Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissance.

Paris: Giraudet for Bachelier, 1824.

First edition, very rare, and a fine copy in original state, of Carnot’s only published work, which led directly to the first and second laws of thermodynamics. “Carnot, one of the most original thinkers among physical scientists, applied himself to the analysis of the cyclical operation of [heat] engines” (Dibner). “Carnot’s treatise on the motive power of heat, which contains the first (albeit imperfect) statement of the second law of thermodynamics, was written to address a practical engineering problem that had occupied French physicists since 1815 – namely, how heat could be used most economically in the production of motive power … Carnot’s originality lay in his recognition that the motive power of a heat engine was independent of the nature of the substance generating it – that it was a function, instead, of the transfer of heat from a warmer to a colder body. He also introduced the fundamental thermodynamic concept of completeness of cycle, in which the engine and working substance return to their original conditions. Carnot’s achievement was largely ignored by his contemporaries, and the Réflexions remained forgotten until rediscovered by William Thomson (Lord Kelvin) in the 1840s; Kelvin, one of the founders of modern thermodynamics, said of Carnot’s work that ‘nothing in the whole range of natural philosophy is more remarkable than the establishment of general laws by such a process of reasoning’ (quoted in Fox, p. 1). The first edition of Réflexions was published in an edition of six hundred copies (see Fox, p. 23, illustrating the printer’s bill)” (Norman). The Réflexions is now regarded as one of the great rarities of 19th-century science, and copies such as ours in completely original state are extremely difficult to find.

“After a concise review of the industrial, political, and economic importance of the steam engine, Carnot [in the Réflexions] raised two problems that he felt prevented further development of both the utility and the theory of steam engines. Does there exist an assignable limit to the motive power of heat, and hence to the improvement of steam engines? Are there agents preferable to steam in producing this motive power? As Carnot conceived it, the Réflexions was nothing more, nor less, than a ‘deliberate examination’ of these questions. Both were timely problems and, although French engineers had investigated them for a decade, no generally accepted solutions had been reached. In the absence of a clear concept of efficiency, proposed steam-engine designs were judged largely on practicality, safety, and fuel economy … The usual approach to these problems was either an empirical study of the fuel input and the work output of individual engines or the application of the mathematical theory of gases to the abstract operations of a specific type of engine. In his choice of problems Carnot was firmly in this engineering tradition; his method of attacking them, however, was radically new and is the essence of his contribution to the science of heat.

“Previous work on steam engines, as Carnot saw it, had failed for want of a sufficiently general theory, applicable to all imaginable heat engines and based on established principles. As the foundations for his study Carnot carefully set out three premises. The first was the impossibility of perpetual motion, a principle that had long been assumed in mechanics and had recently played an important role in the work of Lazare Carnot [Sadi’s father]. As his second premise Carnot used the caloric theory of heat, which, in spite of some opposition, was the most accepted and most developed theory of heat available. In the Réflexions, heat (calorique) was always treated as a weightless fluid that could neither be created nor be destroyed in any process. As an element in Carnot’s demonstrations this assumption asserted that the quantity of heat absorbed or released by a body in any process depends only on the initial and final states of the body. The final premise was that motive power can be produced whenever there exists a temperature difference. The production of motive power was due ‘not to an actual consumption of caloric, but to its transportation from a warm body to a cold body.’ Making the analogy with a waterwheel, Carnot observed that this motive power must depend on both the amount of caloric employed and the size of the temperature interval through which it falls. In his concept of reversibility Carnot also implicitly assumed the converse of this premise, that the expenditure of motive power will return caloric from the cold body to the warm body.

