God, waterwheels, and molecules: Saint-Venant's anticipation of energy conservation

Historical Studies in the Physical and Biological Sciences

Volumn 31, Issue 2, 2001, Pages 285-353

  Darrigol, Olivier ^a  

^a CNRS   (France)

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[No Author keywords available]

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CHRISTIA;

EID: 0035594059     PISSN: 08909997     EISSN: None     Source Type: Journal    
DOI: 10.1525/hsps.2001.31.2.285     Document Type: Review

References (378)

1. Cf. Peter Harman, Energy, force, and matter. The conceptual development of nineteenth century physics (Cambridge, 1982), 33-44; Thomas Kuhn, "Energy conservation as an example of simultaneous discovery" (1959), in The essential tension: Selected studies in scientific tradition and change (Chicago, 1977) 66-104, for conversions, engines, and Naturphilosophie; Timothy Lenoir, The strategy of life: Theology and mechanics in 19th-century biology (Dordrecht, 1982) for physiology; Peter Heimann, "Conversion of forces and the conservation of energy," Centaurus, 18 (1974), 147-161 for convertibility and theology; Donald Cardwell, James Joule: A biography (Manchester, 1989), for engines and kinetic conceptions of heat.
2. Cf. Peter Harman, Energy, force, and matter. The conceptual development of nineteenth century physics (Cambridge, 1982), 33-44; Thomas Kuhn, "Energy conservation as an example of simultaneous discovery" (1959), in The essential tension: Selected studies in scientific tradition and change (Chicago, 1977) 66-104, for conversions, engines, and Naturphilosophie; Timothy Lenoir, The strategy of life: Theology and mechanics in 19th-century biology (Dordrecht, 1982) for physiology; Peter Heimann, "Conversion of forces and the conservation of energy," Centaurus, 18 (1974), 147-161 for convertibility and theology; Donald Cardwell, James Joule: A biography (Manchester, 1989), for engines and kinetic conceptions of heat.
3. Cf. Peter Harman, Energy, force, and matter. The conceptual development of nineteenth century physics (Cambridge, 1982), 33-44; Thomas Kuhn, "Energy conservation as an example of simultaneous discovery" (1959), in The essential tension: Selected studies in scientific tradition and change (Chicago, 1977) 66-104, for conversions, engines, and Naturphilosophie; Timothy Lenoir, The strategy of life: Theology and mechanics in 19th-century biology (Dordrecht, 1982) for physiology; Peter Heimann, "Conversion of forces and the conservation of energy," Centaurus, 18 (1974), 147-161 for convertibility and theology; Donald Cardwell, James Joule: A biography (Manchester, 1989), for engines and kinetic conceptions of heat.
4. Cf. Peter Harman, Energy, force, and matter. The conceptual development of nineteenth century physics (Cambridge, 1982), 33-44; Thomas Kuhn, "Energy conservation as an example of simultaneous discovery" (1959), in The essential tension: Selected studies in scientific tradition and change (Chicago, 1977) 66-104, for conversions, engines, and Naturphilosophie; Timothy Lenoir, The strategy of life: Theology and mechanics in 19th-century biology (Dordrecht, 1982) for physiology; Peter Heimann, "Conversion of forces and the conservation of energy," Centaurus, 18 (1974), 147-161 for convertibility and theology; Donald Cardwell, James Joule: A biography (Manchester, 1989), for engines and kinetic conceptions of heat.
5. Cf. Peter Harman, Energy, force, and matter. The conceptual development of nineteenth century physics (Cambridge, 1982), 33-44; Thomas Kuhn, "Energy conservation as an example of simultaneous discovery" (1959), in The essential tension: Selected studies in scientific tradition and change (Chicago, 1977) 66-104, for conversions, engines, and Naturphilosophie; Timothy Lenoir, The strategy of life: Theology and mechanics in 19th-century biology (Dordrecht, 1982) for physiology; Peter Heimann, "Conversion of forces and the conservation of energy," Centaurus, 18 (1974), 147-161 for convertibility and theology; Donald Cardwell, James Joule: A biography (Manchester, 1989), for engines and kinetic conceptions of heat.
6. Kuhn (ref. 1); On the construction and the diffusion of the new doctrine, cf. Crosbie Smith, The science of energy: A cultural history of energy physics in Victorian Britain (London, 1998); Ernst Mach, Die Prinzipien der Wärmelehre (Leipzig, 1896), 317-318, 321, also Die Geschichte und die Wurzel des Satzes der Erhaltung der Arbeit (Prague, 1872); Max Planck, Das Prinzip der Erhaltung der Energie (Leipzig, 1888), 5th edn. (1924), viii, 1, 154-156.
7. Kuhn (ref. 1); On the construction and the diffusion of the new doctrine, cf. Crosbie Smith, The science of energy: A cultural history of energy physics in Victorian Britain (London, 1998); Ernst Mach, Die Prinzipien der Wärmelehre (Leipzig, 1896), 317-318, 321, also Die Geschichte und die Wurzel des Satzes der Erhaltung der Arbeit (Prague, 1872); Max Planck, Das Prinzip der Erhaltung der Energie (Leipzig, 1888), 5th edn. (1924), viii, 1, 154-156.
8. Kuhn (ref. 1); On the construction and the diffusion of the new doctrine, cf. Crosbie Smith, The science of energy: A cultural history of energy physics in Victorian Britain (London, 1998); Ernst Mach, Die Prinzipien der Wärmelehre (Leipzig, 1896), 317-318, 321, also Die Geschichte und die Wurzel des Satzes der Erhaltung der Arbeit (Prague, 1872); Max Planck, Das Prinzip der Erhaltung der Energie (Leipzig, 1888), 5th edn. (1924), viii, 1, 154-156.
9. Kuhn (ref. 1); On the construction and the diffusion of the new doctrine, cf. Crosbie Smith, The science of energy: A cultural history of energy physics in Victorian Britain (London, 1998); Ernst Mach, Die Prinzipien der Wärmelehre (Leipzig, 1896), 317-318, 321, also Die Geschichte und die Wurzel des Satzes der Erhaltung der Arbeit (Prague, 1872); Max Planck, Das Prinzip der Erhaltung der Energie (Leipzig, 1888), 5th edn. (1924), viii, 1, 154-156.
10. Adhémar Barré de Saint-Venant, "Sur les théorèmes de la mécanique générale," Archives de l'Académie des Sciences, Pochette de séance, 14 Apr 1834.
11. Wilson Scott, The conflict between atomism and conservation theory, 1644 to 1860 (London, 1970), described the "hard-body school" of French mechanics, and its challenge by French engineers. This book contains much that is relevant to this paper. Scott mainly wanted to explain why hard atoms lived into the second half of the 19th century. He did not directly discuss the relation between the emergence of co iservative mechanics and early energetic reasoning.
12. This aspect has been treated by Ivor Grattan-Guinness, "Work of the workers: Advances in engineering mechanics and instruction in France, 1800-1830," Annals of science, 41 (1984), 1-33; by Jean-Pierre Séris, Machine et communication: Du théâtre des machines à la mécanique industrielle (Paris, 1987); and by François Vatin, Le travail. Economie et physique, 1780-1830 (Paris, 1993), who overemphasizes economic connections.
13. This aspect has been treated by Ivor Grattan-Guinness, "Work of the workers: Advances in engineering mechanics and instruction in France, 1800-1830," Annals of science, 41 (1984), 1-33; by Jean-Pierre Séris, Machine et communication: Du théâtre des machines à la mécanique industrielle (Paris, 1987); and by François Vatin, Le travail. Economie et physique, 1780-1830 (Paris, 1993), who overemphasizes economic connections.
14. This aspect has been treated by Ivor Grattan-Guinness, "Work of the workers: Advances in engineering mechanics and instruction in France, 1800-1830," Annals of science, 41 (1984), 1-33; by Jean-Pierre Séris, Machine et communication: Du théâtre des machines à la mécanique industrielle (Paris, 1987); and by François Vatin, Le travail. Economie et physique, 1780-1830 (Paris, 1993), who overemphasizes economic connections.
15. Smith (ref. 2), introduction.
16. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
17. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
18. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
19. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
20. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
21. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
22. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
23. Gottfried Wilhelm Leibniz, ̂Essay de dynamique,̂ 1692, in Pierre Costabel, Leibniz et la dynamique (Paris, 1960), Engl. transl. (Paris, 1973), 108-131, on 112 (effet entier = cause totale); "Specimen dynamicum pro admirandis naturae legibus circa corporum vires et mutuas actiones detegendis et ad suas causas revocandis," Acta eruditorum (1695), in Mathematische Schriften, ed. Carl Immanuel Gerhardt, in Leibniz, Werke, 6 (Halle, 1860), 234-245, on 235 (God); "Essay de dynamique sur les loix du mouvement, ou il est montré, qu'il ne se conserve pas la même quantité de mouvement, mais la même force absolue, ou bien la même quantité de l'action motrice," 1698, in ibid., 215-230, on 220 (quote). Cf. Costabel, La signification d'un débat sur trente ans (1728-1758): La question des forces vives (Paris, 1983); Erwin Hiebert, Historical roots of the energy principle (Madison, 1962), 77-82; Séris (ref. 5), 235-264.
24. Leibniz, "Essay" (ref. 7) (1692), Proposition (4). Suppose that a body of mass 2 acquires the velocity 1 after falling from a height of 1. It can be replaced by a body of mass 1 with velocity 2 without violating the Cartesian conservation law. The velocity of this new body can raise it to height 4. From this height, it can be made to act on a lever to raise the former body to the height 2. The net result of the whole process is the raising of a body without any effort, which implies the possibility of perpetual motion.
25. Leibniz, "Essay" (ref. 7) (1698), 217.
26. 2 not conserved). In order to convert velocity into vertical ascension, Huygens used inclined reflecting planes (the weights must be stopped at the top of their rise). Leibniz's perpetual-motion argument is similar to the one by which he showed that the conservation of mv implied the possibility of perpetual motion (cf. note 8). On Huygens' pendulum studies, cf. Christiane Vilain, "La question du centre d'oscillation de 1660 à 1690," Physis, 37 (2000), 21-52.
27. 2 not conserved). In order to convert velocity into vertical ascension, Huygens used inclined reflecting planes (the weights must be stopped at the top of their rise). Leibniz's perpetual-motion argument is similar to the one by which he showed that the conservation of mv implied the possibility of perpetual motion (cf. note 8). On Huygens' pendulum studies, cf. Christiane Vilain, "La question du centre d'oscillation de 1660 à 1690," Physis, 37 (2000), 21-52.
