MOTIVE POWER OF HEAT

THAT distinguished member of the profession of engineering whose whole life has been an honor to his profession and to his country; and who, elevated to the highest office within the gift of the French Nation, has proven by the quiet dignity and the efficiency with which he has performed his august duties that he is a worthy member of a noble family, already rendered famous by an earlier Sadi Carnot, now immortal in the annals of science, and is himself deserving of enrollment in a list of great men which includes that other distinguished engineer, our own first president, George Washington.

The Carnot Cycle! What memories this name must stir in every engineer! To some it will recall early struggles to comprehend the nature of heat engines; to others it represents the ideal of performance sought after in design and operation. Many will recall the keen delight that came from a thorough understanding of the Carnot cycle which forms one of the principal foundations of thermodynamics. Every student of this subject can now write the elementary principles of this cycle in our modern terms of heat and thermodynamics. How many have given a thought to the conception and development of the idea when many of the laws of physics as now stated were either imperfectly known or not yet discovered? What could be more interesting than to read the thoughts of the originator of the Carnot cycle and to follow his reasonings that led to his great discovery?

The pages that follow contain a reprint of a book written by Dr. Robert H. Thurston and published in 1890 by John Wiley and Sons, to whom acknowledgement is made for permission to reprint this manuscript. The text contains an introduction by Dr. Thurston followed by his translation from the French edition published by Gauthier-Villars of Sadi Carnot's brochure on "Reflexions sur la Puissance Motrice du Feu," together with a sketch of Sadi Carnot's brief life written by his brother Henri and appearing in the same edition.

The translator, Dr. Thurston, one of the founders of The American Society of Mechanical Engineers and its first President, was one of America's outstanding engineers. His writings influenced in a large measure the development of mechanical engineering in the English-speaking world. When Dr. Thurston writes of Sadi Carnot in the first sentence of his introduction

-"Carnot was perhaps the greatest genius in the department of physical science at least that this century has produced"-, one receives a new conception of the stature of Carnot which is further expanded in Dr. Thurston's later paragraphs. Our admiration of Carnot's genius increases when it is realized that this essay was published at an age of twenty-eight so that he must have conceived the idea at a still earlier age; Dr. Thurston suggests at twenty-four.

Henri Carnot's short account of his brother's life enhances further one's appreciation of the discoverer of the Carnot cycle. Sadi Carnot was born, reared and educated during the turbulent times of the French Revolution and Napoleonic era. In fact, his father had a part in these stirring events. He was trained for the army and studied military engineering. One can only conjecture as to the causes that turned his thoughts to the principles underlying the operation of heat engines. Perhaps then as now, war was directing people's thoughts from common-place affairs and stirring the imagination in fields of endeavor never before considered.

Carnot's "Reflexions sur La Puissance Motrice du Feu" appeared first as a small book published in Paris in 1824. In Carnot's time, the nature of heat as now understood, was not generally known. Carnot employs the older conception of heat as a substance that is present everywhere which he calls "caloric". If "quantity of heat" is used in place of caloric, his ideas become more plain. Fortunately, as Dr. Thurston points out, his reasoning and conclusions are independent of the nature of heat and thus his analysis holds true under our later ideas. Also, as Dr. Thurston states, Carnot did not conceive that a portion of the heat was converted into work. The discovery of the relation of heat and work by Joule came later. Some of Carnot's ideas of specific heats may also need revision in view of later physical discoveries.

An engineer will find much of secondary interest in Carnot's book. For instance, he seemed famliar with the development of the steam engine by English engineers and the efficiencies obtained. He speaks of the highest steam pressures as 6 atmospheres (75 lb gage) and condensation temperatures of 40⁰ C (1040⁰ F) corresponding to 27.8 inches vacuum. Carnot had a clear conception of the value of feed water heating which he describes in several paragraphs. One is surprised to find in the later part of his essay a clear conception of the cycle of the combustion gas turbine, which is only now undergoing commercial development. combustion gas turbine.

