Abstract
It is fortunate that the two memoirs Carnot submitted to the Academy of sciences in Paris in 1778 and 1780 have survived in its archives. They give access to the form and content of his thinking about mechanics and the science of machines when he was a young and hopeful officer 5 or 6 years out of engineering school. The present chapter traces the development of his thinking from these, its earliest recorded expressions, through to the publication, in (1803a), of his Principes fondamentaux de l’équilibre et du mouvement. The method is to compare these earlier and later versions to the Essai sur les machines en général, and to continue to an analysis of Sadi Carnot’s Réflexions sur la puissance motrice du feu of 1824 in order to bring out its filiation with his father’s work. The relevant, theoretical sections of the early two memoirs are reprinted by Charles Gillispie in his Lazare Carnot Savant (Gillispie 1971, Appendices B and C, pp 270–340). Readers may wish to refer points in the discussion, or indeed the discussion as a whole, to the original texts.
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Notes
- 1.
- 2.
Probably relying on memory while working at Cherbourg, he had in mind line 129 of de rerum natura , Book I, but spoiled the scansion by inverting the word order; he also displaced the gerundive from the end of line 131. The entire passage reads
Qua propter bene cum superis de rebus
habenda
nobis est ratio, solis lunaeque meatus
qua fiant ratione, et qua vi quaeque
gerantur
in terris, tum cum primis ratione sagaci
unde anima atque animi constet natura
videndum,
et quae res nobis vigilantibus obvia
mentis
terrificet morbo adfectis somnoque
sepultis,
cernere uti videamur eos audireque
coram,
morte obita quorum tellus amplectitur
ossa.
A translation of the words Carnot chose might read: “Let us look to an account of how all things come to pass and of the forces that govern them”.
- 3.
For a discussion of the contest centered upon the winning memoir, and for the importance of Coulomb’s work on friction, see Gillmor (1971), chap. IV. The judges were d’Alembert, Bézout, Bossut, Condorcet, and Trudaine de Montigny.
- 4.
Gillispie (1971), Appendix B, § 43, Corollary 13.
- 5.
Gillispie (1971), Appendix B, § 46, Corollary 16.
- 6.
It would be perfectly possible to see embedded in this Carnot’s principle of continuity, but there is no evidence that he then saw there.
- 7.
Gillispie (1971), Appendix C, § 100.
- 8.
See above Chapter 2, pp 20–22.
- 9.
See above Chapter 2, pp 25–28.
- 10.
See above Chapter 2, pp 19–23.
- 11.
See above Chapter 3, p 54.
- 12.
See above Chapter 2, p 30.
- 13.
«THÉORÈME FONDAMENTAL. Principe général de l’équilibre & du mouvement dans les machines . XXXIV» (Carnot 1786 , p 68).
- 14.
Carnot (1786), § XLI, pp 75–76.
- 15.
«Théorème 1 er. Principe général de l’équilibre dans les machines » (Gillispie 1971, Appendix C, § 133).
- 16.
«Théorème II. Principe général du mouvement dans les machines » (Gillispie 1971, Appendix C, § 140).
- 17.
«Corollaire II. Des machines qui se meuvent uniformément» (Gillispie 1971, Appendix C, § 143).
- 18.
«Corollaire I er. Du mouvement dans les machines a poids » (Gillispie 1971, Appendix C, § 142).
- 19.
«Scholie» (Gillispie 1971, Appendix C, § 148).
- 20.
«[…] le travail absolu ou la peine […]» (Gillispie 1971, Appendix C, § 153, footnote).
- 21.
Gillispie (1971), Appendix C.
- 22.
See, for example, the following works: L’entropie. Son rôle dans le développement historique de la thermodynamique by Brunold (1930, pp 37–38), Some factors in the early development of the concepts of power, work, and energy by Cardwell (1967, pp 209–224), Histoire de la mécanique by Dugas (1955, pp 324–331) and Lectures de mécanique. La mécanique enseignée par les auteurs originaux by Jouguet (1924, II, p 72).
- 23.
Please see above Chapter 2, p 19, ft 7.
- 24.
The geometric figures missing from the 1778 Ms. may be reconstituted from Figs. 2, 3, and 4 of PI. I of the Principes fondamentaux de l’équilibre et du mouvement , which fit the argument of the 1778 memoir.
- 25.
For the Eq., see Carnot (1803a), § 43, p 26.
- 26.
Carnot (1803a), § 64, p 41.
- 27.
«DÉFINITIONS» (Carnot 1803a, § 136, p 108).
- 28.
«Problème XX» (Carnot 1786, § XX, p 40; see also: Ivi, § X, p. 21).
- 29.
«THÉORÈME XI » (Carnot 1803a, § 168, p 139).
- 30.