28. 2 not conserved). In order to convert velocity into vertical ascension, Huygens used inclined reflecting planes (the weights must be stopped at the top of their rise). Leibniz's perpetual-motion argument is similar to the one by which he showed that the conservation of mv implied the possibility of perpetual motion (cf. note 8). On Huygens' pendulum studies, cf. Christiane Vilain, "La question du centre d'oscillation de 1660 à 1690," Physis, 37 (2000), 21-52.
29. 2 not conserved). In order to convert velocity into vertical ascension, Huygens used inclined reflecting planes (the weights must be stopped at the top of their rise). Leibniz's perpetual-motion argument is similar to the one by which he showed that the conservation of mv implied the possibility of perpetual motion (cf. note 8). On Huygens' pendulum studies, cf. Christiane Vilain, "La question du centre d'oscillation de 1660 à 1690," Physis, 37 (2000), 21-52.
30. Leibniz, "Essay" (ref. 7) (1692), 94; cf. Arthur Erich Haas, Die Entwicklungsgeschichte des Satzes von der Erhaltung der Kraft (Vienna, 1909), 22.
31. Leibniz, "Essay" (ref. 7) (1692), 94; cf. Arthur Erich Haas, Die Entwicklungsgeschichte des Satzes von der Erhaltung der Kraft (Vienna, 1909), 22.
32. Leibniz, "Essay" (ref. 7) (1698), 229; Isaac Newton, Opticks (London, 1704), reprint (1931) of 4th edn. (1730), query 31, p. 398 (collidons), 400 (quote). Cf. Wilson Scott, "The significance of 'hard bodies' in the history of scientific thought," Isis, 50 (1959), 199-210.
33. Leibniz, "Essay" (ref. 7) (1698), 229; Isaac Newton, Opticks (London, 1704), reprint (1931) of 4th edn. (1730), query 31, p. 398 (collidons), 400 (quote). Cf. Wilson Scott, "The significance of 'hard bodies' in the history of scientific thought," Isis, 50 (1959), 199-210.
34. Leibniz, "Essay" (ref. 7) (1698), 229; Isaac Newton, Opticks (London, 1704), reprint (1931) of 4th edn. (1730), query 31, p. 398 (collidons), 400 (quote). Cf. Wilson Scott, "The significance of 'hard bodies' in the history of scientific thought," Isis, 50 (1959), 199-210.
35. Leibniz, "Essay" (ref. 7) (1698), 219. Leibriz was aware of Huygens' study of collisions, in which the conservation of live force was expressed (though without proof and in different terms): cf. Costabel, Signification (ref. 7), 20.
36. Leibniz, "Essay" (ref. 7) (1698), 219. Leibriz was aware of Huygens' study of collisions, in which the conservation of live force was expressed (though without proof and in different terms): cf. Costabel, Signification (ref. 7), 20.
37. Leibniz, "Essay" (ref. 7) (1692), 114, and "Essay" (1698), 220, 230-231; "Observatio mechanica de resistantia frictionis," in Ernst Gerland, ed., Leibnizens nachgelassene Schriften physikalischen, mechanischen und technischen Inhalts (Leipzig, 1906), 115-118.
38. Leibniz, "Essay" (ref. 7) (1692), 114, and "Essay" (1698), 220, 230-231; "Observatio mechanica de resistantia frictionis," in Ernst Gerland, ed., Leibnizens nachgelassene Schriften physikalischen, mechanischen und technischen Inhalts (Leipzig, 1906), 115-118.
39. Leibniz, "Essay" (ref. 7) (1692), 114, and "Essay" (1698), 220, 230-231; "Observatio mechanica de resistantia frictionis," in Ernst Gerland, ed., Leibnizens nachgelassene Schriften physikalischen, mechanischen und technischen Inhalts (Leipzig, 1906), 115-118.
40. Jean Bernoulli, "Discours sur les lois de communication du mouvement" (1724), in Bernoulli, Opera ommia, vol. 3 (Lausanne, 1742), 7-107, on 38 (cause = effect), 8-10 (no hard bodies); and "De vera notione virium virarum earumque usu in dynamicis" (1735), ibid., 239-260, on 239-240 (facultas agendi), 213 (inelastic collisions). Cf. Scott (ref. 4), 22-23.
41. Jean Bernoulli, "Discours sur les lois de communication du mouvement" (1724), in Bernoulli, Opera ommia, vol. 3 (Lausanne, 1742), 7-107, on 38 (cause = effect), 8-10 (no hard bodies); and "De vera notione virium virarum earumque usu in dynamicis" (1735), ibid., 239-260, on 239-240 (facultas agendi), 213 (inelastic collisions). Cf. Scott (ref. 4), 22-23.
42. Jean Bernoulli, "Discours sur les lois de communication du mouvement" (1724), in Bernoulli, Opera ommia, vol. 3 (Lausanne, 1742), 7-107, on 38 (cause = effect), 8-10 (no hard bodies); and "De vera notione virium virarum earumque usu in dynamicis" (1735), ibid., 239-260, on 239-240 (facultas agendi), 213 (inelastic collisions). Cf. Scott (ref. 4), 22-23.
43. Jean Bernoulli, "Discours" (ref. 15), 84, 89-93; Daniel Bernoulli, Hydrodynamica, sive de viribus et motibus fluidorum commentarii (Strasbourg, 1738), 200-203. Cf. Clifford Truesdell, "Early kinetic theory of gases," in Truesdell, Essays in the history of mechanics (Berlin, 1968), 272-304, on 276-281.
44. Jean Bernoulli, "Discours" (ref. 15), 84, 89-93; Daniel Bernoulli, Hydrodynamica, sive de viribus et motibus fluidorum commentarii (Strasbourg, 1738), 200-203. Cf. Clifford Truesdell, "Early kinetic theory of gases," in Truesdell, Essays in the history of mechanics (Berlin, 1968), 272-304, on 276-281.
45. Jean Bernoulli, "Discours" (ref. 15), 84, 89-93; Daniel Bernoulli, Hydrodynamica, sive de viribus et motibus fluidorum commentarii (Strasbourg, 1738), 200-203. Cf. Clifford Truesdell, "Early kinetic theory of gases," in Truesdell, Essays in the history of mechanics (Berlin, 1968), 272-304, on 276-281.
46. Daniel Bernoulli (ref. 16), 258-260. Cf. René Dugas, Histoire de la mécanique (Neuchâtel, 1950), 275-278; Clifford Truesdell, "Rational fluid mechanics, 1687-1765," in Leonhard Euler, Opera omnia, series 2, vol. 12 (Lausanne, 1954), i-cxxv, on xxiii-xxxi. Bernoulli did not have a concept of internal pressure and therefore could not write "Bernoulli's equation." He reasoned in terms of the impulsive increase of live force that the fluid would experience if a portion of the wall were suddenly removed.
47. Daniel Bernoulli (ref. 16), 258-260. Cf. René Dugas, Histoire de la mécanique (Neuchâtel, 1950), 275-278; Clifford Truesdell, "Rational fluid mechanics, 1687-1765," in Leonhard Euler, Opera omnia, series 2, vol. 12 (Lausanne, 1954), i-cxxv, on xxiii-xxxi. Bernoulli did not have a concept of internal pressure and therefore could not write "Bernoulli's equation." He reasoned in terms of the impulsive increase of live force that the fluid would experience if a portion of the wall were suddenly removed.
48. Daniel Bernoulli (ref. 16), 258-260. Cf. René Dugas, Histoire de la mécanique (Neuchâtel, 1950), 275-278; Clifford Truesdell, "Rational fluid mechanics, 1687-1765," in Leonhard Euler, Opera omnia, series 2, vol. 12 (Lausanne, 1954), i-cxxv, on xxiii-xxxi. Bernoulli did not have a concept of internal pressure and therefore could not write "Bernoulli's equation." He reasoned in terms of the impulsive increase of live force that the fluid would experience if a portion of the wall were suddenly removed.
49. Bernoulli (ref. 16), ii, 30.
50. Ibid., 12, 124.
51. Bernoulli (ref. 16), 163-165: cf. Séris (ref. 5), 299-318; See also D. Bernoulli's "Recherches sur la manière la plus avantageuse de suppléer à l'action du vent sur les grands vaisseaux," in Académie des sciences, Paris, Recueil des pièces qui ont rapporté les prix, 7 (1768), 1-99, discussed in Grattan-Guinness (ref. 5), 5.
52. Bernoulli (ref. 16), 163-165: cf. Séris (ref. 5), 299-318; See also D. Bernoulli's "Recherches sur la manière la plus avantageuse de suppléer à l'action du vent sur les grands vaisseaux," in Académie des sciences, Paris, Recueil des pièces qui ont rapporté les prix, 7 (1768), 1-99, discussed in Grattan-Guinness (ref. 5), 5.
53. Bernoulli (ref. 16), 163-165: cf. Séris (ref. 5), 299-318; See also D. Bernoulli's "Recherches sur la manière la plus avantageuse de suppléer à l'action du vent sur les grands vaisseaux," in Académie des sciences, Paris, Recueil des pièces qui ont rapporté les prix, 7 (1768), 1-99, discussed in Grattan-Guinness (ref. 5), 5.
54. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
55. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
56. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
57. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
58. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
59. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
60. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
61. Daniel Bernoulli (ref. 16), 9.3.33-9.3.37; Antoine Parent, "Sur la plus grande perfection possible des machines," MAS (1704), 323-338. Cf. Donald Cardwell, "Some factors in the early development of the concepts of power, work, and energy," British journal for the history of science, 3 (1967), 209-224, on 211-212, and Turning points in western technology: A study of technology, science, and history (New York, 1972), 62-64; Josiah Morton Briggs, "Antoine Parent," DSB, vol. 10 (1974), 319-320; Séris (ref. 5), 285-299; Bruno Belhoste and Jean-François Belhoste, "La théorie des machines et les roues hydrauliques," in B. Belhoste et al., Le moteur hydraulique en France au XIXe siècle: Concepteurs, inventeurs et constructeurs (Paris, 1990), 1-32; Terry Reynolds, Stronger than a hundred men: A history of the vertical water wheel (Baltimore, 1983).
62. Cf. Belhoste (ref. 21). Parent's expression of the "natural effect" probably resulted from Mariotte's expression of the impact force of a fluid vein by the weight of a fluid cylinder with the vein's section and a length equal to the height equivalent to the fluid velocity. With this estimate which neglected the vena contracta in Mariotte's efflux-impact experiments, the "natural effect" equals the influx of half live force. Daniel Bernoulli (ref. 16), 9.3.31, noted the erroneousness of the "common view" (Parent's), but nevertheless reproduced it.
63. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
64. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
65. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
66. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
67. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
68. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
69. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
70. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1974), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
71. John Smeaton, Experimental enquiry concerning the natural powers of wind and water to turn mills and other machines depending on a circular motion, TRS, also in Smeaton, reprint of TRS papers (London, 1794). Cf. Pierre Simon Girard's introduction to the French translation (Paris, 1810); Paul N. Wilson, "The waterwheels of John Smeaton," The Newcomen Society, Transactions, 30 (1955), 25-49; Harold Dorn, "John Smeaton," DSB, vol. 12 (1975), 461-463; Cardwell (ref. 21). "Some factors," 213; Turning point, 69-82; Trevor Turner, "John Smeaton, FRS (1724-1792)," Endeavour, 118 (1914), 29-33; Norman Smith, "Scientific work," in John Smeaton, FRS, ed. A.W. Skempton (London, 1986), 35-57; Séris (ref. 5), 318-331.
72. Smeaton (ref. 23), 6-7.
73. Ibid., 26, 30.
74. Smeaton, "Experimental examination of the quantity of power necessary to be employed in giving different degrees of velocity to heavy bodies from a state of rest," TRS (1776), also in Smeaton, reprints (ref. 23), 71-77. Cf. Silvio Bergia and Paola Fantazzini, "La descrizione dei fenomeni meccanici in termini energetici nell'opera di John Smeaton," Giornale di fisica, 22 (1981), 295-310, 23 (1982), 59-73. Smeaton never used the words "live force" or vis viva, probably because he could not afford to contradict the Newtonian definition of force. His charge against waterwheel theorists does not appear to be justified.
75. Smeaton, "Experimental examination of the quantity of power necessary to be employed in giving different degrees of velocity to heavy bodies from a state of rest," TRS (1776), also in Smeaton, reprints (ref. 23), 71-77. Cf. Silvio Bergia and Paola Fantazzini, "La descrizione dei fenomeni meccanici in termini energetici nell'opera di John Smeaton," Giornale di fisica, 22 (1981), 295-310, 23 (1982), 59-73. Smeaton never used the words "live force" or vis viva, probably because he could not afford to contradict the Newtonian definition of force. His charge against waterwheel theorists does not appear to be justified.
76. Smeaton, "Experimental examination of the quantity of power necessary to be employed in giving different degrees of velocity to heavy bodies from a state of rest," TRS (1776), also in Smeaton, reprints (ref. 23), 71-77. Cf. Silvio Bergia and Paola Fantazzini, "La descrizione dei fenomeni meccanici in termini energetici nell'opera di John Smeaton," Giornale di fisica, 22 (1981), 295-310, 23 (1982), 59-73. Smeaton never used the words "live force" or vis viva, probably because he could not afford to contradict the Newtonian definition of force. His charge against waterwheel theorists does not appear to be justified.
77. Smeaton, "New fundamental experiments upon collisions of bodies," TRS (1782), also in Smeaton, reprints (ref. 23), 102-109.
78. Ibid., 109.
79. Jean le Rond d'Alembert, Traité de dynamique (Paris, 1743), 2nd edn. (1758), xvi-xvii. Cf. Dugas (ref. 17), 236-239; Thomas L. Hankins, "Eighteenth-century attempts to resolve the vis viva controversy," Isis, 56 (1965), 281-297, on 283-284, and Hankins, "Introduction," in d'Alembert, Traité (New York, 1968), ix-xxxvi; Craig Fraser, "d'Alembert's principle: The original formulation and application in Jean d'Alembert's 'Traité de dynamique' (1743)," Centaurus, 28 (1985), 31-61, 145-159.
80. Jean le Rond d'Alembert, Traité de dynamique (Paris, 1743), 2nd edn. (1758), xvi-xvii. Cf. Dugas (ref. 17), 236-239; Thomas L. Hankins, "Eighteenth-century attempts to resolve the vis viva controversy," Isis, 56 (1965), 281-297, on 283-284, and Hankins, "Introduction," in d'Alembert, Traité (New York, 1968), ix-xxxvi; Craig Fraser, "d'Alembert's principle: The original formulation and application in Jean d'Alembert's 'Traité de dynamique' (1743)," Centaurus, 28 (1985), 31-61, 145-159.
81. Jean le Rond d'Alembert, Traité de dynamique (Paris, 1743), 2nd edn. (1758), xvi-xvii. Cf. Dugas (ref. 17), 236-239; Thomas L. Hankins, "Eighteenth-century attempts to resolve the vis viva controversy," Isis, 56 (1965), 281-297, on 283-284, and Hankins, "Introduction," in d'Alembert, Traité (New York, 1968), ix-xxxvi; Craig Fraser, "d'Alembert's principle: The original formulation and application in Jean d'Alembert's 'Traité de dynamique' (1743)," Centaurus, 28 (1985), 31-61, 145-159.
82. Jean le Rond d'Alembert, Traité de dynamique (Paris, 1743), 2nd edn. (1758), xvi-xvii. Cf. Dugas (ref. 17), 236-239; Thomas L. Hankins, "Eighteenth-century attempts to resolve the vis viva controversy," Isis, 56 (1965), 281-297, on 283-284, and Hankins, "Introduction," in d'Alembert, Traité (New York, 1968), ix-xxxvi; Craig Fraser, "d'Alembert's principle: The original formulation and application in Jean d'Alembert's 'Traité de dynamique' (1743)," Centaurus, 28 (1985), 31-61, 145-159.
83. Jean le Rond d'Alembert, Traité de dynamique (Paris, 1743), 2nd edn. (1758), xvi-xvii. Cf. Dugas (ref. 17), 236-239; Thomas L. Hankins, "Eighteenth-century attempts to resolve the vis viva controversy," Isis, 56 (1965), 281-297, on 283-284, and Hankins, "Introduction," in d'Alembert, Traité (New York, 1968), ix-xxxvi; Craig Fraser, "d'Alembert's principle: The original formulation and application in Jean d'Alembert's 'Traité de dynamique' (1743)," Centaurus, 28 (1985), 31-61, 145-159.
84. D'Alembert (ref. 29), 3-4.
85. Ibid., 44. On d'Alembert's concept of matter, cf. Scott (ref. 4), 48-49.
86. Ibid., 44. On d'Alembert's concept of matter, cf. Scott (ref. 4), 48-49.
87. Ibid., 58. The definition of mass is only implicit in d'Alembert's text.
88. Ibid., 60-70. The expression, "principle of virtual velocities," and the credit to Jean Bernoulli are owing to Lagrange. In its modern expression, this principle requires the virtual work of all external forces acting on a connected system (of rigid bodies and inextensible threads) in equilibrium to vanish for any infinitesimal change of the configuration of the system.
89. Ibid., 72. Cf. Carnot's notion of "geometrical motion," discussed below.
90. Ibid., 252.
91. Joseph Louis de Lagrange, Méchanique analitique (Paris, 1788), 195, 223-226. The notation is modern.
92. Ibid., 167; Lagrange, Mécanique analitique, 2nd edn. (Paris, 1811), 309-310. Haas' (ref. 11), 70-71, showed that for Lagrange the conservation of vis viva was not completely general. Dugas (ref. 17), 330, erred on this point.
93. Ibid., 167; Lagrange, Mécanique analitique, 2nd edn. (Paris, 1811), 309-310. Haas' (ref. 11), 70-71, showed that for Lagrange the conservation of vis viva was not completely general. Dugas (ref. 17), 330, erred on this point.
94. Ibid., 167; Lagrange, Mécanique analitique, 2nd edn. (Paris, 1811), 309-310. Haas' (ref. 11), 70-71, showed that for Lagrange the conservation of vis viva was not completely general. Dugas (ref. 17), 330, erred on this point.
95. Ibid., 167; Lagrange, Mécanique analitique, 2nd edn. (Paris, 1811), 309-310. Haas' (ref. 11), 70-71, showed that for Lagrange the conservation of vis viva was not completely general. Dugas (ref. 17), 330, erred on this point.
96. Lagrange (ref. 36), 207. Daniel Bernouilli had already obtained the particular case of Lagrange's theorem in which the mass points of the system interact through gravitational forces only: "Remarque sur le principe de la conservation des forces vives pris dans un sens général," Académie Royale des Sciences, Berlin, Histoire, 1748, 356-366.
97. Lagrange (ref. 36), 207. Daniel Bernouilli had already obtained the particular case of Lagrange's theorem in which the mass points of the system interact through gravitational forces only: "Remarque sur le principe de la conservation des forces vives pris dans un sens général," Académie Royale des Sciences, Berlin, Histoire, 1748, 356-366.
98. Pierre Simon de Laplace, Traité de mécanique céleste, vol. 1 (Paris, 1799), 36, 52; Siméon Denis Poisson, Traité de mécanique (Paris, 1811), 209-210, 213.
99. Pierre Simon de Laplace, Traité de mécanique céleste, vol. 1 (Paris, 1799), 36, 52; Siméon Denis Poisson, Traité de mécanique (Paris, 1811), 209-210, 213.
100. Charles de Borda, "Sur l'écoulement des fluides par les orifices des vases," MAS (1766), 579-607. Cf. Jean Mascart, La vie et les travaux du chevalier Jean-Charles de Borda (1733-1799) (Lyon, 1919), 83-98, 100, 119; Dugas (ref. 17), 292-295.
101. Charles de Borda, "Sur l'écoulement des fluides par les orifices des vases," MAS (1766), 579-607. Cf. Jean Mascart, La vie et les travaux du chevalier Jean-Charles de Borda (1733-1799) (Lyon, 1919), 83-98, 100, 119; Dugas (ref. 17), 292-295.
102. Charles de Borda, "Sur l'écoulement des fluides par les orifices des vases," MAS (1766), 579-607. Cf. Jean Mascart, La vie et les travaux du chevalier Jean-Charles de Borda (1733-1799) (Lyon, 1919), 83-98, 100, 119; Dugas (ref. 17), 292-295.
103. Borda (ref. 40), 590. Cf. Scott (ref. 4), 114-118.
104. Borda (ref. 40), 590. Cf. Scott (ref. 4), 114-118.
105. Borda (ref. 40), 591.
106. Charles de Borda, "Expériences sur la résistance des fluides," MAS, 1767, 495-503, and ref. 40, 605 (d'Alembert's paradox). Cf. Dugas (ref. 17), 298-300.
