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hail. The geographer, profiting by a favourable wind, was
to explore, without danger or fatigue, as well those polar
zones which the accumuhited ice of centuries seems to
wish to conceal for ever from our curiosity, as those
central parts of Africa, New Holland, Java, Sumatra,
and Borneo, forbidden to our enterprises not less by a
deadly climate than by the fierce animals and tribes
which live there. Certain generals thought it an urgent
duty to study the systems of fortification and artillery
which it would be necessary to oppose to enemies moving
in balloons ; others elaborated new principles of tactics
applicable to aerial battles. One would say that projects
such as these, which might have been fathered on Ariosto,
should certainly have satisfied the most adventurous and
enthusiastic spirits : such was not the case, however.
The discovery of balloons, notwithstanding the brilliant
accessories with which each one enthusiastically sur-
rounded it, appeared to be only the forerunner of still
greater discoveries ; henceforward nothing was to be im-
possible to one who had conquered the atmosphere. This
idea was continually reproducing itself; it put on every
shape ; youth seized it with joy ; old age made it the
text of a thousand bitter i-egrets. See the Marechale de
Villeroi, an octogenarian and an invalid : she is led to
one of the windows of the Tuileries almost by force, for
she does not believe in balloons ; the balloon neverthe-
less detaches itself from its moorings ; our colleague,
Charles, seated in tlie cradle, gaily salutes the spectators,



£loge op vauban. 13

and soars majestically into the air. Oh ! on the instant
passing without transition from the most complete in-
credulity to an unbounded confidence in the powers of
the human mind, the old Marechale falls on her knees,
and, her eyes bathed in tears, gasps forth these sad
words : " Yes, it is decided, now it is certain ; they will
discover the secret of never dying, but it will he when I
am dead ! "

Carnot, being of a rigorous turn of mind (though he
was not yet eighty years of age), took good care not to
go so far as the Marechale de Villeroi. Nevertheless, he
appeared in the ranks of the enthusiasts. He then be-
lieved, and always did so afterwards, in the possibility of
directing balloons, and consequently in the applications
which science and the art of war had hoped from them.
The archives of the Academy ought to contain a paper
in which Captain Carnot of the engineers submitted to
the authorities an arrangement of light oars, which, in
his opinion, should attain the desired end. This paper
has not yet been discovered. I will continue my re-
searches for it, and if the work seems likely to add to
the reputation of our fellow academician, the public shall
not be deprived of it. Perhaps I shall join with it a
memoir of the same nature, also unpublished, by another
academician, the illustrious Meunier.

ELOGE OP VAUBAN BY CARNOT. HIS DISCUSSIONS

WITH M. DE MONTALEMBERT.

A certain literary society of a very small town once
on a time gave itself the title, on its own full authority,
of Daucjliter of the French Academy. Voltaire thought
that they should not refuse it this title : " Indeed, I
esteem her," said he, " as a very virtuous daughter.



14 CARNOT.

since she has never given occasion for any talk about
her."

Such an epigram would not have been applicable to
the Academy of Dijou. This celebrated society did not
shun the public gaze, either when it proposed the ques-
tion, " Whether the reestablishment of the arts and
sciences had contributed to the refinement of manners,"
nor, more especially, when it rewarded the discourse in
which Jean-Jacques pronounced in the negative. Time
has done ample justice to the paradox ; but it ought not
to have effaced the remembrance of the generous pro-
ceeding which, in giving to Rousseau an unexpected
celebrity, attached him for ever to the brilliant career in
which he met with competitors and rivals, but not with a
master.

To the merit which I have just related, the Academy
of Dijon can add that of having called forth the first pro-
duction of Carnot's which the press took possession of, —
the Eloge of Vauban.

