Nicolas-Léonard-Sadi Carnot was, perhaps, the greatest genius, in the
department of physical science at least, that this century has
produced. By this I mean that he possessed in highest degree that
combination of the imaginative faculty with intellectual acuteness,
great logical power and capacity for learning, classifying and
organizing in their proper relations, all the facts, phenomena, and
laws of natural science which distinguishes the real genius from other
men and even from the simply talented man. Only now and then, in the
centuries, does such a genius come into view. Euclid was such in
mathematics; Newton was such in mechanics; Bacon and Compte were such
in logic and philosophy; Lavoisier and Davy were such in chemistry;
and Fourier, Thomson, Maxwell, and Clausius were such in mathematical
physics. Among engineers, we have the examples of Watt as inventor and
philosopher, Rankine as his mathematical complement, developing the
theory of that art of which Watt illustrated the practical side; we
have Hirn as engineer-experimentalist, and philosopher, as well;
Corliss as inventor and constructor; and a dozen creators of the
machinery of the textile manufactures, in which, in the adjustment of
cam-work, the highest genius of the mechanic appears.
But Carnot exhibited that most marked characteristic of real genius, the
power of applying such qualities as I have just enumerated to great
purposes and with great result while still a youth. Genius is not
dependent, as is talent, upon the ripening and the growth of years for
its prescience; it is ready at the earliest maturity, and sometimes
earlier, to exhibit its marvellous works; as, for example, note Hamilton
the mathematician and Mill the logician; the one becoming master of a
dozen languages when hardly more than as many years of age, reading
Newton’s Principia at sixteen and conceiving that wonderful system,
quaternions, at eighteen; the other competent to begin the study of
Greek at three, learning Latin at seven and reading Plato before he was
eight. Carnot had done his grandest work of the century in his province
of thought, and had passed into the Unseen, at thirty-six; his one
little volume, which has made him immortal, was written when he was but
twenty-three or twenty-four. It is unnecessary, here, to enter into the
particulars of his life; that has been given us in ample detail in the
admirable sketch by his brother which is here republished. It will be
quite sufficient to indicate, in a few words, what were the conditions
amid which he lived and the relation of his work to that great science
of which it was the first exposition.
At the time of Carnot, the opinion of the scientific world was divided,
as it had been for centuries, on the question of the true nature of heat
and light, and as it still is, to a certain extent, regarding
electricity. On the one hand it was held by the best-known physicists
that heat is a substance which pervades all bodies in greater or less
amount, and that heating and cooling are simply the absorption and the
rejection of this “imponderable substance” by the body affected; while,
on the other hand, it was asserted by a small but increasing number that
heat is a “mode of motion,” a form of energy, not only imponderable, but
actually immaterial; a quality of bodies, not a substance, and that it
is identical, in its nature, with other forms of recognizable energy,
as, for example, mechanical energy. A quarter of a century before Carnot
wrote, the experiments of Rumford and of Davy had been crucial in the
settlement of the question and in the proof of the correctness of the
second of the two opposing parties; but their work had not become so
generally known or so fully accepted as to be acknowledged as
representative of the right views of the subject. The prevalent opinion,
following Newton, was favorable to the first hypothesis; and it was in
deference to this opinion that Carnot based his work on an inaccurate
hypothesis; though, fortunately, the fact did not seriously militate
against its value or his credit and fame.
“With true philosophical caution, he avoids committing himself to this
hypothesis; though he makes it the foundation of his attempt to discover
how work is produced from heat.”[1]
The results of Carnot’s reasoning are, fortunately, mainly independent
of any hypothesis as to the nature of heat or the method or mechanism of
development and transfer or transformation of its energy. Carnot was in
error in assuming no loss of heat in a completed cycle and in thus
ignoring the permanent transformation of a definite proportion into
mechanical energy; but his proposition that efficiency increases with
increase of temperature-range is still correct; as is his assertion of
its independence of the nature of the working substance.
Carnot’s “_Réflexions sur la Puissance Motrice du Feu_,” published in
1824, escaped notice at the time, was only now and then slightly
referred to later, until Clapeyron seized upon its salient ideas and
illustrated them by the use of the Watt diagram of energy, and might,
perhaps, have still remained unknown to the world except for the fact
that Sir William Thomson, that greatest of modern mathematical
physicists, fortunately, when still a youth and at the commencement of
his own great work, discovered it, revealed its extraordinary merit,
and, readjusting Carnot’s principles in accordance with the modern views
of heat-energy, gave it the place that it is so well entitled to in the
list of the era-making books of the age. But it still remained
inaccessible to all who could not find the original paper until, only a
few years since, it was reprinted by Gauthier-Villars, the great
publishing house of Paris, accompanied by a biographical sketch by the
younger brother, which it has been thought wise to reproduce with the
translation of Carnot’s book. In making the translation, also, this
later text has been followed; and now, for the first time, so far as is
known to the writer, the work of Carnot is made accessible to the reader
in English.