Carnot was a real scientist and a study of his text serves to increase one's appreciation of his clear conception of the heat cycle in spite of lack of physical and experimental data. We do him honor by the term "Carnot cycle" applied to the principles that he developed.

In closing, I express the deep appreciation of the Society to one of our fellow members, Mr. Robert H. Roy of Baltimore, Md., who personally undertook to set up and print this edition and thus to make again available an intensely interesting book of historical value to engineers.

A. G.

The Johns Hopkins University

November 28, 1942

NICOLAS-LEONARD-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 qualitites 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 marvelous 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 Henri, herewith published. It will be quite sufficient it 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 on 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 in-accurate 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 in-dependent of any hypothesis as to the nature of heat or the method or mechanism of development and transfer or transfor- mation 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 "Reflexions sur la Puissance Motrice du Feu," published in 1824, escaped notice at the time, was only now and then
* Tait: Thermodynamics, p.13.

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 inac-cessible 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 Mon. Henri 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 these generale que la puissance motrice est en quantite' invariable dans la Nature; qu'elle n'est jamais, a proprement parler, ni produite, ni detruite. A la verite, elle change de forme, c'est a dire qu'elle produit tantot un genre de mouvement, tantot un autre; mais elle n'est jamais aneantie." 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 Encyclopedia 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 a la chaleur que doivent etre attribues' les grands mouvements gui frappent nos regards sur la terre; c'est a elle que sont dues les agitations de l'atmosphere, l'ascension des nuages, la chut des pluies et des autres meteores, les courants d'eau qui sillonnent la surface du globe et dont l'homme est parvenue a employer pour son usage une faible partie; enfin les tremblements de terre, les eruptions volcanigue reconnaissent aussi pour cause le chaleur."

Carnot was the first to declare that the quantity of work done by heat, in any given case of application in 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.*

• Account of Carnot's Theory of the Motive Power of Heat; Sir Wm. Thomson; Trans. Roy. Soc. of Edinburgh, xvi, 1849; and Math. and Phys. Papers, xli. vol. 1 (Cambridge, 1882), p.113. In this paper the corrections due to the introduction of the dynamic theory are first applied.
  

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 ou' il existe une differnce de temperature, il peut y avoir production de puissance motrice;" and again, this extra-anticipation of modern science: "le maximum de puissance resultant de l'emploi de la vapeur est aussi le maximum de puissance motrice realisab1e par quelque moyen que ce soit."

"La puissance motrice de la chaleur est independante des agents mis en oeuvre pour la realiser; sa guantite est fixee uniguement par les temperatures des corps entre lesquels se fait, en dernier resultat, le transport du calorique."

"Lorsqu'un gaz passe, sans changer de temperature, d'un volume et d'une pression determine a un autre pression egalement determinees, le quantite de calorique absorbee ou abandonnee est toujours la meme, quelle que soit la nature du gaz choisi comme sujet d'experience."

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 difference entre le chaleur specifique sous pression constante et la chaleur specifique sous volume constant est la meme 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 Brard, 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 degres inferieurs que dans les degres superieurs."

We today 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 faculte de rendre utile une plus grand 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 Horn-blower 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 today 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 flatter de mettre jamais a profit, dans la pratigue, toute la puissance des combustibles. Les tentatives que l'on ferait pour approcher ce resultat seraient meme plus nuisible qu'utile, si elles faisait negliger d'autres considerations importantes. L'economie du combustibles n'est qu'une des conditions a remplir par les machines a feu; dans beaucoup de circonstances, elle n'est que secondaire: elle doit souvent cedar le pas a la surete, a la solidite, a la duree de la machine, au peu de place qu'il faut lui faire occuper, au peu de frais de son etablissement, etc. Savoir apprecier, dans chaque cas, a leur juste valeur, les considerations de convenance et d'economie qui peuvent presenter; savoir discerner les plus importantes de celles qui sont seulement accessoires, les balancier toutes con venablement entre elles, afin de parvenir, par les moyens les plus faciles, au meilleur resultat: tel doit etre le principal talent de l'homme appele a diriger, a co-ordonner entre eux les travaux de ses semblables, a 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 who 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.