The intrepidity, the disinterestedness, and the science
of the illustrious marshal had already received, from the
tongue of Fontenelle, an homage to which it seemed
difficult to add. What speech indeed could more
Avorthily characterize a military life than these few
figures ? " Vauban caused work to be done at 300 for-
tresses ; he constructed 33 new ones ; he conducted 53
sieges ; he was present at 140 actions of importance."
And does not this other sentence seem as though bor-
rowed from Plutarch ? " The morals of Vauban held
out pei'fectly against the most brilliant dignities, and
never even wavered. In a word, he was a Roman
whom it seemed as if our age had stolen from the best
times of the Repu])lic ! "



ELOGE OF VAUBAN. 15

The eloge from which these two passages are taken
had always appeared to me so eloquent and true, that, at
the moment when I first discovered an oi'ation on Vau-
ban amongst tlie productions of our colleague, I burst
out into heartfelt abuse at the academic programme
which, taking advantage of the inexperience of a young
man, had exposed him to so formidable a comparison.
Indeed, I should not have been more uneasy, if I had
discovered that Carnot had endeavoured to rewrite La
Mecanique of Lagi'ange, Athalie, or the Fables of La
Fontaine. These fears were superfluous. The Bur-
gundian members of the Academy of Dijon were right
in thinking that the Burgundian Vauban might still be-
come an interesting subject of study, even after the bril-
liant portrait traced by Fontenelle. And, in truth, the
Secretary of the Academy of Sciences had prudently
left in the shade one of the finest points of the illustrious
marshal.

It would seem that the eloge of Vauban, from the pen
of an officer of engineers, must consist principally of an
exact appreciation of the means of attack and defence
with which the illustrious marshal endowed the art of
■vvar. This was not the plan, howevei", which Carnot
adopted. It was principally for the qualities of the
heart, for virtue, and for patriotism, that Vauban seemed
to him worthy of admiration. " He was," said he, " one
of those men whom nature gives to the world formed
entirely for benevolence ; gifted, like the bee, with an
innate activity for the general welfare ; who cannot
separate their lot from that of the Republic, and who,
intimate members of society, live and flourish, or suffer
and languish, with it."

Prince Henry of Prussia was present at the assembly



16 CARNOT.

of the Academy of Dijon, at which the eloge of Vauban
was read and rewarded. He expressed, in the most
unequivocal terms, the great pleasure that the discourse
had given him ; and assured the author of his profound
esteem, both verbally and in writing. Piqued with
emulation, the Prince de Conde, who presided at the
assembly, as governor of Burgundy, outdid the marks of
favour which were shown to the young engineer officer
by the brother of Frederic the Great.

Had Carnot then flattered the prejudices of the nobles ?
Were his principles in 1784 so different from those which
afterwards directed all his actions, as necessarily to re-
ceive the suffrages of the great ? Listen, Gentlemen,
and judge !

The Dime Roy ale (the King's Tithe), that writing
which, under Louis XIV., brought about the complete
disgrace of Vauban, and of which Fontenelle had the
prudence not even to mention the title, in enumerating
the works of the illustrious marshal, was called by Car-
not a simple and pathetic exposition of facts ; a woi^c in
which " every thing is striking by its precision and truth-
fulness." The assessment of the taxes, in France, in the
eyes of the young officer, was " barbarous ; " the manner
of gathering them " more barbarous still." According to
him, the true object of a government is to oblige every
individual of the State to labour; the method which he
points out for obtaining this result would be (I quote
from the text) to cause riches to pass from those hands
Avhere they are superfluous, into those where they are
necessary. Carnot gives his adhesion unreservedly to
this precept of Vauban's ; the laws ought to prevent the
frightful misery of the one class and the excessive opu-
lence of the other ; he sets his face against the odious



ON EQUALIZING PROPERTY. 17

multiplicity of privileges from which the more numerous
classes of the population had then so much to suffer ;
finally, after having divided mankind into two categories,
the workers and the idlers, he goes so far as to say of
these latter, who alone, according to him, have been
taken into account in the constitution of modern society,
that " they do not begin to be useful till the moment in
wliich they die, for they do not vivify the earth except
by reentering it." Such, Gentlemen, are the bold
opinions wdiich an Academy rewarded in 1784 ; which
called forth from Buffon, who certainly cannot be ac-
cused of having been an innovator in matters of govern-
ment, these words so flattering to the successful orator :
— " Your style is noble and flowing ; you have done, sir,
an agreeable and useful work ; " and which inspired the
brother of an absolute king with the desire of attaching
Carnot, Avhose " friend " he declared himself to be, to the
service of Prussia ; which gained for the young officer
the favour of the prince whom Worms and Coblentz
witnessed a few years afterwards at the head of the
emigration ! Who then will dare to call our revolution
of 1789 an effect without a cause, a meteor of whose
arrival there had been no warning ? The moral trans-
formations of society are subjected to the law of con-
tinuity; they rise and grow hke the productions of the
earth, by imperceptible gradations.