The original manuscript of Carnot has been deposited by his brother in
the archives of the French Academy of Sciences, and thus insured
perpetual care. The work of Carnot includes not only the treatise which
it is the principal object of this translation to give to our readers,
but also a considerable amount of hitherto unpublished matter which has
been printed by his brother, with the new edition of the book, as
illustrative of the breadth and acuteness of the mind of the Founder of
the Science of Thermodynamics.
These previously unpublished materials consist of memoranda relating to
the specific heats of substances, their variations, and various other
facts and data, and principles as well; some of which are now recognized
as essential elements of the new science, even of its fundamental part.
The book is particularly rich in what have been generally supposed to be
the discoveries of later writers, and in enunciations of principles now
recognized as those forming the base and the supporting framework of
that latest of the sciences. As stated by Tait, in his history of
Thermodynamics, the “two grand things” which Carnot originated and
introduced were his idea of a “cycle” and the notion of its
“reversibility,” when perfect. “Without this work of Carnot, the modern
theory of energy, and especially that branch of it which is at present
by far the most important in practice, the dynamical theory of heat,
could not have attained its now enormous development.” These
conceptions, original with our author, have been, in the hands of his
successors, Clausius and other Continental writers, particularly, most
fruitful of interesting and important results; and Clapeyron’s happy
thought of so employing the Watt diagram of energy as to render them
easy of comprehension has proved a valuable aid in this direction.
The exact experimental data needed for numerical computations in
application of Carnot’s principles were inaccessible at the date of his
writing; they were supplied, later, by Mayer, by Colding, by Joule, and
by later investigators. Even the idea of equivalence, according to
Hypolyte Carnot, was not originally familiar to the author of this
remarkable work; but was gradually developed and defined as he
progressed with his philosophy. It is sufficiently distinctly enunciated
in his later writings. He then showed a familiarity with those notions
which have been ascribed generally to Mayer and which made the latter
famous, and with those ideas which are now usually attributed to Joule
with similar result. He seems actually to have planned the very kind of
research which Joule finally carried out. All these advanced views must,
of course, have been developed by Carnot before 1832, the date of his
illness and death, and ten or fifteen years earlier than they were made
public by those who have since been commonly considered their
discoverers. These until lately unpublished notes of Carnot contain
equally well-constructed arguments in favor of the now accepted theory
of heat as energy. While submitting to the authority of the greatest
physicists of his time, and so far as to make their view the basis of
his work, to a certain extent, he nevertheless adhered privately to the
true idea. His idea of the equivalence of heat and other forms of energy
was as distinct and exact as was his notion of the nature of that
phenomenon. He states it with perfect accuracy.
In making his measures of heat-energy, he assumes as a unit a measure
not now common, but one which may be easily and conveniently reduced to
the now general system of measurement. He takes the amount of power
required to exert an energy equal to that needed to raise one cubic
meter of water through a height of one meter, as his unit; this is 1000
kilogrammeters, taken as his unit of motive power; while he says that
this is the equivalent of 2.7 of his units of heat; which latter
quantity would be destroyed in its production of this amount of power,
or rather work. His unit of heat is thus seen to be 1000 ÷ 2.7, or 370
kilogrammeters. This is almost identical with the figure obtained by
Mayer, more than ten years later, and from presumably the same
approximate physical data, the best then available, in the absence of a
Regnault to determine the exact values. Mayer obtained 365, a number
which the later work of Regnault enabled us to prove to be 15 per cent.
too low, a conclusion verified experimentally by the labors of Joule and
his successors. Carnot was thus _a_ discoverer of the equivalence of the
units of heat and work, as well as the revealer of the principles which
have come to be known by his name. Had he lived a little longer, there
can be little doubt that he would have established the facts, as well as
the principles, by convincing proof. His early death frustrated his
designs, and deprived the world of one of its noblest intellects, just
when it was beginning its marvellous career.
The following sentence from Carnot illustrates in brief his wonderful
prescience; one can hardly believe it possible that it should have been
written in the first quarter of the nineteenth century: “_On peut donc
poser en thèse générale que la puissance motrice est en quantité
invariable dans la Nature; qu’elle n’est jamais, à proprement parler, ni
produite, ni détruite. A la vérité, elle change de forme, c’est a dire
qu’elle produit tantôt un genre de mouvement, tantôt un autre; mais elle
n’est jamais anéantie._” It is this man who has probably inaugurated the
development of the modern science of thermodynamics and the whole range
of sciences dependent upon it, and who has thus made it possible to
construct a science of the energetics of the universe, and to read the
mysteries of every physical phenomenon of nature; it is this man who has
done more than any contemporary in his field, and who thus displayed a
more brilliant genius than any man of science of the nineteenth century:
yet not even his name appears in the biographical dictionaries; and in
the Encyclopædia Britannica it is only to be found incidentally in the
article on Thermodynamics.
