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Studies and Heritage of Réflexions sur la puissance motrice du feu

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Lazare and Sadi Carnot

Part of the book series: History of Mechanism and Machine Science ((HMMS,volume 19))

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Abstract

In order to describe a possible scientific and historical panorama of the role played by the physical foundations of Réflexions sur la puissance motrice du feu when it was first published in this section, we’ve selected scientific studies and historical studies regarding Sadi Carnot ’s theory. As we have presented in previous chapters, this theory was essentially based on three anomalies of the paradigm at the time: the novelty of the cycle both as a device of reasoning and an, ad absurdum proof in calculus and the use and doubts regarding caloric . Therefore, for our purposes, we focus on: the contemporary birth of the theory of heat and its developments (Fourier , Lamè ), the scientific studies on cycles (Hoyer ), and the developments of thermodynamics devoted to the physics and mathematics of the nineteenth century regarding the dynamical effects of heat based on Sadi Carnot and Clapeyron’s arguments (Reech ). Finally, we examine a thermodynamics textbook (Saint–Robert 1865, 1870c) used at the end of the nineteenth century which was fundamentally devoted to Lazare and Sadi’s typical scientific approach.

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Notes

  1. 1.

    The content of this chapter is based on Pisano (2001, 2005), Drago and Pisano (2008), Pisano and Capecchi (2009). (The discussion on Sadi Carnot Reech and Hoyer was also previously arranged by one of us in his lauream dissertation in Physics ).

  2. 2.

    See also next 1990 edition.

  3. 3.

    Grattan-Guinness (1969), p 230.

  4. 4.

    The prize was only conferred in 1812.

  5. 5.

    Lamé (1861a), p XII, line 21.

  6. 6.

    Fourier (1878), p 4, line 27. (Id., 1822, p vij, line 25). We listed the references of both the French edition (Fourier 1822) and the English edition (Fourier 1878).

  7. 7.

    Fourier (1878), p 4, line 35. (Id., 1822, p viij, line 12).

  8. 8.

    Fourier (1878), p 5, line 15. (Id., 1822, p ix, line 10). Author’s italics.

  9. 9.

    E.g.,: Denis Papin (1691), Thomas Savery (1698), Boulton & Watt company in Soho , near Birmingham (1776–1800), Richard Trevithick (1801) with the first steam engine called “Catch me who can ”; Stephenson (1813).

  10. 10.

    Singer ([1954–58] 1993), IV, pp 152–221, Dickinson (1939), chaps. 1 and 2, Tredgold (1838), II; Fox and Weisz (2009).

  11. 11.

    Fourier (1878), p 2, line 3. (Id., 1822, p ij, line 24).

  12. 12.

    Fourier (1878), p 2, line 16. (Id., 1822, p iij, line 14).

  13. 13.

    Fourier (1878), p 6, line 11. (Id., 1822, p xj, line 4).

  14. 14.

    Fourier (1878), p 41, line 3. (Id., 1822, p 39 line 23). Author’s italics.

  15. 15.

    Fourier (1878), p 42, line 34. (Id., 1822, p 42, line 11).

  16. 16.

    Fourier (1878), p 26, line 11. (Id., 1822, p 18, line 10).

  17. 17.

    \( ^{17} \)Fourier (1878), p 112, line 15 (Id., 1822, pp 134–135, line 19). Author’s italics.

  18. 18.

    David Keston , Joseph Fourier , Politician & Scientist, also available via: http://www.todayinsci.com/F/Fourier_JBJ/FourierPoliticianScientistBio.htm

  19. 19.

    “[…] most complex effects of all the natural forces, and thus has the thought of Newton been confirmed: quod tam paucis tam multa proestet geometria gloriatur. But whatever may be the range of mechanical theories, they do not apply to the effects of heat . These make up a special order of phenomena, which cannot be explained by the principles of motion and equilibrium.” (Fourier 1878, p 1–2, line 27, 1822, pp ij–iij, line 20). Author’s italics.

