always be true, and it is more convenient for someone analyzing games to see the moves sorted by score. The order in which the engine found them is only of interest to the engine author, and can still be deduced from the time or node count printed with the line. Right-clicking a line in this window, and then moving the mouse vertically with the right button kept down, will make XBoard play through the PV listed there. The use of the board window as 'variation board' will normally end when you release the right button, or when the opponent plays a move. But beware: in Analysis mode, moves thus played out might be added to the game, depending on the setting of the option 'Play moves of clicked PV', when you initiate the click left of the PV in the score area. The Engine-Output pane for each engine will contain a header displaying the multi-PV status and a list of excluded moves in Analysis mode, which are also responsive to right-clicking: Clicking the words 'fewer' or 'more' will alter the number of variations shown at each depth, through the engine's MultiPV option, while clicking in between those and moving the mouse horizontally adjust the option 'Multi-PV Margin'. (In so far the engines support those.) @item Show Move History @cindex Show Move History, Menu Item Shows or hides a list of moves of the current game. The shifted @kbd{Alt+H} key is a keyboard equivalent. This list allows you to move the display to any earlier position in the game by clicking on the corresponding move. @item Show Evaluation Graph @cindex Show Evaluation Graph, Menu Item Shows or hides a window which displays a graph of how the engine score(s) evolved as a function of the move number. The shifted @kbd{Alt+E} key is a keyboard equivalent. The title bar shows the score (and search depth at which it was obtained) of the currently displayed position numerically. Clicking on the graph will bring the corresponding position in the board display. A button 3 click will toggle the display mode between plain and differential (showing the difference in score between successive half moves). Using the mouse wheel over the window will change the scale of the low-score region (from -1 to +1). @item Show Game List @cindex Show Game List, Menu Item Shows or hides the list of games generated by the last @samp{Load Game} command. The shifted @kbd{Alt+G} key is a keyboard equivalent. The line describing each game is built from a selection of the PGN tags. Which tags contribute, and in what order, can be changed by the @samp{Game list tags} menu dialog, which can be popped up through the 'Tags' button below the Game List. Display can be restricted to a sub-set of the games meeting certain criteria. A text entry below the game list allows you to type a text that the game lines must contain in order to be displayed. Games can also be selected based on their Elo PGN tag, as set in the @samp{Load Game Options} dialog, which can be popped up through the 'Thresholds' button below the Game List. Finally they can be selected based on containing a position similar to the one currently displayed in the main window, by pressing the 'Position' button below the Game List, (which searches the entire list for the position), or the 'Narrow' button (which only searches the already-selected games). What counts as similar enough to be selected can also be set in the @samp{Load Game Options} dialog, and ranges from an exact match to just the same material. @item Tags @cindex Tags, Menu Item Pops up a window which shows the PGN (portable game notation) tags for the current game. For now this is a duplicate of the @samp{Edit Tags} item in the @samp{Edit} menu. @item Comments @cindex Comments, Menu Item Pops up a window which shows any comments to or variations on the current move. For now this is a duplicate of the @samp{Edit Comment} item in the @samp{Edit} menu. @item ICS Input Box @cindex ICS Input Box, Menu Item If this option is set in ICS mode, XBoard creates an extra window that you can use for typing in ICS commands. The input box is especially useful if you want to type in something long or do some editing on your input, because output from ICS doesn't get mixed in with your typing as it would in the main terminal window. @item ICS Chat/Console @cindex ICS Chat/Console, Menu Item This menu item opens a window in which you can interact with the ICS, and conduct upto 5 chats with other ICS users (or channels), so you don't have to use the messy xterm from which you launched XBoard for that. The window has a text entry at the bottom where you can type your commands and messages unhindered by the stream of ICS output. The latter will be displayed in a large pane above the input field, the ICS Console. This pane can be vertically split into two, however, where half of it is then used to display selected ICS output, belonging to a chat with another user, or output from an ICS channel. Such output will then not appear in the Console pane. To use the window, write the name of your chat partner, the channel number, or the words 'shouts', 'whispers', 'cshouts' in the upper field (ending with <Enter>). Everything you type in the lowest field will then automatically be sent to the mentioned party, while everything that party sends to you will appear in the central text box, rather than appear in the ICS console. The row of buttons allow you to choose between chat; to start a new chat, just select an empty button, and complete the @samp{Chat partner} field. There are several keyboard accelerators to control this window: <Esc> will close the private chat, and assign the input field to the @item Board @cindex Board, Menu Item Summons a dialog where you can customize the look of the chess board. Here you can specify the directory from which piece images should be taken, when you don't want to use the built-in piece images (see @code{pieceImageDirectory} option), external images to be used for the board squares (@code{liteBackTextureFile} and @code{darkBackTextureFile} options), and square and piece colors for the default pieces. The current combination of these settings can be assigned a 'theme' name by typing one in the text entry in the lower-left of the dialog, and closing the latter with OK. It will then appear in the themes listbox next time you open the dialog, where you can recall the complete settings combination with a double-click. @item Game List Tags @cindex Game List Tags, Menu Item a duplicate of the Game List dialog in the Options menu. @end table @node Mode Menu @section Mode Menu @cindex Menu, Mode @cindex Mode Menu @table @asis @item Machine White @cindex Machine White, Menu Item Tells the chess engine to play White. The @kbd{Ctrl-W} key is a keyboard equivalent. @item Machine Black @cindex Machine Black, Menu Item Tells the chess engine to play Black. The @kbd{Ctrl-B} key is a keyboard equivalent. @item Two Machines @cindex Two Machines, Menu Item Plays a game between two chess engines. The @kbd{Ctrl-T} key is a keyboard equivalent. @item Analysis Mode @cindex Analysis Mode, Menu Item @cindex null move @cindex move exclusion XBoard tells the chess engine to start analyzing the current game/position and shows you the analysis as you move pieces around. The @kbd{Ctrl-A} key is a keyboard equivalent. Note: Some chess engines do not support Analysis mode. To set up a position to analyze, you do the following: 1. Select Edit Position from the Mode Menu 2. Set up the position. Use the middle and right buttons to bring up the white and black piece menus. 3. When you are finished, click on either the Black or White clock to tell XBoard which side moves first. 4. Select Analysis Mode from the Mode Menu to start the analysis. You can now play legal moves to create follow-up positions for the engine to analyze, while the moves will be remembered as a stored game, and then step backward through this game to take the moves back. Note that you can also click on the clocks to set the opposite side to move (adding a so-called @samp{null move} to the game). You can also tell the engine to exclude some moves from analysis. (Engines that do not support the exclude-moves feature will ignore this, however.) The general way to do this is to play the move you want to exclude starting with a double click on the piece. When you use drag-drop moving, the piece you grab with a double click will also remain on its square, to show you that you are not really making the move, but just forbid it from the current position. Playing a thus excluded move a second time will include it again. Excluded moves will be listed as text in a header line in the Engine Output window, and you can also re-include them by right-clicking them there. This header line will also contain the words 'best' and 'tail'; right-clicking those will exclude the currently best move, or all moves not explicitly listed in the header line. Once you leave the current position all memory of excluded moves will be lost when you return there. Selecting this menu item while already in @samp{Analysis Mode} will toggle the participation of the second engine in the analysis. The output of this engine will then be shown in the lower pane of the Engine Output window. The analysis function can also be used when observing games on an ICS with an engine loaded (zippy mode); the engine then will analyze the positions as they occur in the observed game. @item Analyze Game @cindex Analyze Game, Menu Item This option subjects the currently loaded game to automatic analysis by the loaded engine. The @kbd{Ctrl-G} key is a keyboard equivalent. XBoard will start auto-playing the game from the currently displayed position, while the engine is analyzing the current position. The game will be annotated with the results of these analyses. In particlar, the score and depth will be added as a comment, and the PV will be added as a variation. Normally the analysis would stop after reaching the end of the game. But when a game is loaded from a multi-game file while @samp{Analyze Game} was already switched on, the analysis will continue with the next game in the file until the end of the file is reached (or you switch to another mode). The time the engine spends on analyzing each move can be controlled through the command-line option @samp{-timeDelay}, which can also be set from the @samp{Load Game Options} menu dialog. Note: Some chess engines do not support Analysis mode. @item Edit Game Duplicate of the item in the Edit menu. Note that @samp{Edit Game} is the idle mode of XBoard, and can be used to get you out of other modes. E.g. to stop analyzing, stop a game between two engines or stop editing a position. @item Edit Position Duplicate of the item in the Edit menu. @item Training @cindex Training, Menu Item Training mode lets you interactively guess the moves of a game for one of the players. You guess the next move of the game by playing the move on the board. If the move played matches the next move of the game, the move is accepted and the opponent's response is auto-played. If the move played is incorrect, an error message is displayed. You can select this mode only while loading a game (that is, after selecting @samp{Load Game} from the File menu). While XBoard is in @samp{Training} mode, the navigation buttons are disabled. @item ICS Client @cindex ICS Client, Menu Item This is the normal mode when XBoard is connected to a chess server. If you have moved into Edit Game or Edit Position mode, you can select this option to get out. To use xboard in ICS mode, run it in the foreground with the -ics option, and use the terminal you started it from to type commands and receive text responses from the chess server. See @ref{Chess Servers} below for more information. XBoard activates some special position/game editing features when you use the @kbd{examine} or @kbd{bsetup} commands on ICS and you have @samp{ICS Client} selected on the Mode menu. First, you can issue the ICS position-editing commands with the mouse. Move pieces by dragging with mouse button 1. To drop a new piece on a square, press mouse button 2 or 3 over the square. This brings up a menu of white pieces (button 2) or black pieces (button 3). Additional menu choices let you empty the square or clear the board. Click on the White or Black clock to set the side to play. You cannot set the side to play or drag pieces to arbitrary squares while examining on ICC, but you can do so in @kbd{bsetup} mode on FICS. In addition, the menu commands @samp{Forward}, @samp{Backward}, @samp{Pause}, and @samp{Stop Examining} have special functions in this mode; see below. @item Machine Match @cindex Machine match, Menu Item Starts a match between two chess programs, with a number of games and other parameters set through the @samp{Tournament Options} menu dialog. When a match is already running, selecting this item will make XBoard drop out of match mode after the current game finishes. @item Pause @cindex Pause, Menu Item Pauses updates to the board, and if you are playing against a chess engine, also pauses your clock. To continue, select @samp{Pause} again, and the display will automatically update to the latest position. The @samp{P} button and keyboard @kbd{Pause} key are equivalents. If you select Pause when you are playing against a chess engine and it is not your move, the chess engine's clock will continue to run and it will eventually make a move, at which point both clocks will stop. Since board updates are paused, however, you will not see the move until you exit from Pause mode (or select Forward). This behavior is meant to simulate adjournment with a sealed move. If you select Pause while you are observing or examining a game on a chess server, you can step backward and forward in the current history of the examined game without affecting the other observers and examiners, and without having your display jump forward to the latest position each time a move is made. Select Pause again to reconnect yourself to the current state of the game on ICS. If you select @samp{Pause} while you are loading a game, the game stops loading. You can load more moves manually by selecting @samp{Forward}, or resume automatic loading by selecting @samp{Pause} again. @end table @node Action Menu @section Action Menu @cindex Menu, Action @cindex Action, Menu @table @asis @item Accept @cindex Accept, Menu Item Accepts a pending match offer. The @kbd{F3} key is a keyboard equivalent. If there is more than one offer pending, you will have to type in a more specific command instead of using this menu choice. @item Decline @cindex Decline, Menu Item Declines a pending offer (match, draw, adjourn, etc.). The @kbd{F4} key is a keyboard equivalent. If there is more than one offer pending, you will have to type in a more specific command instead of using this menu choice. @item Call Flag @cindex Call Flag, Menu Item Calls your opponent's flag, claiming a win on time, or claiming a draw if you are both out of time. The @kbd{F5} key is a keyboard equivalent. You can also call your opponent's flag by clicking on his clock. @item Draw @cindex Draw, Menu Item Offers a draw to your opponent, accepts a pending draw offer from your opponent, or claims a draw by repetition or the 50-move rule, as appropriate. The @kbd{F6} key is a keyboard equivalent. @item Adjourn @cindex Adjourn, Menu Item Asks your opponent to agree to adjourning the current game, or agrees to a pending adjournment offer from your opponent. The @kbd{F7} key is a keyboard equivalent. @item Abort @cindex Abort, Menu Item Asks your opponent to agree to aborting the current game, or agrees to a pending abort offer from your opponent. The @kbd{F8} key is a keyboard equivalent. An aborted game ends immediately without affecting either player's rating. @item Resign @cindex Resign, Menu Item Resigns the game to your opponent. The @kbd{F9} key is a keyboard equivalent. @item Stop Observing @cindex Stop Observing, Menu Item Ends your participation in observing a game, by issuing the ICS observe command with no arguments. ICS mode only. The @kbd{F10} key is a keyboard equivalent. @item Stop Examining @cindex Stop Examining, Menu Item Ends your participation in examining a game, by issuing the ICS unexamine command. ICS mode only. The @kbd{F11} key is a keyboard equivalent. @item Upload to Examine @cindex Upload to Examine, Menu Item Create an examined game of the proper variant on the ICS, and send the game there that is currenty loaded in XBoard (e.g. through pasting or loading from file). You must be connected to an ICS for this to work. @item Adjudicate to White @itemx Adjudicate to Black @itemx Adjudicate Draw @cindex Adjudicate to White, Menu Item @cindex Adjudicate to Black, Menu Item @cindex Adjudicate Draw, Menu Item Terminate an ongoing game in Two-Machines mode (including match mode), with as result a win for white, for black, or a draw, respectively. The PGN file of the game will accompany the result string by the comment "user adjudication". @end table @node Engine Menu @section Engine Menu @cindex Engine Menu @cindex Menu, Engine @table @asis @item Edit Engine List @cindex Edit Engine List, Menu Item Opens a window that shows the list of engines registered for use by XBoard, together with the options that would be used with them when you would select them from the @samp{Load Engine} dialogs. You can then edit this list, e.g. for re-ordering the engines, or adding uncommon options needed by this engine (e.g. to cure non-compliant behavior). @item Load New 1st Engine @itemx Load New 2nd Engine @cindex Load Engine, Menu Item Pops up a dialog where you can select or specify an engine to be loaded. You can even replace engines during a game, without disturbing that game. (Beware that after loading an engine, XBoard will always be in Edit Game mode, so you will have to tell the new engine what to do before it does anything!) When you select an already installed engine from the ‘Select Engine from List’ listbox, all other fields of the dialog will be ignored. In other cases, you have to specify the engine executable, possible arguments on the engine command line (if the engine docs say the engine needs any), and the directory where the engine should look for its files (if this cannot be deduced automatically from the specification of the engine executable). You will also have to specify (with the aid of checkboxes) if the engine is UCI. If ‘Add this engine to the list’ is ticked (which it is by default), the engine will be added to the list of installed engines in your settings file, (provided you save the settings!), so that next time you can select it from the listbox. You can also specify a ‘nickname’, under which the engine will then appear in that drop-down list, and even choose to use that nickname for it in PGN files for engine-engine games. The info you supply with the checkboxes whether the engine should use GUI book, or (for variant engines) automatically switch to the current variant when loaded, will also be included in the list. For obsolete XBoard engines, which would normally take a long delay to load because XBoard is waiting for a response they will not give, you can tick ‘WB protocol v1’ to speed up the loading process. @item Engine #N Settings @cindex Engine #N Settings, Menu Item Pop up a menu dialog to alter the settings specific to the applicable engine. For each parameter the engine allows to be set, a control element will appear in this dialog that can be used to alter the value. Depending on the type of parameter (text string, number, multiple choice, on/off switch, instantaneous signal) the appropriate control will appear, with a description next to it. XBoard has no idea what these values mean; it just passes them on to the engine. How this dialog looks is completely determined by the engine, and XBoard just passes it on to the user. Many engines do not have any parameters that can be set by the user, and in that case the dialog will be empty (except for the OK and cancel buttons). UCI engines usually have many parameters. (But these are only visible with a sufficiently modern version of the Polyglot adapter needed to run UCI engines, e.g. Polyglot 2.0.1.) For native XBoard engines this is less common. @subsection Common Settings @cindex Common Settings, Menu Item Pops up a sub-menu where you can set some engine parameters common to most engines, such as hash-table size, tablebase cache size, maximum number of processors that SMP engines can use. The shifted @kbd{Alt+U} key is a keyboard equivalent. Older XBoard/WinBoard engines might not respond to these settings, but UCI engines always should. It is also possible to specify a GUI opening book here, i.e. an opening book that XBoard consults for any position a playing engine gets in. It then forces the engine to play the book move, rather than to think up its own, if that position is found in the book. The book can switched on and off independently for either engine. The way book moves are chosen can be influenced through the settings of book depth and variety. After both sides have played more moves than the specified depth, the book will no longer be consulted. When the variety is set to 50, moves will be played with the probability specified in the book. When set to 0, only the move(s) with the highest probability will be played. When set to 100, all listed moves will be played with equal pobability. Other settings interpolate between that. @item Hint @cindex Hint, Menu Item Displays a move hint from the chess engine. @item Book @cindex Book, Menu Item Displays a list of possible moves from the chess engine's opening book. The exact format depends on what chess engine you are using. With GNU Chess 4, the first column gives moves, the second column gives one possible response for each move, and the third column shows the number of lines in the book that include the move from the first column. If you select this option and nothing happens, the chess engine is out of its book or does not support this feature. @item Move Now @cindex Move Now, Menu Item Forces the chess engine to move immediately. Chess engine mode only. The @kbd{Ctrl-M} key is a keyboard equivalent. Many engines won't respond to this. @item Retract Move @cindex Retract Move, Menu Item Retracts your last move. In chess engine mode, you can do this only after the chess engine has replied to your move; if the chess engine is still thinking, use @samp{Move Now} first. In ICS mode, @samp{Retract Move} issues the command @samp{takeback 1} or @samp{takeback 2} depending on whether it is your opponent's move or yours. The @kbd{Ctrl-X} key is a keyboard equivalent. @item Recently Used Engines @cindex Recently Used Engines, In Menu At the bottom of the engine menu there can be a list of names of engines that you recently loaded through the Load Engine menu dialog in previous sessions. Clicking on such a name will load that engine as first engine, so you won't have to search for it in your list of installed engines, if that is very long. The maximum number of displayed engine names is set by the @code{recentEngines}command-line option. @end table @node Options Menu @section Options Menu @cindex Menu, Options @cindex Options Menu @subsection General Options @cindex General Options, Menu Item The following items to set option values appear in the dialog summoned by the general Options menu item. @table @asis @item Absolute Analysis Scores @cindex Absolute Analysis Scores, Menu Item Controls if scores on the Engine Output window during analysis will be printed from the white or the side-to-move point-of-view. @item Almost Always Queen @cindex Almost Always Queen, Menu Item If this option is on, 7th-rank pawns automatically change into Queens when you pick them up, and when you drag them to the promotion square and release them there, they will promote to that. But when you drag such a pawn backwards first, its identity will start to cycle through the other available pieces. This will continue until you start to move it forward; at which point the identity of the piece will be fixed, so that you can safely put it down on the promotion square. If this option is off, what happens depends on the option @code{alwaysPromoteToQueen}, which would force promotion to Queen when true. Otherwise XBoard would bring up a dialog box whenever you move a pawn to the last rank, asking what piece you want to promote to. @item Animate Dragging @cindex Animate Dragging, Menu Item If Animate Dragging is on, while you are dragging a piece with the mouse, an image of the piece follows the mouse cursor. If Animate Dragging is off, there is no visual feedback while you are dragging a piece, but if Animate Moving is on, the move will be animated when it is complete. @item Animate Moving @cindex Animate Moving, Menu Item If Animate Moving is on, all piece moves are animated. An image of the piece is shown moving from the old square to the new square when the move is completed (unless the move was already animated by Animate Dragging). If Animate Moving is off, a moved piece instantly disappears from its old square and reappears on its new square when the move is complete. The shifted @kbd{Ctrl-A} key is a keyboard equivalent. @item Auto Flag @cindex Auto Flag, Menu Item If this option is on and one player runs out of time before the other, XBoard will automatically call his flag, claiming a win on time. The shifted @kbd{Ctrl-F} key is a keyboard equivalent. In ICS mode, Auto Flag will only call your opponent's flag, not yours, and the ICS may award you a draw instead of a win if you have insufficient mating material. In local chess engine mode, XBoard may call either player's flag and will not take material into account (?). @item Auto Flip View @cindex Auto Flip View, Menu Item If the Auto Flip View option is on when you start a game, the board will be automatically oriented so that your pawns move from the bottom of the window towards the top. If you are playing a game on an ICS, the board is always oriented at the start of the game so that your pawns move from the bottom of the window towards the top. Otherwise, the starting orientation is determined by the @code{flipView} command line option; if it is false (the default), White's pawns move from bottom to top at the start of each game; if it is true, Black's pawns move from bottom to top. @xref{User interface options}. @item Blindfold @cindex Blindfold, Menu Item If this option is on, XBoard displays the board as usual but does not display pieces or move highlights. You can still move in the usual way (with the mouse or by typing moves in ICS mode), even though the pieces are invisible. @item Drop Menu @cindex Drop Menu, Menu Item Controls if right-clicking the board in crazyhouse / bughouse will pop up a menu to drop a piece on the clicked square (old, deprecated behavior) or allow you to step through an engine PV (new, recommended behavior). @item Enable Variation Trees @cindex Enable Variation Trees, Menu Item If this option is on, playing a move in Edit Game or Analyze mode while keeping the Shift key pressed will start a new variation. You can then recall the previous line through the @samp{Revert} menu item. When off, playing a move will truncate the game and append the move irreversibly. @item Headers in Engine Output Window @cindex Headers in Engine Output Window, Menu Item Controls the presence of column headers above the variations and associated information printed by the engine, on which you can issue button 3 clicks to open or close the columns. Available columns are search depth, score, node count, time used, tablebase hits, search speed and selective search depth. @item Hide Thinking @cindex Hide Thinking, Menu Item If this option is off, the chess engine's notion of the score and best line of play from the current position is displayed as it is thinking. The score indicates how many pawns ahead (or if negative, behind) the chess engine thinks it is. In matches between two machines, the score is prefixed by @samp{W} or @samp{B} to indicate whether it is showing White's thinking or Black's, and only the thinking of the engine that is on move is shown. The shifted @kbd{Ctrl-H} key is a keyboard equivalent. @item Highlight Last Move @cindex Highlight Last Move, Menu Item If Highlight Last Move is on, after a move is made, the starting and ending squares remain highlighted. In addition, after you use Backward or Back to Start, the starting and ending squares of the last move to be unmade are highlighted. @item Highlight with Arrow @cindex Highlight with Arrow, Menu Item Causes the highlighting described in