Throughout his little book, we find numerous proofs of his clearness of
view and of the wonderful powers of mind possessed by him. He opens his
treatise by asserting that “_C’est à la chaleur que doivent être
attribués les grands mouvements qui frappent nos regards sur la terre;
c’est à elle que sont dues les agitations de l’atmosphère, l’ascension
des nuages, la chute des pluies et des autres météores, les courants
d’eau qui sillonnent la surface du globe et dont l’homme est parvenue à
employer pour son usage une faible partie; enfin les tremblements de
terre, les éruptions volcaniques reconnaissent aussi pour cause la
chaleur._”
Carnot was the first to declare that the maximum of work done by heat,
in any given case of application of the heat-energy, is determined
solely by the range of temperature through which it fell in the
operation, and is entirely independent of the nature of the working
substance chosen as the medium of transfer of energy and the vehicle of
the heat. His assumption of the materiality of heat led, logically, to
the conclusion that the same quantity of heat was finally stored in the
refrigerator as had, initially, left the furnace, and that the effect
produced was a consequence of a fall of temperature analogous to a fall
of water; but, aside from this error—which he himself was evidently
inclined to regard as such,—his process and argument are perfectly
correct.[2]
Throughout his whole work are distributed condensed assertions of
principles now well recognized and fully established, which indicate
that he not only had anticipated later writers in their establishment,
but that he fully understood their real importance in a theory of
heat-energy and of heat-engines. In fact, he often italicizes them,
placing them as independent paragraphs to more thoroughly impress the
reader with their fundamental importance. Thus he says: “_Partout où il
existe une différence de température, il peut y avoir production de
puissance motrice_;” and again, this extraordinary anticipation of
modern science: “_le maximum de puissance résultant de l’emploi de la
vapeur est aussi le maximum de puissance motrice réalisable par quelque
moyen que ce soit_.”
“_La puissance motrice de la chaleur est indépendante des agents mis en
œuvre pour la réaliser; sa quantité est fixée uniquement par les
températures des corps entre lesquels se fait, en dernier résultat, le
transport du calorique._”
“_Lorsqu’un gaz passe, sans changer de température, d’un volume et d’une
pression déterminés à une autre pression également déterminée, la
quantité de calorique absorbée ou abandonnée est toujours la même,
quelle que soit la nature du gaz choisi comme sujet d’expérience._”
Perhaps as remarkable a discovery as any one of the preceding (and one
which, like those, has been rediscovered and confirmed by later
physicists; one which was the subject of dispute between Clausius, who
proved its truth by the later methods which are now the source of his
fame, and the physicists of his earlier days, who had obtained
inaccurate measures of the specific heats of the gases;—values which
were finally corrected by Regnault, thus proving Carnot and Clausius to
be right—is thus stated by Carnot, and is italicized in his manuscript
and book:
“_La différence entre la chaleur spécifique sous pression constante et
la chaleur spécifique sous volume constant est la même pour tous les
gaz._”
He bases his conclusion upon the simplest of thermodynamic
considerations. He says that the increase of volumes with the same
differences of temperature are the same, according to Gay-Lussac and
Dalton; and that, therefore, according to the laws of thermodynamics as
he has demonstrated them, the heat absorbed with equal augmentations of
volume being the same, the two specific heats are constant, and their
difference as well. As will be seen on referring to the text, he bases
upon this principle a determination of the specific heats of constant
volume, taking as his values of the determined specific heats of
constant pressure those of Delaroche and Bérard, making the constant
difference 0.300, that of air at constant pressure being taken as the
standard and as unity. The establishment of this point, in the face of
the opposition, and apparently of the facts, of the best physicists of
his time, was one of those circumstances which did so much to win for
Clausius his great fame. How much greater credit, then, should be given
Carnot, who not only anticipated the later physicists in this matter,
but who must have enunciated his principle under far more serious
discouragements and uncertainty!
It must be remembered, when reading Carnot, that all the “constants of
nature” were, in his time, very inaccurately ascertained. It is only
since the time of Regnault’s grand work that it has been the rule that
such determinations have been published only when very exactly
determined. No change has been attempted in Carnot’s figures, in any
respect; as it would be far less satisfactory to read a paraphrased
work, and the exact figures are now easily accessible to every one, and
his computations may all be made, if desired, on the basis of modern
data. Sir William Thomson has already performed this task in the paper
appended.