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 canons 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-

R.H. Thurston

Cornell University

9

As THE life of Sadi Carnot was not marked by any notable event, his biography would have occupied only a few lines; but a scientific work by him, after remaining long in obscurity, brought again to light many years after his death, has caused his name to be placed among those of great inventors. In regard to his person, his mind, his character, nothing whatever has been known. Since there remains a witness of his private life the sole witness, has he not a duty to fulfill? Ought he not to satisfy the natural and legitimate interest which attaches to any man whose work has deserved a portion of glory?

Nicolas-Leonard-Sadi Carnot was born June 1, 1796, in the smaller Luxembourg. This was that part of the palace where our father then dwelt as a member of the Directory. Our father had a predilection for the name of Sadi, which recalled to his mind ideas of wisdom and poetry. His firstborn had borne this name, and despite the fate of this poor child, who lived but a few months, he called the second also Sadi, in memory of the celebrated Persian poet and moralist.

Scarcely a year had passed when the proscription, which included the Director, obliged him to give up his life, or at least his liberty, to the conspirators of fructidor. Our mother carried her son far from the palace in which violation of law had just triumphed. She fled to St. Omer, with her family, while her husband was exiled to Switzerland, then to Germany. Our mother often said to me, "Thy brother was born in the midst of the cares and agitations of grandeur, thou in the calm of an obscure retreat. Your constitutions show this difference of origin."

My brother in fact was of delicate constitution. He increased his strength later, by means of varied and judicious bodily exercises. He was of medium size, endowed with extreme sensibility and at the same time with extreme energy, more than reserved, almost rude, but singularly courageous on occasion. When he felt himself to be contending against injustice, nothing could restrain him. The following is an anecdote in illustration.

The Directory had given place to the Consulate. Carnot, after two years of exile, returned to his country and was appointed Minister of War. Bonaparte at the same time was still in favor with the republicans. He remembered that Carnot had assisted him in the beginning of his military career, and he resumed the intimate relation which had existed between them during the Directory. When the minister went to Malmaison to work with the First Consul, he often took with him his son, then about four years old, to stay with Madame Bonaparte, who was greatly attached to him.

She was one day with some other ladies in a small boat on a pond, the ladies rowing the boat themselves, when Bonaparte, unexpectedly appearing, amused himself by picking up stones and throwing them near the boat, spattering water on the fresh toilets of the rowers. The ladies dared not manifest their displeasure, but the little Sadi, after having looked on at the affair for some time, suddenly placed himself boldly before the conqueror of Marengo, and threatening him with his fist, he cried, "Beast of a First Consul, will you stop tormenting those ladies!"

Bonaparte, at this unexpected attack, stopped and looked in astonishment at the child. Then he was seized with a fit of laughter in which all the spectators of the scene joined.

At another time, when the minister, wishing to return to Paris, sought his son, who had been left with Madame Bonaparte, it was discovered that he had run away. They found him a long way off, in a mill, the mechanism of which he was trying to understand. This desire had been in the child's mind for days, and the honest miller, not knowing who he was, was kindly answering all his questions. Curiosity, especially in regard to mechanics and physics, was one of the essential traits of Sadi's mind.

On account of this disposition so early manifested, Carnot did not hesitate to give a scientific direction to the studies of his son. He was able to undertake this task himself when the monarchical tendencies of the new government had determined him to retire. For a few months only Sadi followed the course of M. Bourdon at the Charlemagne Lycee to prepare himself for the Polytechnic School.

The pupil made rapid progress. He was just sixteen years old when he was admitted to the school, the twenty-fourth on the list. This was in 1812. The following year he left it, first in artillery. But he was considered too young for the school of Metz, and he continued his studies at Paris for a year. To this circumstance is due the fact that he took part in March, 1814, in the military exploits of Vincennes, and not of the butte Chaumont, as almost all the historians of the siege of Paris declared. M. Chasles, one of Sadi's school-fellows, took pains to rectify this error at a seance of the Institute in 1869. If the pupils of the Polytechnic School did not earlier enter into the campaign, it was not because they had not asked to do so. I find in my brother's papers the copy of an address to the Emperor, signed by them December 29, 1813:

"SIRE: The country needs all its defenders. The pupils of the Polytechnic School, faithful to their motto, ask to be permitted to hasten to the frontiers to share the glory of the brave men who are consecrating themselves to the safety of France. The battalion, proud of having contributed to the defeat of the enemy, will return to the school to cultivate the sciences and prepare for new services."