Highlight Last Move to be done by drawing an arrow between the highlighted squares, so that it is visible even when the width of the grid lines is set to zero. @item Move Sound @cindex Move Sound, Menu Item Enables the sounding of an audible signal when the computer performs a move. For the selection of the sound, see @samp{Sound Options}. If you turn on this option when using XBoard with the Internet Chess Server, you will probably want to give the @kbd{set bell 0} command to the ICS, since otherwise the ICS will ring the terminal bell after every move (not just yours). (The @file{.icsrc} file is a good place for this; see @ref{ICS options}.) @item One-Click Moving @cindex One-Click Moving, Menu Item If this option is on, XBoard does not wait for you to click both the from- and the to-square, or drag the piece, but performs a move as soon as it is uniqely specified. This applies to clicking an own piece that only has a single legal move, clicking an empty square or opponent piece where only one of your pieces can move (or capture) to. Furthermore, a double-click on a piece that can only make a single capture will cause that capture to be made. Promoting a Pawn by clicking its to-square will suppress the promotion popup or other methods for selecting an under-promotion, and make it promote to Queen. @item Periodic Updates @cindex Periodic Updates, Menu Item If this option is off (or if you are using a chess engine that does not support periodic updates), the analysis window will only be updated when the analysis changes. If this option is on, the Analysis Window will be updated every two seconds. @item Play Move(s) of Clicked PV @cindex Play Move(s) of Clicked PV, Menu Item If this option is on, right-clicking a PV in the Engine Output window during Analyze mode will cause the first move of that PV to be played. You could also play more than one (or no) PV move by moving the mouse to engage in the PV walk such a right-click will start, to seek out another position along the PV where you want to continue the analysis, before releasing the mouse button. @item Ponder Next Move @cindex Ponder Next Move, Menu Item If this option is off, the chess engine will think only when it is on move. If the option is on, the engine will also think while waiting for you to make your move. The shifted @kbd{Ctrl-P} key is a keyboard equivalent. @item Popup Exit Message @cindex Popup Exit Message, Menu Item If this option is on, when XBoard wants to display a message just before exiting, it brings up a modal dialog box and waits for you to click OK before exiting. If the option is off, XBoard prints the message to standard error (the terminal) and exits immediately. @item Popup Move Errors @cindex Popup Move Errors, Menu Item If this option is off, when you make an error in moving (such as attempting an illegal move or moving the wrong color piece), the error message is displayed in the message area. If the option is on, move errors are displayed in small pop-up windows like other errors. You can dismiss an error pop-up either by clicking its OK button or by clicking anywhere on the board, including down-clicking to start a move. @item Scores in Move List @cindex Scores in Move List, Menu Item If this option is on, XBoard will display the depth and score of engine moves in the Move List, in the format of a PGN comment. @item Show Coords @cindex Show Coords, Menu Item If this option is on, XBoard displays algebraic coordinates along the board's left and bottom edges. @item Show Target Squares @cindex Show Target Squares, Menu Item If this option is on, all squares a piece that is 'picked up' with the mouse can legally move to are highighted with a fat colored dot in yellow (non-captures) or red (captures). Special moves might have other colors (e.g. magenta for promotion, cyan for a partial move). Legality testing must be on for XBoard to know how the piece moves. @item Sticky Windows @cindex Sticky Windows, Menu Item Controls whether the auxiliary windows such as Engine Output, Move History and Evaluation Graph should keep touching XBoard's main window when you move the latter. @item Test Legality @cindex Test Legality, Menu Item If this option is on, XBoard tests whether the moves you try to make with the mouse are legal and refuses to let you make an illegal move. The shifted @kbd{Ctrl-L} key is a keyboard equivalent. Moves loaded from a file with @samp{Load Game} are also checked. If the option is off, all moves are accepted, but if a local chess engine or the ICS is active, they will still reject illegal moves. Turning off this option is useful if you are playing a chess variant with rules that XBoard does not understand. (Bughouse, suicide, and wild variants where the king may castle after starting on the d file are generally supported with Test Legality on.) @item Top-Level Dialogs @cindex Top-Level Dialogs, Menu Item Controls whether the auxiliary windows will appear as icons in the task bar and independently controllable, or whether they open and minimize all together with the main window. @item Flash Moves @itemx Flash Rate @cindex Flash Moves, Menu Item @cindex Flash Rate, Menu Item If this option is non-zero, whenever a move is completed, the moved piece flashes the specified number of times. The flash-rate setting determines how rapidly this flashing occurs. @item Animation Speed @cindex Animation Speed, Menu Item Determines the duration (in msec) of an animation step, when @samp{Animate Moving} is swiched on. @item Zoom factor in Evaluation Graph @cindex Zoom factor in Evaluation Graph, Menu Item Sets the valueof the @code{evalZoom} option, indicating the factor by which the score interval (-1,1) should be blown up on the vertical axis of the Evaluation Graph. @end table @subsection Time Control @cindex Time Control, Menu Item Pops up a sub-menu where you can set the time-control parameters interactively. The shifted @kbd{Alt+T} key is a keyboard equivalent. Allows you to select classical or incremental time controls, set the moves per session, session duration, and time increment. Also allows specification of time-odds factors for one or both engines. If an engine is given a time-odds factor N, all time quota it gets, be it at the beginning of a session or through the time increment or fixed time per move, will be divided by N. @subsection Adjudications @cindex Adjudications, Menu Item Pops up a sub-menu where you can enable or disable various adjudications that XBoard can perform in engine-engine games. The shifted @kbd{Alt+J} key is a keyboard equivalent. You can instruct XBoard to detect and terminate the game on checkmate or stalemate, even if the engines would not do so, to verify engine result claims (forfeiting engines that make false claims), rather than naively following the engine, to declare draw on positions which can never be won for lack of mating material, (e.g. KBK), or which are impossible to win unless the opponent seeks its own demise (e.g. KBKN). For these adjudications to work, @samp{Test Legality} should be switched on. It is also possible to instruct XBoard to enforce a 50-move or 3-fold-repeat rule and automatically declare draw (after a user-adjustable number of moves or repeats) even if the engines are prepared to go on. It is also possible to have XBoard declare draw on games that seem to drag on forever, or adjudicate a loss if both engines agree (for 3 consecutive moves) that one of them is behind more than a user-adjustable score threshold. For the latter adjudication to work, XBoard should be able to properly understand the engine's scores. To facilitate the latter, you can inform xboard here if the engines report scores from the viewpoint of white, or from that of their own color. @subsection ICS Options @cindex ICS Options, Menu Item The following options occur in a dialog summoned by the ICS Options menu item. @table @asis @item Auto Kibitz @cindex Auto Kibitz, Menu Item Setting this option when playing with or aginst a chess program on an ICS will cause the last line of thinking output of the engine before its move to be sent to the ICS in a kibitz command. In addition, any kibitz message received through the ICS from an opponent chess program will be diverted to the engine-output window, (and suppressed in the console), where you can play through its PV by right-clicking it. @item Auto Comment @cindex Auto Comment, Menu Item If this option is on, any remarks made on ICS while you are observing or playing a game are recorded as a comment on the current move. This includes remarks made with the ICS commands @kbd{say}, @kbd{tell}, @kbd{whisper}, and @kbd{kibitz}. Limitation: remarks that you type yourself are not recognized; XBoard scans only the output from ICS, not the input you type to it. @item Auto Observe @cindex Auto Observe, Menu Item If this option is on and you add a player to your @code{gnotify} list on ICS, XBoard will automatically observe all of that player's games, unless you are doing something else (such as observing or playing a game of your own) when one starts. The games are displayed from the point of view of the player on your gnotify list; that is, his pawns move from the bottom of the window towards the top. Exceptions: If both players in a game are on your gnotify list, if your ICS @code{highlight} variable is set to 0, or if the ICS you are using does not properly support observing from Black's point of view, you will see the game from White's point of view. @item Auto Raise Board @cindex Auto Raise Board, Menu Item If this option is on, whenever a new game begins, the chessboard window is deiconized (if necessary) and raised to the top of the stack of windows. @item Auto Save @cindex Auto Save, Menu Item If this option is true, at the end of every game XBoard prompts you for a file name and appends a record of the game to the file you specify. Disabled if the @code{saveGameFile} command-line option is set, as in that case all games are saved to the specified file. @xref{Load and Save options}. @item Background Observe @cindex Background Observe, Menu Item Setting this option will make XBoard suppress display of any boards from observed games while you are playing. In stead the last such board will be remembered, and shown to you when you right-click the board. This allows you to peek at your bughouse partner's game when you want, without disturbing your own game too much. @item Dual Board @cindex Dual Board, Menu Item Setting this option in combination with @samp{Background Observe} will display boards of observed games while you are playing on a second board next to that of your own game. @item Get Move List @cindex Get Move List, Menu Item If this option is on, whenever XBoard receives the first board of a new ICS game (or a different game from the one it is currently displaying), it retrieves the list of past moves from the ICS. You can then review the moves with the @samp{Forward} and @samp{Backward} commands or save them with @samp{Save Game}. You might want to turn off this option if you are observing several blitz games at once, to keep from wasting time and network bandwidth fetching the move lists over and over. When you turn this option on from the menu, XBoard immediately fetches the move list of the current game (if any). @item Quiet Play @cindex Quiet Play, Menu Item If this option is on, XBoard will automatically issue an ICS @kbd{set shout 0} command whenever you start a game and a @kbd{set shout 1} command whenever you finish one. Thus, you will not be distracted by shouts from other ICS users while playing. @item Seek Graph @cindex Seek Graph, Menu Item Setting this option will cause XBoard to display an graph of currently active seek ads when you left-click the board while idle and logged on to an ICS. @item Auto-Refresh Seek Graph @cindex Auto-Refresh Seek Graph, Menu Item In combination with the @samp{Seek Graph} option this will cause automatic update of the seek graph while it is up. This only works on FICS and ICC, and requires a lot of bandwidth on a busy server. @item Auto-InputBox PopUp @cindex Auto-InputBox PopUp, Menu Item Controls whether the ICS Input Box will pop up automatically when you type a printable character to the board window in ICS mode. @item Quit After Game @cindex Quit After Game, Menu Item Controls whether XBoard will automatically disconnect from the ICS and close when the game currently in progress finishes. @item Premove @itemx Premove White @itemx Premove Black @itemx First White Move @itemx First Black Move @cindex Premove, Menu Item @cindex Premove White, Menu Item @cindex Premove Black, Menu Item @cindex First White Move, Menu Item @cindex First Black Move, Menu Item If this option is on while playing a game on an ICS, you can register your next planned move before it is your turn. Move the piece with the mouse in the ordinary way, and the starting and ending squares will be highlighted with a special color (red by default). When it is your turn, if your registered move is legal, XBoard will send it to ICS immediately; if not, it will be ignored and you can make a different move. If you change your mind about your premove, either make a different move, or double-click on any piece to cancel the move entirely. You can also enter premoves for the first white and black moves of the game. @item ICS Alarm @itemx ICS Alarm Time @cindex ICS Alarm, Menu Item @cindex ICS Alarm Time, Menu Item When this option is on, an alarm sound is played when your clock counts down to the icsAlarmTime in an ICS game. (By default, the time is 5 seconds, but you can pecify other values with the Alarm Time spin control.) For games with time controls that include an increment, the alarm will sound each time the clock counts down to the icsAlarmTime. By default, the alarm sound is the terminal bell, but on some systems you can change it to a sound file using the soundIcsAlarm option; see below. @item Colorize Messages @cindex Colorize Messages, Menu Item Ticking this options causes various types of ICS messages do be displayed with different foreground or background colors in the console. The colors can be individually selected for each type, through the accompanying text edits. @end table @subsection Tournament Options @cindex Tournament Options, Menu Item Summons a dialog where you can set options important for playing automatic matches between two or more chess programs (e.g. by using the @samp{Machine Match} menu item in the @samp{Mode} menu). @table @asis @item Tournament file @cindex Tournament file, Menu item To run a tournament, XBoard needs a file to record its progress, so it can resume the tourney when it is interrupted. When you want to conduct anything more complex than a simple two-player match with the currently loaded engines, (i.e. when you select a list of participants), you must not leave this field blank. When you enter the name of an existing tournament file, XBoard will ignore all other input specified in the dialog, and will take the corresponding info from that tournament file. This resumes an interrupted tournament, or adds another XBoard agent playing games for it to those that are already doing so. Specifying a not-yet-existing file will cause XBoard to create it, according to the tournament parameters specified in the rest of the dialog, before it starts the tournament on ‘OK’. Provided that you specify participants; without participants no tournament file will be made, but other entered values (e.g. for the file with opening positions) will take effect. Default: configured by the @code{defaultTourneyName} option. @item Sync after round @itemx Sync after cycle @cindex Sync after round, Menu Item @cindex Sync after cycle, Menu Item The sync options, when on, will cause WinBoard to refrain from starting games of the next round or cycle before all games of the previous round or cycle are finished. This guarantees correct ordering in the games file, even when multiple XBoard instances are concurrently playing games for the same tourney. Default: sync after cycle, but not after round. @item Select Engine @itemx Tourney participants @cindex Select Engine, Menu Item @cindex Tourney participants, Menu Item With the Select Engine drop-down list you can pick an engine from your list of installed engines in the settings file, to be added to the tournament. The engines selected so far will be listed in the ‘Tourney participants’ memo. The latter is a normal text edit, so you can use normal text-editing functions to delete engines you selected by accident, or change their order. Do not type names yourself there, because names that do not exactly match one of the names from the drop-down list will lead to undefined behavior. @item Tourney type @cindex Tourney type, Menu Item Here you can specify the type of tournament you want. XBoard’s intrinsic tournament manager support round-robins (type = 0), where each participant plays every other participant, and (multi-)gauntlets, where one (or a few) so-called ‘gauntlet engines’ play an independent set of opponents. In the latter case, you specify the number of gauntlet engines. E.g. if you specified 10 engines, and tourney type = 2, the first 2 engines each play the remaining 8. A value of -1 instructs XBoard to play Swiss; for this to work an external pairing engine must be specified through the @code{pairingEngine} option. Each Swiss round will be considered a tourney cycle in that case. Default:0 @item Number of tourney cycles @itemx Default number of Games @cindex Number of tourney cycles, Menu Item @cindex Default number of Games, Menu Item You can specify tourneys where every two opponents play each other multiple times. Such multiple games can be played in a row, as specified by the ‘number of games per pairing’, or by repeating the entire tournament schedule a number of times (specified by the ‘number of tourney cycles’). The total number of times two engine meet will be the product of these two. Default is 1 cycle; the number of games per pairing is the same as the default number of match games, stored in your settings file through the @code{defaultMatchGames} option. @item Save Tourney Games @cindex Save Tourney Games, Menu Item File where the tournament games are saved (duplicate of the item in the @samp{Save Game Options}). @item Game File with Opening Lines @itemx File with Start Positions @itemx Game Number @itemx Position Number @itemx Rewind Index after @cindex Game File with Opening Lines, Menu Item @cindex File with Start Positions, Menu Item @cindex Game Number, Menu Item @cindex Position Number, Menu Item @cindex Rewind Index after, Menu Item These items optionally specify the file with move sequences or board positions the tourney games should start from. The corresponding numbers specify the number of the game or position in the file. Here a value -1 means automatic stepping through all games on the file, -2 automatic stepping every two games. The Rewind-Index parameter causes a stepping index to reset to one after reaching a specified value. A setting of -2 for the game number will also be effective in a tournament without specifying a game file, but playing from the GUI book instead. In this case the first (odd) games will randomly select from the book, but the second (even) games will select the same moves from the book as the previous game. (Note this leads to the same opening only if both engines use the GUI book!) Default: No game or position file will be used. The default index if such a file is used is 1. @item Disable own engine bools be default @cindex Disable own engine books be default, Menu Item Setting this option reverses the default situation for use of the GUI opening book in tournaments from what it normally is, namely not using it. So unless the engine is installed with an option to explicitly specify it should not use the GUI book (i.e. @code{-firstHasOwnBookUCI true}), it will be made to use the GUI book. @item Replace Engine @itemx Upgrade Engine @cindex Replace Engine, Menu Item @cindex Upgrade Engine, Menu Item With these two buttons you can alter the participants of an already running tournament. After opening the Match Options dialog on an XBoard that is playing for the tourney, you will see all the tourney parameters in the dialog fields. You can then replace the name of one engine by that of another by editing the @samp{participants} field. (But preserve the order of the others!) Pressing the button after that will cause the substitution. With the @samp{Upgrade Engine} button the substitution will only affect future games. With @samp{Replace Engine} all games the substituted engine has already played will be invalidated, and they will be replayed with the substitute engine. In this latter case the engine must not be playing when you do this, but otherwise there is no need to pause the tournament play for making a substitution. @item Clone Tourney @cindex CloneTourney, Menu Item Pressing this button after you have specified an existing tournament file will copy the contents of the latter to the dialog, and then puts the originally proposed name for the tourney file back. You can then run a tourney with the same parameters (possibly after changing the proposed name of the tourney file for the new tourney) by pressing 'OK'. @end table @subsection Load Game Options @cindex Load Game Options, Menu Item Summons a dialog where you can set the @code{autoDisplayComment} and @code{autoDisplayTags} options, (which control popups when viewing loaded games), and specify the rate at which loaded games are auto-played, in seconds per move (which can be a fractional number, like 1.6). This rate is also used with the @code{Analyze Game} menu item. You can also set search criteria for determining which games will be displayed in the Game List for a multi-game file, and thus be eligible for loading: @table @asis @item Elo of strongest player @itemx Elo of weakest player @itemx year @cindex Elo of strongest player, Menu Item @cindex Elo of weakest player, Menu Item @cindex year, Menu Item These numeric fields set thresholds (lower limits) on the Elo rating of the mentioned player, or the date the game was played. Defaults: 0 @item Final nr of pieces @cindex Final nr of pieces, Menu Item Here you can enter a range (e.g. 8-10), and only games will be selected that has a number of men in this range on the board in their final position. @item Search mode @cindex Search mode, Menu Item @cindex find position, Menu Item @cindex narrow, Menu Item This setting determines which positions in a game will be considered a match to the position currently displayed in the board window when you press the @samp{find position} button in the Game List. You can search for an exact match, a position that has all shown material in the same place, but might contain additional material, a position that has all Pawns in the same place, but can have the shown material anywhere, a position that can have all shown material anywhere, or a position that has material between certain limits anywhere. For the latter you have to place the material that must be present in the four lowest ranks of the board, and optional additional material in the four highest ranks of the board. You can request the optional material to be balanced. The @samp{narrow} button is similar in fuction to the @samp{find position} button, but only searches in the already selected games, rather than the complete game file, and can thus be used to refine a search based on multiple criteria. @item number of consecutive positions @cindex number of consecutive positions, Menu Item When you are searching by material, rather than for an exact match, this parameter indicates forhowmany consecutive game positions the same amount of material must be on the board before it is considered a match. @item Also match reversed colors @itemx Also match left-right flipped position @cindex Also match reversed colors, Menu Item @cindex Also match left-right flipped position, Menu Item When looking for matching positions rather than by material, these settings determine whether mirror images (in case of a vertical flip in combination with color reversal) will be also considered a match. The left-right flipping is only useful after all castling rights have expired (or in Xiangqi). @end table @subsection Save Game Options @cindex Save Game Options, Menu Item Summons a dialog where you can specify the files on which XBoard should automatically save any played or entered games, (the @code{saveGameFile} option), or the final position of such games (the @code{savePositionfile} option). You can also select 'auto-save' without a file name, in which case XBoard will prompt the user for a file name after each game. In ICS mode you can limit the auto-saving to your own games (i.e. suppress saving of observed games). You can also set the default value for the PGN Event tag that will be used for each new game you start. Various options for the format of the game can be specified as well, such as whether scores and depths of engine games should be saved as comments, and if a tag with info about the score with which the engine came out of book should be included. For Chess, always set the format to PGN, rather than "old save stye"! @subsection Game List @cindex Game List Tags, Menu Item Pops up a dialog where you can select the PGN tags that should appear on the lines in the game list, and their order. @subsection Sound Options @cindex Sound Options, Menu Item Summons a dialog where you can specify the sounds that should accompany various events that can occur XBoard. Most events are only relevant to ICS play, but the move sound is an important exception. For each event listed in the dialog, you can select a standard sound from a menu. You can also select a user-supplied sound file, by typing its name into the designated text-edit field first, and then selecting "Above WAV File" from the menu for the event. A dummy event has been provided for trying out the sounds with the "play" button next to it. The directory with standard sounds, and the external program for playing the sounds can be specified too, but normally you would not touch these once XBoard is properly installed. When a move sound other than 'None' is selected, XBoard alerts you by playing that sound after each of your opponent's moves (or after every move if you are observing a game on the Internet Chess Server). The sound is not played after moves you make or moves read from a saved game file. @subsection Save Settings Now @cindex Save Settings Now, Menu Item Selecting this menu item causes the current XBoard settings to be written to the settings file, so they will also apply in future sessions. Note that some settings are 'volatile', and are not saved, because XBoard considers it too unlikely that you want those to apply next time. In particular this applies to the Chess program names, and all options giving information on those Chess programs (such as their directory, if they have their own opening book, if they are UCI or native XBoard), or the variant you are playing. Such options would still be understood when they appear in the settings file in case they were put there with the aid of a text editor, but they would disappear from the file as soon as you save the settings. Note that XBoard no longer pays attention to options values specified in the .Xresources file. (Specifying key bindings there will still work, though.) To alter the default of volatile options, you can use the following method: Rename your ~/.xboardrc settings file (to ~/.yboardrc, say), and create a new file ~/.xboardrc, which only contains the options @example -settingsFile ~/.yboardrc -saveSettingsFile ~/.yboardrc @end example @noindent This will cause your settings to be saved on ~/.yboardrc in the future, so that ~/.xboardrc is no longer overwritten. You can then safely specify volatile options in ~/.xboardrc, either before or after the settingsFile options. Note that when you specify persistent options after the settingsFile options in ~/.xboardrc, you will essentially turn them into volatile options with the specified value as default, because that value will overrule the value loaded from the settings file (being read later). @subsection Save Settings on Exit @cindex Save Settings on Exit, Menu Item Setting this option has no immediate effect, but causes the settings to be saved when you quit XBoard. What happens then is otherwise identical to what happens when you use select "Save Settings Now", see there. @node Help Menu @section Help Menu @cindex Menu, Help @cindex Help Menu @table @asis @item Info XBoard @cindex Info XBoard, Menu Item Displays the XBoard documentation in info format. For this feature to work, you must have the GNU info program installed on your system, and the file @file{xboard.info} must either be present in the current working directory, or have been installed by the @samp{make install} command when you built XBoard. @item Man XBoard @cindex Man XBoard, Menu Item Displays the XBoard documentation in man page format. The @kbd{F1} key is a keyboard equivalent. For this feature to work, the file @file{xboard.6} must have been installed by the @samp{make install} command when you built XBoard, and the directory it was placed in must be on the search path for your system's @samp{man} command. @item About XBoard @cindex About XBoard, Menu Item Shows the current XBoard version number. @end table @node Keys @section Other Shortcut Keys @cindex Keys @cindex Shortcut keys @table @asis @item Show Last Move @cindex Show Last Move, Shortcut Key By hitting @kbd{Enter} the last move will be re-animated. @item Load Next Game @cindex Load Next Game, Menu Item Loads the next game from the last game record file you loaded. The @kbd{Alt+PgDn} key triggers this action. @item Load Previous Game @cindex Load Previous Game, Menu Item Loads the previous game from the last game record file you loaded. The @kbd{Alt+PgUp} key triggers this action. Not available if the last game was loaded from a pipe. @item Reload Same Game @cindex Reload Same Game, Menu Item Reloads the last game you loaded. Not available if the last game was loaded from a pipe. Currently no keystroke is assigned to this ReloadGameProc. @item Reload Same Position @cindex Reload Same Position, Menu Item Reloads the last position you loaded. Not available if the last position was loaded from a pipe. Currently no keystroke is assigned to this ReloadPositionProc. @end table In the Xaw build of XBoard you can add or remove shortcut keys using the X resources @code{paneA.translations}. Here is an example of what could go into your @file{.Xdefaults} file: @example XBoard*paneA.translations: \ Shift<Key>?: MenuItem(Help.About) \n\ Ctrl<Key>y: MenuItem(Action.Accept) \n\ Ctrl<Key>n: MenuItem(Action.Decline) \n\ Ctrl<Key>i: MenuItem(Nothing) @end example @noindent So the key should always be bound to the action 'MenuItem', with the (hierarchical) name of the menu item as argument. There are a few actions available for which no menu item exists: Binding a key to @code{Nothing} makes it do nothing, thus removing it as a shortcut key. Other such functions that can be bound to keys are: @example AboutGame, DebugProc (switches the -debug option on or off), LoadNextGame, LoadPrevGame, ReloadGame, ReloadPosition. @end example @node Options @chapter Options @cindex Options @cindex Options This section documents the command-line options to XBoard. You can set these options in two ways: by typing them on the shell command line you use to start XBoard, or by editing the settings file (usually ~/.xboardrc) to alter the value of the setting that was saved there. Some of the options cannot be changed while XBoard is running; others set the initial state of items that can be changed with the @ref{Options} menu. Most of the options have both a long name and a short name. To turn a boolean option on or off from the command line, either give its long name followed by the value true or false (@samp{-longOptionName true}), or give just the short name to turn the option on (@samp{-opt}), or the short name preceded by @samp{x} to turn the option off (@samp{-xopt}). For options that take strings or numbers as values, you can use the long or short option names interchangeably. @menu * Chess engine options:: Controlling the chess engine. * UCI + WB Engine Settings:: Setting some very common engine parameters * Tournament options:: Running tournaments and matches between engines. * ICS options:: Connecting to and using ICS. * Load and Save options:: Input/output options. * User interface options:: Look and feel options. * Adjudication Options:: Control adjudication of engine-engine games. * Other options:: Miscellaneous. @end menu @node Chess engine options @section Chess Engine Options @cindex options, Chess engine @cindex Chess engine options @table @asis @item -tc or -timeControl minutes[:seconds] @cindex tc, option @cindex timeControl, option Each player begins with his clock set to the @code{timeControl} period. Default: 5 minutes. The additional options @code{movesPerSession} and @code{timeIncrement} are mutually exclusive. @item -mps or -movesPerSession moves @cindex mps, option @cindex movesPerSession, option When both players have made @code{movesPerSession} moves, a new @code{timeControl} period is added to both clocks. Default: 40 moves. @item -inc or -timeIncrement seconds @cindex inc, option @cindex timeIncrement, option If this option is specified, @code{movesPerSession} is ignored. Instead, after each player's move, @code{timeIncrement} seconds are added to his clock. Use @samp{-inc 0} if you want to require the entire game to be played in one @code{timeControl} period, with no increment. Default: -1, which specifies @code{movesPerSession} mode. @item -clock/-xclock or -clockMode true/false @cindex clock, option @cindex clockMode, option Determines whether or not to display the chess clocks. If clockMode is false, the clocks are not shown, but the side that is to play next is still highlighted. Also, unless @code{searchTime} is set, the chess engine still keeps track of the clock time and uses it to determine how fast to make its moves. @item -st or -searchTime minutes[:seconds] @cindex st, option @cindex searchTime, option Tells the chess engine to spend at most the given amount of time searching for each of its moves. Without this option, the chess engine chooses its search time based on the number of moves and amount of time remaining until the next time control. Setting this option also sets clockMode to false. @item -depth or -searchDepth number @cindex sd, option @cindex searchDepth, option Tells the chess engine to look ahead at most the given number of moves when searching for a move to make. Without this option, the chess engine chooses its search depth based on the number of moves and amount of time remaining until the next time control. With the option, the engine will cut off its search early if it reaches the specified depth. @item -firstNPS number @itemx -secondNPS number @cindex firstNPS, option @cindex secondNPS, option Tells the chess engine to use an internal time standard based on its node count, rather then wall-clock time, to make its timing decisions. The time in virtual seconds should be obtained by dividing the node count through the given number, like the number was a rate in nodes per second. Xboard will manage the clocks in accordance with this, relying on the number of nodes reported by the engine in its thinking output. If the given number equals zero, it can obviously not be used to convert nodes to seconds, and the time reported by the engine is used to decrement the XBoard clock in stead. The engine is supposed to report in CPU time it uses, rather than wall-clock time, in this mode. This option can provide fairer conditions for engine-engine matches on heavily loaded machines, or with very fast games (where the wall clock is too inaccurate). @code{showThinking} must be on for this option to work. Default: -1 (off). Not many engines might support this yet! @item -firstTimeOdds factor @itemx -secondTimeOdds factor @cindex firstTimeOdds, option @cindex secondTimeOdds, option Reduces the time given to the mentioned engine by the given factor. If pondering is off, the effect is indistinguishable from what would happen if the engine was running on an n-times slower machine. Default: 1. @item -timeOddsMode mode @cindex timeOddsMode, option This option determines how the case is handled where both engines have a time-odds handicap. If mode=1, the engine that gets the most time will always get the nominal time, as specified by the time-control options, and its opponent's time is renormalized accordingly. If mode=0, both play with reduced time. Default: 0. @item -hideThinkingFromHuman true/false Controls the Hide Thinking option. @xref{Options Menu}. Default: true. (Replaces the Show-Thinking option of older xboard versions.) @item -thinking/-xthinking or -showThinking true/false @cindex thinking, option @cindex showThinking, option Forces the engine to send thinking output to xboard. Used to be the only way to control if thinking output was displayed in older xboard versions, but as the thinking output in xboard 4.3 is also used for several other purposes (adjudication, storing in PGN file) the display of it is now controlled by the new option Hide Thinking. @xref{Options Menu}. Default: false. (But if xboard needs the thinking output for some purpose, it makes the engine send it despite the setting of this option.) @item -ponder/-xponder or -ponderNextMove true/false @cindex ponder, option @cindex ponderNextMove, option Sets the Ponder Next Move menu option. @xref{Options Menu}. Default: true. @item -smpCores number Specifies the maximum number of CPUs an SMP engine is allowed to use. Only works for engines that support the XBoard/WinBoard-protocol cores feature. @item -mg or -matchGames n @cindex mg, option @cindex matchGames, option Automatically runs an n-game match between two chess engines, with alternating colors. If the @code{loadGameFile} or @code{loadPositionFile} option is set, XBoard starts each game with the given opening moves or the given position; otherwise, the games start with the standard initial chess position. If the @code{saveGameFile} option is set, a move record for the match is appended to the specified file. If the @code{savePositionFile} option is set, the final position reached in each game of the match is appended to the specified file. When the match is over, XBoard displays the match score and exits. Default: 0 (do not run a match). @item -mm/-xmm or -matchMode true/false @cindex mm, option @cindex matchMode, option Setting @code{matchMode} to true is equivalent to setting @code{matchGames} to 1. @item -sameColorGames n @cindex sameColorGames, option Automatically runs an n-game match between two chess engines, without alternating colors. Otherwise the same applies as for the @samp{-matchGames} option, over which it takes precedence if both are specified. (See there.) Default: 0 (do not run a match). @item -fcp or -firstChessProgram program @cindex fcp, option @cindex firstChessProgram, option Name of first chess engine. Default: @file{Fairy-Max}. @item -scp or -secondChessProgram program @cindex scp, option @cindex secondChessProgram, option Name of second chess engine, if needed. A second chess engine is started only in Two Machines (match) mode. Default: @file{Fairy-Max}. @item -fe or -firstEngine nickname @cindex fe, option @cindex firstEngine, option This is an alternative to the @code{fcp} option for specifying the first engine, for engines that were already configured (using the @samp{Load Engine} dialog) in XBoard's settings file. It will not only retrieve the real name of the engine, but also all options configured with it. (E.g. if it is UCI, whether it should use book.) @item -se or -secondEngine nickname @cindex se, option @cindex secondEngine, option As @code{fe}, but for the second engine. @item -fb/-xfb or -firstPlaysBlack true/false @cindex fb, option @cindex firstPlaysBlack, option In games between two chess engines, firstChessProgram normally plays white. If this option is true, firstChessProgram plays black. In a multi-game match, this option affects the colors only for the first game; they still alternate in subsequent games. @item -fh or -firstHost host @itemx -sh or -secondHost host @cindex fh, option @cindex firstHost, option @cindex sh, option @cindex secondHost, option Hosts on which the chess engines are to run. The default for each is @file{localhost}. If you specify another host, XBoard uses @file{rsh} to run the chess engine there. (You can substitute a different remote shell program for rsh using the @code{remoteShell} option described below.) @item -fd or -firstDirectory dir @itemx -sd or -secondDirectory dir @cindex fd, option @cindex firstDirectory, option @cindex sd, option @cindex secondDirectory, option Working directories in which the chess engines are to be run. The default is "", which means to run the chess engine in the same working directory as XBoard itself. (See the CHESSDIR environment variable.) This option is effective only when the chess engine is being run on the local host; it does not work if the engine is run remotely using the -fh or -sh option. @item -initString string or -firstInitString @itemx -secondInitString string @cindex initString, option @cindex firstInitString, option @cindex secondInitString, option The string that is sent to initialize each chess engine for a new game. Default: @example new random @end example @noindent Setting this option from the command line is tricky, because you must type in real newline characters, including one at the very end. In most shells you can do this by entering a @samp{\} character followed by a newline. Using the character sequence @samp{\n} in the string should work too, though. If you change this option, don't remove the @samp{new} command; it is required by all chess engines to start a new game. You can remove the @samp{random} command if you like; including it causes GNU Chess 4 to randomize its move selection slightly so that it doesn't play the same moves in every game. Even without @samp{random}, GNU Chess 4 randomizes its choice of moves from its opening book. Many other chess engines ignore this command entirely and always (or never) randomize. You can also try adding other commands to the initString; see the documentation of the chess engine you are using for details. @item -firstComputerString string @itemx -secondComputerString string @cindex firstComputerString, option @cindex secondComputerString, option The string that is sent to the chess engine if its opponent is another computer chess engine. The default is @samp{computer\n}. Probably the only useful alternative is the empty string (@samp{}), which keeps the engine from knowing that it is playing another computer. @item -reuse/-xreuse or -reuseFirst true/false @itemx -reuse2/-xreuse2 or -reuseSecond true/false @cindex reuse, option @cindex reuseFirst, option @cindex reuse2, option @cindex reuseSecond, option If the option is false, XBoard kills off the chess engine after every game and starts it again for the next game. If the option is true (the default), XBoard starts the chess engine only once and uses it repeatedly to play multiple games. Some old chess engines may not work properly when reuse is turned on, but otherwise games will start faster if it is left on. @item -firstProtocolVersion version-number @itemx -secondProtocolVersion version-number @cindex firstProtocolVersion, option @cindex secondProtocolVersion, option This option specifies which version of the chess engine communication protocol to use. By default, version-number is 2. In version 1, the "protover" command is not sent to the engine; since version 1 is a subset of version 2, nothing else changes. Other values for version-number are not supported. @item -firstScoreAbs true/false @itemx -secondScoreAbs true/false @cindex firstScoreAbs, option @cindex secondScoreAbs, option If this option is set, the score reported by the engine is taken to be that in favor of white, even when the engine plays black. Important when XBoard uses the score for adjudications, or in PGN reporting. @item -niceEngines priority @cindex niceEngines, option This option allows you to lower the priority of the engine processes, so that the generally insatiable hunger for CPU time of chess engines does not interfere so much with smooth operation of XBoard (or the rest of your system). Negative values could increase the engine priority, which is not recommended. @item -firstOptions string @itemx -secondOptions string @cindex firstOptions, option @cindex secondOptions, option The given string is a comma-separated list of (option name=option value) pairs, like the following example: "style=Karpov,blunder rate=0". If an option announced by the engine at startup through the feature commands of the XBoard/WinBoard protocol matches one of the option names (i.e. "style" or "blunder rate"), it would be set to the given value (i.e. "Karpov" or 0) through a corresponding option command to the engine. This provided that the type of the value (text or numeric) matches as well. @item -firstNeedsNoncompliantFEN string @itemx -secondNeedsNoncompliantFEN string @cindex firstNeedsNoncompliantFEN, option @cindex secondNeedsNoncompliantFEN, option The castling rights and e.p. fields of the FEN sent to the mentioned engine with the setboard command will be replaced by the given string. This can for instance be used to run engines that do not understand Chess960 FENs in variant fischerandom, to make them at least understand the opening position, through setting the string to "KQkq -". (Note you also have to give the e.p. field!) Other possible applications are to provide work-arounds for engines that want to see castling and e.p. fields in variants that do not have castling or e.p. (shatranj, courier, xiangqi, shogi) so that XBoard would normally omit them (string = "- -"), or to add variant-specific fields that are not yet supported by XBoard (e.g. to indicate the number of checks in 3check). @item -shuffleOpenings @cindex shuffleOpenings, option Forces shuffling of the opening setup in variants that normally have a fixed initial position. Shufflings are symmetric for black and white, and exempt King and Rooks in variants with normal castling. Remains in force until a new variant is selected. @item -fischerCastling @cindex fischerCastling, option Specifies Fischer castling (as in Chess960) should be enabled in variants that normally would not have it. Remains in force until a new variant is selected. @end table @node UCI + WB Engine Settings @section UCI + WB Engine Settings @cindex Engine Settings @cindex Settings, Engine @table @asis @item -fUCI or -firstIsUCI true/false @itemx -sUCI or -secondIsUCI true/false @cindex fUCI, option @cindex sUCI, option @cindex firstIsUCI, option @cindex secondIsUCI, option Indicates if the mentioned engine executable file is an UCI engine, and should be run with the aid of the Polyglot adapter rather than directly. Xboard will then pass the other UCI options and engine name to Polyglot on its command line, according to the option @code{adapterCommand}. @item -fUCCI @itemx -sUCCI @itemx -fUSI @itemx -sUSI @cindex fUCCI, option @cindex sUCCI, option @cindex fUSI, option @cindex sUSI, option Options similar to @code{fUCI} and @code{sUCI}, except that they use the indicated engine with the protocol adapter specified in the @samp{uxiAdapter} option. This can then be configured for running an UCCI or USI adapter, as the need arises. @item -adapterCommand string @cindex adapterCommand, option The string conatins the command that should be issued by XBoard to start an engine that is accompanied by the @code{fUCI} option. Any identifier following a percent sign in the command (e.g. %fcp) will be considered the name of an XBoard option, and be replaced by the value of that option at the time the engine is started. For starting the second engine, any leading "f" or "first" in the option name will first be replaced by "s" or "second", before finding its value. Default: 'polyglot -noini -ec "%fcp" -ed "%fd"' @item -uxiAdapter string @cindex uxiAdapter, option Similar to @code{adapterCommand}, but used for engines accompanied by the @code{fUCCI} or @code{fUSI} option, so you can configure XBoard to be ready to handle more than one flavor of non-native protocols. Default: "" @item -polyglotDir filename @cindex polyglotDir, option Gives the name of the directory in which the Polyglot adapter for UCI engines resides. Default: "". @item -usePolyglotBook true/false @cindex usePolyglotBook, option Specifies if the Polyglot book should be used as GUI book. @item -polyglotBook filename @cindex polyglotBook, option Gives the filename of the opening book. The book is only used when the @code{usePolyglotBook} option is set to true, and the option @code{firstHasOwnBookUCI} or @code{secondHasOwnBookUCI} applying to the engine is set to false. The engine will be kept in force mode as long as the current position is in book, and XBoard will select the book moves for it. Default: "". @item -fNoOwnBookUCI or -firstXBook or -firstHasOwnBookUCI true/false @itemx -sNoOwnBookUCI or -secondXBook or -secondHasOwnBookUCI true/false @cindex fNoOwnBookUCI, option @cindex sNoOwnBookUCI, option @cindex firstHasOwnBookUCI, option @cindex secondHasOwnBookUCI, option @cindex firstXBook, option @cindex secondXBook, option Indicates if the mentioned engine has its own opening book it should play from, rather than using the external book through XBoard. Default: depends on setting of the option @code{discourageOwnBooks}. @item -discourageOwnBooks true/false @cindex discourageOwnBooks, option When set, newly loaded engines will be assumed to use the GUI book, unless they explicitly specify differently. Otherwise they will be assumed to not use the GUI book, unless the specify differently (e.g. with @code{firstXBook}). Default: false. @item -bookDepth n @cindex bookDepth, option Limits the use of the GUI book to the first n moves of each side. Default: 12. @item -bookVariation n @cindex bookVariation, option A value n from 0 to 100 tunes the choice of moves from the GUI books from totally random to best-only. Default: 50 @item -mcBookMode @cindex mcBookMode, option When this volatile option is specified, the probing algorithm of the GUI book is altered to always select the move that is most under-represented based on its performance. When all moves are played in approximately the right proportion, a book miss will be reported, to give the engine opportunity to explore a new move. In addition score of the moves will be kept track of during the session in a book buffer. By playing an match in this mode, a book will be built from scratch. The only output are the saved games, which can be converted to an actual book later, with the @samp{Save Games as Book} command. This command can also be used to pre-fill the book buffer before adding new games based on the probing algorithm. @item -fn string or -firstPgnName string @itemx -sn string or -secondPgnName string @cindex firstPgnName, option @cindex secondPgnName, option @cindex fn, option @cindex sn, option Indicates the name that should be used for the engine in PGN tags of engine-engine games. Intended to allow you to install verions of the same engine with different settings, and still distinguish them. Default: "". @item -defaultHashSize n @cindex defaultHashSize, option Sets the size of the hash table to n MegaBytes. Together with the EGTB cache size this number is also used to calculate the memory setting of XBoard/WinBoard engines, for those that support the memory feature of the XBoard/WinBoard protocol. Default: 64. @item -defaultCacheSizeEGTB n @cindex defaultCacheSizeEGTB, option Sets the size of the EGTB cache to n MegaBytes. Together with the hash-table size this number is also used to calculate the memory setting of XBoard/WinBoard engines, for those that support the memory feature of the XBoard/WinBoard protocol. Default: 4. @item -defaultPathEGTB filename @cindex defaultPathEGTB, option Gives the name of the directory where the end-game tablebases are installed, for UCI engines. Default: "/usr/local/share/egtb". @item -egtFormats string @cindex egtFormats, option Specifies which end-game tables are installed on the computer, and where. The argument is a comma-separated list of format specifications, each specification consisting of a format name, a colon, and a directory path name, e.g. "nalimov:/usr/local/share/egtb". If the name part matches that of a format that the engine requests through a feature command, xboard will relay the path name for this format to the engine through an egtpath command. One egtpath command for each matching format will be sent. Popular formats are "nalimov" DTM tablebases and "scorpio" bitbases. Default: "". @item -firstChessProgramNames=@{names@} This option lets you customize the drop-down list of chess engine names that appears in the @samp{Load Engine} and @samp{Match Options} dialog. It consists of a list of strings, one per line. When an engine is loaded, the corresponding line is prefixed with "-fcp ", and processed like it appeared on the command line. That means that apart from the engine command, it can contain any list of XBoard options you want to use with this engine. (Commonly used options here are -fd, -firstXBook, -fUCI, -variant.) The value of this option is gradually built as you load new engines through the @samp{Load Engine} menu dialog, with @samp{Add to list} ticked. To change it, edit your settings file with a plain text editor. @end table @node Tournament options @section Tournament options @cindex Tournament Options @cindex Options, Tournament @table @asis @item -defaultMatchGames n @cindex defaultMatchGames, option Sets the number of games that will be used for a match between two engines started from the menu to n. Also used as games per pairing in other tournament formats. Default: 10. @item -matchPause n @cindex matchPause, option Specifies the duration of the pause between two games of a match or tournament between engines as n milliseconds. Especially engines that do not support ping need this option, to prevent that the move they are thinking on when an opponent unexpectedly resigns will be counted for the next game, (leading to illegal moves there). Default: 10000. @item -tf filename or -tourneyFile filename @cindex tf, option @cindex tourneyFile, option Specifies the name of the tournament file used in match mode to conduct a multi-player tournament. This file is a special settings file, which stores the description of the tournament (including progress info), through normal options (e.g. for time control, load and save files), and through some special-purpose options listed below. @item -tt number or -tourneyType number @cindex tt, option @cindex tourneyType, option Specifies the type of tourney: 0 = round-robin, N>0 = (multi-)gauntlet with N gauntlet engines, -1 = Swiss through external pairing engine. Volatile option, but stored in tourney file. @item -cy number or -tourneyCycles number @cindex cy, option @cindex tourneyCycles, option Specifies the number of cycles in a tourney. Volatile option, but stored in tourney file. @item -participants list @cindex participants, option The list is a multi-line text string that specifies engines occurring in the @code{firstChesProgramNames} list in the settings file by their (implied or explicitly given) nicknames, one engine per line. The mentioned engines will play in the tourney. Volatile option, but stored in tourney file. @item -results string @cindex results, option The string of +=- characters lists the result of all played games in a toruney. Games currently playing are listed as *, while a space indicates a game that is not yet played or playing . Volatile option, but stored in tourney file. @item -defaultTourneyName string @cindex defaultTourneyName, option Specifies the name of the tournament file XBoard should propose when the @samp{Match Options} dialog is opened. Any %y, %M, %d, %h, %m, %s in the string are replaced by the current year, month, day of the month, hours, minutes, seconds of the current time, respectively, as two-digit number. A %Y would be replaced by the year as 4-digit number. Default: empty string. @item -pairingEngine filename @cindex pairingEngine, option Specifies the external program to be used to pair the participants in Swiss tourneys. XBoard communicates with this engine in the same way as it communicates with Chess engines. The only commands sent to the pairing engine are “results N string”, (where N is the number of participants, and string the results so far in the format of the results option), and “pairing N”, (where N is the number of the tourney game). To the latter the pairing engine should answer with “A-B”, where A and B are participant numbers (in the range 1-N). (There should be no reply to the results command.) Default: empty string. @item -afterGame string @itemx -afterTourney string @cindex afterGame, option @cindex afterTourney, option When