Each century develops, discusses, and adapts to itself,
in some degree, truths — or, if you prefer it, principles —
of which the conception belonged to the preceding cen-
tury ; this work of the mind usually goes on without
being perceived by the vulgar ; but when the day of
application ai'rives, when principles claim their part in
practice, when they aim at penetrating into political life,



18 CARNOT.

the ancient interests, if they have only this same anti-
quity to invoke in their favour, become excited, resist,
and struggle, and society is shaken to its foundations.
The tableau will be complete, Gentlemen, when I add
that, in these obstinate conflicts, it is never the principles
that succumb.

Carnot, as I have already remarked, had but lightly
touched on the technical part of Vauban's works, in his
^loge ; yet, in the few sentences which he Avrote on this
subject, he took occasion to say that " a certain vulgar,
ignorant, person " took an erroneous view of fortification
in reducing it to the art of tracing on paper lines sub-
jected to certain, more or less, systematic conditions.
These words, in their general sense, seemed as if they
might have passed unnoticed ; but an unfortunate con-
currence of circumstances gave to them an importance
which was not foreseen, and still less desired by their
author. In 1783, a general of infantry, member of this
Academy, M. le Marquis de Montalembert, published,
under the title o? Perpendicular Fortification, an entirely
new system of defence of fortresses. This system was
outrageously opposed by almost the whole corps of mili-
tary engineers. The scion of an illustrious family, the
general officer of the French army, the academician,
might assuredly, without too much vanity, believe him-
self not included in the ignorant vulgar that the author
of the eulogy had lightly designated ; but M. de Mont-
alembert was determined to apply these expressions to
himself, and to revenge himself he published an edition
of Vauban's eloge accompanied by notes, in which offence
and gross affront were carried to the utmost. There was
enough in this pamjihlet to upset the mind of a young
man a thousand times ; nevertheless, under these diffi-



MERITS OF MONTALKMRERT. 19

cult circumstances, Carnot already showed himself such
as he always was afterwards — frank, just, and completely
insensihle to undeserved abuse.

" If your suspicions wdre well founded," wrote he to
his fiery antagonist, " I should have forgotten the first
duties of propriety and decency ; I should have been
wanting, above all, in the infinite respect which military
men owe to a distinguished general : be assured that
there is not a single officer of engineers who has not
learnt with the same pleasure, from M. le Marquis de
Montalembert, how to fortify places well, as from the
brave D'Esse to defend them well."

The appositeness and delicacy of this quotation will be
appreciated when I mention that the brave D'Esse, who,
in 1543, after three months of an heroic resistance, com-
pelled the whole forces of the emperor to raise the siege
of Landrecies, was an ancestor of M. de Montalembert.

Moderation and politeness are almost infallible means
of success against violence and affront ; moreover, in the
quarrels of the press, they must often be looked upon as
the simple result of calculation, and as proofs of ability.
But Carnot's letter allowed no misapprehension as to the
sincerity of his sentiments. " Your work," he wrote to
him who had just criticized so bitterly the principle, the
style, and I might almost add, the punctuation, of his

^loge, " your work is full of genius How that

your casemates are known and proved, fortification will
put on a new face ; it u'ill become a new art. It w^ill be
no longer allowable to employ the revenues of the State
to construct something tolerable, when you have taught

us to cousti'uct something good Although the

corps of engineers has not the advantage of possessing
you, we do not the less consider that we have a right to



