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The great works of art, those of peace as well as those of war,
are not to be undertaken without long studies which save much
groping, miscalculation and useless expense. These studies can
only be based upon a good map. But a map will be only a valueless
phantasy if constructed without basing it upon a solid framework.
As well make stand a human body minus the skeleton. |
But these deep-lying rocks we can not reach, exercise from
afar their attraction which operates upon the pendulum and deforms
the terrestrial spheroid. Geodesy can therefore weigh
them from afar, so to speak, and tell us of their distribution.
Thus will it make us really see those mysterious regions which
Jules Verne only showed us in imagination. |
At the beginning of the eighteenth century, long discussions
arose between the Newtonians who believed the earth flattened,
as the theory of gravitation requires, and Cassini, who, deceived
by inexact measurements, believed our globe elongated. Only
direct observation could settle the question. It was our Academy
of Sciences that undertook this task, gigantic for the epoch. |
Truly, the country where Maupertuis operated was not a desert
and he even enjoyed, it is said, among the Laplanders those sweet
satisfactions of the heart that real arctic voyagers never know.
It was almost the region where, in our days, comfortable steamers
carry, each summer, hosts of tourists and young English people.
But in those days Cook's agency did not exist and Maupertuis
really believed he had made a polar expedition. |
The name of Maupertuis has reached us much scratched by the
claws of Doctor Akakia; the scientist had the misfortune to displease
Voltaire, who was then the king of mind. He was first
praised beyond measure; but the flatteries of kings are as much
to be dreaded as their displeasure, because the days after are
terrible. Voltaire himself knew something of this. |
Is nature governed by caprice, or does harmony rule there?
That is the question. It is when it discloses to us this harmony
that science is beautiful and so worthy to be cultivated. But
whence can come to us this revelation, if not from the accord of
a theory with experiment? To seek whether this accord exists
or if it fails, this therefore is our aim. Consequently these two
terms, which we must compare, are as indispensable the one as
the other. To neglect one for the other would be nonsense. Isolated,
theory would be empty, experiment would be blind; each
would be useless and without interest. |
We reach what may be called the second heroic period of
geodesy. France is torn within. All Europe is armed against
her; it would seem that these gigantic combats might absorb all
her forces. Far from it; she still has them for the service of
science. The men of that time recoiled before no enterprise,
they were men of faith. |
Delambre and M茅chain were commissioned to measure an arc
going from Dunkerque to Barcelona. This time there was no
going to Lapland or to Peru; the hostile squadrons had closed to
us the ways thither. But, though the expeditions are less distant,
the epoch is so troubled that the obstacles, the perils even,
are just as great. |
In France, Delambre had to fight against the ill-will of suspicious
municipalities. One knows that the steeples, which are
visible from so far, and can be aimed at with precision, often
serve as signal points to geodesists. But in the region Delambre
traversed there were no longer any steeples. A certain proconsul
had passed there, and boasted of knocking down all the
steeples rising proudly above the humble abode of the sans-culottes.
Pyramids then were built of planks and covered with
white cloth to make them more visible. That was quite another
thing: with white cloth! What was this rash person who, upon
our heights so recently set free, dared to raise the hateful standard
of the counter-revolution? It was necessary to border the
white cloth with blue and red bands. |
M茅chain operated in Spain; the difficulties were other; but
they were not less. The Spanish peasants were hostile. There
steeples were not lacking: but to install oneself in them with
mysterious and perhaps diabolic instruments, was it not sacrilege?
The revolutionists were allies of Spain, but allies smelling
a little of the stake. |
The fact is that he encountered among his collaborators more
of proud obstinacy than of good will and that a thousand accidents
retarded his work. The plague was nothing, the fear of
the plague was much more redoubtable; all these isles were on
their guard against the neighboring isles and feared lest they
should receive the scourge from them. M茅chain obtained permission
to disembark only after long weeks upon the condition
of covering all his papers with vinegar; this was the antisepsis
of that time. |
It was the moment when all Spain took up arms to defend her
independence against France. Why did this stranger climb the
mountains to make signals? It was evidently to call the French
army. Arago was able to escape the populace only by becoming
a prisoner. In his prison, his only distraction was reading in
the Spanish papers the account of his own execution. The papers
of that time sometimes gave out news prematurely. He had at
least the consolation of learning that he died with courage and
like a Christian. |
The vessel and the prisoners were released. The port should
have been properly reached, since they had on board an astronomer;
but the astronomer was seasick, and the Algerian seamen,
who wished to make Marseilles, came out at Bougie. Thence
Arago went to Algiers, traversing Kabylia on foot in the midst
of a thousand perils. He was long detained in Africa and
threatened with the convict prison. Finally he was able to get
back to France; his observations, which he had preserved and
safeguarded under his shirt, and, what is still more remarkable,
his instruments had traversed unhurt these terrible adventures.
Up to this point, not only did France hold the foremost place,
but she occupied the stage almost alone. |
In the years which follow, she has not been inactive and our
staff-office map is a model. However, the new methods of observation
and calculation have come to us above all from Germany
and England. It is only in the last forty years that France has
regained her rank. She owes it to a scientific officer, General
Perrier, who has successfully executed an enterprise truly audacious,
the junction of Spain and Africa. Stations were installed
on four peaks upon the two sides of the Mediterranean.
For long months they awaited a calm and limpid atmosphere.