Throughout the whole of this treatise, small as it is, we find
distributed a singular number of these anticipations of modern
thermodynamic principles. Studying the relation of heat-energy to work
done, he concludes:
“_La chute du calorique produit plus de puissance motrice dans les
degrés inférieurs que dans les degrés supérieurs._”
We to-day admit that, since the one degree at a low temperature, and the
corresponding quantity of heat, are larger fractions of the total
temperature, and the total heat stored in the substance, than the one
degree at a higher point on the scale of absolute temperature, this
principle of Carnot has become obvious.
In the enunciation of the essential principles of efficiency of the
heat-engine, we find the proofs of this same wonderful prescience. He
asserts that, for best effect: “(1) The temperature of the working fluid
must be raised to the highest degree possible, in order to secure a
commensurate range of temperature; (2) The cooling must be carried to
the lowest point on the scale that may be found practicable; (3) The
passage of the fluid from the upper to the lower limit of temperature
must be produced by expansion;” i.e., “it is necessary that the cooling
of the gas shall occur spontaneously by its rarefaction;” which is
simply his method of stating the now universally understood principle
that, for highest efficiency, the expansion must be adiabatic, from a
maximum to a minimum temperature. He goes on to explain these
principles, and then says that the advantage of high-pressure engines
lies “_essentiellement dans la faculté de rendre utile une plus grande
chute de calorique_.” This principle, as a practical system of
operation, had already, as he tells us, been enunciated by M. Clement,
and had been practised, as we well know, since the days of its
originator, Watt; but Carnot saw clearly the thermodynamic principle
which underlies it, and as clearly states it, for the first time.
He sees clearly, too, the reasons for the attempts of Hornblower and of
Woolf, premature as they proved and as he also sees, in the introduction
of the compound engine, and even suggests that this idea might be still
further developed by the use of a triple-expansion engine, a type which
is to-day just coming into use, more than a half-century after Carnot’s
date. He recognizes the advantages of the compound engine in better
distribution of pressures and in distribution of the work of expansion,
but does not, of course, perceive the then undiscovered limitation of
the efficiency of the simple engine, due to “cylinder condensation,”
which has finally led, perhaps more than any other circumstance, to its
displacement so largely by the multi-cylinder machine. No one has more
exactly and plainly stated the respective advantages to be claimed for
air and the gases, used as working fluids in heat-engines, than does
Carnot; nor does any one to-day better recognize the difficulties which
lie in the path to success in that direction, in the necessity of
finding a means of handling them at high temperatures and of securing
high mean pressures.
His closing paragraph shows his extraordinary foresight, and the
precision with which that wonderful intellect detected the practical
elements of the problem which the engineer, from the days of Savery, of
Newcomen, and of Watt has been called upon to study, and the importance
of the work, which he began, in the development of a theory of the
action, or of the operation, of the heat-engines, which should give
effective assistance in the development of their improved forms:
“_On ne doit pas se flatter de mettre jamais à profit, dans la pratique,
toute la puissance des combustibles. Les tentatives que l’on ferait pour
approcher ce résultat seraient même plus nuisibles qu’utiles, si elles
faisaient négliger d’autres considérations importantes. L’économie du
combustible n’est qu’une des conditions à remplir par les machines à
feu; dans beaucoup de circonstances, elle n’est que secondaire: elle
doit souvent céder le pas à la sûreté, à la solidité, à la durée de la
machine, au peu de place qu’il faut lui faire occuper, au peu de frais
de son établissement, etc. Savoir apprécier, dans chaque cas, à leur
juste valeur, les considérations de convenance et d’économie qui peuvent
se présenter; savoir discerner les plus importantes de celles qui sont
seulement accessoires, les balancer toutes convenablement entre elles,
afin de parvenir, par les moyens les plus faciles, au meilleur résultat:
tel doit être le principal talent de l’homme appelé à diriger, à
co-ordonner entre eux les travaux de ses semblables, à les faire
concourir vers un but utile de quelque genre qu’il soit._”
Such was the work and such the character of this wonderful man. Those
whose desire to follow more closely and to witness the process of
development of the work of which this initial paper of Carnot was the
introductory, should study the contribution of Sir William Thomson to
this development, as published in 1849,—a paper which constitutes that
physicist the virtual discoverer of Carnot and the godfather of the man
and his thoughts. This paper constitutes the final chapter of this
little book.
From that time the additional progress so rapidly made in the new
science was as inevitable as the development of a gold-field, once the
precious metal has been found in paying quantities in the hitherto
unvisited cañons and gorges of a distant and unexplored mountain-range.
But great as is the work since done, and great as have been the
discoveries and the discoverers of later years, none claims our
gratitude and compels our respect in greater degree than does the
original discoverer—