General Carnot was at Anvers, which he had just been defending against the confederate English, Prussians, and Swedes, where the French flag yet floated, when he wrote to his son, April 12, 1814:

"My DEAR SADI: I have learned with extreme pleasure that the battalion of the Polytechnic School has distinguished itself, and that you have performed your first military exploits with honor. When I am recalled, I shall be very glad if the minister of War will give you permission to come to me. You will become acquainted with a fine country and a beautiful city, where I have had the satisfaction of remaining in peace while disaster has overwhelmed so many other places."

Peace being restored, Sadi rejoined his father at Anvers and returned with him into France. In the month of October he left the Polytechnic School, ranking sixth on the list of young men destined to service in the engineer corps, and went to Metz as a cadet sub-lieutenant at the school. Many scientific papers that he wrote there were a cited success. One is particularly referred to as very clever, a memoir on the instrument called the theodolite which is used in ~tronomy and geodesy.

I obtain these details from M. Ornvier, who was of the same rank as Sadi and who, later, was one of the founders of the Ecole Centrale. Among his other comrades besides M. Chasles, the learned geometrician just now referred to, was Gen. Duvivier, lamented victim of the insurrection of June 1848. I ought also to mention M. Robelin, Sadi's most intimate friend, who came to help me nurse him during his last lllness, and who published a notice concerning him in the Revue encylopedigue, t. lv.

The events of 1815 brought General Carnot back into politics during the "Cent Jours" which ended in a fresh catastrophe. This gave Sadi a glimpse of human nature of which he could not speak without disgust. His little sub-lieutenant's room was visited by certain superior officers who did not disdain to mount to the third floor to pay their respects to the son of the new minister. Waterloo put an end to their attentions. The Bourbons reestablished on the throne, Carnot was proscribed and Sadi sent successively into many trying places to pursue his vocation of engineer, to count bricks, to repair walls, and to draw plans destined to be hidden in portfolios. He performed these duties conscientiously and without hope of recompense, for his name, which not long before had brought him so many flatteries, was henceforth the cause of his advancement being long delayed.

In 1818 there came an unlooked-for royal ordinance, authorizing the officers of all branches of the service to present themselves at the examinations for the new corps of the staff. Sadi was well aware that favor had much more to do with this matter than ability, but he was weary of garrison life. The stay in small fortresses to which the nature of his work confined him did not offer sufficient resources to his love of study. Then he hoped, and his hope was realized, that a request for a furlough would be obtained without difficulty, and would insure him the leisure that he sought. In spite of the friendly opposition of some chiefs of the engineer corps, testifying to a sincere regret at the removal from their register of a name which had gained honor among them, Sadi came to Paris to take the examination, and was appointed lieutenant on the staff, January 20, 1819.

He hastened to obtain his furlough, and availed himself of it to lead, in Paris and in the country round about Paris, a studious life interrupted but once, in 1821, by a journey to Germany to visit our father in his exile at Magdeburg. We had then the pleasure of passing some weeks all three together.

When, two years later, death took from us this revered father and I returned alone to France, I found Sadi devoting himself to his scientific studies, which he alternated with the culture of the arts. In this way also, his tastes had marked out for him an original direction, for no one was more opposed than he to the traditional and the conventional. On his music-desk were seen only the compositions of Lully that he had studied, and the concerti of Viotti which he executed. On his table were seen only Pascal, Moliere, or La Fontaine, and he knew his favorite books almost by heart. I call this direction original, because it was anterior to the artistic and literary movement which preceded the revolution of 1830. As to the sympathy of Sadi for the author of the Provinciles, it was due not only to the respect of the young mathematician for one of the masters of science, but his devoutly religious mind regarded with horror hypocrisy and hypocrites.