At last was seen the little thread of light which had traversed
300 kilometers over the sea. The undertaking had succeeded. |
We have become more and more exacting and what our fathers
admired does not satisfy us to-day. But in proportion as we seek
more exactitude, the difficulties greatly increase; we are surrounded
by snares and must be on our guard against a thousand
unsuspected causes of error. It is needful, therefore, to create
instruments more and more faultless. |
The future of French geodesy is at present in the hands of the
Geographic Service of the army, successively directed by General
Bassot and General Berthaut. We can not sufficiently congratulate
ourselves upon it. For success in geodesy, scientific aptitudes
are not enough; it is necessary to be capable of standing
long fatigues in all sorts of climates; the chief must be able to
win obedience from his collaborators and to make obedient his
native auxiliaries. These are military qualities. Besides, one
knows that, in our army, science has always marched shoulder to
shoulder with courage. |
I add that a military organization assures the indispensable
unity of action. It would be more difficult to reconcile the rival
pretensions of scientists jealous of their independence, solicitous
of what they call their fame, and who yet must work in concert,
though separated by great distances. Among the geodesists of
former times there were often discussions, of which some aroused
long echoes. The Academy long resounded with the quarrel of
Bouguer and La Condamine. I do not mean to say that soldiers
are exempt from passion, but discipline imposes silence upon a
too sensitive self-esteem. |
Our hydrographic engineers contribute also to the common
achievement a glorious contingent. The survey of our coasts, of
our colonies, the study of the tides, offer them a vast domain of
research. Finally I may mention the general leveling of France
which is carried out by the ingenious and precise methods of
M. Lallemand. |
With such men we are sure of the future. Moreover, work for
them will not be lacking; our colonial empire opens for them immense
expanses illy explored. That is not all: the International
Geodetic Association has recognized the necessity of a new measurement
of the arc of Quito, determined in days of yore by La
Condamine. It is France that has been charged with this operation;
she had every right to it, since our ancestors had made, so
to speak, the scientific conquest of the Cordilleras. Besides,
these rights have not been contested and our government has
undertaken to exercise them. |
Captains Maurain and Lacombe completed a first reconnaissance,
and the rapidity with which they accomplished their
mission, crossing the roughest regions and climbing the most
precipitous summits, is worthy of all praise. It won the admiration
of General Alfaro, President of the Republic of Ecuador,
who called them 'los hombres de hierro,' the men of iron. |
The final commission then set out under the command of Lieutenant-Colonel
(then Major) Bourgeois. The results obtained
have justified the hopes entertained. But our officers have encountered
unforeseen difficulties due to the climate. More than
once, one of them has been forced to remain several months at
an altitude of 4,000 meters, in the clouds and the snow, without
seeing anything of the signals he had to aim at and which refused
to unmask themselves. But thanks to their perseverance and
courage, there resulted from this only a delay and an increase of
expense, without the exactitude of the measurements suffering
therefrom. |
What I have sought to explain in the preceding pages is how
the scientist should guide himself in choosing among the innumerable
facts offered to his curiosity, since indeed the natural
limitations of his mind compel him to make a choice, even though
a choice be always a sacrifice. I have expounded it first by
general considerations, recalling on the one hand the nature
of the problem to be solved and on the other hand seeking to
better comprehend that of the human mind, which is the principal
instrument of the solution. I then have explained it by
examples; I have not multiplied them indefinitely; I also have
had to make a choice, and I have chosen naturally the questions
I had studied most. Others would doubtless have made a different
choice; but what difference, because I believe they would
have reached the same conclusions. |
Doubtless this classification is relative and depends upon the
weakness of our mind. The facts of slight outcome are the complex
facts, upon which various circumstances may exercise a
sensible influence, circumstances too numerous and too diverse
for us to discern them all. But I should rather say that these
are the facts we think complex, since the intricacy of these circumstances
surpasses the range of our mind. Doubtless a mind vaster
and finer than ours would think differently of them. But what
matter; we can not use that superior mind, but only our own. |
Facts where the laws of chance apply become easy of access to
the scientist who would be discouraged before the extraordinary
complication of the problems where these laws are not applicable.
We have seen that these considerations apply not only to the
physical sciences, but to the mathematical sciences. The method
of demonstration is not the same for the physicist and the mathematician.
But the methods of invention are very much alike.
In both cases they consist in passing up from the fact to the
law, and in finding the facts capable of leading to a law. |
To bring out this point, I have shown the mind of the mathematician
at work, and under three forms: the mind of the mathematical
inventor and creator; that of the unconscious geometer
who among our far distant ancestors, or in the misty years of
our infancy, has constructed for us our instinctive notion of
space; that of the adolescent to whom the teachers of secondary
education unveil the first principles of the science, seeking to
give understanding of the fundamental definitions. Everywhere
we have seen the r么le of intuition and of the spirit of generalization
without which these three stages of mathematicians, if I
may so express myself, would be reduced to an equal impotence. |
And when sciences have no direct bond, they still mutually
throw light upon one another by analogy. When we studied
the laws obeyed by gases we knew we had attacked a fact of great
outcome; and yet this outcome was still estimated beneath its
value, since gases are, from a certain point of view, the image
of the milky way, and those facts which seemed of interest only
for the physicist, ere long opened new vistas to astronomy quite
unexpected. |
And finally when the geodesist sees it is necessary to move his
telescope some seconds to see a signal he has set up with great
pains, this is a very small fact; but this is a fact of great outcome,
not only because this reveals to him the existence of a
small protuberance upon the terrestrial globe, that little hump
would be by itself of no great interest, but because this protuberance
gives him information about the distribution of matter
in the interior of the globe, and through that about the past of
our planet, about its future, about the laws of its development. |