In thermodynamics, Thomson’s search for Carnot’s Reflections is a famous story of how in 1845 a twenty-one year old Irish student named William Thomson went on a search throughout the bookstores of Paris looking for French physicist Sadi Carnot's 1824 memoir Reflections on the Motive Power of Fire; efforts that later functioned to bring the proto-subject of the connection between heat and work to the likes of William Rankine, James Maxwell, and most importantly Rudolf Clausius, the latter of which later coming to lay the foundations of thermodynamics with his 1865 book The Mechanical Theory of Heat.

Early details
In 1839, a young 15-year-old Irish mathematical physics student named William Thomson was in attendance at the Royal Belfast Academical Institution of Northern Ireland, where Scottish educator John Nichol, a professor of astronomy, had that year took the chair of natural philosophy. Upon doing so, Nichol updated the curriculum, introducing students to the new mathematical works of French mathematical physicist Joseph Fourier's particularly his 1822 Analytical Theory of Heat. [1] The mathematical treatment much impressed young Thomson, who became intrigued with Fourier's Théorie analytique de la chaleur and committed himself to study the "Continental" mathematics resisted by a British establishment still working in the shadow of English physicist Isaac Newton. This was Thomson's first stimulator as to the nature of heat.

In 1840, Thomson also came across Edinburgh mathematics professor Philip Kelland's 1837 Theory of Heat, in which it was claimed that Fourier was mostly wrong. [2] In comparing the two, as Thomson told his father, "Fourier is right, and Kelland is wrong." [3] Out of this stimulus, in 1841, at the age of seventeen, Thomson wrote his first scientific paper on Fourier’s analysis of heat under the pseudonym P.Q.R., which was submitted to the Cambridge Mathematical Journal by his father James Thomson (mathematician), titled “On Fourier's expansions of functions in trigonometric series”; and soon two more papers of similar theme soon followed. [4]

At some point during the years 1843 to 1845, William Thomson learned about Carnot through hearing of or reading French engineer Émile Clapeyron's 1834 article Memoir on the Motive Power of Heat, wherein French physicist Sadi Carnot's 1824 work, for the first time, had been referenced and also reinterpreted graphically, using English engineer John Southern's 1796 indicator diagram methodology. [6]

English thermodynamics historian Crosbie Smith states, in his 1998 book The Science of Energy, that this occurred in the late summer of 1843 when William and his older brother
brother James Thomson began initiated a dialogue on the Carnot-Clapeyron theory. [5] Crosbie argues that William developed an interest in the efficiency of heat engines during this period and had begun to engage in discussions about the paper of Carnot on this subject with his older brother James Thomson, a steam engineer, who was in need of such knowledge so to improve the efficiency of engines at a factory where he was employed at the time.

American low-temperature historian Tom Shachtman states, in his 1999 book Absolute Zero, that William learned of Clapeyron’s exegesis of Carnot, in 1845, while doing post-graduate work in the laboratory of Victor Regnault, a former student (1830) and chair of chemistry (1840) of the École Polytechnique (a school founded by Carnot's father, Lazare Carnot), from “colleagues at Regnault’s laboratory”. Shachtman also states that prior to being introduced to Clapeyron's work, Thomson believed that heat depended on caloric as Regnault did. [12]

Paris bookstores
During this time (likely in 1845), Thomson tried to find a copy of Carnot’s Reflections. To his surprise and disappointment there was no copy in the library of the École Polytechnique, and no Paris bookseller had heard of it or its author. [7] As he later recalled: [8]

“I went to every book-shop I could think of, asking for the Puissance Motrice du Feu, by Carnot. ‘Caino? Je ne connais pas cet auteur’ … ‘Ah! Ca-rrr-not! Oui, voice son ouvrgae’, producing a volume on some social question by Hippolyte Carnot [Sadi’s brother]; but the Puissance Motrice du Fue was quite unknown.”