  20. 20.

    Lamé (1852), p V, line 11.

  21. 21.

    Lamé (1852), p VI, line 4.

  22. 22.

    Ibidem, line 24.

  23. 23.

    Lamé (1861b), p. V, line 1. Author’s italics.

  24. 24.

    Lamé (1861b), p VI, line 26.

  25. 25.

    Lamé (1861b), p 2, line 8.

  26. 26.

    Lamé (1861b), p. 16, line 8. Since it is a difficult original print, we changed some letters in the formula “(23)”. Nevertheless, the mathematical content does not change.

  27. 27.

    Generally speaking the analytical theory of heat is not interested in the intimate nature of heat.

  28. 28.

    Fourier (1878), p 22, line 17; Id., 1822, p 12 line 16. See also Fourier (1822), pp 4–6.

  29. 29.

    Ferdnand or Ferdinand or Frederick or Frédéric Reech, French marine engineer, entered the École du génie maritime in Brest after graduating from École polytechnique (1825). Upon the completion of his naval training, he was promoted to the rank of lieutenant in 1829. He soon devoted himself exclusively to teaching and research in geometry, mechanics, thermodynamics , and hydrodynamics . Reech was director of the École du génie maritime (1831–1870) and in 1854 was transferred back to Paris, where he devoted himself to teaching and also became a professor at Université Sorbonne, Paris. Reech published ten memoirs, ranging from a brochure supporting his unsuccessful candidacy for membership at the Académie des sciences : e.g., notes on mechanics, mathematics physics applied to mechanics and topics of applied thermodynamics. Most remember him for his contribution to the first formulation of the hydraulic–model law of gravitational similitude: the necessary proportionality between the velocity of a ship and the square root of its length (more generally known as Froude’s law of similarity). This law was included in his lectures as early as 1831, but it is first mentioned in his memoir from 1844 and then discussed in detail in his course notes from 1852. In 1870, Reech retired from active duty and returned to Lorient in Brittany , a fascinating region in the North West of France. He was also a member of the Association française pour l’avancement des sciences (1875–1883). At his request, he was buried in Soultz–sous–Forêts , close to the village of his birth. Truesdell included Reech in his summary of thermodynamic views (Truesdell and Bharatha 1977; see also Drago and Pisano 2008).

  30. 30.

    He rebuilt the definition of integral, which, in a global conception of differential calculus concerning the calculus of an area for a given function, we can consider is the first mathematical operation.

  31. 31.

    Reech (1853), p 357, line 14. (Translation is ours: RP; Author’s italic).

  32. 32.

    Reech explicitly stated four main hypotheses–premises for this reasoning on Sadi Carnot ’s theory.

  33. 33.

    Reech (1851), p 602. (Capital letters and italics from the original; the translation is ours: RP).

  34. 34.

    Reech (1852), p 21, line 23. (Capital letters and italics from the original; the translation is ours: RP).

  35. 35.

    We have kept Reech ’s original symbols. Consequently, the letter q indicates the quantity of heat , which is indicated by the letter Q in Sadi Carnot ’s work .

  36. 36.

    Sadi Carnot used a single machine to operate first in a direct manner and then in an inverse manner.

  37. 37.

    Carnot (1978), p 25, line 10.

  38. 38.

    The result was presented by Sadi Carnot in Notes sur les mathématiques, la physique et autres sujets (III.Folio 7v; see also Carnot 1878b, p 95, 1896, p 191).

  39. 39.

    As Hoyer also remarked , it should be noted that in Réflexions sur la puissance motrice du feu (Carnot 1978, p 46) Sadi Carnot cites Delaroche and Bérard’s experiments , which both showed that specific heat at constant pressure was equal to \( {c_p} = \Delta q = \int\limits_4^2 {dq = 0.267kcal} \); (m = 1 kg).