“The analysis of heat engines began … with an abstract, three-stage steam-engine cycle. The incompleteness of this cycle proved troublesome, and Carnot pushed the abstraction one step further, producing the ideal heat engine and the cycle that now bear his name. The ‘Carnot engine’ consisted simply of a cylinder and piston, a working substance that he assumed to be a perfect gas, and two heat reservoirs maintained at different temperatures. The new cycle incorporated the isothermal and adiabatic expansions and the isothermal compression of the steam engine, but Carnot added a final adiabatic compression in which motive power was consumed to heat the gas to its original, boiler temperature. In describing the engine’s properties, Carnot introduced two fundamental thermodynamic concepts, completeness and reversibility. At the end of each cycle the engine and the working substance returned to their original conditions. This complete cycle not only provided an unambiguous definition of the input and output of the engine, but also rendered superfluous the detailed examination of each stage of the cycle. With each cycle the engine transferred a certain quantity of caloric from the high-temperature reservoir to the low-temperature reservoir and thereby produced a certain amount of motive power. Since each stage of the cycle could be reversed, the entire engine was reversible. Running backward, the engine consumed as much motive power as it produced running forward and returned an equal amount of caloric to the high-temperature reservoir. Joined together but operating in opposite directions, two engines would therefore produce no net effect.

“Carnot then postulated the existence of an engine that, by virtue of design or working substance, would produce more motive power than a ‘Carnot engine’ operating over the same temperature interval and with the same amount of caloric. A reversed ‘Carnot engine’ would be able to return to the boiler all of the caloric transported to the condenser by the hypothetical engine. Yet the reversed ‘Carnot engine’ would consume only a portion of the motive power produced by the hypothetical engine, leaving the remainder available for external work. Together these two engines would form a larger engine whose only net effect was the production of motive power in unlimited quantities. Since such a perpetual motion machine violated his first premise, Carnot concluded that no engine whatsoever produced more motive power than a ‘Carnot engine.’ Formulating the result now known as ‘Carnot’s theorem’, he stated that ‘the motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.’

“To elucidate further the motive power of heat, Carnot turned his attention to the physical properties of gases, a subject in which there had been considerable activity for over a decade. By 1823 a sizable body of experimental data on adiabatic and isothermal processes and on specific heats had been assimilated into the caloric theory of heat and mathematized by Laplace and Poisson. Combining the results of this activity with the concepts involved in his fundamental theorem, Carnot derived a series of seven theorems. With the exception of a long footnote in which he attempted to cast his results in algebraic form, Carnot developed his theorems in a synthetic, geometric manner that, although clear and logically rigorous, was in sharp contrast with the mathematical analysis dominant in the scientific community. Nonetheless, at least three of the theorems represented major advances. The first, that the quantity of heat absorbed or released in isothermal changes is the same for all gases, was experimentally established by Dulong in 1828, but without any reference to Carnot. In a very subtle verbal argument, Carnot also demonstrated that ‘the difference between specific heat under constant pressure and specific heat under constant volume is the same for all gases.’ The final theorem proved that the fall of caloric produces more motive power when the temperature interval is located lower rather than higher on the temperature scale. Although aware of the uncertainties introduced by some assumptions and experimental data for specific heat changes, Carnot was able to calculate motive power values and to verify the theorem …

“In the final section of the Réflexions, Carnot returned to his original questions on steam engines. With experimental data taken from the current literature he verified that all gases produce the same amount of motive power and was able to estimate the ideal limit for its production. In a review of the most common types of steam engines, Carnot sought to apply his findings to the practical questions of steam-engine design and operation. His contributions, however, fell short of his original goal. His conclusions—that steam ought to be used expansively (adiabatically), over a large temperature interval, and without conduction losses—were already widely recognized by engineers of his time. Because of difficulties in engine construction even the problem of the best working substance was not conclusively answered.

“Although the Réflexions was regarded by contemporaries as primarily an essay on steam engines, Carnot’s most important innovations lay in a new approach to the study of heat. While he accepted, and in some theorems furthered, the theory of heat developed by Laplace and Poisson, Carnot also shifted the emphasis from the microscopic to the macroscopic. Rather than build upon the notion of gas particles surrounded by atmospheres of caloric, he began with the directly measurable entities of volume, pressure, temperature, and work …