In June of 1848, still not having found an a copy of Carnot’s publication, Thomson published a paper titled “On an Absolute Thermometric Scale Founded on Carnot’s Theory of the Motive Power of Heat” read to the Cambridge Philosophical Society, based on Clapeyron’s 1834 paper. [6] In a foot note to his paper, Thomson states: [9]

“Having never met with the original work, it is only through a paper by M. Clapeyron, on the same subject, published in the Journal de l’École Polytechnique, Vol. xiv. 1834, and translated in the first volume of Taylor’s Scientific Memoirs, that the Author has become acquainted with Carnot’s Theory.”

Thomson also recalls, in retrospect, in a November 5th, 1881 note, that:

“A few months later through the kindness of my late colleague Professor Lewis Gordon, I received a copy of Carnot’s original work and was thus able to give to the Royal Society of Edinburgh my ‘Account of Carnot’s Theory’ (Jan. 2nd, 1849).”

The article referred to above is the 1849 “An Account of Carnot’s Theory of the Motive Power of Heat”, in which the term "thermo-dynamic" was coined. [10]

By 1850, through Thomson's and Clapeyron's writings, the work of Carnot, via Clapeyron's paper, reached the likes of German physicist Rudolf Clausius. Without even seeing Carnot's paper directly, Clausius was so drawn into the subject that he wrote the famous 1850 paper "On the Moving Force of Heat", giving his views on Carnot's heat engine theories. In a foot note, Clausius states: [11]

“I have not been able to obtain a copy of this book [Reflections], and am acquainted with it only through the work of Clapeyron and Thomson, from the latter of whom are quoted the extracts afterwards given.”

The supposition, in Carnot’s work, that caught Clausius’ attention was the postulate, expressly stated, that “the quantity of heat remains unchanged” (in the process), which equates to the argument that “no change occurs in the condition of the working body” (during the work cycle). Conversely, according the view of Clausius, as developed in the mechanical equivalence of heat, a certain amount of heat would consumed in the working body during an irreversible passage of heat in the cyclical production of work. These corrections were employed and remolded in Clausius' famous Mechanical Theory of Heat (1850-1875).

1. Fourier, Joseph. (1822). Analytical Theory of Heat (Théorie Analytique de la Chaleur). Cambridge.
2. Kelland, Philip. (1837). Theory of Heat. Cambridge.
3. Lindley, David. (2004). Degrees Kelvin - a Tale of Genius, Invention, and Tragedy, (pg. 19). Washington, D.C.: Joseph Henry Press.
4. (a) P.Q.R (1841) "On Fourier's expansions of functions in trigonometric series" Cambridge Mathematical Journal 2, 258-259.
(b) P.Q.R (1841). "Note on a passage in Fourier's 'Heat'" Cambridge Mathematical Journal 3, 25-27.
(c) P.Q.R (1842). "On the uniform motion of heat and its connection with the mathematical theory of electricity" Cambridge Mathematical Journal 3, 71-84.
5. Smith, Crosbie. (1998). The Science of Energy - a Cultural History of Energy Physics in Victorian Britain (pgs. 39-44). Chicago: The University of Chicago Press.
6. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX, [1843] 446, 566).
7. Laidler, Keith J. (2002). Energy and the Unexpected, (pg. 31). Oxford University Press.
8. Thomson, William. (1889-94). Popular Lectures and Addresses. 3 vols. 2: 458n [1892]. London: Macmillan.
9. Thomson, William. (1848). “On an Absolute Thermometric Scale Founded on Carnot’s Theory of the Motive Power of Heat” (pgs. 100-06), Cambridge Philosophical Society Proceedings for June 5; and Phil. Mag., Oct. 1848.
10. Thomson, William. (1849). “An Account of Carnot’s Theory of the Motive Power of Heat – with Numerical Results Deduced from Regnault’s Experiments on Steam”, (127-203) Transactions of the Edinburgh Royal Society, xiv.; Annales de Chime, xxxv. 1852.
11. Clausius, Rudolf. (1850). "On the Motive Power of Heat, and on the Laws Which Can be Deduced from it for the Theory of Heat" (author footnote, pg 1). Poggendorff's Annalen der Physik, LXXIX, 368, 500.
12. Shachtman, Tom. (1999). Absolute Zero and the Quest for Absolute Cold (pgs. 94-95). Mariner Books.

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