20 CAKNOT.

reckon you amongst its most illustrious members. Who-
ever extends our knowledge, whoever furnishes us with
new means of being useful to France, becomes our com-
rade, our chief, and our benefactor." M. de Montalem-
bert did not resist such explicit and flattering testimony.
The most formal disavowal of the unlucky pamphlet
quickly followed Carnot's answer ; on the other hand, it
must be confessed that the higher authorities of the en-
gineers were so irritated at the praises which a simple
captain had allowed himself to bestow on systems which
they had authoritatively rejected, that a " lettre de
cachet" and the Bastille signified to our member that,
on the eve of our great revolution, liberty of discussion,
that precious conquest of modern philosophy, had not
yet penetrated amongst military usages. Such rigour
seems inexplicable, even when one makes every allow-
ance for the requirements of esprit de corps and the sus-
ceptibilities of self-esteem ; Carnot had shown himself,
indeed, both in his dloge and in his letter to Montalem-
bert, the warmest defender of the department to which
he belonged, and which, said he, " professes to sacrifice
its time and its life for the State." Had this man then,
I demand, forgotten the duties of his position, who, when
called on to judge between the services of a regimental
ofRcer and those of the engineer on whom devolves the
dangerous honour of tracing parallels, of commanding in
the trench, or of directing the head of a sap, expressed
himself so nobly : " The officer of engineers is in the
midst of peril, but he is there alone and silent ; he sees
death, but he must gaze on it with coolness ; he may not
rush on it like the heroes of battle ; he sees it appi'oach
with tranquillity ; he seeks the spot where the lightning
bursts forth, not to act but to observe ; not to get excited,
but to deliberate."



POWEK OF MACHINES. 21

Perhaps, Gentlemen, I should not have insisted at
such length on this painful episode in Carnot's life, if I
had not had opportunity of perceiving how far removed
are such times from ours ; if I had not seen, when ac-
companying our most illustrious officers of engineers in
the inspection of some fortified towns, in the discussion
of the amelioration they might be susceptible of, the
simple sous-lieutenant freely oppose his ideas, reflections,
and systems, with full liberty, to the opinions of the gen-
erals ; surrender only after having been victoriously
refuted ; and come forth from the animated contest, not,
as formerly, to go to the Bastille, but with fresh chances
of advancement.

Those on whom the duty devolves of incessantly
referring to the ameliorations of which our social state
is susceptible, would become discouraged. Gentlemen, if,
when occasion presents itself, we did not show the public
that their endeavours have been sometimes crowned with
success.

ESSAY ON MACHINES. NEW THEOREM ON THE LOSS

OF POWER.

The first — nay, more, the principal — scientific produc-
tion of Carnot, bears the date of the year 1783 ; it is
entitled Essay on Machines in general.

They who would seek in the essay of our member the
technical description or special study of any one of the
machines in particular, simple or composite, from which
man has been able to derive so many advantages, would
lalioiir to no purpose. Such was not, indeed, the end
which the; author had in view.

jV macliine, considei-ed generally, is the assemblage of
a more or less considerable number of fixed or movable



22 CARNOT.

pieces, by the aid of which forces of all sorts ordinarily
produce effects which their direct action could not bring
about. Take, for instance, the stone-mason with his
hand on the handle of a very simple machine, the winch
of the lifting-jack or the roller ; he turns about enormous
blocks, or inclines them to suit his convenience, or raises
them to the summit of the highest buildings, when, with-
out the machine, he could not stir them a hair's breadth.

At sight of these effects, the ignorant make great out-
cry at the marvel ; they persuade themselves that ma-
chines multiply force, and this false idea, radically false,
leads them into fantastic and generally very complicated
conceptions, which take away an immense quantity of
capital every year, in pure loss, from agriculture, and
manufacturing industry, and commerce.

With a force of any nature whatsoever, that which
must be valued in money, that which the fabricator buys
from the engineei*, may be easily referred to a very sim-
ple effect, of which every one has a clear idea. Let the
force be supposed directly applied to the raising of a
weight ; the height to which the force raises the weight
in a certain time is observed, and these two data from
experiment, the weight and the height, multiplied together
form a product which is the exact value of the force em-
ployed. This product, indeed, for a given time and the
same height, cannot be augmented or diminished with-
out the force augmenting or diminishing in the same
proportion ; so tluit, for example, if it becomes double,'
triple, or decuple, it is the result of the force being mul-
tiplied by two, tliree, or ten.