107. Charles de Borda, "Expériences sur la résistance des fluides," MAS, 1767, 495-503, and ref. 40, 605 (d'Alembert's paradox). Cf. Dugas (ref. 17), 298-300.
108. Charles de Borda, "Mémoire sur les roues hydrauliques," MAS (1767), 270-287, on 273. Borda showed that the maximum weight raised by the wheel to a given height was only half of the weight of the water whose descent from the same height set the wheel into motion. Cf. Belhoste (ref. 21) and Séris (ref. 5), 331-341.
109. Charles de Borda, "Mémoire sur les roues hydrauliques," MAS (1767), 270-287, on 273. Borda showed that the maximum weight raised by the wheel to a given height was only half of the weight of the water whose descent from the same height set the wheel into motion. Cf. Belhoste (ref. 21) and Séris (ref. 5), 331-341.
110. Borda (ref. 44), 274.
111. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
112. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
113. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
114. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
115. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
116. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
117. Lazare Carnot, Essai sur les machines en général (Paris, 1783). Cf. Charles Coulston Gillispie and A.P. Youschkewitch, Lazare Carnot savant (Princeton, 1971), chapt. 3; Dugas (ref. 17), 309-317; Scott (ref. 4), 91 -101; Patrice Bailhache, "Lazare Carnot entre d'Alembert et Lagrange: Originalité de la mécanique," in Jean Paul Charnay, ed., Lazare Carnot ou le savant citoyen (Paris, 1990), 544-555; Antonino Drago, "Le lien entre mathématique et physique dans la mécanique de Lazare Carnot," ibid., 501-515; Séris (ref. 5), chapt. 6; Craig Fraiser, The approach of Jean d'Alembert and Lazare Carnot to the theory of a constrained dynamical system (PhD diss., University of Toronto, 1981), pt. 2.
118. Lazare Carnot, Principes fondamentaux de l'équilibre et du mouvement (Paris, 1803), xi, 1-2, 49. This is a reworked version of the essay of 1783 (ref. 46).
119. Ibid., 118, 127.
120. Ibid., 108, 127.
121. Ibid., 108, 177, theorems XI-XVI.
122. Ibid., theorems XVI, XII. In the last statement, the geometrical character of the motion excludes variations of an internal potential energy.
123. Ibid., 245-246, 37, 246.
124. Ibid., 38 (moment of activity), 231 (salaries), 181-182 (theorem). In his analytical mechanics, Lagrange gave the infinitesimal version of this theorem. But he did so only in symbols, having neither name nor physical interpretation for the moment of activity.
125. Ibid., 255-262, 257 (quote). A few years earlier, the French Academy of Sciences, Histoires, 1775, 61-65, had decided no longer to examine suggestions for perpetual motion, considering that even in the total absence of friction "a motive force could only produce an effect equal to its cause."
126. Ibid., 255-262, 257 (quote). A few years earlier, the French Academy of Sciences, Histoires, 1775, 61-65, had decided no longer to examine suggestions for perpetual motion, considering that even in the total absence of friction "a motive force could only produce an effect equal to its cause."
127. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
128. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
129. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
130. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
131. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
132. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
133. Cf. Gillispie (ref. 46). Coulomb's memoirs are "Théorie des machines simples en ayant égart au frottement et à la raideur des cordages," Académie des Sciences, Mémoires présentés par divers savants étrangers, 10 (1781), 161-332; "Résultats de plusieurs expériences destinées à déterminer la quantité d'action que les hommes peuvent fournir par leur travail journalier, suivant les différentes manières dont ils employent leurs forces," Institut National des Sciences et Arts, Sciences mathématiques et physiques, Mémoires, 2 (1799), 380-428. The first is discussed in Dugas (ref. 17), 306; the second in Grattan-Guinness (ref. 5), 8, and Vatin (ref. 5), 70-92; both in Charles Stewart Gillmor, Coulomb and the evolution of physics and engineering in eighteenth-century France (Princeton, 1971), 41, 77-79, 129-136. See also Charles Coulomb, "Observations théoriques et expérimentales sur l'effet des moulins à vent, et sur la figure de leurs ailes," MAS (1781), 65-81, par. 20: "L'effet d'une machine dans laquelle il n'y a ni force ni frottement, est toujours proportionnel à la quantité de force vive dépensée par l'agent qui a produit cet effet."
134. Cf. Bruno Belhoste, "Un modèle à l'épreuve. L'Ecole Polytechnique de 1794 au second Empire," in Bruno Belhoste, Amy Dahan, and Antoine Picon, La formation polytechnicienne, 1794-1994 (Paris, 1994), 9-30.
135. Jean Hachette, Traité élémentaire des machines (Paris, 1811), 2nd. edn (1819), x. Cf. Lorraine Daston, "The physicalist tradition in early nineteenth century French geometry," Studies in history and philosophy of science, 17 (1986), 269-295; Konstantinos Chatzis, "Mécanique rationnelle et mécanique des machines," in Belhoste et al. (ref. 56), 95-108, on 96-97; Séris (ref. 5), 377-407.
136. Jean Hachette, Traité élémentaire des machines (Paris, 1811), 2nd. edn (1819), x. Cf. Lorraine Daston, "The physicalist tradition in early nineteenth century French geometry," Studies in history and philosophy of science, 17 (1986), 269-295; Konstantinos Chatzis, "Mécanique rationnelle et mécanique des machines," in Belhoste et al. (ref. 56), 95-108, on 96-97; Séris (ref. 5), 377-407.
137. Jean Hachette, Traité élémentaire des machines (Paris, 1811), 2nd. edn (1819), x. Cf. Lorraine Daston, "The physicalist tradition in early nineteenth century French geometry," Studies in history and philosophy of science, 17 (1986), 269-295; Konstantinos Chatzis, "Mécanique rationnelle et mécanique des machines," in Belhoste et al. (ref. 56), 95-108, on 96-97; Séris (ref. 5), 377-407.
138. Jean Hachette, Traité élémentaire des machines (Paris, 1811), 2nd. edn (1819), x. Cf. Lorraine Daston, "The physicalist tradition in early nineteenth century French geometry," Studies in history and philosophy of science, 17 (1986), 269-295; Konstantinos Chatzis, "Mécanique rationnelle et mécanique des machines," in Belhoste et al. (ref. 56), 95-108, on 96-97; Séris (ref. 5), 377-407.
139. Jean Hachette, Programme du cours élémentaire de machines pour l'an 1808 [at the Ecole Polytechnique]; [followed by] Essai sur ta compositions des machines par MM. Lanz et Bétancourt (Paris, 1808), v; ref. 57, xxii. On cinématique, see André-Marie Ampère, Essai de philosophie des sciences (Paris, 1834), 50-52, which relates to Carnot's geometrical motions and to the Essai by Lanz et Bétancourt.
140. Jean Hachette, Programme du cours élémentaire de machines pour l'an 1808 [at the Ecole Polytechnique]; [followed by] Essai sur ta compositions des machines par MM. Lanz et Bétancourt (Paris, 1808), v; ref. 57, xxii. On cinématique, see André-Marie Ampère, Essai de philosophie des sciences (Paris, 1834), 50-52, which relates to Carnot's geometrical motions and to the Essai by Lanz et Bétancourt.
141. Jean Hachette, Programme du cours élémentaire de machines pour l'an 1808 [at the Ecole Polytechnique]; [followed by] Essai sur ta compositions des machines par MM. Lanz et Bétancourt (Paris, 1808), v; ref. 57, xxii. On cinématique, see André-Marie Ampère, Essai de philosophie des sciences (Paris, 1834), 50-52, which relates to Carnot's geometrical motions and to the Essai by Lanz et Bétancourt.
142. Jean Hachette, Programme du cours élémentaire de machines pour l'an 1808 [at the Ecole Polytechnique]; [followed by] Essai sur ta compositions des machines par MM. Lanz et Bétancourt (Paris, 1808), v; ref. 57, xxii. On cinématique, see André-Marie Ampère, Essai de philosophie des sciences (Paris, 1834), 50-52, which relates to Carnot's geometrical motions and to the Essai by Lanz et Bétancourt.
143. Joseph Louis de Lagrange, Théorie des fonctions analytiques contenant les principes du calcul différentiel dégagés de toutes considérations d'infiniment petits ou d'évanouissans, de limites ou de fluxions, et réduits à l'analyse algébrique des quantités finies (Paris, 1898), 223-277 (applications à la mécanique), on 275.
144. Hachette (ref. 57), x, viii.
145. Ibid., xvii, 93-98.
146. Claude Burdin, "Considérations générales sir les machines en mouvement," Journal des mines, 37 (1815), 319-346, on 337. Cf. Séris (ref. 5), 411-412.
147. Claude Burdin, "Considérations générales sir les machines en mouvement," Journal des mines, 37 (1815), 319-346, on 337. Cf. Séris (ref. 5), 411-412.
148. Alexis Petit, "Sur l'emploi du principe des forces vives dans le calcul de l'effet des machines," CR, 8 (1818), 287-305, on 287, 290. Cf. Grattan-Guinness (ref. 5), 10.
149. Alexis Petit, "Sur l'emploi du principe des forces vives dans le calcul de l'effet des machines," CR, 8 (1818), 287-305, on 287, 290. Cf. Grattan-Guinness (ref. 5), 10.
150. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
151. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
152. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
153. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
154. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
155. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
156. Louis Navier, "Détails historiques sur l'emploi du principe des forces vives dans la théorie des machines, et sur diverses roues hydrauliques," CR, 9 (1918), 146-159; Bernard Forest de Bélidor, Architecture hydraulique, ou l'art de construire, d'élever, et de ménager les eaux pour les besoins de la vie, ed. by Louis Navier (Paris, 1819), esp. 103-120, 376-396. Cf. Gaspard de Prony, biography of Navier, in Louis Navier, Résumé des leçons données à l'Ecole des Ponts et Chaussées sur l'application de la mécanique à l'établissement des constructions et des machines. Première section: De la Résistance des corps solides, 3rd edn., annotated by A. de Saint-Venant (Paris, 1864), xxxix-li, lv-lxxxiii, on lvii-lviii, and "Historique," ibid, xc-cccxi; Grattan-Guinness (ref. 5), 12; Séris, (ref. 5), 419-428; Konstantinos Chatzis, "Economie, machines et mécanique rationnelle: La naissance du concept de travail chez les ingénieurs-savants français, entre 1819 et 1829," Annales des Ponts et Chaussées, 82 (1997), 10-20, on 11-12.