non-empty, the given string will be executed as a system command after each tournament game, orafterthe tourney completes, respectively. This can be used, for example, to autmatically run a cross-table generator on the PGN file where games are saved, to update the tourney standings. Default: "" @item -syncAfterRound true/false @itemx -syncAfterCycle true/false @cindex syncAfterRound, option @cindex syncAfterCycle, option Controls whether different instances of XBoard concurrently running the same tournament will wait for each other. Defaults: sync after cycle, but not after round. @item -seedBase number @cindex seedBase, option Used to store the seed of the pseudo-random-number generator in the tourneyFile, so that separate instances of XBoard working on the same tourney can take coherent 'random' decisions, such as picking an opening for a given game number. @end table @node ICS options @section ICS options @cindex ICS options @cindex Options, ICS @table @asis @item -ics/-xics or -internetChessServerMode true/false @cindex ics, option @cindex internetChessServerMode, option Connect with an Internet Chess Server to play chess against its other users, observe games they are playing, or review games that have recently finished. Default: false. @item -icshost or -internetChessServerHost host @cindex icshost, option @cindex internetChessServerHost, option The Internet host name or address of the chess server to connect to when in ICS mode. Default: @code{chessclub.com}. Another popular chess server to try is @code{freechess.org}. If your site doesn't have a working Internet name server, try specifying the host address in numeric form. You may also need to specify the numeric address when using the icshelper option with timestamp or timeseal (see below). @item -icsport or -internetChessServerPort port-number @cindex icsport, option @cindex internetChessServerPort, option The port number to use when connecting to a chess server in ICS mode. Default: 5000. @item -icshelper or -internetChessServerHelper prog-name @cindex icshelper, option @cindex internetChessServerHelper, option An external helper program used to communicate with the chess server. You would set it to "timestamp" for ICC (chessclub.com) or "timeseal" for FICS (freechess.org), after obtaining the correct version of timestamp or timeseal for your computer. See "help timestamp" on ICC and "help timeseal" on FICS. This option is shorthand for @code{-useTelnet -telnetProgram program}. @item -telnet/-xtelnet or -useTelnet true/false @cindex telnet, option @cindex useTelnet, option This option is poorly named; it should be called useHelper. If set to true, it instructs XBoard to run an external program to communicate with the Internet Chess Server. The program to use is given by the telnetProgram option. If the option is false (the default), XBoard opens a TCP socket and uses its own internal implementation of the telnet protocol to communicate with the ICS. @xref{Firewalls}. @item -telnetProgram prog-name @cindex telnetProgram, option This option is poorly named; it should be called helperProgram. It gives the name of the telnet program to be used with the @code{gateway} and @code{useTelnet} options. The default is @file{telnet}. The telnet program is invoked with the value of @code{internetChessServerHost} as its first argument and the value of @code{internetChessServerPort} as its second argument. @xref{Firewalls}. @item -gateway host-name @cindex gateway, option If this option is set to a host name, XBoard communicates with the Internet Chess Server by using @file{rsh} to run the @code{telnetProgram} on the given host, instead of using its own internal implementation of the telnet protocol. You can substitute a different remote shell program for @file{rsh} using the @code{remoteShell} option described below. @xref{Firewalls}. @item -internetChessServerCommPort or -icscomm dev-name @cindex internetChessServerCommPort, option @cindex icscomm, option If this option is set, XBoard communicates with the ICS through the given character I/O device instead of opening a TCP connection. Use this option if your system does not have any kind of Internet connection itself (not even a SLIP or PPP connection), but you do have dial-up access (or a hardwired terminal line) to an Internet service provider from which you can telnet to the ICS. The support for this option in XBoard is minimal. You need to set all communication parameters and tty modes before you enter XBoard. Use a script something like this: @example stty raw -echo 9600 > /dev/tty00 xboard -ics -icscomm /dev/tty00 @end example Here replace @samp{/dev/tty00} with the name of the device that your modem is connected to. You might have to add several more options to these stty commands. See the man pages for @file{stty} and @code{tty} if you run into problems. Also, on many systems stty works on its standard input instead of standard output, so you have to use @samp{<} instead of @samp{>}. If you are using linux, try starting with the script below. Change it as necessary for your installation. @example #!/bin/sh -f # configure modem and fire up XBoard # configure modem ( stty 2400 ; stty raw ; stty hupcl ; stty -clocal stty ignbrk ; stty ignpar ; stty ixon ; stty ixoff stty -iexten ; stty -echo ) < /dev/modem xboard -ics -icscomm /dev/modem @end example @noindent After you start XBoard in this way, type whatever commands are necessary to dial out to your Internet provider and log in. Then telnet to ICS, using a command like @kbd{telnet chessclub.com 5000}. Important: See the paragraph below about extra echoes, in @ref{Limitations}. @item -icslogon or -internetChessServerLogonScript file-name @cindex icslogon, option @cindex internetChessServerLogonScript, option @cindex .icsrc Whenever XBoard connects to the Internet Chess Server, if it finds a file with the name given in this option, it feeds the file's contents to the ICS as commands. The default file name is @file{.icsrc}. Usually the first two lines of the file should be your ICS user name and password. The file can be either in $CHESSDIR, in XBoard's working directory if CHESSDIR is not set, or in your home directory. @item -msLoginDelay delay @cindex msLoginDelay, option If you experience trouble logging on to an ICS when using the @code{-icslogon} option, inserting some delay between characters of the logon script may help. This option adds @code{delay} milliseconds of delay between characters. Good values to try are 100 and 250. @item -icsinput/-xicsinput or -internetChessServerInputBox true/false @cindex icsinput, option @cindex internetChessServerInputBox, option Sets the ICS Input Box menu option. @xref{Mode Menu}. Default: false. @item -autocomm/-xautocomm or -autoComment true/false @cindex autocomm, option @cindex autoComment, option Sets the Auto Comment menu option. @xref{Options Menu}. Default: false. @item -autoflag/-xautoflag or -autoCallFlag true/false @cindex autoflag, option @cindex autoCallFlag, option Sets the Auto Flag menu option. @xref{Options Menu}. Default: false. @item -autobs/-xautobs or -autoObserve true/false @cindex autobs, option @cindex autoObserve, option Sets the Auto Observe menu option. @xref{Options Menu}. Default: false. @item -autoKibitz @cindex autoKibitz, option Enables kibitzing of the engines last thinking output (depth, score, time, speed, PV) before it moved to the ICS, in zippy mode. The option @code{showThinking} must be switched on for this option to work. Also diverts similar kibitz information of an opponent engine that is playing you through the ICS to the engine-output window, as if the engine was playing locally. @item -seekGraph true/false or -sg @cindex seekGraph, option @cindex sg, option Enables displaying of the seek graph by left-clicking the board when you are logged on to an ICS and currently idle. The seek graph show all players currently seeking games on the ICS, plotted according to their rating and the time control of the game they seek, in three different colors (for rated, unrated and wild games). Computer ads are displayed as squares, human ads are dots. Default: false. @item -autoRefresh true/false @cindex autoRefresh, option Enables automatic updating of the seek graph, by having the ICS send a running update of all newly placed and removed seek ads. This consumes a substantial amount of communication bandwidth, and is only supported for FICS and ICC. Default: false. @item -backgroundObserve true/false @cindex backgroundObserve, option When true, boards sent to you by the ICS from other games while you are playing (e.g. because you are observing them) will not be automatically displayed. Only a summary of time left and material of both players will appear in the message field above the board. XBoard will remember the last board it has received this way, and will display it in stead of the position in your own game when you press the right mouse button. No other information is stored on such games observed in the background; you cannot save such a game later, or step through its moves. This feature is provided solely for the benefit of bughouse players, to enable them to peek at their partner's game without the need to logon twice. Default: false. @item -dualBoard true/false @cindex dualBoard, option In combination with -backgroundObserve true, this option will display the board of the background game side by side with that of your own game, so you can have it in view permanently. Any board or holdings info coming in will be displayed on the secondary board immediately. This feature is still experimental and largely unfinished. There is no animation or highlighting of moves on the secondary board. Default: false. @item -disguisePromotedPieces true/false @cindex disguisePromotedPieces, option When set promoted Pawns in crazyhouse/bughouse are displayed identical to primordial pieces of the same type, rather than distinguishable. Default: true. @item -moves/-xmoves or -getMoveList true/false @cindex moves, option @cindex getMoveList, option Sets the Get Move List menu option. @xref{Options Menu}. Default: true. @item -alarm/-xalarm or -icsAlarm true/false @cindex alarm, option @cindex icsAlarm, option Sets the ICS Alarm menu option. @xref{Options Menu}. Default: true. @item -icsAlarmTime ms @cindex icsAlarmTime, option Sets the time in milliseconds for the ICS Alarm menu option. @xref{Options Menu}. Default: 5000. @item lowTimeWarning true/false @cindex lowTimeWarning, option Controls a color change of the board as a warning your time is running out. @xref{Options Menu}. Default: false. @item -pre/-xpre \fRor\fB -premove true/false @cindex pre, option @cindex premove, option Sets the Premove menu option. @xref{Options Menu}. Default: true. @item -prewhite/-xprewhite or -premoveWhite @itemx -preblack/-xpreblack or -premoveBlack @itemx -premoveWhiteText string @itemx -premoveBlackText string @cindex prewhite, option @cindex premoveWhite, option @cindex preblack, option @cindex premoveBlack, option @cindex premoveWhiteText, option @cindex premoveBlackText, option Set the menu options for specifying the first move for either color. @xref{Options Menu}. Defaults: false and empty strings, so no pre-moves. @item -quiet/-xquiet or -quietPlay true/false @cindex quiet, option @cindex quietPlay, option Sets the Quiet Play menu option. @xref{Options Menu}. Default: false. @item -colorizeMessages or -colorize/-xcolorize @cindex Colors @cindex colorize, option @cindex colorizeMessages, option Setting colorizeMessages to true tells XBoard to colorize the messages received from the ICS. Colorization works only if your xterm supports ISO 6429 escape sequences for changing text colors. Default: true. @item -colorShout foreground,background,bold @itemx -colorSShout foreground,background,bold @itemx -colorCShout foreground,background,bold @itemx -colorChannel1 foreground,background,bold @itemx -colorChannel foreground,background,bold @itemx -colorKibitz foreground,background,bold @itemx -colorTell foreground,background,bold @itemx -colorChallege foreground,background,bold @itemx -colorRequest foreground,background,bold @itemx -colorSeek foreground,background,bold @itemx -colorNormal foreground,background,bold @cindex Colors @cindex colorShout, option @cindex colorSShout, option @cindex colorCShout, option @cindex colorChannel1, option @cindex colorChannel, option @cindex colorKibitz, option @cindex colorTell, option @cindex colorChallenge, option @cindex colorRequest, option @cindex colorSeek, option @cindex colorNormal, option These options set the colors used when colorizing ICS messages. All ICS messages are grouped into one of these categories: shout, sshout, channel 1, other channel, kibitz, tell, challenge, request (including abort, adjourn, draw, pause, and takeback), or normal (all other messages). Each foreground or background argument can be one of the following: black, red, green, yellow, blue, magenta, cyan, white, or default. Here ``default'' means the default foreground or background color of your xterm. Bold can be 1 or 0. If background is omitted, ``default'' is assumed; if bold is omitted, 0 is assumed. @item -soundProgram progname @cindex soundProgram, option @cindex Sounds If this option is set to a sound-playing program that is installed and working on your system, XBoard can play sound files when certain events occur, listed below. The default program name is "play". If any of the sound options is set to "$", the event rings the terminal bell by sending a ^G character to standard output, instead of playing a sound file. If an option is set to the empty string "", no sound is played for that event. @item -soundDirectory directoryname @cindex soundDirectory, option @cindex Sounds This option specifies where XBoard will look for sound files, when these are not given as an absolute path name. @item -soundShout filename @itemx -soundSShout filename @itemx -soundCShout filename @itemx -soundChannel filename @itemx -soundChannel1 filename @itemx -soundKibitz filename @itemx -soundTell filename @itemx -soundChallenge filename @itemx -soundRequest filename @itemx -soundSeek filename @cindex soundShout, option @cindex soundSShout, option @cindex soundCShout, option @cindex soundChannel, option @cindex soundChannel1, option @cindex soundKibitz, option @cindex soundTell, option @cindex soundChallenge, option @cindex soundRequest, option @cindex soundSeek, option These sounds are triggered in the same way as the colorization events described above. They all default to "", no sound. They are played only if the colorizeMessages is on. CShout is synonymous with SShout. @item -soundMove filename @cindex soundMove, option This sound is used by the Move Sound menu option. Default: "$". @item -soundIcsAlarm filename @cindex soundIcsAlarm, option This sound is used by the ICS Alarm menu option. Default: "$". @item -soundIcsWin filename @cindex soundIcsWin, option This sound is played when you win an ICS game. Default: "" (no sound). @item -soundIcsLoss filename @cindex soundIcsLoss, option This sound is played when you lose an ICS game. Default: "" (no sound). @item -soundIcsDraw filename @cindex soundIcsDraw, option This sound is played when you draw an ICS game. Default: "" (no sound). @item -soundIcsUnfinished filename @cindex soundIcsUnfinished, option This sound is played when an ICS game that you are participating in is aborted, adjourned, or otherwise ends inconclusively. Default: "" (no sound). @end table @node Load and Save options @section Load and Save options @cindex Options, Load and Save @cindex Load and Save options @table @asis @item -lgf or -loadGameFile file @itemx -lgi or -loadGameIndex index @cindex lgf, option @cindex loadGameFile, option @cindex lgi, option @cindex loadGameIndex, option If the @code{loadGameFile} option is set, XBoard loads the specified game file at startup. The file name @file{-} specifies the standard input. If there is more than one game in the file, XBoard pops up a menu of the available games, with entries based on their PGN (Portable Game Notation) tags. If the @code{loadGameIndex} option is set to @samp{N}, the menu is suppressed and the N th game found in the file is loaded immediately. The menu is also suppressed if @code{matchMode} is enabled or if the game file is a pipe; in these cases the first game in the file is loaded immediately. Use the @file{pxboard} shell script provided with XBoard if you want to pipe in files containing multiple games and still see the menu. If the loadGameIndex specifies an index -1, this triggers auto-increment of the index in @code{matchMode}, which means that after every game the index is incremented by one, causing each game of the match to be played from the next game in the file. Similarly, specifying an index value of -2 causes the index to be incremented every two games, so that each game in the file is used twice (with reversed colors). The @code{rewindIndex} option causes the index to be reset to the first game of the file when it has reached a specified value. @item -rewindIndex n Causes a position file or game file to be rewound to its beginning after n positions or games in auto-increment @code{matchMode}. See @code{loadPositionIndex} and @code{loadGameIndex}. default: 0 (no rewind). @item -td or -timeDelay seconds @cindex td, option @cindex timeDelay, option Time delay between moves during @samp{Load Game} or @samp{Analyze File}. Fractional seconds are allowed; try @samp{-td 0.4}. A time delay value of -1 tells XBoard not to step through game files automatically. Default: 1 second. @item -sgf or -saveGameFile file @cindex sgf, option @cindex saveGameFile, option If this option is set, XBoard appends a record of every game played to the specified file. The file name @file{-} specifies the standard output. @item -autosave/-xautosave or -autoSaveGames true/false @cindex autosave, option @cindex autoSaveGames, option Sets the Auto Save menu option. @xref{Options Menu}. Default: false. Ignored if @code{saveGameFile} is set. @item -onlyOwnGames true/false @cindex onlyOwnGames, option Suppresses auto-saving of ICS observed games. Default: false. @item -lpf or -loadPositionFile file @itemx -lpi or -loadPositionIndex index @cindex lpf, option @cindex loadPositionFile, option @cindex lpi, option @cindex loadPositionIndex, option If the @code{loadPositionFile} option is set, XBoard loads the specified position file at startup. The file name @file{-} specifies the standard input. If the @code{loadPositionIndex} option is set to N, the Nth position found in the file is loaded; otherwise the first position is loaded. If the loadPositionIndex specifies an index -1, this triggers auto-increment of the index in @code{matchMode}, which means that after every game the index is incremented by one, causing each game of the match to be played from the next position in the file. Similarly, specifying an index value of -2 causes the index to be incremented every two games, so that each position in the file is used twice (with the engines playing opposite colors). The @code{rewindIndex} option causes the index to be reset to the first position of the file when it has reached a specified value. @item -spf or -savePositionFile file @cindex spf, option @cindex savePositionFile, option If this option is set, XBoard appends the final position reached in every game played to the specified file. The file name @file{-} specifies the standard output. @item -positionDir directory @cindex positionDir, option Specifies the directory where file browsing should start when using the @samp{Load Position} menu item. @item -pgnExtendedInfo true/false @cindex pgnExtendedInfo, option If this option is set, XBoard saves depth, score and time used for each move that the engine found as a comment in the PGN file. Default: false. @item -pgnEventHeader string @cindex pgnEventHeader, option Sets the name used in the PGN event tag to string. Default: "Computer Chess Game". @item -pgnNumberTag true/false @cindex pgnNumberTag, option Include the (unique) sequence number of a tournament game into the saved PGN file as a 'number' tag. Default: false. @item -saveOutOfBookInfo true/false @cindex saveOutOfBookInfo, option Include the information on how the engine(s) game out of its opening book in a special 'annotator' tag with the PGN file. Default: true. @item -oldsave/-xoldsave or -oldSaveStyle true/false @cindex oldsave, option @cindex oldSaveStyle, option Sets the Old Save Style menu option. @xref{Options Menu}. Default: false. @item -gameListTags string @cindex gameListTags, option The character string lists the PGN tags that should be printed in the Game List, and their order. The meaning of the codes is e=event, s=site, d=date, o=round, p=players, r=result, w=white Elo, b=black Elo, t=time control, v=variant, a=out-of-book info, c=result comment. Default: "eprd" @item -ini or -settingsFile filename @itemx -saveSettingsFile filename @itemx @@filename @cindex saveSettingsFile, option @cindex SettingsFile, option @cindex init, option @cindex at sign, option When XBoard encounters an option -settingsFile (or -ini for short), or @@filename, it tries to read the mentioned file, and substitutes the contents of it (presumaby more command-line options) in place of the option. In the case of -ini or -settingsFile, the name of a successfully read settings file is also remembered as the file to use for saving settings (automatically on exit, or on user command). An option of the form @@filename does not affect saving. The option -saveSettingsFile does specify a name of the file to use for saving, without reading any options from it, and is thus also effective when the file did not exist yet. So the settings will be saved to the file specified in the last -saveSettingsFile or succesfull -settingsFile / -ini command, if any, and in /etc/xboard/xboard.conf otherwise. Usualy the latter is only accessible for the system administrator, though, and will be used to contain system-wide default setings, amongst which a -saveSettingsFile and -settingsFile options to specify a settings file accessible to the individual user, such as ~/.xboardrc in the user's home directory. @item -saveSettingsOnExit true/false @cindex saveSettingsOnExit, option Controls saving of options on the settings file. @xref{Options Menu}. Default: true. @end table @node User interface options @section User interface options @cindex User interface options @cindex Options, User interface @table @asis @item -display @itemx -geometry @itemx -iconic @itemx -name @cindex display, option @cindex geometry, option @cindex iconic, option @cindex resource name, option These and most other standard Xt options are accepted. @item -noGUI @cindex noGUI, option Suppresses all GUI functions of XBoard (to speed up automated ultra-fast engine-engine games, which you don't want to watch). There will be no board or clock updates, no printing of moves, and no update of the icon on the task bar in this mode. @item -logoSize N @cindex logoSize, option This option controls the drawing of player logos next to the clocks. The integer N specifies the width of the logo in pixels; the logo height will always be half the width. When N = 0, no logos will be diplayed. Default: 0. @item -firstLogo imagefile @itemx -secondLogo imagefile @cindex firstLogo, option @cindex secondLogo, option Specify the images to be used as player logos when @code{logoSize} is non-zero, next to the white and black clocks, respectively. @item -autoLogo true/false @item -logoDir filename @cindex autoLogo, option @cindex logoDir, option When @code{autoLogo} is set, XBoard will search for a PNG image file with the name of the engine or ICS in the directory specified. For a human player it will look for a file <username>.png in this directory, but only when ~/.logo.png does not provide one. by @code{logoDir}. @item -recentEngines number @itemx -recentEngineList list @cindex recentEngines, option @cindex recentEngineList, option When the number is larger than zero, it determines how many recently used engines will be appended at the bottom of the @samp{Engines} menu. The engines will be saved in your settings file as the option @code{recentEngineList}, by their nicknames, and the most recently used one will always be sorted to the top. If the list after that is longer than the specified number, the last one is discarded. Changes in the list will only become visible the next session, provided you saved the settings. Default: 6. @item -autoInstall list @cindex autoInstall, option When the list is set to a non-empty string, XBoard will scan the operating system's plugin directory for engines supporting UCI and XBoard protocol at startup. When it finds an engine that was installed after it last saved its settings, a line to launch that engine (as per specs in the plugin file) is appended to the -firstChessProgramNames list of installed engines. In the future it will be possible to use the list to limit this automatic adding of engines to a certain types of variants. @item -oneClickMove true/false @cindex oneClickMove, option When set, this option allows you to enter moves by only clicking the to- or from-square, when only a single legal move to or from that square is possible. Double-clicking a piece (or clicking an already selected piece) will instruct that piece to make the only capture it can legally do. Default: false. @item -monoMouse true/false @cindex monoMouse, option When set button 1 clicks on empty squares in Edit Position mode will be interpreted as button 3 clicks, so they place a piece. Default: false. @item -movesound/-xmovesound or -ringBellAfterMoves true/false @cindex movesound, option @cindex bell, option @cindex ringBellAfterMoves, option Sets the Move Sound menu option. @xref{Options Menu}. Default: false. For compatibility with old XBoard versions, -bell/-xbell are also accepted as abbreviations for this option. @item -exit/-xexit or -popupExitMessage true/false @cindex exit, option @cindex popupExitMessage, option Sets the Popup Exit Message menu option. @xref{Options Menu}. Default: true. @item -popup/-xpopup or -popupMoveErrors true/false @cindex popup, option @cindex popupMoveErrors, option Sets the Popup Move Errors menu option. @xref{Options Menu}. Default: false. @item -queen/-xqueen or -alwaysPromoteToQueen true/false @cindex queen, option @cindex alwaysPromoteToQueen, option Sets the Always Queen menu option. @xref{Options Menu}. Default: false. @item -sweepPromotions true/false @cindex sweepPromotion, option Sets the @samp{Almost Always Promote to Queen} menu option. @xref{Options Menu}. Default: false. @item -legal/-xlegal or -testLegality true/false @cindex legal, option @cindex testLegality, option Sets the Test Legality menu option. @xref{Options Menu}. Default: true. @item -size or -boardSize (sizeName | n1,n2,n3,n4,n5,n6,n7) @cindex size, option @cindex boardSize, option @cindex board size Determines how large the board will be, by selecting the pixel size of the pieces and setting a few related parameters. The sizeName can be one of: Titanic, giving 129x129 pixel pieces, Colossal 116x116, Giant 108x108, Huge 95x95, Big 87x87, Large 80x80, Bulky 72x72, Medium 64x64, Moderate 58x58, Average 54x54, Middling 49x49, Mediocre 45x45, Small 40x40, Slim 37x37, Petite 33x33, Dinky 29x29, Teeny 25x25, or Tiny 21x21. Xboard installs with a set of scalable (svg) piece images, which it scales to any of the requested sizes. The square size can further be continuously scaled by sizing the board window, but this only adapts the size of the pieces, and has no effect on the width of the grid lines or the font choice (both of which would depend on he selected boardSize). The default depends on the size of your screen; it is approximately the largest size that will fit without clipping. You can select other sizes or vary other layout parameters by providing a list of comma-separated values (with no spaces) as the argument. You do not need to provide all the values; for any you omit from the end of the list, defaults are taken from the nearest built-in size. The value @code{n1} gives the piece size, @code{n2} the width of the black border between squares, @code{n3} the desired size for the clockFont, @code{n4} the desired size for the coordFont, @code{n5} the desired size for the messageFont, @code{n6} the smallLayout flag (0 or 1), and @code{n7} the tinyLayout flag (0 or 1). All dimensions are in pixels. If the border between squares is eliminated (0 width), the various highlight options will not work, as there is nowhere to draw the highlight. If smallLayout is 1 and @code{titleInWindow} is true, the window layout is rearranged to make more room for the title. If tinyLayout is 1, the labels on the menu bar are abbreviated to one character each and the buttons in the button bar are made narrower. @item -overrideLineGap n @cindex overrideLineGap, option When n >= 0, this forces the width of the black border between squares to n pixels for any board size. Mostly used to suppress the grid entirely by setting n = 0, e.g. in xiangqi or just getting a prettier picture. When n < 0 this the size-dependent width of the grid lines is used. Default: -1. @item -coords/-xcoords or -showCoords true/false @cindex coords, option @cindex showCoords, option Sets the Show Coords menu option. @xref{Options Menu}. Default: false. The @code{coordFont} option specifies what font to use. @item -autoraise/-xautoraise or -autoRaiseBoard true/false @cindex autoraise, option @cindex autoRaiseBoard, option Sets the Auto Raise Board menu option. @xref{Options Menu}. Default: true. @item -autoflip/-xautoflip or -autoFlipView true/false @cindex autoflip, option @cindex autoFlipView, option Sets the Auto Flip View menu option. @xref{Options Menu}. Default: true. @item -flip/-xflip or -flipView true/false @cindex flip, option @cindex flipView, option If Auto Flip View is not set, or if you are observing but not participating in a game, then the positioning of the board at the start of each game depends on the flipView option. If flipView is false (the default), the board is positioned so that the white pawns move from the bottom to the top; if true, the black pawns move from the bottom to the top. In any case, the Flip menu option (see @ref{Options Menu}) can be used to flip the board after the game starts. @item -title/-xtitle or -titleInWindow true/false @cindex title, option @cindex titleInWindow, option If this option is true, XBoard displays player names (for ICS games) and game file names (for @samp{Load Game}) inside its main window. If the option is false (the default), this information is displayed only in the window banner. You probably won't want to set this option unless the information is not showing up in the banner, as happens with a few X window managers. @item -buttons/-xbuttons or -showButtonBar True/False @cindex buttons, option @cindex showButtonBar, option If this option is False, xboard omits the [<<] [<] [P] [>] [>>] button bar from the window, allowing the message line to be wider. You can still get the functions of these buttons using the menus or their keyboard shortcuts. Default: true. @item -evalZoom factor @cindex evalZoom, option The score interval (-1,1) is blown up on the vertical axis of the Evaluation Graph by the given factor. Default: 1 @item -evalThreshold n @cindex evalThreshold, option Score below n (centiPawn) are plotted as 0 in the Evaluation Graph. Default: 25 @item -mono/-xmono or -monoMode true/false @cindex mono, option @cindex monoMode, option Determines whether XBoard displays its pieces and squares with two colors (true) or four (false). You shouldn't have to specify @code{monoMode}; XBoard will determine if it is necessary. @item -showTargetSquares true/false @cindex showTargetSquares, option Determines whether XBoard can highlight the squares a piece has legal moves to, when you grab that piece with the mouse. Default: false. @item -flashCount count @itemx -flashRate rate @itemx -flash/-xflash @cindex flashCount, option @cindex flashRate, option @cindex flash, option @cindex xflash, option These options enable flashing of pieces when they land on their destination square. @code{flashCount} tells XBoard how many times to flash a piece after it lands on its destination square. @code{flashRate} controls the rate of flashing (flashes/sec). Abbreviations: @code{flash} sets flashCount to 3. @code{xflash} sets flashCount to 0. Defaults: flashCount=0 (no flashing), flashRate=5. @item -highlight/-xhighlight or -highlightLastMove true/false @cindex highlight, option @cindex highlightLastMove, option Sets the Highlight Last Move menu option. @xref{Options Menu}. Default: false. @item -highlightMoveWithArrow true/false @cindex highlight Arrow, option @cindex highlightMoveWithArrow, option Sets the Highlight with Arrow menu option. @xref{Options Menu}. Default: false. @item -blind/-xblind or -blindfold true/false @cindex blind, option @cindex blindfold, option Sets the Blindfold menu option. @xref{Options Menu}. Default: false. @item -periodic/-xperiodic or -periodicUpdates true/false @cindex periodic, option @cindex periodicUpdates, option Controls updating of current move andnode counts in analysis mode. Default: true. @item -fSAN @itemx -sSAN @cindex fSAN, option @cindex sSAN, option Causes the PV in thinking output of the mentioned engine to be converted to SAN before it is further processed. Warning: this might lose engine output not understood by the parser, and uses a lot of CPU power. Default: the PV is displayed exactly as the engine produced it. @item -showEvalInMoveHistory true/false @cindex showEvalInMoveHistory, option Controls whether the evaluation scores and search depth of engine moves are displayed with the move in the move-history window. Default: true. @item -clockFont font @cindex clockFont, option @cindex Font, clock The font used for the clocks. If the option value is a pattern that does not specify the font size, XBoard tries to choose an appropriate font for the board size being used. Default Xaw: -*-helvetica-bold-r-normal--*-*-*-*-*-*-*-*. Default GTK: Sans Bold %d. @item -coordFont font @cindex coordFont, option @cindex Font, coordinates The font used for rank and file coordinate labels if @code{showCoords} is true. If the option value is a pattern that does not specify the font size, XBoard tries to choose an appropriate font for the board size being used. Default Xaw: -*-helvetica-bold-r-normal--*-*-*-*-*-*-*-*. Default GTK: Sans Bold %d. @item -messageFont font @cindex messageFont, option @cindex Font, message The font used for popup dialogs, menus, etc. If the option value is a pattern that does not specify the font size, XBoard tries to choose an appropriate font for the board size being used. Default Xaw: -*-helvetica-medium-r-normal--*-*-*-*-*-*-*-*. Default GTK: Sans Bold %d. @cindex tagsFont, option @cindex Font, tags The font used in the Edit Tags dialog. If the option value contains %d, XBoard will replace it by an appropriate font for the board size being used. (Only used in GTK build.) Default: Sans Normal %d. @cindex commentFont, option @cindex Font, comment The font used in the Edit Comment dialog. If the option value contains %d, XBoard will replace it by an appropriate font for the board size being used. (Only used in GTK build.) Default: Sans Normal %d. @cindex icsFont, option @cindex Font, ics The font used to display ICS output in the ICS Chat window. As ICS output often contains tables aligned by spaces, a mono-space font is recommended here. If the option value contains %d, XBoard will replace it by an appropriate font for the board size being used. (Only used in GTK build.) Default: Monospace Normal %d. @cindex moveHistoryFont, option @cindex Font, moveHistory The font used in Move History and Engine Output windows. As these windows display mainly moves, one could use a figurine font here. If the option value contains %d, XBoard will replace it by an appropriate font for the board size being used. (Only used in GTK build.) Default: Sans Normal %d. @cindex gameListFont, option @cindex Font, gameList The font used in the listbox of the Game List window. If the option value contains %d, XBoard will replace it by an appropriate font for the board size being used. (Only used in GTK build.) Default: Sans Bold %d. @item -fontSizeTolerance tol @cindex fontSizeTolerance, option In the font selection algorithm, a nonscalable font will be preferred over a scalable font if the nonscalable font's size differs by @code{tol} pixels or less from the desired size. A value of -1 will force a scalable font to always be used if available; a value of 0 will use a nonscalable font only if it is exactly the right size; a large value (say 1000) will force a nonscalable font to always be used if available. Default: 4. @item -pid or -pieceImageDirectory dir @cindex pid, option @cindex pieceImageDirectory, option This options control what piece images xboard uses. XBoard will look in the specified directory for an image in png or svg format for every piece type, with names like BlackQueen.svg, WhiteKnight.svg etc. When neither of these is found (or no valid directory is specified) XBoard will first ty to use an image White/BlackTile.svg in that same directory, and if that is not present either use the svg piece that was installed with it (from the source-tree directory @samp{svg}). Both svg and png images will be scaled by XBoard to the required size, but the png pieces lose much in quality when scaled too much. Default: "". @item -inscriptions utf8string @cindex inscriptions, option The positions in the utf8string correspond to XBoard's piece types, and for each type a glyph can be defined. This glyph will then be rendered on top of the image for the piece. This is useful in combination with the White/BlackTile.svg images, which could be the image of a blank Shogi tile, for writing the kanji piece name on top of it on the fly. Default: "". @item -whitePieceColor color @itemx -blackPieceColor color @itemx -lightSquareColor color @itemx -darkSquareColor color @itemx -highlightSquareColor color @itemx -preoveHighlightColor color @itemx -lowTimeWarningColor color @cindex Colors @cindex whitePieceColor, option @cindex blackPieceColor, option @cindex lightSquareColor, option @cindex darkSquareColor, option @cindex highlightSquareColor, option @cindex premoveHighlightColor, option @cindex lowTimeWarningColor, option Colors to use for the pieces, squares, and square highlights. Defaults: @example -whitePieceColor #FFFFCC -blackPieceColor #202020 -lightSquareColor #C8C365 -darkSquareColor #77A26D -highlightSquareColor #FFFF00 -premoveHighlightColor #FF0000 -lowTimeWarningColor #FF0000 @end example On a grayscale monitor you might prefer: @example -whitePieceColor gray100 -blackPieceColor gray0 -lightSquareColor gray80 -darkSquareColor gray60 -highlightSquareColor gray100 -premoveHighlightColor gray70 -lowTimeWarningColor gray70 @end example The PieceColor options only work properly if the image files defining the pieces were pure black & white (possibly anti-aliased to produce gray scales and semi-transparancy), like the pieces images that come with the install. Their effect on colored pieces is undefined. The SquareColor option only have an effect when no board textures are used. @item -trueColors true/false @cindex trueColors, option When set, this option suppresses the effect of the PieceColor options mentioned above. This is recommended for images that are already colored. @item -useBoardTexture true/false @itemx -liteBackTextureFile filename @itemx -darkBackTextureFile filename @cindex useBoardTexture, option @cindex liteBackTextureFile, option @cindex darkBackTextureFile, option Indicate the png image files to be used for drawing the board squares, and if they should be used rather than using simple colors. The algorithm for cutting squares out of a given bitmap is such that the picture is perfectly reproduced when a bitmap the size of the complete board is given. If the filename ends in "-NxM.png", with integer N and M, it is assumed to contain a bitmap of a complete board of N files and M ranks, and XBoard will scale it to exactly match the current square size. If N=M=0 it scales the entire bitmap to the size of the board, irrespective of the number of files and ranks of the latter. Without any -NxM suffix textures are only blown up by an integer factor when they are smaller than the square size, or, when the name starts with "xq", too small to cover the complete Xiangqi board. Default: false and "" @item -drag/-xdrag or -animateDragging true/false @cindex drag, option @cindex animateDragging, option Sets the Animate Dragging menu option. @xref{Options Menu}. Default: true. @item -animate/-xanimate or -animateMoving true/false @cindex animate, option @cindex animateMoving, option Sets the Animate Moving menu option. @xref{Options Menu}. Default: true. @item -animateSpeed n @cindex -animateSpeed, option Number of milliseconds delay between each animation frame when Animate Moves is on. @item -autoDisplayComment true/false @itemx -autoDisplayTags true/false @cindex -autoDisplayComment, option @cindex -autoDisplayTags, option If set to true, these options cause the window with the move comments, and the window with PGN tags, respectively, to pop up automatically when such tags or comments are encountered during the replaying a stored or loaded game. Default: true. @item -pasteSelection true/false @cindex -pasteSelection, option If this option is set to true, the Paste Position and Paste Game options paste from the currently selected text. If false, they paste from the clipboard. Default: false. @item -autoCopyPV true|false @cindex autoCopyPV, option When this option is set, the position displayed on the board when you terminate a PV walk (initiated by a right-click on board or engine-output window) will be automatically put on the clipboard as FEN. Default: false. @item -dropMenu true|false @cindex dropMenu, option This option allows you to emulate old behavior, where the right mouse button brings up the (now deprecated) drop menu rather than displaying the position at the end of the principal variation. Default: False. @item -pieceMenu true|false @cindex pieceMenu, option This option allows you to emulate old behavior, where the right mouse button brings up the (now deprecated) piece menu in Edit Position mode. From this menu you can select the piece to put on the square you clicked to bring up the menu, or select items such as @kbd{clear board}. You can also @kbd{promote} or @kbd{demote} a clicked piece to convert it into an unorthodox piece that is not directly in the menu, or give the move to @kbd{black} or @kbd{white}. @item -variations true|false @cindex variations, option When this option is on, you can start new variations in Edit Game or Analyze mode by holding the Shift key down while entering a move. When it is off, the Shift key will be ignored. Default: False. @item -appendPV true|false @cindex appendPV, option When this option is on, a button 3 click left of a PV in the Engine Output window will play the first move of that PV in Analyze mode, or as many moves as you walk through it by moving the mouse. Default: False. @item -absoluteAnalysisScores true|false @cindex absoluteAnalysisScores, option When true, scores on the Engine Output window during analysis will be printed from the white point-of-view, rather than the side-to-move point-of-view. Default: False. @item -scoreWhite true|false @cindex scoreWhite, option When true, scores will always be printed from the white point-of-view, rather than the side-to-move point-of-view. Default: False. @item -memoHeaders true|false @cindex memoHeaders, option When true, column headers will be displayed in the Engine Output window for the depth, score, time and nodes data. A button 3 click on these headers will hide or show the corresponding data. (Not intended for dynamic use, as already printed data of the current search will not be affected!) Defaul: False. @end table @node Adjudication Options @section Adjudication Options @cindex Options, adjudication @table @asis @item -adjudicateLossThreshold n @cindex adjudicateLossThreshold, option If the given value is non-zero, XBoard adjudicates the game as a loss if both engines agree for a duration of 6 consecutive ply that the score is below the given score threshold for that engine. Make sure the score is interpreted properly by XBoard, using @code{-firstScoreAbs} and @code{-secondScoreAbs} if needed. Default: 0 (no adjudication) @item -adjudicateDrawMoves n @cindex adjudicateDrawMoves, option If the given value is non-zero, XBoard adjudicates the game as a draw if after the given number of moves it was not yet decided. Default: 0 (no adjudication) @item -checkMates true/false @cindex checkMates, option If this option is set, XBoard detects all checkmates and stalemates, and ends the game as soon as they occur. Legality-testing must be switched on for this option to work. Default: true @item -testClaims true/false @cindex testClaims, option If this option is set, XBoard verifies all result claims made by engines, and those who send false claims will forfeit the game because of it. Legality-testing must be switched on for this option to work. Default: true @item -materialDraws true/false @cindex materialDraws, option If this option is set, XBoard adjudicates games as draws when there is no sufficient material left to inflict a checkmate. This applies to KBKB with like bishops (any number, actually), and to KBK, KNK and KK. Legality-testing must be switched on for this option to work. Default: true @item -trivialDraws true/false @cindex trivialDraws, option If this option is set, XBoard adjudicates games as draws that cannot be usually won without opponent cooperation. This applies to KBKB with unlike bishops, and to KBKN, KNKN, KNNK, KRKR and KQKQ. The draw is called after 6 ply into these end-games, to allow quick mates that can occur in some exceptional positions to be found by the engines. KQKQ does not really belong in this category, and might be taken out in the future. (When bitbase-based adjudications are implemented.) Legality-testing must be on for this option to work. Default: false @item -ruleMoves n @cindex ruleMoves, option If the given value is non-zero, XBoard adjudicates the game as a draw after the given number of consecutive reversible moves. Engine draw claims are always accepted after 50 moves, irrespective of the given value of n. @item -repeatsToDraw n If the given value is non-zero, xboard adjudicates the game as a draw if a position is repeated the given number of times. Engines draw claims are always accepted after 3 repeats, (on the 3rd occurrence, actually), irrespective of the value of n. Beware that positions that have different castling or en-passant rights do not count as repeats, XBoard is fully e.p. and castling aware! @end table @node Other options @section Other options @cindex Options, miscellaneous @table @asis @item -ncp/-xncp or -noChessProgram true/false @cindex ncp, option @cindex noChessProgram, option If this option is true, XBoard acts as a passive chessboard; it does not start a chess engine at all. Turning on this option also turns off clockMode. Default: false. @item -viewer @itemx -viewerOptions string @cindex viewer, option @cindex viewerOptions, option Presence of the volatile option @code{viewer} on the command line will cause the value of the persistent option @code{viewerOptions} as stored in the settings file to be appended to the command line. The @code{view} option will be used by desktop associations with game or position file types, so that @code{viewerOptions} can be used to configure the exact mode XBoard will start in when it should act on such a file (e.g. in -ncp mode, or analyzing with your favorite engine). The options are also automatically appended when Board is invoked with a single argument not being an option name, which is then assumed to be the name of a @code{loadGameFile} or (when the name ends in .fen) a @code{loadPositionFile}. Default: "-ncp -engineOutputUp false -saveSettingsOnExit false". @item -tourneyOptions string @cindex tourneyOptions, option When XBoard is invoked with a single argument that is a file with .trn extension, it will assume this argument to be the value of a @code{tourneyFile} option, and apped the value of the persistent option @code{tourneyOptions} as stored in the settings file to the command line. Thus the value of @code{tourneyOptions} can be used to configure XBoard to automatically start running a tournament when it should act on such a file. Default: "-ncp -mm -saveSettingsOnExit false". @item -mode or -initialMode modename @cindex mode, option @cindex initalMode, option If this option is given, XBoard selects the given modename from the Mode menu after starting and (if applicable) processing the loadGameFile or loadPositionFile option. Default: "" (no selection). Other supported values are MachineWhite, MachineBlack, TwoMachines, Analysis, AnalyzeFile, EditGame, EditPosition, and Training. @item -variant varname @cindex variant, option Activates (sometimes partial) support for playing chess variants against a local engine or editing variant games. This flag is not needed in ICS mode. Recognized variant names are: @example normal Normal chess wildcastle Shuffle chess, king can castle from d file nocastle Shuffle chess, no castling allowed fischerandom Fischer Random shuffle chess bughouse Bughouse, ICC/FICS rules crazyhouse Crazyhouse, ICC/FICS rules losers Lose all pieces or get mated (ICC wild 17) suicide Lose all pieces including king (FICS) giveaway Try to have no legal moves (ICC wild 26) twokings Weird ICC wild 9 kriegspiel Opponent's pieces are invisible atomic Capturing piece explodes (ICC wild 27) 3check Win by giving check 3 times (ICC wild 25) shatranj An ancient precursor of chess (ICC wild 28) xiangqi Chinese Chess (on a 9x10 board) shogi Japanese Chess (on a 9x9 board & piece drops) capablanca Capablanca Chess (10x8 board, with Archbishop and Chancellor pieces) gothic similar, with a better initial position caparandom An FRC-like version of Capablanca Chess (10x8) janus A game with two Archbishops (10x8 board) courier Medieval intermediate between shatranj and modern Chess (on 12x8 board) falcon Patented 10x8 variant with two Falcon pieces berolina Pawns capture straight ahead, and move diagonally cylinder Pieces wrap around the board edge knightmate King moves as Knight, and vice versa super Superchess (shuffle variant with 4 exo-pieces) makruk Thai Chess (shatranj-like, P promotes on 6th rank) asean ASEAN Chess (a modernized version of Makruk) spartan Spartan Chess (black has unorthodox pieces) great Great Shatranj, a 10x8 variant without sliders grand Grand Chess, on 10x10 with Capablanca pieces lion Mighty-Lion Chess, with a multi-capturing Lion elven Eleven Chess, with Lion and crowned sliders on 10x10 chu Chu Shogi, historic 12x12 variant with 2x46 pieces fairy A catchall variant in which all piece types known to XBoard can participate (8x8) unknown Catchall for other unknown variants @end example In the shuffle variants, XBoard does shuffle the pieces, although you can still do it by hand using Edit Position. Some variants are supported only in ICS mode, including bughouse, and kriegspiel. Berolina and cylinder chess are only partially supported, and can only be played with legality testing off. Apart from these standard variants, engines can define variants of arbitrary names, briefing XBoard transparently on the rules for piece movement, board size and initial setup, so that they work nearly as well as fully-supported standard variants. (But obviously only while using that engine.) The user might have to alter the adjudication settings for some variants, however. E.g. it makes no sense to adjudicate a draw after 50 reversible moves in variants that have a 64-move rule, or no similar rule at all. @item -boardHeight N @cindex boardHeight, option Allows you to set a non-standard number of board ranks in any variant. If the height is given as -1, the default height for the variant is used. Default: -1 @item -boardWidth N @cindex boardWidth, option Allows you to set a non-standard number of board files in any variant. If the width is given as -1, the default width for the variant is used. With a non-standard width, the initial position will always be an empty board, as the usual opening array will not fit. Default: -1 @item -holdingsSize N @cindex holdingsSize, option Allows you to set a non-standard size for the holdings in any variant. If the size is given as -1, the default holdings size for the variant is used. The first N piece types will go into the holdings on capture, and you will be able to drop them on the board in stead of making a normal move. If size equals 0, there will be no holdings. Default: -1 @item -defaultFrcPosition N @cindex defaultFrcPosition, option Specifies the number of the opening position in shuffle games like Chess960. A value of -1 means the position is randomly generated by XBoard at the beginning of every game. Default: -1 @item -pieceToCharTable string @cindex pieceToCharTable, option The characters that are used to represent the piece types XBoard knows in FEN diagrams and SAN moves. The string argument has to specify an even number of pieces (or it will be ignored), as white and black pieces have to be given separately (in that order). The last letter for each color will be the King. The letters before that will be PNBRQ and then a whole host of fairy pieces in an order that has not fully crystallized yet (currently FEACWMOHIJGDVLSU, F=Ferz, Elephant, A=Archbishop, C=Chancellor, W=Wazir, M=Commoner, O=Cannon, H=Nightrider). You should list at least all pieces that occur in the variant you are playing. If you have fewer characters in the string than XBoard has pieces, the pieces not mentioned will get assigned a period, and will not be usable in the variant. You can also explicitly assign pieces a period, in which case they will not be counted in deciding which captured pieces can go into the holdings. A tilde '~' as a piece name does mean this piece is used to represent a promoted Pawn in crazyhouse-like games, i.e. on capture it turns back to a Pawn. A '+' similarly indicates the piece is a shogi-style promoted piece, that should revert to its non-promoted version on capture (rather than to a Pawn). Note that promoted pieces are represented by pieces 11 further in the list (27 in variant chu). To get around the limitation of the alphabet, piece IDs can also be 'dressed letters', i.e. a single letter (upper case for white, lower case for black) followed by a single quote or an exclamation point. You should not have to use this option often: each variant has its own default setting for the piece representation in FEN, which should be sufficient in normal use. Default: "" @item -pieceNickNames string @cindex pieceNickNames, option The characters in the string are interpreted the same way as in the @code{pieceToCharTable} option. But on input, piece-ID letters are first looked up in the nicknames, and only if not defined there, in the normal pieceToCharTable. This allows you to have two letters designate the same piece, (e.g. N as an alternative to H for Horse in Xiangqi), to make reading of non-compliant notations easier. Default: "" @item -colorNickNames string @cindex colorNickNames, option The side-to-move field in a FEN will be first matched against the letters in the string (first character for white, second for black), before it is matched to the regular 'w' and 'b'. This makes it easier to read non-compliant FENs, which, say, use 'r' for white. Default: "" @item -debug/-xdebug or -debugMode true/false @cindex debug, option @cindex debugMode, option Turns on debugging printout. @item -debugFile filename or -nameOfDebugFile filename @cindex debugFile, option @cindex nameOfDebugFile, option Sets the name of the file to which XBoard saves debug information (including all communication to and from the engines). A @kbd{%d} in the given file name (e.g. game%d.debug) will be replaced by the unique sequence number of a tournament game, so that the debug output of each game will be written on a separate file. @item -engineDebugOutput number @cindex engineDebugOutput, option Specifies how XBoard should handle unsolicited output from the engine, with respect to saving it in the debug file. The output is further (hopefully) ignored. If number=0, XBoard refrains from writing such spurious output to the debug file. If number=1, all engine output is written faithfully to the debug file. If number=2, any protocol-violating line is prefixed with a '#' character, as the engine itself should have done if it wanted to submit info for inclusion in the debug file. This option is provided for the benefit of applications that use the debug file as a source of information, such as the broadcaster of live games TLCV / TLCS. Such applications can be protected from spurious engine output that might otherwise confuse them. @item -rsh or -remoteShell shell-name @cindex rsh, option @cindex remoteShell, option Name of the command