Appreciating the useful and the beautiful, Sadi frequented the museum of the Louvre and the Italian Theatre, as well as the Jardin des Plantes and the Conservatoire des Arts et Metiers. Music was almost a passion with him. He probably inherited this from our mother, who was an excellent pianist, to whom Dalayrac and especially Monsigny, her compatriot, had given instruction. Not content with being able to play well on the violin, Sadi carried to great length his theoretical studies.

His insatiable intellect, moreover, would not allow him to remain a stranger to any branch of knowledge. He diligently followed the course of the College of France and of the Sorbonne, He visited the workshops with eager interest, and made himself familiar with the processes of manufacture; mathematical sciences, natural history, industrial art, political economy,-all these he cultivated with equal ardor. I have seen him not only practise as an amusement, but search theoretically into, gymnastics, fencing, swimming, dancing, and even skating. In even these things Sadi acquired a superiority which astonished specialists when by chance he forgot himself enough to speak of them for the satisfaction of his own mind was the only aim that he sought.

He had such a repugnance to bringing himself forward that, in his intimate conversations with a few friends, he kept them ignorant of the treasures of science which he had accumulated. They never knew of more than a small part of them. How was it that he determined to formulate his ideas about the motive power of heat, and especially to publish them? I still ask myself this question, -I, who lived with him in the little apartment where our father was confined in the Rue du Parc-Royal while the police of the first Restoration were threatening him. Anxious to be perfectly clear, Sadi made me read some passages of his manuscript in order to convince himself that it would be understood by persons occupied with other studies.

Perhaps a solitary life in small garrisons, in the work-room and in the chemical laboratory, had increased his natural reserve. In small companies, however, he was not at all taciturn. He took part voluntarily in the gayest plays, abandoning himself to lively chat. "The time passed in laughing is well spent," he once wrote. His language was at such times full of wit, keen without malice, original without eccentricity, sometimes paradoxical, but without other pretension than that of an innocent activity of intelligence. He had a very warm heart under a cold manner. He was obliging and devoted, sincere and true in his dealings.

Towards the end of 1826, a new royal ordinance having obliged the staff lieutenants to return to the ranks, Sadi asked and obtained a return to the engineer corps, in which he received the following year, as his rank of seniority, the grade of captain.

Military service, however, weighed upon him. Jealous of his liberty, in 1828, he laid aside his uniform that he might be free to come and go at will. He took advantage of his leisure to make journeys and to visit our principal centres of industry.

He frequently visited M. Clement Desormes, professor at the Conservatoire des Arts et Metiers, who had made great advances in applied chemistry. M. Desormes willingly took counsel with him. He was a native of Bourgogne, our family country, which circumstance, I believe, brought them together.

It was before this period (in 1824) that Sadi had published his Reflexions sur la puissance motrice de feu. He had seen how little progress had been made in the theory of machines in which this power was employed. He had ascertained that the improvements made in their arrangement were effected tentatively, and almost by chance. He comprehended that in order to raise this important art above empiricism, and to give it the rank of a science, it was necessary to study the phenomena of the production of motion by heat, from the most general point of view, independently of any mechanism, of any special agent; and such had been the thought of his life.

Did he foresee that this small brochure would become the foundation of a new science? He must have attached much importance to it to publish it, and bring himself out of his voluntary obscurity. In fact (as his working notes prove), he perceived the exist in relation between heat and mechanical work; and after having established the principle to which savants have given his name, he devoted himself to the researches which should enable him to establish with certainty the second principle, that of equivalence, which he already clearly divined. Thermodynamics was established from that time. But these researches were rudely interrupted by a great event-the- revolution of July, 1830.

Sadi welcomed it enthusiastically-not, however, it is evident, as a personal advantage.

Several old members of the Convention were still living, even of those who had become celebrated; no favor of the new government was accorded them. To the son of Philippe-Egalite was ascribed a saying which, if it was untrue, at least agreed well with the sentiment of his position: "I can do nothing for the members of the Convention themselves," he said, "but for their families whatever they will."