  40. 40.

    Hoyer (1976), p 223, line 22. Author’s italics.

  41. 41.

    Hoyer (1976), p 226, line 22. Italic style from the author.

  42. 42.

    In the Reference section of our book, we attempted to compile a list of Saint–Robert’s works. (Cfr.: Drago 1993b; Pisano 2005). Recently the first popular and scientific St Robert’s celebration (after those by Accademia di Torino in ’70s of the past century) was organized by the Comune di Castagnole delle Lanze (Piemonte, Italy) and Associazione Culturale Conte Paolo Ballada di Saint Robert (Ibidem). The event has celebrated both the man and scientific works. It has been patronaged by European Society for the History of Science and scientifically-historically supported by one of us (RP).

  43. 43.

    Saint–Robert (1869), IV, pp 151–170, 1870c, pp 431–450.

  44. 44.

    His physical mathematical approach to thermodynamics concerning the role played by physics and mathematics of the nineteenth century was studied by Drago (1993a, b) and one of us (Pisano 2005). We also remember Cerruti (1999, pp 95–178) for a work in which he dedicated enough space to Ballada even though his topic was not strictly related to Saint–Robert.

  45. 45.

    Marie François Sadi Carnot (1837–1894) became the fourth President of the Third French Republic . On June 24, 1894, Sante Geronimo Caserio (1873–1894), an Italian anarchist , fatally stabbed President Carnot after his public banquet, to avenge Auguste Vaillant (1861–1894) and Emile Henry (1872–1894). Thus, Caserio assassinated the president who died after midnight on 25 June. The Board of Pardons decided against all appeals for clemency on August 14. Caserio was executed by guillotine in Lyon at 5 am, August 16, 1894. President Carnot was honored with an elaborate funeral ceremony in the Panthéon , Paris.

  46. 46.

    Cfr.: Carnot (1986), pp 216–217.

  47. 47.

    Saint–Robert (1870c), pp 447–448, line 24.

  48. 48.

    Saint–Robert (1870c), p 449, line 7.

  49. 49.

    See Chapters 6 and 7.

  50. 50.

    The book was also reviewed in Les mondes Revue hebdomadaire des sciences et de leurs applications aux arts et l'industrie (Moigno 1865, VIII, pp 514–515). In the secondary literature, a book by Saint–Robert entitled Traité de thermodynamique seemed to have been circulated. Its existence is doubtful since any reference–frontispieces–editions seems to be lacking.

  51. 51.

    We avoid any possible contribution to the discussion regarding the steam engine, or rather motive power by heat et al. in society, since this is not the main subject of our research. Historical foundations on physics and mathematics in the theory are considered here.

  52. 52.

    We should note that Maxwell ’s (1831–1879) textbook was published in 1870, and accumulated many new editions.

  53. 53.

    Saint–Robert (1865), pp V–VI, line 1. Author’s italics. On Joule see: Joule (1844).

  54. 54.

    Saint–Robert (1865), p 1, line 1.

  55. 55.

    Author’s italics.

  56. 56.

    Saint–Robert (1865), p 1, line 6.

  57. 57.

    Saint–Robert (1870c), pp VI–VII, line 2. (Author’s Capital letters).

  58. 58.

    Let us note that this part of the theory is constructed pedagogically like that which appears today in polytechnic engineering institutes, usually known as technical physics.

  59. 59.

    [also available in .pdf via: http://www.brera.unimi.it/sisfa/atti/index.html]

  60. 60.

    [also available in .pdf via: http://www.brera.unimi.it/sisfa/atti/index.html]

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  1. Department of History, Princeton University, Princeton, New Jersey, USA

    Charles Coulston Gillispie

  2. SCité University of Lille 1, Lille, France

    Raffaele Pisano

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Gillispie, C.C., Pisano, R. (2014). Studies and Heritage of Réflexions sur la puissance motrice du feu . 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_10

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