used to run programs remotely. The default is @file{rsh} or @file{remsh}, determined when XBoard is configured and compiled. @item -ruser or -remoteUser user-name @cindex ruser, option @cindex remoteUser, option User name on the remote system when running programs with the @code{remoteShell}. The default is your local user name. @item -userName username @cindex userName, option Name under which the Human player will be listed in the PGN file. Default is the login name on your local computer. @item -delayBeforeQuit number @itemx -delayAfterQuit number @cindex delayBeforeQuit, option @cindex delayAfterQuit, option These options order pauses before and after sending the "quit" command to an engine that must be terminated. The pause between quit and the previous command is specified in milliseconds. The pause after quit is used to schedule a kill signal to be sent to the engine process after the number of specified seconds plus one. This signal is a different one as the terminiation signal described in the protocol specs which engines can suppress or ignore, and which is sent directly after the "quit" command. Setting @code{delayAfterQuit} to -1 will suppress sending of the kill signal. Default: 0 @item -searchMode n @cindex searchMode, option The integer n encodes the mode for the @samp{find position} function. Default: 1 (= Exact position match) @item -eloThresholdBoth elo @itemx -eloThresholdAny elo @cindex eloThresholdBoth, option @cindex eloThresholdAny, option Defines a lower limit for the Elo rating, which has to be surpassed before a game will be considered when searching for a board position. Default: 0 @item -dateThreshold year @cindex dateThreshold, option Only games not played before the given year will be considered when searching for a board position @end table @node Chess Servers @chapter Chess Servers @cindex ICS @cindex ICS, addresses @cindex Internet Chess Server An @dfn{Internet Chess Server}, or @dfn{ICS}, is a place on the Internet where people can get together to play chess, watch other people's games, or just chat. You can use either @code{telnet} or a client program like XBoard to connect to the server. There are thousands of registered users on the different ICS hosts, and it is not unusual to meet 200 on both chessclub.com and freechess.org. Most people can just type @kbd{xboard -ics} to start XBoard as an ICS client. Invoking XBoard in this way connects you to the Internet Chess Club (ICC), a commercial ICS. You can log in there as a guest even if you do not have a paid account. To connect to the largest Free ICS (FICS), use the command @kbd{xboard -ics -icshost freechess.org} instead, or substitute a different host name to connect to your favorite ICS. For a full description of command-line options that control the connection to ICS and change the default values of ICS options, see @ref{ICS options}. While you are running XBoard as an ICS client, you use the terminal window that you started XBoard from as a place to type in commands and read information that is not available on the chessboard. The first time you need to use the terminal is to enter your login name and password, if you are a registered player. (You don't need to do this manually; the @code{icsLogon} option can do it for you. @pxref{ICS options}.) If you are not registered, enter @kbd{g} as your name, and the server will pick a unique guest name for you. Some useful ICS commands include @table @kbd @item help <topic> @cindex help, ICS command to get help on the given <topic>. To get a list of possible topics type @dfn{help} without topic. Try the help command before you ask other people on the server for help. For example @kbd{help register} tells you how to become a registered ICS player. @item who <flags> @cindex who, ICS command to see a list of people who are logged on. Administrators (people you should talk to if you have a problem) are marked with the character @samp{*}, an asterisk. The <flags> allow you to display only selected players: For example, @kbd{who of} shows a list of players who are interested in playing but do not have an opponent. @item games @cindex games, ICS command to see what games are being played @item match <player> [<mins>] [<inc>] to challenge another player to a game. Both opponents get <mins> minutes for the game, and <inc> seconds will be added after each move. If another player challenges you, the server asks if you want to accept the challenge; use the @kbd{accept} or @kbd{decline} commands to answer. @item accept @itemx decline @cindex accept, ICS command @cindex decline, ICS command to accept or decline another player's offer. The offer may be to start a new game, or to agree to a @kbd{draw}, @kbd{adjourn} or @kbd{abort} the current game. @xref{Action Menu}. If you have more than one pending offer (for example, if more than one player is challenging you, or if your opponent offers both a draw and to adjourn the game), you have to supply additional information, by typing something like @kbd{accept <player>}, @kbd{accept draw}, or @kbd{draw}. @item draw @itemx adjourn @itemx abort @cindex draw, ICS command @cindex adjourn, ICS command @cindex abort, ICS command asks your opponent to terminate a game by mutual agreement. Adjourned games can be continued later. Your opponent can either @kbd{decline} your offer or accept it (by typing the same command or typing @kbd{accept}). In some cases these commands work immediately, without asking your opponent to agree. For example, you can abort the game unilaterally if your opponent is out of time, and you can claim a draw by repetition or the 50-move rule if available simply by typing @kbd{draw}. @item finger <player> @cindex finger, ICS command to get information about the given <player>. (Default: yourself.) @item vars @cindex vars, ICS command to get a list of personal settings @item set <var> <value> @cindex set, ICS command to modify these settings @item observe <player> @cindex observe, ICS command to observe an ongoing game of the given <player>. @item examine @itemx oldmoves @cindex examine, ICS command @cindex oldmoves, ICS command to review a recently completed game @end table Some special XBoard features are activated when you are in examine mode on ICS. See the descriptions of the menu commands @samp{Forward}, @samp{Backward}, @samp{Pause}, @samp{ICS Client}, and @samp{Stop Examining} on the @ref{Edit Menu}, @ref{Mode Menu}, and @ref{Action Menu}. @node Firewalls @chapter Firewalls By default, XBoard communicates with an Internet Chess Server by opening a TCP socket directly from the machine it is running on to the ICS. If there is a firewall between your machine and the ICS, this won't work. Here are some recipes for getting around common kinds of firewalls using special options to XBoard. Important: See the paragraph in the below about extra echoes, in @ref{Limitations}. Suppose that you can't telnet directly to ICS, but you can telnet to a firewall host, log in, and then telnet from there to ICS. Let's say the firewall is called @samp{firewall.example.com}. Set command-line options as follows: @example xboard -ics -icshost firewall.example.com -icsport 23 @end example @noindent Then when you run XBoard in ICS mode, you will be prompted to log in to the firewall host. This works because port 23 is the standard telnet login service. Do so, then telnet to ICS, using a command like @samp{telnet chessclub.com 5000}, or whatever command the firewall provides for telnetting to port 5000. If your firewall lets you telnet (or rlogin) to remote hosts but doesn't let you telnet to port 5000, you may be able to connect to the chess server on port 23 instead, which is the port the telnet program uses by default. Some chess servers support this (including chessclub.com and freechess.org), while some do not. If your chess server does not allow connections on port 23 and your firewall does not allow you to connect to other ports, you may be able to connect by hopping through another host outside the firewall that you have an account on. For instance, suppose you have a shell account at @samp{foo.edu}. Follow the recipe above, but instead of typing @samp{telnet chessclub.com 5000} to the firewall, type @samp{telnet foo.edu} (or @samp{rlogin foo.edu}), log in there, and then type @samp{telnet chessclub.com 5000}. Suppose that you can't telnet directly to ICS, but you can use rsh to run programs on a firewall host, and that host can telnet to ICS. Let's say the firewall is called @samp{rsh.example.com}. Set command-line options as follows: @example xboard -ics -gateway rsh.example.com -icshost chessclub.com @end example @noindent Then when you run XBoard in ICS mode, it will connect to the ICS by using @file{rsh} to run the command @samp{telnet chessclub.com 5000} on host @samp{rsh.example.com}. Suppose that you can telnet anywhere you want, but you have to run a special program called @file{ptelnet} to do so. First, we'll consider the easy case, in which @samp{ptelnet chessclub.com 5000} gets you to the chess server. In this case set command line options as follows: @example xboard -ics -telnet -telnetProgram ptelnet @end example @noindent Then when you run XBoard in ICS mode, it will issue the command @samp{ptelnet chessclub.com 5000} to connect to the ICS. Next, suppose that @samp{ptelnet chessclub.com 5000} doesn't work; that is, your @file{ptelnet} program doesn't let you connect to alternative ports. As noted above, your chess server may allow you to connect on port 23 instead. In that case, just add the option @samp{-icsport ""} to the above command. But if your chess server doesn't let you connect on port 23, you will have to find some other host outside the firewall and hop through it. For instance, suppose you have a shell account at @samp{foo.edu}. Set command line options as follows: @example xboard -ics -telnet -telnetProgram ptelnet -icshost foo.edu -icsport "" @end example @noindent Then when you run XBoard in ICS mode, it will issue the command @samp{ptelnet foo.edu} to connect to your account at @samp{foo.edu}. Log in there, then type @samp{telnet chessclub.com 5000}. ICC timestamp and FICS timeseal do not work through some firewalls. You can use them only if your firewall gives a clean TCP connection with a full 8-bit wide path. If your firewall allows you to get out only by running a special telnet program, you can't use timestamp or timeseal across it. But if you have access to a computer just outside your firewall, and you have much lower netlag when talking to that computer than to the ICS, it might be worthwhile running timestamp there. Follow the instructions above for hopping through a host outside the firewall (foo.edu in the example), but run timestamp or timeseal on that host instead of telnet. Suppose that you have a SOCKS firewall that will give you a clean 8-bit wide TCP connection to the chess server, but only after you authenticate yourself via the SOCKS protocol. In that case, you could make a socksified version of XBoard and run that. If you are using timestamp or timeseal, you will to socksify it, not XBoard; this may be difficult seeing that ICC and FICS do not provide source code for these programs. Socksification is beyond the scope of this document, but see the SOCKS Web site at http://www.socks.permeo.com/. If you are missing SOCKS, try http://www.funbureau.com/. @node Environment @chapter Environment variables @cindex Environment variables @cindex CHESSDIR Game and position files are found in a directory named by the @code{CHESSDIR} environment variable. If this variable is not set, the current working directory is used. If @code{CHESSDIR} is set, XBoard actually changes its working directory to @code{$CHESSDIR}, so any files written by the chess engine will be placed there too. @node Limitations @chapter Limitations and known bugs @cindex Limitations @cindex Bugs There is no way for two people running copies of XBoard to play each other without going through an Internet Chess Server. Under some circumstances, your ICS password may be echoed when you log on. If you are connecting to the ICS by running telnet on an Internet provider or firewall host, you may find that each line you type is echoed back an extra time after you hit @key{Enter}. If your Internet provider is a Unix system, you can probably turn its echo off by typing @kbd{stty -echo} after you log in, and/or typing @key{^E}@key{Enter} (Ctrl+E followed by the Enter key) to the telnet program after you have logged into ICS. It is a good idea to do this if you can, because the extra echo can occasionally confuse XBoard's parsing routines. The game parser recognizes only algebraic notation. Many of the following points used to be limitations in XBoard 4.2.7 and earlier, but are now fixed: The internal move legality tester in XBoard 4.3.xx does look at the game history, and is fully aware of castling or en-passant-capture rights. It permits castling with the king on the d file because this is possible in some "wild 1" games on ICS. The piece-drop menu does not check piece drops in bughouse to see if you actually hold the piece you are trying to drop. But this way of dropping pieces should be considered an obsolete feature, now that pieces can be dropped by dragging them from the holdings to the board. Anyway, if you would attempt an illegal move when using a chess engine or the ICS, XBoard will accept the error message that comes back, undo the move, and let you try another. FEN positions saved by XBoard do include correct information about whether castling or en passant are legal, and also handle the 50-move counter. The mate detector does not understand that non-contact mate is not really mate in bughouse. The only problem this causes while playing is minor: a "#" (mate indicator) character will show up after a non-contact mating move in the move list. XBoard will not assume the game is over at that point, not even when the option Detect Mates is on. Edit Game mode always uses the rules of the selected variant, which can be a variant that uses piece drops. You can load and edit games that contain piece drops. The (obsolete) piece menus are not active, but you can perform piece drops by dragging pieces from the holdings. Fischer Random castling is fully understood. You can enter castlings by dragging the King on top of your Rook. You can probably also play Fischer Random successfully on ICS by typing castling moves into the ICS Interaction window. The menus may not work if your keyboard is in Caps Lock or Num Lock mode. This seems to be a problem with the Athena menu widget, not an XBoard bug. Also see the ToDo file included with the distribution for many other possible bugs, limitations, and ideas for improvement that have been suggested. @node Problems @chapter Reporting problems @cindex Bugs @cindex Bug reports @cindex Reporting bugs @cindex Problems @cindex Reporting problems You can report bugs and problems with XBoard using the bug tracker at @code{https://savannah.gnu.org/projects/xboard/} or by sending mail to @code{<bug-xboard@@gnu.org>}. It can also be useful to report or discuss bugs in the WinBoard Forum at @code{http://www.open-aurec.com/wbforum/}, WinBoard development section. Please use the @file{script} program to start a typescript, run XBoard with the @samp{-debug} option, and include the typescript output in your message. Also tell us what kind of machine and what operating system version you are using. The command @samp{uname -a} will often tell you this. If you improve XBoard, please send a message about your changes, and we will get in touch with you about merging them in to the main line of development. @node Contributors @chapter Authors and contributors @cindex Authors @cindex Contributors Chris Sears and Dan Sears wrote the original XBoard. They were responsible for versions 1.0 through 1.2. The color scheme was taken from Wayne Christopher's @code{XChess} program. Tim Mann was primarily responsible for XBoard versions 1.3 through 4.2.7, and for WinBoard (a port of XBoard to Microsoft Win32) from its inception through version 4.2.7. John Chanak contributed the initial implementation of ICS mode. Evan Welsh wrote @code{CMail}, and Patrick Surry helped in designing, testing, and documenting it. Elmar Bartel contributed the new piece bitmaps introduced in version 3.2. Jochen Wiedmann converted the documentation to texinfo. Frank McIngvale added click/click moving, the Analysis modes, piece flashing, ZIICS import, and ICS text colorization to XBoard. Hugh Fisher added animated piece movement to XBoard, and Henrik Gram added it to WinBoard. Mark Williams contributed the initial (WinBoard-only) implementation of many new features added to both XBoard and WinBoard in version 4.1.0, including copy/paste, premove, icsAlarm, autoFlipView, training mode, auto raise, and blindfold. Ben Nye contributed X copy/paste code for XBoard. In a fork from version 4.2.7, Alessandro Scotti added many elements to the user interface of WinBoard, including the board textures and font-based rendering, the evaluation-graph, move-history and engine-output window. He was also responsible for adding the UCI support. H. G. Muller continued this fork of the project, producing version 4.3. He made WinBoard castling- and e.p.-aware, added variant support with adjustable board sizes, the crazyhouse holdings, and the fairy pieces. In addition he added most of the adjudication options, made WinBoard more robust in dealing with buggy and crashing engines, and extended time control with a time-odds and node-count-based modes. Most of the options that initially were WinBoard only have now been back-ported to XBoard. Michel van den Bergh provided the code for reading Polyglot opening books. Meanwhile, some work continued on the GNU XBoard project maintained at savannah.gnu.org, but version 4.2.8 was never released. Daniel Mehrmann was responsible for much of this work. Most recently, Arun Persaud worked with H. G. Muller to merge all the features of the never-released XBoard/WinBoard 4.2.8 of the GNU XBoard project and the never-released 4.3.16 from H. G.'s fork into a unified XBoard/WinBoard 4.4, which is now available both from the savannah.gnu.org web site and the WinBoard forum. @node CMail @chapter CMail @cindex cmail The @file{cmail} program can help you play chess by email with opponents of your choice using XBoard as an interface. You will usually run @file{cmail} without giving any options. @menu * CMail options:: Invoking CMail. * CMail game:: Starting a CMail game. * CMail answer:: Answering a move. * CMail multi:: Multiple games in one message. * CMail completion:: Completing a game. * CMail trouble:: Known CMail problems. @end menu @node CMail options @section CMail options @table @asis @item -h Displays @file{cmail} usage information. @item -c Shows the conditions of the GNU General Public License. @xref{Copying}. @item -w Shows the warranty notice of the GNU General Public License. @xref{Copying}. @item -v @itemx -xv Provides or inhibits verbose output from @file{cmail} and XBoard, useful for debugging. The @code{-xv} form also inhibits the cmail introduction message. @item -mail @itemx -xmail Invokes or inhibits the sending of a mail message containing the move. @item -xboard @itemx -xxboard Invokes or inhibits the running of XBoard on the game file. @item -reuse @itemx -xreuse Invokes or inhibits the reuse of an existing XBoard to display the current game. @item -remail Resends the last mail message for that game. This inhibits running XBoard. @item -game <name> The name of the game to be processed. @item -wgames <number> @itemx -bgames <number> @itemx -games <number> Number of games to start as White, as Black or in total. Default is 1 as white and none as black. If only one color is specified then none of the other color is assumed. If no color is specified then equal numbers of White and Black games are started, with the extra game being as White if an odd number of total games is specified. @item -me <short name> @itemx -opp <short name> A one-word alias for yourself or your opponent. @item -wname <full name> @itemx -bname <full name> @itemx -myname <full name> @itemx -oppname <full name> The full name of White, Black, yourself or your opponent. @item -wna <net address> @itemx -bna <net address> @itemx -na <net address> @itemx -oppna <net address> The email address of White, Black, yourself or your opponent. @item -dir <directory> The directory in which @file{cmail} keeps its files. This defaults to the environment variable @code{$CMAIL_DIR} or failing that, @code{$CHESSDIR}, @file{$HOME/Chess} or @file{~/Chess}. It will be created if it does not exist. @item -arcdir <directory> The directory in which @file{cmail} archives completed games. Defaults to the environment variable @code{$CMAIL_ARCDIR} or, in its absence, the same directory as cmail keeps its working files (above). @item -mailprog <mail program> The program used by cmail to send email messages. This defaults to the environment variable @code{$CMAIL_MAILPROG} or failing that @file{/usr/ucb/Mail}, @file{/usr/ucb/mail} or @file{Mail}. You will need to set this variable if none of the above paths fit your system. @item -logFile <file> A file in which to dump verbose debugging messages that are invoked with the @samp{-v} option. @item -event <event> The PGN Event tag (default @samp{Email correspondence game}). @item -site <site> The PGN Site tag (default @samp{NET}). @item -round <round> The PGN Round tag (default @samp{-}, not applicable). @item -mode <mode> The PGN Mode tag (default @samp{EM}, Electronic Mail). @item Other options Any option flags not listed above are passed through to XBoard. Invoking XBoard through CMail changes the default values of two XBoard options: The default value for @samp{-noChessProgram} is changed to true; that is, by default no chess engine is started. The default value for @samp{-timeDelay} is changed to 0; that is, by default XBoard immediately goes to the end of the game as played so far, rather than stepping through the moves one by one. You can still set these options to whatever values you prefer by supplying them on CMail's command line. @xref{Options}. @end table @node CMail game @section Starting a CMail Game Type @file{cmail} from a shell to start a game as white. After an opening message, you will be prompted for a game name, which is optional---if you simply press @key{Enter}, the game name will take the form @samp{you-VS-opponent}. You will next be prompted for the short name of your opponent. If you haven't played this person before, you will also be prompted for his/her email address. @file{cmail} will then invoke XBoard in the background. Make your first move and select @samp{Mail Move} from the @samp{File} menu. @xref{File Menu}. If all is well, @file{cmail} will mail a copy of the move to your opponent. If you select @samp{Exit} without having selected @samp{Mail Move} then no move will be made. @node CMail answer @section Answering a Move When you receive a message from an opponent containing a move in one of your games, simply pipe the message through @file{cmail}. In some mailers this is as simple as typing @kbd{| cmail} when viewing the message, while in others you may have to save the message to a file and do @kbd{cmail < file} at the command line. In either case @file{cmail} will display the game using XBoard. If you didn't exit XBoard when you made your first move then @file{cmail} will do its best to use the existing XBoard instead of starting a new one. As before, simply make a move and select @samp{Mail Move} from the @samp{File} menu. @xref{File Menu}. @file{cmail} will try to use the XBoard that was most recently used to display the current game. This means that many games can be in progress simultaneously, each with its own active XBoard. If you want to look at the history or explore a variation, go ahead, but you must return to the current position before XBoard will allow you to mail a move. If you edit the game's history you must select @samp{Reload Same Game} from the @samp{File} menu to get back to the original position, then make the move you want and select @samp{Mail Move}. As before, if you decide you aren't ready to make a move just yet you can either select @samp{Exit} without sending a move or just leave XBoard running until you are ready. @node CMail multi @section Multi-Game Messages It is possible to have a @file{cmail} message carry more than one game. This feature was implemented to handle IECG (International Email Chess Group) matches, where a match consists of one game as white and one as black, with moves transmitted simultaneously. In case there are more general uses, @file{cmail} itself places no limit on the number of black/white games contained in a message; however, XBoard does. @node CMail completion @section Completing a Game Because XBoard can detect checkmate and stalemate, @file{cmail} handles game termination sensibly. As well as resignation, the @samp{Action} menu allows draws to be offered and accepted for @file{cmail} games. For multi-game messages, only unfinished and just-finished games will be included in email messages. When all the games are finished, they are archived in the user's archive directory, and similarly in the opponent's when he or she pipes the final message through @file{cmail}. The archive file name includes the date the game was started. @node CMail trouble @section Known CMail Problems It's possible that a strange conjunction of conditions may occasionally mean that @file{cmail} has trouble reactivating an existing XBoard. If this should happen, simply trying it again should work. If not, remove the file that stores the XBoard's PID (@file{game.pid}) or use the @samp{-xreuse} option to force @file{cmail} to start a new XBoard. Versions of @file{cmail} after 2.16 no longer understand the old file format that XBoard used to use and so cannot be used to correspond with anyone using an older version. Versions of @file{cmail} older than 2.11 do not handle multi-game messages, so multi-game correspondence is not possible with opponents using an older version. @node Other programs @chapter Other programs you can use with XBoard @cindex Other programs Here are some other programs you can use with XBoard @menu * GNU Chess:: The GNU Chess engine. * Fairy-Max:: The Fairy-Max chess engine. * HoiChess:: The HoiChess chess engine. * Crafty:: The Crafty chess engine. @end menu @node GNU Chess @section GNU Chess The GNU Chess engine is available from: ftp://ftp.gnu.org/gnu/gnuchess/ You can use XBoard to play a game against GNU Chess, or to interface GNU Chess to an ICS. @node Fairy-Max @section Fairy-Max Fairy-Max is a derivative from the once World's smallest Chess program micro-Max, which measures only about 100 lines of source code. The main difference with micro-Max is that Fairy-Max loads its move-generator tables from a file, so that the rules for piece movement can be easily configured to implement unorthodox pieces. Fairy-Max can therefore play a large number of variants, normal Chess being one of those. In addition it plays Knightmate, Capablanca and Gothic Chess, Shatranj, Courier Chess, Cylinder chess, Berolina Chess, while the user can easily define new variants. It can be obtained from: http://home.hccnet.nl/h.g.muller/dwnldpage.html @node HoiChess @section HoiChess HoiChess is a not-so-very-strong Chess engine, which comes with a derivative HoiXiangqi, able to play Chinese Chess. It can be obtained from the standard Linux repositories through: sudo apt-get install hoichess @node Crafty @section Crafty Crafty is a chess engine written by Bob Hyatt. You can use XBoard to play a game against Crafty, hook Crafty up to an ICS, or use Crafty to interactively analyze games and positions for you. Crafty is a strong, rapidly evolving chess program. This rapid pace of development is good, because it means Crafty is always getting better. This can sometimes cause problems with backwards compatibility, but usually the latest version of Crafty will work well with the latest version of XBoard. Crafty can be obtained from its author's FTP site: ftp://ftp.cis.uab.edu/hyatt/. To use Crafty with XBoard, give the -fcp and -fd options as follows, where <crafty's directory> is the directory in which you installed Crafty and placed its book and other support files. @ifnottex @node Copyright @unnumbered Copyright @include copyright.texi @end ifnottex @node Copying @unnumbered GNU GENERAL PUBLIC LICENSE @include gpl.texinfo @c noman @node Index @unnumbered Index @printindex cp @contents @c end noman @bye

