Part 2

It has seemed to the Editor and to the Publishers that the product of the wonderful genius of Carnot,—the great foundation-stone of one of the most marvellous and important of modern sciences, the first statement of the grand though simple laws of Thermodynamics,—as illustrated in this one little treatise, should be made accessible to all who desire to study the work in English, and preserved, so far as its publication in this form could accomplish it, as a permanent memorial, in a foreign tongue, of such grand truths, and of such a great genius as was their discoverer. It is with this purpose that Publishers and Editor have cooperated in this project.

The book consists, as will be seen on inspection, of the translation of Carnot’s Réflexions sur la Puissance Motrice du Feu, preceded by a notice written by the Editor calling attention to its remarkable features, and its extraordinary character as the product of a most remarkable genius; and by a biographical sketch of the great author, written by his brother, Mons. Hyppolyte Carnot, which sketch we find in the French copy of the work as published by Gauthier-Villars, the latest reproduction of the book in the original tongue. To the main portion of the book, Carnot’s Réflexions, is appended the celebrated paper of Sir William Thomson, his “Account of Carnot’s Theory,” in which that great physicist first points out to the world the treasure so long concealed, unnoticed, among the scientific literature, already mainly antiquated, of the first quarter of the nineteenth century. The distinguished writer of this paper has kindly interested himself in the scheme of the Editor, and has consented to its insertion as a natural and desirable commentary upon the older work, and especially as exhibiting the relations of the fundamental principles discovered and enunciated by Carnot to the modern view of the nature of thermodynamic phenomena—relations evidently understood by that writer, but not by the leaders of scientific thought of his time, and therefore ignored by him in the construction of his new science.

The Appendix contains a number of Carnot’s own notes, too long to be inserted in the body of the paper in its present form, and which have therefore been removed to their present location simply as a matter of convenience in bookmaking.

The dedication of the work to the grandnephew of the author, who by a singular coincidence happens to-day to occupy the highest position that any citizen can aspire to reach in that now prosperous Republic, will be recognized as in all respects appropriate by every reader of the work of the earlier Sadi Carnot who is familiar with the character, the history, the attainments, the achievements, of the later Sadi Carnot in so many and widely diverse fields. The Carnot talent and the Carnot character are equally observable in both men, widely as they are separated in time and in the nature of their professional labors. Both are great representatives of a noble family, whose honor and fame they have both splendidly upheld.

The Publishers offer this little book to its readers as a small, yet in one sense not unimportant, contribution to the great cause of modern science, as a relic, a memorial, a corner-stone.

NOTE BY THE EDITOR.

“Je me suis proposé de grands desseins dans ce petit ouvrage,” as Bernardin de Saint-Pierre says in the preface to his pathetic story of Paul et Virginie. I have sought to present to the great English-speaking world the work of a genius hitherto only known to a few men of science, and not well known, even among the people of France, for whose credit he has done so much. In placing before the readers of this translation his book—small of size but great in matter as it is—I feel that I have accomplished an easy task, but one of real importance. I have been asked, as Corresponding Member for the United States of the Société des Ingénieurs Civils de France, to communicate to my colleagues scientific and professional memoirs and whatever may be of interest to them—“en un mot, que nous resserrions les liens qui font des ingénieurs en général une seule famille.” That were a pleasant task; but a grander and a more agreeable one still is that of bringing “nearer in heart and thought” the members of that still larger community, the men of science of the world, and of weaving still more firmly and closely those bonds of kindly thought and feeling which are growing continually more numerous and stronger as the nations are brought to see that humanity is larger and more important than political divisions, and that the labors of educated men and of the guiding minds in the great industries are constantly doing more to promote a true brotherhood of mankind than ever have, or ever can, the greatest statesmen.

When the wonderful intellectual accomplishments of men like the elder Sadi Carnot become known and appreciated by the world, much more will have been accomplished in this direction. It is perhaps from this point of view that the importance of such work will be most fully recognized. When the little treatise which is here for the first time published in English becomes familiar to those for whom it is intended, it will be, to many at least, a matter of surprise no less than pleasure to discover that France has produced a writer on this now familiar subject whose inspiration anticipated many of the principles that those founders of the modern science, Rankine and Clausius, worked out through the tedious and difficult methods of the higher mathematics, and which were hailed by their contemporaries as marvellous discoveries.

NOTE TO SECOND EDITION.

The present edition of this little work is improved by the removal of a few errata observed in the first issue, and by the addition of a recent and excellent portrait of Lord Kelvin, as a frontispiece to his era-making paper, at page 127. This picture, taken within the last year, is thought by the friends of its distinguished subject to be one of the best yet produced. That it is satisfactory to him and his friends is indicated by the fact that the original of this reproduction was presented to the writer by Lady Kelvin, in 1895, immediately after it was taken, and the autograph supplied by her distinguished husband. The Editor takes this occasion to acknowledge cordially the letters of appreciation and commendation received from those who have agreed with M. Haton de la Goupillière that the translation of Carnot and its publication in this manner, with the famous paper of Lord Kelvin, will be considered as worthy of approval by English-speaking readers as well as “appreciated by the whole French nation.”

I. THE WORK OF SADI CARNOT.

BY THE EDITOR.

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.”

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.

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.”