157. Lagrange (ref. 59), 275; Bélidor (ref. 64), 376, 112.
158. Lagrange (ref. 59), 275; Bélidor (ref. 64), 376, 112.
159. Navier's Bélidor (ref. 64), 376. Cf. Vatin (ref. 5), 57-69.
160. Joseph Montgolfier, "Sur la possibilité de substituer le bélier hydraulique à l'ancienne machine de Marly," JEP, 14 (1808), 289-316, on 290-292; Navier's Bélidor (ref. 64), 380, 376. Daniel Bernoulli had already discussed the poor efficiency of the Marly machine (ref. 16), 9.2.27). Hachette (ref. 57), 1811, xiv-xv, also quoted Montgolfier's dictum that live force is what we pay for.
161. Joseph Montgolfier, "Sur la possibilité de substituer le bélier hydraulique à l'ancienne machine de Marly," JEP, 14 (1808), 289-316, on 290-292; Navier's Bélidor (ref. 64), 380, 376. Daniel Bernoulli had already discussed the poor efficiency of the Marly machine (ref. 16), 9.2.27). Hachette (ref. 57), 1811, xiv-xv, also quoted Montgolfier's dictum that live force is what we pay for.
162. Joseph Montgolfier, "Sur la possibilité de substituer le bélier hydraulique à l'ancienne machine de Marly," JEP, 14 (1808), 289-316, on 290-292; Navier's Bélidor (ref. 64), 380, 376. Daniel Bernoulli had already discussed the poor efficiency of the Marly machine (ref. 16), 9.2.27). Hachette (ref. 57), 1811, xiv-xv, also quoted Montgolfier's dictum that live force is what we pay for.
163. Joseph Montgolfier, "Sur la possibilité de substituer le bélier hydraulique à l'ancienne machine de Marly," JEP, 14 (1808), 289-316, on 290-292; Navier's Bélidor (ref. 64), 380, 376. Daniel Bernoulli had already discussed the poor efficiency of the Marly machine (ref. 16), 9.2.27). Hachette (ref. 57), 1811, xiv-xv, also quoted Montgolfier's dictum that live force is what we pay for.
164. Gaspard Coriolis, Du calcul de l'effet des machines ou considérations sur l'emploi des moteurs et leur évaluation, pour servir d'introduction à l'étude spéciale des machines (Paris, 1829), iii, 105. Cf. Haas (ref. 11), 75-79; Grattan-Guinness (ref. 5), 13; Chatzis (ref. 64), 16-20; Vatin (ref. 5), 70-92.
165. Gaspard Coriolis, Du calcul de l'effet des machines ou considérations sur l'emploi des moteurs et leur évaluation, pour servir d'introduction à l'étude spéciale des machines (Paris, 1829), iii, 105. Cf. Haas (ref. 11), 75-79; Grattan-Guinness (ref. 5), 13; Chatzis (ref. 64), 16-20; Vatin (ref. 5), 70-92.
166. Gaspard Coriolis, Du calcul de l'effet des machines ou considérations sur l'emploi des moteurs et leur évaluation, pour servir d'introduction à l'étude spéciale des machines (Paris, 1829), iii, 105. Cf. Haas (ref. 11), 75-79; Grattan-Guinness (ref. 5), 13; Chatzis (ref. 64), 16-20; Vatin (ref. 5), 70-92.
167. Gaspard Coriolis, Du calcul de l'effet des machines ou considérations sur l'emploi des moteurs et leur évaluation, pour servir d'introduction à l'étude spéciale des machines (Paris, 1829), iii, 105. Cf. Haas (ref. 11), 75-79; Grattan-Guinness (ref. 5), 13; Chatzis (ref. 64), 16-20; Vatin (ref. 5), 70-92.
168. Gaspard Coriolis, Du calcul de l'effet des machines ou considérations sur l'emploi des moteurs et leur évaluation, pour servir d'introduction à l'étude spéciale des machines (Paris, 1829), iii, 105. Cf. Haas (ref. 11), 75-79; Grattan-Guinness (ref. 5), 13; Chatzis (ref. 64), 16-20; Vatin (ref. 5), 70-92.
169. Coriolis (ref. 68), i; Gaspard Coriolis, "Observations sur le choix d'une nouvelle dénomination et d'une nouvelle unité de dynamique," Académie des Sciences, pochette de séance for 7 Aug 1826. On the practically important issue of the unit of work, cf. Haas (ref. 11), 82-83.
170. Coriolis (ref. 68), i; Gaspard Coriolis, "Observations sur le choix d'une nouvelle dénomination et d'une nouvelle unité de dynamique," Académie des Sciences, pochette de séance for 7 Aug 1826. On the practically important issue of the unit of work, cf. Haas (ref. 11), 82-83.
171. Coriolis (ref. 68), i; Gaspard Coriolis, "Observations sur le choix d'une nouvelle dénomination et d'une nouvelle unité de dynamique," Académie des Sciences, pochette de séance for 7 Aug 1826. On the practically important issue of the unit of work, cf. Haas (ref. 11), 82-83.
172. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
173. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
174. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
175. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
176. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
177. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
178. Jean Victor Poncelet, Cours de mécanique appliqué aux machines (Metz, 1826), and Cours de mécanique industrielle fait aux artistes et ouvriers messins, pendant les hivers de 1827 à 1828, et de 1828 à 1829 (Metz, 1829), x. The course for the Ecole de Metz still used Navier's "quantity of action" and a more conventional introduction of mechanical concepts. Cf. Grattan-Guinness (ref. 5), 18-20, 29; Bruno Belhoste and Antoine Picon, "Les caractères généraux de l'enseignement à l'Ecole d'Application de l'Artillerie et du Génie de Metz," in Belhoste and Picon, L'Ecole d'Application de l'Artillerie et du Génie de Metz (1802-1870), Enseignements et recherches (Paris, 1996), 18-31; Belhoste and Louis Lemaître, "J. V. Poncelet, les ingénieurs militaires et les roues et turbines hydrauliques," in Belhoste et al. (ref. 21), 33-89; Konstantinos Chatzis, "Jean-Victor Poncelet et la 'science des machines' à l'Ecole de Metz; 1825-1870," ibid., 32-43; Séris (ref. 5), 429-437.
179. Poncelet (ref. 70, 1829) vii; 2nd edn. (1839), 115. Cf. Scott (ref. 4), 167-176. The principle of live forces implies all other principles of mechanics only in the case of a single degree of freedom.
180. Poncelet (ref. 70, 1829) vii; 2nd edn. (1839), 115. Cf. Scott (ref. 4), 167-176. The principle of live forces implies all other principles of mechanics only in the case of a single degree of freedom.
181. Poncelet (ref. 70, 1829), 55, 91. In the same section, Poncelet confused the work needed to extract coal from mines with the work provided by this coal to thermal machines: energetic thinking was still in its infancy.
182. Jean-Baptiste Bélanger, Notes sur la mécanique appliquée aux principes de la stabilité des constructions et à la dynamique des machines, litographed course (1842-43) at the Ponts et Chaussées; Cours de mécanique, ou résumé des leçons sur la dynamique, la statique, et leurs applications à l'art de l'ingénieur (Paris, 1847); François Arago and Charles Dupin, "Rapport sur un mémoire de Poncelet intitulé Cours de mécanique appliquée aux machines, Académie des Sciences, Procès verbaux des séances, 8 (1827), 527-531, on 531. On Bélanger, cf. Chatzis (ref. 57), 104-107.
183. Jean-Baptiste Bélanger, Notes sur la mécanique appliquée aux principes de la stabilité des constructions et à la dynamique des machines, litographed course (1842-43) at the Ponts et Chaussées; Cours de mécanique, ou résumé des leçons sur la dynamique, la statique, et leurs applications à l'art de l'ingénieur (Paris, 1847); François Arago and Charles Dupin, "Rapport sur un mémoire de Poncelet intitulé Cours de mécanique appliquée aux machines, Académie des Sciences, Procès verbaux des séances, 8 (1827), 527-531, on 531. On Bélanger, cf. Chatzis (ref. 57), 104-107.
184. Jean-Baptiste Bélanger, Notes sur la mécanique appliquée aux principes de la stabilité des constructions et à la dynamique des machines, litographed course (1842-43) at the Ponts et Chaussées; Cours de mécanique, ou résumé des leçons sur la dynamique, la statique, et leurs applications à l'art de l'ingénieur (Paris, 1847); François Arago and Charles Dupin, "Rapport sur un mémoire de Poncelet intitulé Cours de mécanique appliquée aux machines, Académie des Sciences, Procès verbaux des séances, 8 (1827), 527-531, on 531. On Bélanger, cf. Chatzis (ref. 57), 104-107.
185. Jean-Baptiste Bélanger, Notes sur la mécanique appliquée aux principes de la stabilité des constructions et à la dynamique des machines, litographed course (1842-43) at the Ponts et Chaussées; Cours de mécanique, ou résumé des leçons sur la dynamique, la statique, et leurs applications à l'art de l'ingénieur (Paris, 1847); François Arago and Charles Dupin, "Rapport sur un mémoire de Poncelet intitulé Cours de mécanique appliquée aux machines, Académie des Sciences, Procès verbaux des séances, 8 (1827), 527-531, on 531. On Bélanger, cf. Chatzis (ref. 57), 104-107.
186. Cf. J.L. Heilbron, Weighing imponderables and other quantitative science around 1800 (Berkeley, 1993), 1-16.
187. Cf. Robert Fox, "The rise and fall of Laplacian physics," HSPS, 4 (1974), 89-136; Michael Crosland, The Society of Arcueil (Cambridge, 1967); Heilbron (ref. 74), 1-7, 141-149.
188. Cf. Robert Fox, "The rise and fall of Laplacian physics," HSPS, 4 (1974), 89-136; Michael Crosland, The Society of Arcueil (Cambridge, 1967); Heilbron (ref. 74), 1-7, 141-149.
189. Cf. Robert Fox, "The rise and fall of Laplacian physics," HSPS, 4 (1974), 89-136; Michael Crosland, The Society of Arcueil (Cambridge, 1967); Heilbron (ref. 74), 1-7, 141-149.
190. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
191. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
192. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
193. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
194. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
195. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
196. On Laplace, cf. Heilbron, ref. 74, 157-165 (capillarity), 171-184 (sound). On Poisson, cf. D.H. Arnold, "The mécanique physique of Siméon Denis Poisson: The evolution and isolation in France of his approach to physical theory," Archive for the history of exact sciences, 28 (1983), 243-367; 29 (1983), 37-94. On Navier's contribution, cf. Saint-Venant, "Historique," in Navier, Résumé, ref. 64, cxii-cxlix; Bruno Belhoste, "Navier, Saint-Venant et la création de la mécanique des fluides visqueux," Annales des Ponts et Chaussés, 82 (1997), 4-9. On Cauchy, cf. Belhoste, Augustin Cauchy: A biography (New York, 1991), 93-102; Amy Dahan, Mathématisations: Augustin Cauchv et l'école française (Paris, 1992).
197. Laplace, "Sur l'action capillaire" (1806), in Oeuvres complètes, 14 vols. (Paris, 1878-1912), vol. 4, 233-277; Exposition du système du monde, 3rd ed. (1808), 296, 301, 317, 318 (shape of molecules); [on sound] (1821-1823), in Oeuvres, vol. 13, 277-282. Cf. Heilbron (ref. 74), 171-184. Laplace seems not to have discussed the internal structure of molecules. He represented all matter as made of material points. But he discussed neither the kind of distribution (discrete or continuous) nor the kind of cohesion (perfect solid or balance of internal central forces) of the points within a molecule.
198. Laplace, "Sur l'action capillaire" (1806), in Oeuvres complètes, 14 vols. (Paris, 1878-1912), vol. 4, 233-277; Exposition du système du monde, 3rd ed. (1808), 296, 301, 317, 318 (shape of molecules); [on sound] (1821-1823), in Oeuvres, vol. 13, 277-282. Cf. Heilbron (ref. 74), 171-184. Laplace seems not to have discussed the internal structure of molecules. He represented all matter as made of material points. But he discussed neither the kind of distribution (discrete or continuous) nor the kind of cohesion (perfect solid or balance of internal central forces) of the points within a molecule.
199. Laplace, "Sur l'action capillaire" (1806), in Oeuvres complètes, 14 vols. (Paris, 1878-1912), vol. 4, 233-277; Exposition du système du monde, 3rd ed. (1808), 296, 301, 317, 318 (shape of molecules); [on sound] (1821-1823), in Oeuvres, vol. 13, 277-282. Cf. Heilbron (ref. 74), 171-184. Laplace seems not to have discussed the internal structure of molecules. He represented all matter as made of material points. But he discussed neither the kind of distribution (discrete or continuous) nor the kind of cohesion (perfect solid or balance of internal central forces) of the points within a molecule.
200. Laplace, "Sur l'action capillaire" (1806), in Oeuvres complètes, 14 vols. (Paris, 1878-1912), vol. 4, 233-277; Exposition du système du monde, 3rd ed. (1808), 296, 301, 317, 318 (shape of molecules); [on sound] (1821-1823), in Oeuvres, vol. 13, 277-282. Cf. Heilbron (ref. 74), 171-184. Laplace seems not to have discussed the internal structure of molecules. He represented all matter as made of material points. But he discussed neither the kind of distribution (discrete or continuous) nor the kind of cohesion (perfect solid or balance of internal central forces) of the points within a molecule.
201. Poisson, Nouvelle théorie de l'action capillaire (Paris, 1831); "Mémoire sur l'équilibre et le mouvement des corps élastiques" (1828), MAS, 8 (1829), 357-570, 623-627, on 365-366, 398-399; Augustin Cauchy, "Sur l'équilibre et le mouvement d'un système de points matériels sollicités par des forces d'attraction ou de répulsion mutuelle," in Exercices de mathématique. 3e année (Paris, 1828), 188-212, on 202-205. Cf. Arnold, ref. 76, Part 6, 347-360; Part 8, 60-63. Saint-Venant's contribution is discussed below.
202. Poisson, Nouvelle théorie de l'action capillaire (Paris, 1831); "Mémoire sur l'équilibre et le mouvement des corps élastiques" (1828), MAS, 8 (1829), 357-570, 623-627, on 365-366, 398-399; Augustin Cauchy, "Sur l'équilibre et le mouvement d'un système de points matériels sollicités par des forces d'attraction ou de répulsion mutuelle," in Exercices de mathématique. 3e année (Paris, 1828), 188-212, on 202-205. Cf. Arnold, ref. 76, Part 6, 347-360; Part 8, 60-63. Saint-Venant's contribution is discussed below.
203. Poisson, Nouvelle théorie de l'action capillaire (Paris, 1831); "Mémoire sur l'équilibre et le mouvement des corps élastiques" (1828), MAS, 8 (1829), 357-570, 623-627, on 365-366, 398-399; Augustin Cauchy, "Sur l'équilibre et le mouvement d'un système de points matériels sollicités par des forces d'attraction ou de répulsion mutuelle," in Exercices de mathématique. 3e année (Paris, 1828), 188-212, on 202-205. Cf. Arnold, ref. 76, Part 6, 347-360; Part 8, 60-63. Saint-Venant's contribution is discussed below.
204. Poisson, Nouvelle théorie de l'action capillaire (Paris, 1831); "Mémoire sur l'équilibre et le mouvement des corps élastiques" (1828), MAS, 8 (1829), 357-570, 623-627, on 365-366, 398-399; Augustin Cauchy, "Sur l'équilibre et le mouvement d'un système de points matériels sollicités par des forces d'attraction ou de répulsion mutuelle," in Exercices de mathématique. 3e année (Paris, 1828), 188-212, on 202-205. Cf. Arnold, ref. 76, Part 6, 347-360; Part 8, 60-63. Saint-Venant's contribution is discussed below.
205. Laplace, Traité de mécanique céleste, vol. 5 (1825), 99.
206. Poisson (ref. 78) (1828), 361.
207. Cf. Arnold (ref. 76). The engineers' recourse to the molecular picture for finding the basic properties of matter should not be confused with a taste for molecular speculation. Saint-Venant, Coriolis, Bélanger, and Poncelet tried as much as possible to reason from macroscopic quantities when dealing with engineering problems.
208. Gaspard Coriolis, Leçons sur la mécanique, lithographed course at Centrale (1830-1831, 1836-1837 ); Eric Brizay's unpublished analysis of these courses; Coriolis, "Sur le principe des forces vives dans les mouvements relatifs des machines," JEP, 21e cahier (1832), 268-302; "Sur la manière d'établir les différents principes de la mécanique pour des systèmes de corps, en les considérants comme des assemblages de molécules," JEP, 24e cahier (1835), 93-125. Poncelet must have had a similar derivation of the principle of live forces in mind, since he included the work of internal forces. Bélanger (ref. 73), (1847), 220, also gave a molecular derivation of the principle of virtual velocities.
209. Gaspard Coriolis, Leçons sur la mécanique, lithographed course at Centrale (1830-1831, 1836-1837 ); Eric Brizay's unpublished analysis of these courses; Coriolis, "Sur le principe des forces vives dans les mouvements relatifs des machines," JEP, 21e cahier (1832), 268-302; "Sur la manière d'établir les différents principes de la mécanique pour des systèmes de corps, en les considérants comme des assemblages de molécules," JEP, 24e cahier (1835), 93-125. Poncelet must have had a similar derivation of the principle of live forces in mind, since he included the work of internal forces. Bélanger (ref. 73), (1847), 220, also gave a molecular derivation of the principle of virtual velocities.
210. Gaspard Coriolis, Leçons sur la mécanique, lithographed course at Centrale (1830-1831, 1836-1837 ); Eric Brizay's unpublished analysis of these courses; Coriolis, "Sur le principe des forces vives dans les mouvements relatifs des machines," JEP, 21e cahier (1832), 268-302; "Sur la manière d'établir les différents principes de la mécanique pour des systèmes de corps, en les considérants comme des assemblages de molécules," JEP, 24e cahier (1835), 93-125. Poncelet must have had a similar derivation of the principle of live forces in mind, since he included the work of internal forces. Bélanger (ref. 73), (1847), 220, also gave a molecular derivation of the principle of virtual velocities.
211. Gaspard Coriolis, Leçons sur la mécanique, lithographed course at Centrale (1830-1831, 1836-1837 ); Eric Brizay's unpublished analysis
212. A.M. Ampère, "Sur la détermination des proportions dans lesquelles les corps se combinent d'après les nombres et la disposition respective des molécules dont leurs particules intégrantes sont composées," Annales de chimie, 90 (1814), 43-86; "Idées de Mr. Ampère sur la chaleur et la lumière," Bibliothèque universelle des sciences, belles-lettres et arts, rédigée à Genève, 1 (1832), 225-235; "Note sur la chaleur et sur la lumière considérées comme résultant de mouvements vibratoires," CR, 58 (1835), 432-444. Cf. Myriam Scheidecker-Chevalier and Robert Locqueneux, "La théorie mathématique de la combinaison chimique d'André-Marie Ampère," Revue d'histoire des sciences, 47 (1994), 309-332. Saint-Venant mentioned Ampere's conception of heat in his memoir of 1844 on the discontinuity of matter.
213. A.M. Ampère, "Sur la détermination des proportions dans lesquelles les corps se combinent d'après les nombres et la disposition respective des molécules dont leurs particules intégrantes sont composées," Annales de chimie, 90 (1814), 43-86; "Idées de Mr. Ampère sur la chaleur et la lumière," Bibliothèque universelle des sciences, belles-lettres et arts, rédigée à Genève, 1 (1832), 225-235; "Note sur la chaleur et sur la lumière considérées comme résultant de mouvements vibratoires," CR, 58 (1835), 432-444. Cf. Myriam Scheidecker-Chevalier and Robert Locqueneux, "La théorie mathématique de la combinaison chimique d'André-Marie Ampère," Revue d'histoire des sciences, 47 (1994), 309-332. Saint-Venant mentioned Ampere's conception of heat in his memoir of 1844 on the discontinuity of matter.
214. A.M. Ampère, "Sur la détermination des proportions dans lesquelles les corps se combinent d'après les nombres et la disposition respective des molécules dont leurs particules intégrantes sont composées," Annales de chimie, 90 (1814), 43-86; "Idées de Mr. Ampère sur la chaleur et la lumière," Bibliothèque universelle des sciences, belles-lettres et arts, rédigée à Genève, 1 (1832), 225-235; "Note sur la chaleur et sur la lumière considérées comme résultant de mouvements vibratoires," CR, 58 (1835), 432-444. Cf. Myriam Scheidecker-Chevalier and Robert Locqueneux, "La théorie mathématique de la combinaison chimique d'André-Marie Ampère," Revue d'histoire des sciences, 47 (1994), 309-332. Saint-Venant mentioned Ampere's conception of heat in his memoir of 1844 on the discontinuity of matter.