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\[\mathop{\Phi^{(3)}\/}\nolimits\!\left(a,a^{\prime};b,b^{\prime};c;x,y\right)=% \frac{\left(a,bx;q\right)_{\infty}}{\left(c,x;q\right)_{\infty}}\sum_{n,r\geqq 0% }\frac{\left(a^{\prime},b^{\prime};q\right)_{n}\left(x;q\right)_{r}\left(c/a;q% \right)_{n+r}a^{r}y^{n}}{\left(q,c/a;q\right)_{n}\left(q,bx;q\right)_{r}}.\]

http://www.astroscu.unam.mx/massive_stars/submission/2011/11020155831.tex

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\begin{center}{\Large\bf First detection of a magnetic field in the fast rotating runaway Oe star $zeta$,Ophiuchi}\end{center} \centerline{\bf S. Hubrig$^1$, L.M. Oskinova$^2$, M. Sch"oller$^3$ }{\footnotesize $^1$ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482~Potsdam, Germany $^2$ Universit"at Potsdam, Institut f"ur Physik und Astronomie, 14476~Potsdam, Germany $^3$ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748~Garching, Germany } The star $zeta$,Ophiuchi is one of the brightest massive stars in the northern hemisphere and was intensively studied in various wavelength domains. The currently available observational material suggests that certain observed phenomena are related to the presence of a magnetic field. We acquired spectropolarimetric observations of $zeta$,Oph with FORS,1 mounted on the 8-m Kueyen telescope of the VLT to investigate if a magnetic field is indeed present in this star. Using all available absorption lines, we detect a mean longitudinal magnetic field $left< B_zright>_{rm all}= 141pm45$,G, confirming the magnetic nature of this star. We review the X-ray properties of $zeta$,Oph with the aim to understand whether the X-ray emission of $zeta$,Oph is dominated by magnetic or by wind instability processes. {\bf Reference: AN, in print} \\{\it Status:} Manuscript has been accepted \\ {\it Comments:} {\it On the web at:} {\tt http://arxiv.org/abs/1101.5500} {\it Preprints from:} {\tt mschoell@eso.org} \vspace*{5mm}

https://mirror.mwt.me/ctan/macros/latex/contrib/misc/hexdump.sty

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%%% File Hexdump.sty %%% Reads an ASCII hexdump file and puts it formated into %%% the document %%% %%% Author : Thomas Hillebrand (thillebrand@my-deja.com) %%% Date : 04/17/2000 %%% Version: 0.1 %%% \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{hexdump}[2000/21/06 v0.1 format hexdumps] % % Test weather the package 'moreverb.sty' is loaded % \RequirePackage{moreverb} % % % Dump title, defaults to 'Dump' % The command \dumpname{} sets the title of the dump % \newcommand{\dump@head}{Dump} % Default title is 'Dump' \newcommand{\dumpname}[1]{\renewcommand{\dump@head}{#1}} % % Set the fontsize, default is \scriptsize, % use \dumpfontsize{<size>} to change it % \newcommand{\dump@font@size}{\scriptsize} \newcommand{\dumpfontsize}[1]{\renewcommand{\dump@font@size}{#1}} % % Calculate the width % \newlength{\dumpwidth} % Variable for textwidth \settowidth{\dumpwidth}% {\dump@font@size\texttt{00000000\space\space{}FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FF FFFFFFFFFFFFFFFF}} % The double \space puts two spaces between address and values % % Define new counter, arabic numbers % reset counter, if chapter changes % \newcounter{dumpcount}[chapter] \renewcommand{\thedumpcount}{\thechapter.\arabic{dumpcount}\space} % % Now to the page 'list of dumps' % Set titleword with \dumptocname, this is used for the lod page. % \newcommand{\dump@word}{directory} \newcommand{\dumptocname}[1]{\renewcommand{\dump@word}{#1}} % % Define own list of dumps, use \listofdumps % First let's define the top line of the list of dumps % then define an entry in the lod file \newcommand{\listofdumps}{\chapter*{\dump@head\dump@word}\@starttoc{lod}} \newcommand{\dcaption}[1]{\addcontentsline{lod}{table}% {\protect\numberline{\thedumpcount}#1}#1} % % Now to the main thing: the dump itself. % Define \inputdump{<file>}{<caption>} % command to read hex-dump file and put it formatted into document % Parameter #1 : Floatposition - this is optional % Parameter #2 : Filename % Parameter #3 : Caption % % A label is also defined: use \ref{dumpname:filename} (see example). % \newcommand{\inputdump}[3][htbp]{% \begin{table}[#1] \begin{center} \begin{minipage}{\dumpwidth} \refstepcounter{dumpcount} \rule[0.1\baselineskip]{\dumpwidth}{.8pt} \dump@head \space \thedumpcount{}:\space\dcaption{#3} \label{\dump@head:#2} % Label contains title and filename \newline \rule[0.33\baselineskip]{\dumpwidth}{.8pt} \ttfamily\dump@font@size \verbatimtabinput{#2} \rule[0.75\baselineskip]{\dumpwidth}{.8pt} \end{minipage} \end{center} \end{table} } % end newcommand % % End of file hexdump.sty % %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Here's a sample tex file % %\documentclass{book} %\usepackage{hexdump} % %\dumpsize{\tiny} % will give _very_ small dumps, better use default setting %\dumptocname{directoy} %\dumpname{Dump} % %\begin{document} %\listofdumps % the title will be 'Dumpdirectory', see above % %\capter{Bar} % %\inputdump{test.hex} % assumed that file test.hex contains the dump % %The dump is shown in dump \ref{Dump:test.hex}. %\end{document} % %%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Now to the legal stuff: % % Copyright (c) Thomas Hillebrand 2000 % % Usage of this file is unlimited, but I guarantee for nothing - except % that it uses space on your harddisk. As usual, use this file at your % own risk. % % You are encouraged to modify this file, but please be so kind to e-mail % me your modifications. Maybe they are included in the next release... %

http://m2matlabdb.ma.tum.de/exercise/iter11t.tex?ME_ID=139&target=latex

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\begin{aufgabe}{Anwendungen des cg-Verfahrens}{schriftlich}{20}{iter11i} Wir untersuchen zwei Problemstellungen aus der Mechanik. Wir vergleichen analytische Berechnungen mit Ergebnissen, die durch numerische Methoden ermittelt wurden. \begin{center} Saite (Fall i) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Balken (Fall ii) \mbox{\includegraphics[width=0.5\textwidth]{AUX/saite.eps} \includegraphics[width=0.5\textwidth]{AUX/balken.eps}} \end{center} \begin{itemize} \item[i)] \textbf{Die Saite}. Eine Saite ist ein mit einer Kraft $S$ vorgespanntes, biegeschlaffes Seil. Durch vertikale Auslenkung $w$ kann die Saite eine vertikal aufgebrachte Last $q_0$ aufnehmen. Unter der Annahme kleiner Auslenkung wird diese Gesetzmäßigkeit durch die folgende Differentialgleichung 2. Ordnung beschrieben: \[ \frac{d^2 w}{dx^2} = -\frac{q}{S}. \] Die Auslenkungslinie berechnet sich für $q$ = $q_0$ = const. analytisch zu \[ w_{s,exakt}(x) = \frac{q_0}{2S} x \left (l-x \right ). \] \item[ii)] \textbf{Der Balken}. Unter Annahme kleiner Durchbiegungen gilt für den Balken mit Biegesteifigkeit $EI$ die folgende Differentialgleichung 4. Ordnung: \[ \frac{d^4 w}{dx^4} = \frac{q}{EI} \] Wir betrachten einen beidseitig eingespannten Balken unter Gleichstreckenlast $q_0$ = const. Dann erhält man für die Biegelinie \[ w_{b,exakt}(x) = \frac{q_0}{24 EI} x^2 (x-l)^2 . \] \end{itemize} Ein numerisches Verfahren zur Diskretisierung einer Differential\-gleichung (d.h. Über\-führung der Differentialgleichung in ein System von $n$ linearen Gleichungen) ist das Verfahren der Finiten Differenzen. Man erhält (unter vereinfachter Betrachtung der Randbedingungen) $A\cdot w_h = f$ mit \begin{itemize} \small \item[i)] \[ A_{Saite} = \begin{bmatrix} 2 & -1 & & & \\ -1 & 2 & -1 & & \\ & \ddots & \ddots & \ddots & \\ & & -1 & 2 & -1 \\ & & & -1 & 2 \\ \end{bmatrix} ~~~~~ f_{Saite} = \frac{q_0}{S} \cdot h^2 \begin{bmatrix} 1 \\ 1 \\ \vdots \\ 1 \\ \end{bmatrix} \] \item[ii)] \[ A_{Balken} = \begin{bmatrix} 6&-4&1& & & & \\\noalign{\medskip}-4&6&-4&1& & & \\\noalign{\medskip}1&-4&6&-4&1& & \\\noalign{\medskip} & \ddots &\ddots&\ddots&\ddots&\ddots& \\\noalign{\medskip} & &1&-4&6&-4&1\\\noalign{\medskip} & & &1&-4&6&-4\\\noalign{\medskip} & & & &1&-4&6 \end{bmatrix} ~~~~~ f_{Balken} = \frac{q_0}{EI} \cdot h^4 \begin{bmatrix} 1 \\ 1 \\ \vdots \\ 1 \\ \end{bmatrix} \] \end{itemize} $h = l/(n+1)$ ist die Schrittweite der Diskretisierung. Die Randwerte $w(0)$ und $w(l)$ sind in obiger Darstellung bereits eliminiert, d.h. $(w_h)_1 = w(h)$ und $(w_h)_n = w(l-h)$. Allgemein gilt \[ (w_h)_k = w(\frac{l \cdot k}{n+1}). \] \begin{itemize} \item[a)] Implementieren Sie die exakten Verschiebungsfunktionen in Matlab unter Verwendung der Signaturen \\ \texttt{function w = w\_saite\_exakt(x, l, q\_0, S)} \\ \texttt{function w = w\_balken\_exakt((x, l, q\_0, EI)}. \item[b)] Stellen Sie die Gleichungssysteme für die Saite und den Balken in Matlab auf (Dabei sei die Anzahl der Unbekannten variabel).\\ \textit{Hinweise:} Verwenden Sie den \texttt{spdiags}-Befehl. Verwenden Sie zwei Script-Files. \item[c)] Lösen Sie die Gleichungssysteme mit dem cg-Verfahren für $n = 10$ (Saite) bzw. $n = 100$ (Balken). Die Abbruchbedingung sei $tol=10^{-4}$ für das relative Residuum bei maximal $1000$ Iterationen. Der Startvektor sei der Nullvektor. Ausserdem seien $q_0 = 5$~kN/m, $l=10$~m, $S = 1000$~kN und $EI = 4000$~kNm$^2$. \item[d)] Bestimmen Sie die Verschiebungsfiguren der Saite (mit $n=10$) und des Balkens (mit $n=100$) anhand der numerischen Lösung. Stellen Sie die exakte Lösung für $w$ zum Vergleich im selben Plot dar. % \item[e)] Plotten Sie den relativen lokalen Fehler in der euklidischen Norm % \[ \frac{\norm{w_{exakt,h}-w_h}}{\norm{w_{exakt,h}}} \] % für unterschiedlich feine Diskretisierungen $10 \leq n \leq 100$, für beide Probleme im doppelt-logarithmischen Maßstab (mit \texttt{loglog}). \item[e)] Plotten Sie die Kondition der Matrizen $A_{Saite}$ und $A_{Balken}$ für $10 \leq n \leq 100$. \item[f)] Plotten Sie die Anzahl der benötigten Iterationen, um eine Abbruchbedingung von $tol=10^{-11}$ zu erreichen, für $10 \leq n \leq 100$. \item[g)] Welchen Zusammenhang beobachten Sie zwischen den Konditionen der Matrizen und der Anzahl der benötigten Iterationen? \end{itemize} \textit{Hinweis:} Eine Implementierung des cg-Verfahrens in Matlab können Sie unter {\small \begin{center} \texttt{http://matlabdb.mathematik.uni-stuttgart.de} \end{center}} herunterladen. Sie können auch die Matlab-Funktion \texttt{pcg} verwenden, verwenden Sie dabei die Option \texttt{M=[]}, um \texttt{pcg} ohne Vorkonditionierer aufzurufen. (Siehe auch \texttt{help pcg}). \end{aufgabe}

https://ctan.math.washington.edu/tex-archive/info/examples/Einfuehrung2/15-05-17.ltx

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%% %% Ein Beispiel der DANTE-Edition %% %% 2. Auflage %% %% Beispiel 15-05-17 auf Seite 821. %% %% Copyright (C) 2016 Herbert Voss %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% %% %% ==== % Show page(s) 1 %% %% \documentclass[]{exaarticle} \pagestyle{empty} \setlength\textwidth{352.81416pt} \parindent=0pt %StartShownPreambleCommands \usepackage{chemmacros} \usepackage{chemfig} \usepackage{chemnum} %StopShownPreambleCommands \begin{document} \chemname{\chemfig{*6(=-=-(-R)=-)}}{\cmpd{benzene.{H,Me,OH,NH2}}} \begin{tabular}{lll} & \ch{-R} & Name \\\hline \cmpd[sub-only]{benzene.H} & \ch{-H} & Benzol \\ \cmpd[sub-only]{benzene.Me} & \ch{-CH3} & Toluol \\ \cmpd[sub-only]{benzene.OH} & \ch{-OH} & Phenol \\ \cmpd[sub-only]{benzene.NH2} & \ch{-NH2} & Phenylamin (Anilin) \end{tabular} \end{document}

https://heatfinder.net/files/paints/2/car502.tex

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\documentclass[10pt]{article} \usepackage{fullpage} \usepackage{setspace} \usepackage{parskip} \usepackage{titlesec} \usepackage[section]{placeins} \usepackage{xcolor} \usepackage{breakcites} \usepackage{lineno} \usepackage{hyphenat} \PassOptionsToPackage{hyphens}{url} \usepackage[colorlinks = true, linkcolor = blue, urlcolor = blue, citecolor = blue, anchorcolor = blue]{hyperref} \usepackage{etoolbox} \makeatletter \patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{% \errmessage{\noexpand\@combinedblfloats could not be patched}% }% \makeatother \usepackage{natbib} \renewenvironment{abstract} {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize} {\bigskip} \titlespacing{\section}{0pt}{*3}{*1} \titlespacing{\subsection}{0pt}{*2}{*0.5} \titlespacing{\subsubsection}{0pt}{*1.5}{0pt} \usepackage{authblk} \usepackage{graphicx} \usepackage[space]{grffile} \usepackage{latexsym} \usepackage{textcomp} \usepackage{longtable} \usepackage{tabulary} \usepackage{booktabs,array,multirow} \usepackage{amsfonts,amsmath,amssymb} \providecommand\citet{\cite} \providecommand\citep{\cite} \providecommand\citealt{\cite} % You can conditionalize code for latexml or normal latex using this. \newif\iflatexml\latexmlfalse \providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}% \AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}} \usepackage[utf8]{inputenc} \usepackage[ngerman,english]{babel} \usepackage{float} \begin{document} \title{Evaluating the German oncology certification system and its implications for colorectal carcinoma - a national and international comparison of relative survival rates.} \author[1]{Maximilian Richter}% \author[2]{Lena Sonnow}% \author[2]{Amir Mehdizadeh-Shrifi}% \author[3]{Axel Richter}% \author[4]{Rainer Koch}% \author[1]{Alexander Zipprich}% \affil[1]{Martin-Luther-Universit├Ąt Halle-Wittenberg}% \affil[2]{Medizinische Hochschule Hannover}% \affil[3]{HELIOS Klinikum Hildesheim}% \affil[4]{Technische Universit├Ąt Dresden}% \vspace{-1em} \date{\today} \begingroup \let\center\flushleft \let\endcenter\endflushleft \maketitle \endgroup \sloppy \selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/CRC-LZW300/CRC-LZW300} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/Colon-LZW300/Colon-LZW300} \end{center} \end{figure}\selectlanguage{english} \begin{figure}[H] \begin{center} \includegraphics[width=0.70\columnwidth]{figures/rectal-LZW300/rectal-LZW300} \end{center} \end{figure} \selectlanguage{english} \FloatBarrier \end{document}