For the Eq., see Carnot 1803a, § 169, p 143.
- 31.
Carnot (1803a), §175, pp 145-146.
- 32.
See above Chapter 2, p 30.
- 33.
One wonders whether the papers of the chevalier Patrick d’Arcy had been an important source of inspiration to Lazare Carnot , but this is the only place he mentions them (Carnot 1803a, § 195, p 174). The relevant memoirs are: Problème de dynamique (d’Arcy 1752, II, pp 344–356) with an addendum (Ivi, pp 356–361), Suite d’un mémoire de dynamique (Id., 1754, pp 107–108) and Théorèmes de dynamique (Id., 1763, pp 1–8).
- 34.
Carnot cited Coulomb ’s memoir on the employment of manpower, Résultat de plusieurs expériences destinées a déterminer la quantité d’action que les hommes peuvent fournir par leur travail journalier suivant les différentes manières dont ils emploient leurs forces (Coulomb 1799, II, pp 340–428). Coulomb first read this memoir to the Academy in 1778 . See Gillmor (1971), chap. II. Carnot cited further a memoir of Euler, de machinis in genere (Euler 1751, III, p 254).
- 35.
Carnot (1803a), § 293, pp 261–262.
- 36.
Recherche d’une formule propre à représenter la puissance motrice de la vapeur d’eau –the manuscript, Un manuscrit inédit de Sadi Carnot, was published by Gabbey and Herivel ( pp151–166). For a discussion of the question surrounding the date, see footnote 42 below.
- 37.
Hippolyte’s biography is contained in a reprinted edition of the Réflexions sur la puissance motrice du feu published in Paris in 1878 . References in the notes that follow are to the pagination of the facsimile of the first, 1824, edition published by Blanchard in 1953 (Carnot 1953).
- 38.
See above Chapter 1.
- 39.
Carnot (1824) , p 20.
- 40.
See above Chapter 2, pp 25–28.
- 41.
It is agreed that Sadi Carnot must have composed the manuscript of the Recherche d’une formule propre à représenter la puissance motrice de la vapeur d’eau at some time between November 1819 and March 1827. In publishing the text (Gabbey and Herivel ) Drs. Gabbey and Rerivel concluded that a date prior to 1824, when the Réflexions sur la puissance motrice du feu appeared, was more probable than a later one. Mr. James Challey suggests that 1823 is the most probable date of composition because of Sadi Carnot ’s use of the dyname as the unit of motive power , Dupin having coined the word in a report to the Academy in April of that year (Challey 1971, Dictionary of Scientific Biography, III, p 83, n. 3). For reasons indicated in the argument of this section, I agree. Dr. Robert Fox disagrees, however. He kindly provided for me the proofs in his article Watt’s expansive principle in the work of Sadi Carnot and Nicolas Clément (Fox 1970, 233–253). In that paper he explores the relations between Nicolas Clément (1779–1842) and Sadi Carnot very carefully. The main point is to establish the importance to Sadi Carnot’s work of contemporary power technology. This it does admirably. Dr. Fox argues further that the manuscript Recherche represents an attempt by Sadi Carnot to compute a formula for the motive power of steam that would be applicable in actual engines as the highly abstract and unrealistic reasoning of the Réflexions sur la puissance motrice du feu could not be, specifically because in the manuscript memoir Carnot computed the motive power that would be developed in the phase of adiabatic expansion between any two temperatures instead of restricting it to the unreal case of a span of 1°. Dr. Fox may well be right. I doubt it, or doubt at least that this is the whole explanation because it reverses the configuration both of his work and his father’s, which moved from the analysis of machine processes to theory rather than from theory to specific engineering application. Further, it seems more likely that the inclusion of the three–stage cycle applicable only to steam in the early passages of the Réflexions sur la puissance motrice du feu reflects rather the carry–over of an unperfected stage of his analysis into the final product, than it does that he should afterwards have reverted to this imperfect analysis in order to base an applicable calculation on it. There is a possibility that we are both right, and that the manuscript memoir, which does indeed have all the appearance of having been finished, represents the final development that Sadi Carnot , after publishing the Réflexions sur la puissance motrice du feu, then gave to the idea of a three–stage cycle with which he had begun his thinking. If so, it remains a problem that he did not publish it. Since almost all his manuscripts were burned after his death it is unlikely that the question will ever be decisively resolved.
- 42.
Carnot (1824) , pp 21–22.
- 43.
Carnot (1824) , pp 22–23.
- 44.
Carnot (1824), p 38.
- 45.
Carnot (1824), p 32.
- 46.
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Gillispie, C.C., Pisano, R. (2014). The Development of Carnot’s Mechanics. In: Lazare and Sadi Carnot. History of Mechanism and Machine Science, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8011-7_3
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