215. A.M. Ampère, "Sur la détermination des proportions dans lesquelles les corps se combinent d'après les nombres et la disposition respective des molécules dont leurs particules intégrantes sont composées," Annales de chimie, 90 (1814), 43-86; "Idées de Mr. Ampère sur la chaleur et la lumière," Bibliothèque universelle des sciences, belles-lettres et arts, rédigée à Genève, 1 (1832), 225-235; "Note sur la chaleur et sur la lumière considérées comme résultant de mouvements vibratoires," CR, 58 (1835), 432-444. Cf. Myriam Scheidecker-Chevalier and Robert Locqueneux, "La théorie mathématique de la combinaison chimique d'André-Marie Ampère," Revue d'histoire des sciences, 47 (1994), 309-332. Saint-Venant mentioned Ampere's conception of heat in his memoir of 1844 on the discontinuity of matter.
216. Ampère (ref. 83) (1832), 230 (quote) and (ref. 58), 54 (mécanique moléculaire); Carnot, Academy reports, in Chaniay (ref. 46), 656-657.
217. Ampère (ref. 83) (1832), 230 (quote) and (ref. 58), 54 (mécanique moléculaire); Carnot, Academy reports, in Charnay (ref. 46), 656-657.
218. Poisson (ref. 39); Gaspard de Prony, Leçons de mécanique analytique [for the Polytechnique] (2 vols., Paris, 1815); Hachette (ref. 57). Prony's Nouvelle architecture hydraulique (Paris, 1790) reproduced Jorge Juan's theory of collisions from his Examen maritime, théorique et pratique, ou traité de méchanique appliquée à la construction et à la manoeuvre des vaisseaux et autres bâtiments (2 vols., Nantes, 1883), vol. 1, chapt. 6: "De la percussion." Juan supposed a finite compression of the colliding bodies in proportion with their momemtum loss: cf. Scott (ref. 4), 107-109.
219. Poisson (ref. 39); Gaspard de Prony, Leçons de mécanique analytique [for the Polytechnique] (2 vols., Paris, 1815); Hachette (ref. 57). Prony's Nouvelle architecture hydraulique (Paris, 1790) reproduced Jorge Juan's theory of collisions from his Examen maritime, théorique et pratique, ou traité de méchanique appliquée à la construction et à la manoeuvre des vaisseaux et autres bâtiments (2 vols., Nantes, 1883), vol. 1, chapt. 6: "De la percussion." Juan supposed a finite compression of the colliding bodies in proportion with their momemtum loss: cf. Scott (ref. 4), 107-109.
220. Poisson (ref. 39); Gaspard de Prony, Leçons de mécanique analytique [for the Polytechnique] (2 vols., Paris, 1815); Hachette (ref. 57). Prony's Nouvelle architecture hydraulique (Paris, 1790) reproduced Jorge Juan's theory of collisions from his Examen maritime, théorique et pratique, ou traité de méchanique appliquée à la construction et à la manoeuvre des vaisseaux et autres bâtiments (2 vols., Nantes, 1883), vol. 1, chapt. 6: "De la percussion." Juan supposed a finite compression of the colliding bodies in proportion with their momemtum loss: cf. Scott (ref. 4), 107-109.
221. Poisson (ref. 39); Gaspard de Prony, Leçons de mécanique analytique [for the Polytechnique] (2 vols., Paris, 1815); Hachette (ref. 57). Prony's Nouvelle architecture hydraulique (Paris, 1790) reproduced Jorge Juan's theory of collisions from his Examen maritime, théorique et pratique, ou traité de méchanique appliquée à la construction et à la manoeuvre des vaisseaux et autres bâtiments (2 vols., Nantes, 1883), vol. 1, chapt. 6: "De la percussion." Juan supposed a finite compression of the colliding bodies in proportion with their momemtum loss: cf. Scott (ref. 4), 107-109.
222. Lagrange (ref. 59), 271.
223. Navier's Bélidor (ref. 64), x-xi, 76n-80n. Navier borrowed his collision theory from Juan, who imagined "pores" allowing the compression of bodies (ref. 85, 1, 120); but he avoided the notion of live force, which he judged to be too vague (ibid., 123-124).
224. Navier's Bélidor (ref. 64), x-xi, 76n-80n. Navier borrowed his collision theory from Juan, who imagined "pores" allowing the compression of bodies (ref. 85, 1, 120); but he avoided the notion of live force, which he judged to be too vague (ibid., 123-124).
225. Navier's Bélidor (ref. 64), x-xi, 76n-80n. Navier borrowed his collision theory from Juan, who imagined "pores" allowing the compression of bodies (ref. 85, 1, 120); but he avoided the notion of live force, which he judged to be too vague (ibid., 123-124).
226. Coriolis (ref. 68), 39, 93-95; Prony, Girard, and Navier, Rapport, ibid. (1)-(4), on (4).
227. Coriolis (ref. 68), 39, 93-95; Prony, Girard, and Navier, Rapport, ibid. (1)-(4), on (4).
228. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 1829, 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
229. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 1829, 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
230. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 1829, 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
231. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 1829, 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
232. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
233. Poncelet "mécanique appliqué" (ref. 70), 1826, 119-120; 69-72, 124-127, 137; 1839, 190. Cf. Haas (ref. 4), 82. Coriolis reprocuced several bits of Poncelet's reasoning, including his treatment of collisions, without reference to Poncelet's lithographed course. Poncelet reacted in "Notes sur quelques principes relatifs à la science des machines," Bulletin universel des sciences. Feb 1829, 1st section, 1-15. Cf. Grattan-Guinness (ref. 57), 18.
234. Poncelet "mécanique industrielle" (ref. 70), 2nd edn. (1839), 524-697, on 527. On Poncelet's experiments (with collaborators), and on his earlier invention of a curved-paddles vertical waterwheel, cf. Belhoste et Lemaître (ref. 70).
235. Poncelet "mécanique industrielle" (ref. 70), 1839, 529, 530.
236. Cf. André-Marie Ampère, section on collisions of "Cours de physique mathématique," notes taken by Liouville and revised by Ampère, in Carton 11, Chemise 211 of the Fond Ampère at the Académie des Sciences; no trace of Ampere's course at the Ecole Polytechnique has been found; Augustin Cauchy, "Sur un nouveau principe de mécanique," Bulletin des science mathématiques, 12 (1829), 116-121; Siméon Denis Poisson, Traité de mécanique, 2nd edn. (2 vols., Paris, 1833), 2, 26-31.
237. Cf. André-Marie Ampère, section on collisions of "Cours de physique mathématique," notes taken by Liouville and revised by Ampère, in Carton 11, Chemise 211 of the Fond Ampère at the Académie des Sciences; no trace of Ampere's course at the Ecole Polytechnique has been found; Augustin Cauchy, "Sur un nouveau principe de mécanique," Bulletin des science mathématiques, 12 (1829), 116-121; Siméon Denis Poisson, Traité de mécanique, 2nd edn. (2 vols., Paris, 1833), 2, 26-31.
238. Cf. André-Marie Ampère, section on collisions of "Cours de physique mathématique," notes taken by Liouville and revised by Ampère, in Carton 11, Chemise 211 of the Fond Ampère at the Académie des Sciences; no trace of Ampere's course at the Ecole Polytechnique has been found; Augustin Cauchy, "Sur un nouveau principe de mécanique," Bulletin des science mathématiques, 12 (1829), 116-121; Siméon Denis Poisson, Traité de mécanique, 2nd edn. (2 vols., Paris, 1833), 2, 26-31.
239. Cf. Eduardo Benvenuto, "Adhémar-Jean-Claude Barré de Saint-Venant: The man, the scientist, the engineer," in Accademia Nazionale del Lincei, Atti dei convegni Lincei, 140 (1998), 7-34; Chiara Melucci, Scienza, spiritualità, visione politica in A.J.C. Barré de Saint-Venant: Contributi teorici e applicativi nella dinamica dei fluidi e nella scienza del miglioramento del territorio, doctoral diss. (Università degli studi di Genova, 1996), 8-9; Joseph Bertrand, "Eloge historique de Michel Chasles," in Eloges académiques. Nouvelle série (Paris, 1902), 37-47, on 42 (for Chasles' report of the incident). Dates and ranks are from the registers of the Ecole Polytechnique (all biographers have them wrong).
240. Cf. Eduardo Benvenuto, "Adhémar-Jean-Claude Barré de Saint-Venant: The man, the scientist, the engineer," in Accademia Nazionale del Lincei, Atti dei convegni Lincei, 140 (1998), 7-34; Chiara Melucci, Scienza, spiritualità, visione politica in A.J.C. Barré de Saint-Venant: Contributi teorici e applicativi nella dinamica dei fluidi e nella scienza del miglioramento del territorio, doctoral diss. (Università degli studi di Genova, 1996), 8-9; Joseph Bertrand, "Eloge historique de Michel Chasles," in Eloges académiques. Nouvelle série (Paris, 1902), 37-47, on 42 (for Chasles' report of the incident). Dates and ranks are from the registers of the Ecole Polytechnique (all biographers have them wrong).
241. Cf. Eduardo Benvenuto, "Adhémar-Jean-Claude Barré de Saint-Venant: The man, the scientist, the engineer," in Accademia Nazionale del Lincei, Atti dei convegni Lincei, 140 (1998), 7-34; Chiara Melucci, Scienza, spiritualità, visione politica in A.J.C. Barré de Saint-Venant: Contributi teorici e applicativi nella dinamica dei fluidi e nella scienza del miglioramento del territorio, doctoral diss. (Università degli studi di Genova, 1996), 8-9; Joseph Bertrand, "Eloge historique de Michel Chasles," in Eloges académiques. Nouvelle série (Paris, 1902), 37-47, on 42 (for Chasles' report of the incident). Dates and ranks are from the registers of the Ecole Polytechnique (all biographers have them wrong).
242. Cf. Melucci (ref. 93), 9-10, 12; Joseph Boussinesq and Alfred Flamant, Notice sur la vie et les travaux de Barré de Saint-Venant (Paris, 1886).
243. Cf. Melucci (ref. 93), 9-10, 12; Joseph Boussinesq and Alfred Flamant, Notice sur la vie et les travaux de Barré de Saint-Venant (Paris, 1886).
244. Cf. Melucci (ref. 93), 13-15.
245. Melucci (ref. 93), 16 (Versailles), chapt. 2 (hydraulique agricole); A.J.C. Barré de Saint-Venant, Notice sur les travaux et titres scientifiques de M. de Saint-Venant (Paris, 1864).