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\documentclass[twocolumn,twoside]{article} \makeatletter\if@twocolumn\PassOptionsToPackage{switch}{lineno}\else\fi\makeatother \usepackage{amsfonts,amssymb,amsbsy,latexsym,amsmath,tabulary,graphicx,times,xcolor} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Following additional macros are required to function some % functions which are not available in the class used. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{url,multirow,morefloats,floatflt,cancel,tfrupee} \makeatletter \AtBeginDocument{\@ifpackageloaded{textcomp}{}{\usepackage{textcomp}}} \makeatother \usepackage{colortbl} \usepackage{xcolor} \usepackage{pifont} \usepackage[nointegrals]{wasysym} \urlstyle{rm} \makeatletter %%%For Table column width calculation. \def\mcWidth#1{\csname TY@F#1\endcsname+\tabcolsep} %%Hacking center and right align for table \def\cAlignHack{\rightskip\@flushglue\leftskip\@flushglue\parindent\z@\parfillskip\z@skip} 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Botulinum toxin is a bacterial extract which acts at the synaptic level and inhibits the neuronal uptake of acetylcholine causing inhibition of muscular contraction. This property of botox proves to be useful in various muscle spastic disorders. Commercially accessible under the brand label of Botox and is universally used in cosmetic field in managing wrinkles and crow lines correspondingly it has multitude of use in treating innumerable maxillofacial complex disorders like Temperomandibular disorders, Hypertonicity of lips, gummy smiles, Bruxism, trigeminal neuralgia and other types of facial pain. Botox is regarded as minimally invasive procedure with promising results in muscular disorders as well as cosmetic purpose. Botulinum when used in therapeutic doses proves to be boon to mankind. The effects are dose dependent as it comes with the black box warning. Overcoming this disadvantage of botox, the newly emerged Frotox {\textsuperscript{\textregistered}} based on the (Focussed Cold Therapy) is used nowadays and proves to be more efficacious.This article describes in detail about the origin of the toxin, it's commercially available forms. It also describes the clinical technique, its pros and cons with instructions with patient as well as operator point of view. \end{abstract}\def\keywordstitle{Keywords} \begin{keywords}Botulinom toxin A,\newline Botulinom toxin B,\newline Botox,\newline Aesthetics,\newline Cosmetic,\newline Frotox \end{keywords} \twocolumn[ \maketitle {\printKwdAbsBox}] \makeatletter\textsuperscript{*}Corresponding Author\par Name:\ Sweta~Kale~Pisulkar~\\ Phone:\ 9881215746~\\ Email:\ drsweta15@gmail.com \par\vspace*{-11pt}\hrulefill\par{\fontsize{12}{14}\selectfont ISSN: 0975-7538}\par% \textsc{DOI:}\ \href{https://doi.org/10.26452/\@journalDoi}{\textcolor{blue}{\underline{\smash{https://doi.org/10.26452/\@journalDoi}}}}\par% \vspace*{-11pt}\hrulefill\\{\fontsize{9.12}{10.12}\selectfont Production and Hosted by}\par{\fontsize{12}{14}\selectfont Pharmascope.org}\par% \vspace*{-7pt}{\fontsize{9.12}{10.12}\selectfont\textcopyright\ \@copyrightYear\ $|$ All rights reserved.}\par% \vspace*{-11pt}\rule{\linewidth}{1.2pt} \makeatother \section{Introduction} Botulinum toxin originated from the Latin term `\textit{botulus'} meaning `sausage'. Botulinum toxin is a bacterial extract which acts at the synaptic level and inhibits the neuronal uptake of acetylcholine causing inhibition of muscular contraction. This property of botox proves to be useful in various muscle spastic disorders\unskip~\citep{782491:18631692,782491:18631694}. \textbf{Mechanism of Action} The Bacterial extract from clostridium toxin acts at the skeletal muscle synaptic level. The toxins can be serologically differentiated into eight types from ``A, B, C1, C2, D, E, F, and G''. The neurotoxins A, B possesses antigenic variation but have no dissimilar functions and helps in management of various disorders.it can be used in injectable form via intramuscular, Intra-detrusor also intradermallly\unskip~\citep{782491:18631691,782491:18631700}. As injected into the intramuscularly it leads to proteolysis of Synaptosomal associated pro\-tein SNAP-25 in the cytoplasmic region of the neurons, which is essential for discharge of acetyl choline at the synaptic level of neuromuscular junction\unskip~\citep{782491:18631706} . Leading to zero action potential and inhibiting the muscular contraction in return leading to paralysis of particular muscle (Figure~\ref{f-65bfc9b82f97}) The effectivity of botox starts deteriorating and completely vanishes off after 3 months and needs re-administration of the therapy. \begin{table*}[!htbp] \caption{\boldmath {Evolution of Botox as a Therapeutic Agent} } \label{tw-d1d81ba7d274} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.1376\linewidth-2\tabcolsep}p{\dimexpr.3483\linewidth-2\tabcolsep}p{\dimexpr.5141\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}ERA & Scientists and Place & Observation\\ \tblmidrule 1820 & Justinus Kerner & Lethal effect of minute doses and earned himself recognition as pioneer of modern botulinum toxin therapy\\ 1989 & Food and Drug Administration (FDA) & Therapeutic use in management of ocular muscle spasms\\ 1895 & \'{E}mile van Ermengem & Correctly described the toxin as the bacterial source from Clostridium botulinum\\ 1895-1925 & Karl Friedrich Meyer & Developed a toxin extraction technique from the organism grew and inactivated the toxin by heating it. \\ 1970's & & Botulinum was used in management of strabismus coincidentally also noticed that botulinum also reduced wrinkles in the glabella region. \\ Post world war II & In Maryland & Botulinum gained recognition as a weapon at ``Fort Detrick in Maryland. \\ 1946 & Carl Lamanna and James Duff & Formulated the concentration and crystallization technique given by Edward J. Schantz\\ 1978 & Dr. Allen Scott & First clinical test for management of Blepharospasm. \\ 2000 & Food and Drug Administration (FDA) & Neck muscle associated spasticity \\ 2002 & Food and Drug Administration (FDA) & Cosmetic correction for Glabellar frown lines and in removal of the facial wrinkle lines.\\ 2004 & Food and Drug Administration (FDA) & Its use in excessive sweating cases\\ 2009 & Food and Drug Administration (FDA) & Approved for use in Cases of Blepharospasm\\ \tblbottomrule \end{tabulary}\par \end{table*} \textbf{Commercial Forms of Botox} Out of the seven types of botulinum toxins have been isolated only toxin A and B types are available commercially. Three forms of Botulinum toxin A (Botox{\textsuperscript{\textregistered}}, Xeonin{\textsuperscript{\textregistered}}, Dyspord{\textsuperscript{\textregistered}}) and Only one formulation of toxin B (Myobloc{\textsuperscript{\textregistered}}) are available commercially from various therapeutic and enhancing cosmetic procedures\unskip~\citep{782491:18631716}. \bgroup \fixFloatSize{images/1bbe98eb-034c-4a33-899c-e9560c5aa082-upicture1.png} \begin{figure*}[!htbp] \centering \makeatletter\IfFileExists{images/1bbe98eb-034c-4a33-899c-e9560c5aa082-upicture1.png}{\includegraphics{images/1bbe98eb-034c-4a33-899c-e9560c5aa082-upicture1.png}}{} \makeatother \caption{\boldmath {Diagrammatic demonstration on mechanism of action of botox at neuromuscular junction}} \label{f-65bfc9b82f97} \end{figure*} \egroup \textbf{Each vial contains} \begin{enumerate} \item \relax 100 units of Botulinum type A neurotoxin complex. \item \relax 0.5 mg of Human Albumin. \item \relax 0.9 mg of NaCl in a sterile, vacuum dried form devoid of preservatives. \end{enumerate} \textbf{Applications} Botulinum toxin (BT) is known to have multitudes of uses in cosmetic as well as therapeutic effect. Off all the commercially available preparations Botox{\textsuperscript{\textregistered}} is the worldwide commonly used and has maximum approvals\unskip~\citep{782491:18631701,782491:18631695,782491:18631707}. BT-B is approved by DA for its use in cases of cervical dystonia, Hemi-facial related spasms\unskip~\citep{782491:18631710}. The uses of botox are as follows, They can be subdivided grossly into, Cosmetic use and Therapeutic use. Botulinum toxin finds multitudes of use in head and neck area.it deals with both the cosmetic as well as therapeutic use. It has proved as an adjunct to various treatment modalities. The applications in maxillofacial region are as follows, 1. Gummy smile 2. Chronic headaches/migraines 3. Bruxism 4. Trigeminal neuralgia 5. Temperomandibular disorders (TMD's) 6. Masseter hypertrophy 7. Black Triangles 8. Dental implantology and surgery \textbf{Excessive Gingival display} It can be effectively used in patients with gummy smile in which there is display of maxillary gingival tissue while smiling. The gingival complex plays a major role in the overall beauty of a smile\unskip~\citep{782491:18631693} .It can be due to skeletal defect or hyperactivity of lip muscles. The conventional treatment routinely followed is surgical correction of hyperactive Lip muscle. But this method comes with added disadvantage of scar contraction and relapse of the muscle activity\unskip~\citep{782491:18631712,782491:18631702} . Hence, dentists generally prefer botulinum injection therapy over the invasive correction. \textbf{Chronic migraine} Botulinum toxin in case of migraine condition doesn't weakens muscles rather it inhibits the carrier protein and blocks them. In patients treated for cosmetic purpose it was seen that it also improves chronic headaches.Botulinum toxin A injections when used in patients receiving cosmetic botulinum treatment with associated complain of headache it was observed that there was improvement in chronic headache\unskip~\citep{782491:18631704}.\textbf{\space } \textbf{Bruxism} Bruxism is a para-functional activity leading to clenching and grinding of teeth and is usually accompanied with muscular hypertrophy and myofascial pain due to hyper contractibility of muscles. Which often leads to pain in TMJ along with muscle hypertrophy.\textbf{\space } \textbf{Trigeminal neuralgia} ``Trigeminal neuralgia (TN) is defined as sudden, usually unilateral severe brief stabbing recurrent episodes of pain within the distribution of one or more roots of the trigeminal nerve.'' Patients mainly complain of numbness, picking, rubbing, or scratching sensations in the affected areas\unskip~\citep{782491:18631697} There are case reports and evidence proving the efficacy and its duration on trigeminal neuralgia \unskip~\citep{782491:18631709,782491:18631696} ,(Table~\ref{tw-d1d81ba7d274}). \textbf{Temperomandibular disorders} TMD is a canopy term which houses many pathologies related to the joint and/or the masticatory muscular dysfunctions. The symptoms manifested in Temperomandibular pain are clicking of joint, headaches, joint pain, per auricular pain, neck stiffness and associated pain. Occlusal disharmonies and periodontal problems have a major role in aetiology for TMD's.in untreated cases of bruxism, there are microfractures in and around restorations the reason being excessive forces along with increases prevalence of tooth decay and these forces may also cause gingival recession. Some studies state that it relieves pain associated with joint and improvises mouth opening and shows no side effects \unskip~\citep{782491:18631691,782491:18631699}, (Table~\ref{tw-7cb92737a976}). \textbf{Dental implants and surgery} Botulinum has also proved efficaciously in the fields of implantology by allowing unimpeded Osseo integration of implants.as any loading stresses on implants can lead to implant failure. However, there is less evidence based literature of use in implants and needs further research\unskip~\citep{782491:18631714} . Kayikvioglu and colleagues conducted a small open label study to examine therapeutic efficacy as an adjunct in fixation in cases of zygomatic fracture the patients were operated 12-48 hrs. An EMG confirmation was done to assure complete muscle denervation post injection. The temporary effect of paralysis of masseter allowed fewer mini-plate fixation and complications\unskip~\citep{782491:18631715}. \textbf{Massetric hypertrophy} Patients with history of bruxism are commonly found with masseter hypertrophy. The facial appearance of the patients changes due to increase in the size of muscle. The jaw seems swollen and misshaped. Conventional treatment modality to be followed is surgical correction but nowadays minimally invasive technique of injection\unskip~\citep{782491:18631716},(Table~\ref{tw-d1d81ba7d274}). \textbf{Other uses} \textbf{Sialorrhea} Botulinum acts as anticholinergic reduces the salivary secretions and can be effectively used in cases of sialorrhea\unskip~\citep{782491:18631716} .Cosmetic uses for marinette line, crow lines, and nasolabial fold drop (Table~\ref{tw-d1d81ba7d274}). \textbf{Aesthetics \& Black triangle} The war lies in harmonizing between the white and pink. Botox acts as dermal fillers and provides volume to the tissues and enhances the aesthetics. Botox are injected into the interdental spaces and it replaces the lost interdental soft tissue which is of prime importance while replacing missing anterior. Botox replaces the lost and enhances aesthetic to prosthesis. There are lack of case reports pertaining to the botox used as fillers for the lost interdental papilla. The treatment effect lies approximately for 8 months\unskip~\citep{782491:18631716}. \textbf{Contraindications} \begin{enumerate} \item \relax Patients should not be advised management with botox who are: \item \relax Psychologically unstable with unrealistic expectations \item \relax Are on Anti-Cholinergics \item \relax Allergic to any of the composition of botulinum preparation \item \relax Pregnant or lactating females \item \relax Suffering from neuromuscular disorders. \end{enumerate} \begin{table*}[!htbp] \caption{\boldmath {Application of botulinum along with dosage, important landmarks for clinical practise, treatment effectivity evidence based and duration of effectivity} } \label{tw-7cb92737a976} \def\arraystretch{1.1} \ignorespaces \centering \begin{tabulary}{\linewidth}{p{\dimexpr.1543\linewidth-2\tabcolsep}p{\dimexpr.14590000000000002\linewidth-2\tabcolsep}p{\dimexpr.18610000000000007\linewidth-2\tabcolsep}p{\dimexpr.38709999999999994\linewidth-2\tabcolsep}p{\dimexpr.12659999999999998\linewidth-2\tabcolsep}} \tbltoprule \rowcolor{kwdboxcolor}Disorders \mbox{}\protect\newline or \mbox{}\protect\newline Problems & Dose & Muscle Landmarks & Treatment Effect With Evidence Reports & Effect Duration\\ \tblmidrule Gummy smile & 3-5U \mbox{}\protect\newline each Bilaterally & `Yonsei' point & Lip Hyperactivity reduces.\unskip~\citet{782491:18631712,782491:18631702} & 3-4 months\\ Drooping corners of lips & 2-5U \mbox{}\protect\newline each Bilaterally & Trajectory of nasolabial fold to the jaw line. & Improvement of the facial features.\unskip~\citet{782491:18631718} & 3-4 months\\ Bruxism & 25-50U \mbox{}\protect\newline each Bilaterally & Masseter belly & -Muscle relaxation \mbox{}\protect\newline -Also post trauma associated bruxism is treated.\unskip~\citet{782491:18631705} \mbox{}\protect\newline -Equally effective when compared with oral splint therapy and can also be used to treat sleep bruxism\unskip~\citet{782491:18631717} \mbox{}\protect\newline -Tan and Jankovic et al (2000) stated its efficacy stays till 19 weeks at dosage of 25U-100U on masseter.\unskip~\citet{782491:18631691} & -3 months27 \mbox{}\protect\newline -1month \mbox{}\protect\newline (single injection)\\ TMD & 2.5-7.5U \mbox{}\protect\newline each Bilaterally \mbox{}\protect\newline 150 U~& -Masseter and temporalis.\unskip~\citet{782491:18631697} & Freund et al 1999 stated relief in pain, tenderness and also improvement in mouth opening.\unskip~\citet{782491:18631709} \mbox{}\protect\newline Lee et al in (2005) conducted a small open label trial study reported no side effects during management of TMD cases 5-12 month follow up period.\unskip~\citet{782491:18631693} & efficacy was maintained until 19 weeks.\unskip~\citet{782491:18631704}\\ Chronic Migraine & Total of 155U \mbox{}\protect\newline (divided into 7 muscles bilaterally) & Frontalis(20U) \mbox{}\protect\newline Corrugator(10U) \mbox{}\protect\newline Procerus(5U) \mbox{}\protect\newline Trapezius(30U) \mbox{}\protect\newline Temporalis(40U) \mbox{}\protect\newline Occipitalis(30U) \mbox{}\protect\newline Cervical (20U) \mbox{}\protect\newline paraspinal & -Relief in pain also associated chronic headaches are relieved.\unskip~\citet{782491:18631711,782491:18631708} \mbox{}\protect\newline In Randomized controlled trials concluded botulinum beneficial for chronic daily headaches and chronic migraines \unskip~\citet{782491:18631713} & 3 months\\ Trigeminal neuralgia & 25-75U39 & Peri-cranial muscles.\unskip~\citet{782491:18631716} & -88.9\% patients had relief (6 month follow up.13 \mbox{}\protect\newline -Males exhibited better treatment outcomes comparatively. \mbox{}\protect\newline -concluded long-term effectivity of the treatment\unskip~\citet{782491:18631693} & 1-10 months\\ Masseter hypertrophy & 30U each bilaterally & Masseter belly & Injection into the masseter muscles resulted \mbox{}\protect\newline reduction in masseter muscle hyperactivity.\unskip~\citet{782491:18631703} & \\ Oro-mandibular dystonia & 30U & Masseter and/or Sub-mental complex & 67.9\% improvement inspeaking, swallowing, and eating. (10yr follow up study)\unskip~\citet{782491:18631698} & \\ \tblbottomrule \end{tabulary}\par \end{table*} \textbf{Clinical Technique} Botulinum for the treatment has to be freshly prepared before use and has to be injected intradermal and the preparation has to be refrigerated at 2-4\ensuremath{^\circ}C the preparation has to be diluted with sterile saline, and is advised to be used within 4 hours after preparation and to be injected using tuberculin syringe. The site to be injected is to be made aseptic using alcohol with sterile sponge gauze pieces. Aspiration during injecting is to be assessed to avoid involuntary deposition at the undesired site such as facial arteries. The effects of botulinum are short term and is effective for only 4-6 months After care post treatment, the patient should not lie down for the first 4 hours. Exposure to sun must be taken care and avoided also strenuous exercises for a minimum period of 24 hours. Skin manipulation activities to be avoided that shall cause flushing like effect namely acupressure facial massage, heat or cold pack, any topical applications, and consumption of alcohol\unskip~\citep{782491:18631714}. \textbf{Maintenance} The effects are reversible and hence the maintenance has to be taken care off and needs to be administered 2-3 times a year depending on the declining effect. Injections are given with a sparing time for a minimum of three months approximately to avoid the immune response which would prevent Botox from working the next time\unskip~\citep{782491:18631714}. Safety margin of botox that is lethal dose in humans can reach upto40 U/kg BW). \textbf{Frotox as an Alternative} Cold therapy or cryotherapy is a procedure in which the cold energy is focussed and delivered at the targeted area of the nerve fibre. Which is also known as cryoneuromodulation which temporarily interrupts the neuronal connection and immediately freezes the targeted muscle. A close-ended needle that is filled with highly pressurized liquid nitrous oxide which is not released into the skin. Frotox has immediate effect as compared to botox. Frotox works on the specific target which gives the most natural look. Frotox lasts up to 4 months. \section{Results and Discussion} The fundamental aspects in facial aesthetics are mouth and teeth.\ensuremath{^{28}}Botox is non-invasive procedure which has reversible effects, conservative, non-surgical, treatment modality to achieve optimum aesthetics. It becomes easy for the dentists to learn the injecting techniques as they are already aware about the anatomical landmarks to be considered while managing the cases during administration of local anaesthesia thus patients are at ease and comfort. The preparation has to be freshly made before every use. The dilution is prepared by following user guidelines and to be used within 4 hours. The calibrated tuberculin syringe is used. Botulinum is known as the neurotoxin it acts at the synaptic level to inhibit release of the neurotransmitter Acetyl choline and aborts muscular contractions leading to a chemo-denervation process. As the use, knowledge and awareness of botulinum is in increasing day by day in leaps and bounds. Caution has to be taken about the adverse deadly reaction occurring due to its poisonous nature. Dose has to be calibrated and administered. Neither literature nor clinical randomized controlled trials shows any reports with such adverse reactions to botulinum. Some animal studies report that Botulinum after being injected spreads up to 30-45mm away from the target site and causes it to diffuse into adjacent muscles, the consequence of generalized diffusion of toxin is not well known. Systemic toxin spread can lead to consequences suggesting botulism leading to weakening of muscles or paresis, dysphagia and respiratory arrest. These when left untreated can prove to be fatal to mankind\unskip~\citep{782491:18631715}. \section{Conclusions} Botulinum toxin therapy is one of the trending and unique adjunctive treatment modality in the field of dentistry and acts as arsenal in managing the cosmetic as well as the therapeutic fields of Oro-facial complexes as the botulinum comes with the black box warning label onto the vial the doses should be carefully monitored and wisely delivered at the targeted sites for the desired result.as the effects are reversible over a period of time it needs to be revised. There are no such adverse reactions note in the literature evidences and the effect being quick and aesthetic. Though botox has its limitation in being used widely ethically as it is yet to be FDA approved for many of its application and is obvious that BT of\-fers a range of valued results for dentist and will take dental profession to one step ahead in the field of progress. \section{Acknowledgement} None. \textbf{Conflict of Interest} None. \textbf{Funding Support} None. \bibliographystyle{pharmascope_apa-custom} \bibliography{\jobname} \end{document}

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# # ChangeLog for doc/theses/thierry_delisle_PhD/thesis/text/core.tex # # Generated by Trac 1.2.1 # Oct 5, 2022, 7:13:55 AM Tue, 12 Apr 2022 00:49:43 GMT Thierry Delisle <tdelisle@…> [05e33f5] * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) Added a section on fairness goals to chapter 3 Mon, 11 Apr 2022 21:51:28 GMT Thierry Delisle <tdelisle@…> [13888c0] * doc/theses/thierry_delisle_PhD/thesis/Makefile (modified) * doc/theses/thierry_delisle_PhD/thesis/fig/cache-noshare.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/cache-share.fig (added) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) First complete draft of chapter 3. Still very rough but probably ... Sat, 09 Apr 2022 18:51:24 GMT Thierry Delisle <tdelisle@…> [6db62fa] * doc/theses/thierry_delisle_PhD/thesis/Makefile (modified) * doc/theses/thierry_delisle_PhD/thesis/data/cycle.jax (added) * doc/theses/thierry_delisle_PhD/thesis/fig/base.fig (modified) * doc/theses/thierry_delisle_PhD/thesis/fig/base_avg.fig (added) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/eval_micro.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/io.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/thesis.tex (modified) Added some experiments, some graph generation and a whole lot of text Wed, 02 Feb 2022 00:42:31 GMT Thierry Delisle <tdelisle@…> [729c991] * doc/theses/thierry_delisle_PhD/thesis/fig/base.fig (modified) * doc/theses/thierry_delisle_PhD/thesis/glossary.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/eval_macro.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/eval_micro.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/existing.tex (modified) Re-starting work on my thesis. Fri, 15 Jan 2021 02:19:58 GMT Thierry Delisle <tdelisle@…> [bf08316] * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) Merge more of peter's changed. Thu, 14 Jan 2021 03:23:02 GMT Peter A. Buhr <pabuhr@…> [bace538] * doc/bibliography/pl.bib (modified) * doc/theses/thierry_delisle_PhD/thesis/Makefile (modified) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/io.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/runtime.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/thesis.tex (modified) proofread Thierry's chapter 2 and 3, update latex formatting, add ... Mon, 04 Jan 2021 20:49:08 GMT Thierry Delisle <tdelisle@…> [c04a19e] * doc/theses/thierry_delisle_PhD/thesis/Makefile (modified) * doc/theses/thierry_delisle_PhD/thesis/fig/fairness.py (added) * doc/theses/thierry_delisle_PhD/thesis/glossary.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/local.bib (modified) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/existing.tex (modified) Major update to chapter 3 Fri, 30 Oct 2020 16:35:59 GMT Thierry Delisle <tdelisle@…> [b9537e6] * doc/theses/thierry_delisle_PhD/thesis/Makefile (modified) * doc/theses/thierry_delisle_PhD/thesis/fig/system.fig (modified) * doc/theses/thierry_delisle_PhD/thesis/glossary.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/local.bib (added) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/existing.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/front.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/intro.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/io.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/practice.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/text/runtime.tex (modified) * doc/theses/thierry_delisle_PhD/thesis/thesis.tex (modified) A whole bunch of thesis work and existing work Thu, 03 Sep 2020 17:00:13 GMT Thierry Delisle <tdelisle@…> [86c1f1c3] * doc/theses/thierry_delisle_PhD/thesis/Makefile (added) * doc/theses/thierry_delisle_PhD/thesis/fig/base.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/empty.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/emptybit.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/emptytls.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/emptytree.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/resize.fig (added) * doc/theses/thierry_delisle_PhD/thesis/fig/system.fig (added) * doc/theses/thierry_delisle_PhD/thesis/glossary.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/core.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/front.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/intro.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/io.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/practice.tex (added) * doc/theses/thierry_delisle_PhD/thesis/text/runtime.tex (added) * doc/theses/thierry_delisle_PhD/thesis/thesis.tex (added) First draft at my thesis

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First write a $1$ to the answer location. Then assign a processor to each bit. If any bit is $0$, the processor for that bit writes a $0$ to the answer location. We could have many processors trying to write in this step, but they would all be writing the same value ($0$).

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\magnification=1200 \hsize=4in \overfullrule=0pt \nopagenumbers \noindent % % {\bf Emeric Deutsch, A. J. Hildebrand and Herbert S. Wilf} % % \medskip \noindent % % {\bf Longest Increasing Subsequences in Pattern-Restricted Permutations} % % \vskip 5mm \noindent % % % % Inspired by the results of Baik, Deift and Johansson on the limiting distribution of the lengths of the longest increasing subsequences in random permutations, we find those limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3. We show that the (132)-avoiding case is identical to the distribution of heights of ordered trees, and that the (321)-avoiding case has interesting connections with a well known theorem of Erd\H os-Szekeres. \bye

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%% %% The LaTeX Companion, 2ed (second printing August 2004) %% %% Example 3-4-12 on page 158. %% %% Copyright (C) 2004 Frank Mittelbach, Michel Goossens, %% Johannes Braams, David Carlisle, and Chris Rowley %% %% It may be distributed and/or modified under the conditions %% of the LaTeX Project Public License, either version 1.3 %% of this license or (at your option) any later version. %% %% See http://www.latex-project.org/lppl.txt for details. %% \documentclass{ttctexa} \pagestyle{empty} \setcounter{page}{6} \setlength\textwidth{159.0pt} \StartShownPreambleCommands \usepackage{color,fancyvrb} \StopShownPreambleCommands \begin{document} \begin{Verbatim}[frame=single,rulecolor=\color{blue}, framerule=3pt,framesep=1pc,fillcolor=\color{yellow}] A framed verbatim line! \end{Verbatim} \end{document}