However it may be, some of those about him vaguely questioned my brother as to his desires in case one of us should be called to the Chamber of Peers, of which Carnot had been a member in 1815. We had on this occasion a brief conference. Unknown to us both, this distinction could be offered only to a title in some sort hereditary. We could not accept it without forsaking the principles of Carnot, who had combated the heredity of the peerage. The paternal opinion therefore came to second our distaste for the proposition, and dictated our reply.

Sadi frequented the popular reunions at this period without forsaking his role of a simple observer.

Nevertheless he was, when occasion demanded it, a man of prompt and energetic action. One incident will suffice to prove this, and to show the sang-froid which characterized him. On the day of the funeral of Gen. Lamarque, Sadi was walking thoughtfully in the vicinity of the insurrection. A horseman preceding a company, and who was evidently intoxicated, passed along the street on the gallop, brandishing his sabre and striking down the passers-by. Sadi darted forward, cleverly avoided the weapon of the soldier, seized him by the leg, threw him to the earth and laid him in the gutter, then continued on his way to escape from the cheers of the crowd, amazed at this daring deed.

Before 1830, Sadi had formed part of a Renion polytechnique industrielle, made up of old pupils of the school, with a plan of study in common. After 1830, he was a member of the Association polytechnigue, consisting also of graduates, the object being the popular propagation of useful knowledge. The president of this association was M. de Choiseul-Praslin; the vice-presidents, MM. de Tracy, August Comte, etc.

The hopes of the democracy meanwhile seeming to be in abeyance, Sadi devoted himself anew to study, and pursued his scientific labors with all the greater energy, as he brought to bear upon them the political ardor now so completely repressed. He undertook profound researches on the physical properties of gases and vapors, and especially on their elastic tensions. Unfortunately, the tables which he prepared from his comparative experiments were not completed; but happily the excellent works of Victor Regnault, so remarkable for their accuracy, have supplied to science, in this respect, the blanks of which Sadi Carnot was conscious.

His excessive application affected his health towards the end of June, 1832. Feeling temporarily better, he wrote gaily to one of his friends who had written several letters to him: "My delay this time is not without excuse. I have been sick for a long time, and in a very wearisome way. I have had an inflammation of the lungs, followed by scarlet-fever. (Perhaps you know what this horrible disease is.) I had to remain twelve days in bed, without sleep or food, without any occupation, amusing myself with leeches, with drinks, with baths, and other toys out of the same shop. This little diversion is not yet ended, for I am still very feeble."

This letter was written at the end of July.

There was a relapse, then brain fever; then finally, hardly recovered from so many violent illnesses which had weakened him morally and physically, Sadi was carried off in a few hours, August 24, 1832, by an attack of cholera. Towards the last, and as if from a dark presentiment, he had given much attention to the prevailing epidemic, following its course with the attention and penetration that he gave to everything.

Sadi Carnot died in the vigor of life, in the brightness of a career that he bade fair to run with glory, leaving memory of profound esteem and affection in the hearts of many friends.

His copy-books, filled with memoranda, attest the activity of his mind, the variety of his knowledge, his love of humanity, his clear sentiments of justice and of liberty. We can follow therein the traces of all his various studies. But the only work that he actually completed is this which is here published. It will suffice to preserve his name from oblivion.

His moral character has other claims on our recognition. Our only ambition here is to present a sketch of it. But, much better than through the perusal of these few pages, Sadi Carnot can be appreciated by reading the thoughts scattered through his memoranda, which are to be carefully collected. There are many practical rules of conduct which he records for himself; many observations that he desires to fix in his memory; sometimes an impression that has just come to him, grave or gay; sometimes too, though rarely, a trace of ill-humor directed against men or society. He never thought that these notes, the outpouring of his mind, would be read by other eyes than his own, or that they would some day be used to judge him. I find in them, for my part, touching analogies with the thoughts of my father, although the father and son had, unfortunately, lived almost always apart, by force of circumstances.