“Although the exact reasons are impossible to determine, the Réflexions had almost no influence on contemporary science. The original edition had not sold out by 1835; by 1845 booksellers had forgotten it completely. Aside from the reviews in 1824 and the references in obituaries, Carnot’s work was mentioned only twice between 1824 and 1834. Clément recommended the book in his 1824–1825 lectures and Poncelet, writing sometime before 1830, cited it in his Introduction à la mécanique industrielle (Paris, 1839). In Carnot’s obituary Robelin attributed the neglect of the Réflexions to its difficulty, an explanation that would have applied only to engineers and craftsmen unfamiliar with contemporary physics and mathematics. Another explanation points to the failure of the Réflexions to reach conclusions of real value to steam engineers. The silence on the part of physicists like Dulong, who later retraced portions of Carnot’s work, is more difficult to explain. One probable factor, however, was Carnot’s use of the caloric theory and of experimental results such as Clément’s law of saturated vapors. His work was thus especially vulnerable, as he realized himself, when Clément’s law was disproved in 1827 and when problems of radiant heat initiated a period of ‘agnosticism’ concerning the nature of heat.

“In 1834 Clapeyron, with whom Carnot may have been acquainted in 1832, published an analytical reformulation of the Réflexions. While Clapeyron preserved the premises, the theorems, and some of the specific arguments, the emphasis and style were considerably altered. He related the Carnot cycle to the pressure-volume indicator diagram and, emphasizing Carnot’s function, translated Carnot’s synthetic work from the world of heat engines to the realm of the mathematical theory of gases. Carnot’s work attracted no further attention until C. H. A. Holtzman in 1845 and William Thomson in 1848 began working on special aspects of Clapeyron’s paper. Between 1848 and 1850 Thomson, working directly from the Réflexions, published a series of papers that both extended and confirmed Carnot’s results. These papers constituted a strong defence for Carnot’s work, including his use of the caloric theory, at a time when Joule, Julius Mayer, and Helmholtz were establishing the convertibility of heat and work and the principle of energy conservation. In 1850 Clausius showed that Carnot’s theorem was correct as stated but that Carnot’s proof, which assumed no heat was lost, needed modification. Clausius added the statements that in the Carnot engine a certain quantity of heat is destroyed, another quantity is transferred to the colder body, and both quantities stand in a definite relation to the work done. With these additions, which Thomson also adopted in 1851, Carnot’s theorem became the second law of thermodynamics” (DSB).

Sadi Carnot was the eldest son of Lazare Carnot (1753-1823), who, at the time of Sadi’s birth in 1796, was a member of the French Revolutionary government (1795-99). Sadi was named after the medieval Persian poet and philosopher Sa’di of Shiraz. Under his father’s tuition, Sadi Carnot showed great promise and entered the École Polytechnique at the youngest possible age of 16. After graduating in 1814, Carnot went to the École du Génie at Metz to take the two-year course in military engineering. In 1815 Lazare was permanently exiled to Germany, and in 1819 Sadi left military service to live in Paris in his father’s former apartment. He attended courses at various institutions in Paris, and became interested in industrial problems and, in particular, began to study the theory of gases. Sadi visited his father in 1821 in his exiled home in Magdeburg, where he discussed steam engines with Lazare and his brother Hippolyte, who was then living with his father. After returning to Paris, Carnot began the work which led to the mathematical theory of heat and founded the modern theory of thermodynamics. After the publication of Réflexions in 1824, Sadi continued with his research, and although nothing of this was published, notes that Carnot made as his ideas developed have survived. In 1827, Sadi was recalled to full time military duties, but after less than a year he retired permanently and returned to live in Paris where he aimed to continue with his research into the theory of heat. In June 1832 he became ill and had not fully regained his strength when the cholera epidemic of 1832 struck Paris. Although only 36 years of age, he died within a day of contracting the disease.

Bibliotheca Mechanica, p. 63; DSB III, pp. 79-83 (“the first edition of Réflexions … is very rare”); Dibner 155; Norman 404; PMM 285 (“His work led directly to the enunciation of the theory of conservation of energy by Helmholtz in 1847 … The second law of thermodynamics is also implicit in Carnot’s treatise”). Fox, ‘Introduction,’ in Carnot, Reflexions on the motive power of fire, ed. Fox, pp. 1-57.

8vo (220 x 143 mm), pp. [iv], [1], 2-118, with one folding engraved plate. Contemporary marbled wrappers, uncut and mostly unopened, a very faint damp stain to lower left margin, an exceptional copy preserved in its original state. Custom morocco box.

Item #4836

Price: $60,000.00