The product, which gives the direct measure of a
force, serves equally to measure it when it exercises its
action against a resisting body by an intermediate ma-



POWER OF MACHINES. 23

chine ; well, endow this machine, if you please, with the
power of thought and all the perfections imaginable, and
the product of the weight multiplied by the height it will
have passed through in a given time, will be exactly
equal to that obtained by the employment of the same
force without any intermediate operation. The real
effect, then — or, to speak more strongly, the effect of
any machine when properly estimated — will never sur-
pass that which the motive force was capable of pro-
ducing naturally. Doubtless you can, if you like, with
a machine, raise enormous masses, of millions or thou-
sands of millions of pounds ; but since the product of the
weight, multiplied by the height, must remain constant,
the height to which these masses can be raised in a
minute will be millions or thousands of millions of times
smaller than that to which your hand might have raised
one pound in the same time.

Every one will now understand the true meaning of
that aphorism in mechanics. Machines lose in time or
velocity what they gain in power ! Give me a point of
support situated outside the earth, cried Archimedes,
and I will, with the aid of a lever, raise this earth, so
large and massive, by the mere effort of my hand. The
exclamation of the immortal geometer was marvellously
characteristic of machines, in so far as they give to man
the means of realizing effects otherwise millions of mil-
lions of times beyond his natural strength ; but antiquity
would no doubt have admired it much less if any one,
analyzing phenomena more closely, as we have just
done, had added : Yes, doubtless, mathematically speak-
ing, with his fulcrum and lever Archimides might raise
the globe ; but, after forty million centuries of continu-
ous effort (for such a calculation is not, at the present



24 . CARNOT.

day, beyond the limits of science), the movement effected
would be hardly the breadth of a liair.

If the ideal machine, the machine endowed with all
imaginable perfections, adds nothing to the force which
puts it in action, at any rate it takes nothing away from
it ; it transforms the effects by rigorous equivalents. It
is not thus with a real machine ; in this case the power
and the resistance communicate with one another by
means of pieces which we had supposed inflexible, and
which are not so ; by means of chains and cords whose
roughness cannot but be injurious ; the movable parts,
moreover, turn in collars or sockets where great friction
takes place ; all these causes united absorb in pure loss
a very noticeable part of the motive force ; so that the
effect of a machine must always be inferior to that which
would have been engendered by the power acting directly
on the i-esistance.

These results of theory, which are, moreover, com-
pletely confirmed by experience, yet allow that, under
certain points of view, some particular machine may be
recommended without paradox ; that it may be useful
and often even indispensable. For instance, considerations
of solidity or ornament necessitate the carrying to the sum-
mit of certain edifices blocks of stone or marble whose
weight is beyond the strength of the most vigorous work-
man ; suppress the windlass and analogous machines,
and one man will no longer be able to execute the work
which the architect has conceived ; it will be necessary
to unite the strength of thousands of arms at the same
point ; the narrowness of space will prevent that ; the
character of grandeur will disappear from all the monu-
ments of architecture ; the triumphal arch, the palace,
will only be constructed, like the humble cottage, of
little rough stones.



TIIEOKEM IN MECHANICS. 25

You see, Gentlemen, tliat there are cases, it cannot
be too often repeated, in which we must resign ourselves,
whether we will or no, to the loss of force consequent on
machines, since, without their help, certain works would
become impossible.

The losses of force which depend on the flexibility of
the materials of which machines are composed, on the
roughness of cords, and on friction, had been remarked
by the most ancient mechanicians ; modern ones have
gone farther ; their experiments enable them to appreci-
ate these losses and value them in numbers with tolerable
exactness. Science had arrived thus far, when Cai-not
published his Essay. In this work, our member, looking
on machines, and even more generally on every system
of movable bodies, from an entirely new point of view,
indicates a cause unperceived, or at any rate imperfectly
analyzed, by his predecessors, and which in certain cases
must also give rise to considerable losses ; he shows that
we ought, by all means, to avoid abrupt changes of
velocity. Carnot does more ; he finds the mathematical
expression of the loss of active force which such chano-es
occasion ; he shows that it is equal to the active force
by which all the various bodies of the system would be
animated, if each of them were endowed with the com-
plete velocity which it lost at the instant of the abrupt
change being affected.

Such is. Gentlemen, the enunciation of the principle
which, under the name of " Carnot's Theorem," plays so
great a part in the calculation of the effect of machines.

This beautiful and valuable theorem is now well



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