246. Melucci (ref. 93), 16 (Versailles), chapt. 2 (hydraulique agricole); A.J.C. Barré de Saint-Venant, Notice sur les travaux et titres scientifiques de M. de Saint-Venant (Paris, 1864).
247. Saint-Venant remembering Navier, "Mémoire sur les eaux courantes considérées dans un lit de figure variable," unpub. MS, FSV, carton 21. Cf. Benvenuto (ref. 93), 7-9.
248. Saint-Venant remembering Navier, "Mémoire sur les eaux courantes considérées dans un lit de figure variable," unpub. MS, FSV, carton 21. Cf. Benvenuto (ref. 93), 7-9.
249. Saint-Venant, quoted in Benvenuto (ref. 93), 8.
250. Navier (ref. 64, 1864); Joseph Boussinesq, introduction to Saint-Venant, Résistance des fluides: Considerations historiques, physiques et pratiques relatives au problème de l'action dynamique mutuelle d'un fluide et d'un solide, spécialement dans l'état de permanence supposé acquis par leurs mouvements (Paris, 1888), 1-6, on 6; Boussinesq and Flamant (ref. 94), 25. Melucci (ref. 93), 12. The Comte de Déservilliers described Saint-Venant's character as "strong and gentle, full of kindness, benevolence, and ingenuous simplicity, which increased the fascination of this great mind and gave a truly angelic virtue to Saint-Venant."
251. Navier (ref. 64, 1864); Joseph Boussinesq, introduction to Saint-Venant, Résistance des fluides: Considerations historiques, physiques et pratiques relatives au problème de l'action dynamique mutuelle d'un fluide et d'un solide, spécialement dans l'état de permanence supposé acquis par leurs mouvements (Paris, 1888), 1-6, on 6; Boussinesq and Flamant (ref. 94), 25. Melucci (ref. 93), 12. The Comte de Déservilliers described Saint-Venant's character as "strong and gentle, full of kindness, benevolence, and ingenuous simplicity, which increased the fascination of this great mind and gave a truly angelic virtue to Saint-Venant."
252. Navier (ref. 64, 1864); Joseph Boussinesq, introduction to Saint-Venant, Résistance des fluides: Considerations historiques, physiques et pratiques relatives au problème de l'action dynamique mutuelle d'un fluide et d'un solide, spécialement dans l'état de permanence supposé acquis par leurs mouvements (Paris, 1888), 1-6, on 6; Boussinesq and Flamant (ref. 94), 25. Melucci (ref. 93), 12. The Comte de Déservilliers described Saint-Venant's character as "strong and gentle, full of kindness, benevolence, and ingenuous simplicity, which increased the fascination of this great mind and gave a truly angelic virtue to Saint-Venant."
253. Navier (ref. 64, 1864); Joseph Boussinesq, introduction to Saint-Venant, Résistance des fluides: Considerations historiques, physiques et pratiques relatives au problème de l'action dynamique mutuelle d'un fluide et d'un solide, spécialement dans l'état de permanence supposé acquis par leurs mouvements (Paris, 1888), 1-6, on 6; Boussinesq and Flamant (ref. 94), 25. Melucci (ref. 93), 12. The Comte de Déservilliers described Saint-Venant's character as "strong and gentle, full of kindness, benevolence, and ingenuous simplicity, which increased the fascination of this great mind and gave a truly angelic virtue to Saint-Venant."
254. Cf. Saint-Venant to Dupin, 11 Dec 1843, FSV #977. quoted in Benventito (ref. 93), 13. Although (or perhaps because) Cauchy presented Saint-Venant as his top candidate, the votes were more favorable to Morin, Fourneyron, and Combes. Cf. CR, 17 (1843), 1210, 1237.
255. Augustin Cauchy, "Rapport sur divers mémoires de M. Saint-Venant relatifs à la mécanique rationnelle et à la mécanique appliquée," CR, 17 (1843), 1234-1236; article on Saint-Venant and elasticity, in L'univers-Union Catholique, 17 Dec 1843. François Moigno, Leçons de mécanique analytique (Paris, 1868), xxxviii-xxxix. Cf. Benvenuto (ref. 93), 10.
256. Augustin Cauchy, "Rapport sur divers mémoires de M. Saint-Venant relatifs à la mécanique rationnelle et à la mécanique appliquée," CR, 17 (1843), 1234-1236; article on Saint-Venant and elasticity, in L'univers-Union Catholique, 17 Dec 1843. François Moigno, Leçons de mécanique analytique (Paris, 1868), xxxviii-xxxix. Cf. Benvenuto (ref. 93), 10.
257. Augustin Cauchy, "Rapport sur divers mémoires de M. Saint-Venant relatifs à la mécanique rationnelle et à la mécanique appliquée," CR, 17 (1843), 1234-1236; article on Saint-Venant and elasticity, in L'univers-Union Catholique, 17 Dec 1843. François Moigno, Leçons de mécanique analytique (Paris, 1868), xxxviii-xxxix. Cf. Benvenuto (ref. 93), 10.
258. Augustin Cauchy, "Rapport sur divers mémoires de M. Saint-Venant relatifs à la mécanique rationnelle et à la mécanique appliquée," CR, 17 (1843), 1234-1236; article on Saint-Venant and elasticity, in L'univers-Union Catholique, 17 Dec 1843. François Moigno, Leçons de mécanique analytique (Paris, 1868), xxxviii-xxxix. Cf. Benvenuto (ref. 93), 10.
259. Saint-Venant, Cahiers analytiques, FSV, carton 10, ##1914-1927. Cahiers 2, 3, 4 carry dates 1822 for the main text, 1828 for the marginal notes.
260. Saint-Venant, Cahiers analytiques, FSV, carton 10, ##1914-1927. Cahiers 2, 3, 4 carry dates 1822 for the main text, 1828 for the marginal notes.
261. Ibid., Cahiers 2-6.
262. Ibid., Cahier 3.
263. Ibid., marginal notes; "Mécanique," in Cahier 9 (1826, transcribed in 1829).
264. Ibid., with the remark (dated 1828) that friction implies permanent deformation or wearing.
265. By the conservation of force, Saint-Venant presumably meant the invariability of the distance-force laws: something like the conservation of charge or gravitational mass.
266. Ibid., additions of Aug and Sep 1828, and marginal notes of 1834.
267. Ibid., additions of 1828.
268. Ibid.
269. Saint-Venant (ref. 3), published in Alfred Flamant, Mécanique générale (Paris, 1888), ix-xxxii, two years after Saint-Venant's death. As epigraph, Saint-Venant reproduced Laplace's suggestion of a new formulation of mechanics, quoted above, ref. 79. Ivor Grattan-Guinness mentioned the existence of this manuscript in his Convolutions in French mathematics, 1800-40 (3 vols., Basel, 1990), vol. 2, 1238-1239. Benvenuto noted its importance in ref. 93, 17n.
270. Saint-Venant (ref. 3), published in Alfred Flamant, Mécanique générale (Paris, 1888), ix-xxxii, two years after Saint-Venant's death. As epigraph, Saint-Venant reproduced Laplace's suggestion of a new formulation of mechanics, quoted above, ref. 79. Ivor Grattan-Guinness mentioned the existence of this manuscript in his Convolutions in French mathematics, 1800-40 (3 vols., Basel, 1990), vol. 2, 1238-1239. Benvenuto noted its importance in ref. 93, 17n.
271. Saint-Venant (ref. 3), published in Alfred Flamant, Mécanique générale (Paris, 1888), ix-xxxii, two years after Saint-Venant's death. As epigraph, Saint-Venant reproduced Laplace's suggestion of a new formulation of mechanics, quoted above, ref. 79. Ivor Grattan-Guinness mentioned the existence of this manuscript in his Convolutions in French mathematics, 1800-40 (3 vols., Basel, 1990), vol. 2, 1238-1239. Benvenuto noted its importance in ref. 93, 17n.
272. Ibid., xxi-xxii.
273. Saint-Venant, in Flamant (ref. 111), xxix-xxxii. On xxxi, Saint-Venant noted that the two capitals corresponded to the quantities V and T Lagrange had introduced in his Analytical mechanics as potentials for generalized and fictional forces. Saint-Venant's definition of latent capital was similar to Ampère's definition of latent live force in his paper of 1832 on heat and light, discussed above (ref. 83).
274. Saint-Venant, in Flamant (ref. 111), xxxii.
275. Saint-Venant to Savary, 25 Aug, 27 Jul, 10 Sep 1834, Bibliothèque de l'Institut, MS #4226; André-Marie Ampère, "Démonstration générale du principe des vitesses virtuelles dégagée de la considération des infiniments petits,̀ JEP, 6 (1806), 247-269, and "Nouvelle démonstration du principe des vitesses virtuelles," Correspondances de mathématique et de physique, 2 (1826), 35-47. Ampère gave the new proof in his course at the Collège de France of 1826-27 (ref. 93); J.M.C. Duhamel use it in his Cours de mécanique de l'Ecole Polytechnique (Paris, 1845).
276. Saint-Venant to Savary, 25 Aug, 27 Jul, 10 Sep 1834, Bibliothèque de l'Institut, MS #4226; André-Marie Ampère, "Démonstration générale du principe des vitesses virtuelles dégagée de la considération des infiniments petits,̀ JEP, 6 (1806), 247-269, and "Nouvelle démonstration du principe des vitesses virtuelles," Correspondances de mathématique et de physique, 2 (1826), 35-47. Ampère gave the new proof in his course at the Collège de France of 1826-27 (ref. 93); J.M.C. Duhamel use it in his Cours de mécanique de l'Ecole Polytechnique (Paris, 1845).
277. Saint-Venant to Savary, 25 Aug, 27 Jul, 10 Sep 1834, Bibliothèque de l'Institut, MS #4226; André-Marie Ampère, "Démonstration générale du principe des vitesses virtuelles dégagée de la considération des infiniments petits,̀ JEP, 6 (1806), 247-269, and "Nouvelle démonstration du principe des vitesses virtuelles," Correspondances de mathématique et de physique, 2 (1826), 35-47. Ampère gave the new proof in his course at the Collège de France of 1826-27 (ref. 93); J.M.C. Duhamel use it in his Cours de mécanique de l'Ecole Polytechnique (Paris, 1845).
278. Saint-Venant, "Mémoire sur la dynamique des fluides," Archives de l'Académie des Sciences, pochette de séance of 14 Apr 1834. Saint-Venant mistakenly assumed that the sheer stress on a given surface element of the fluid was always in a plane perpendicular to this element and parallel to the fluid velocity. He renounced publication in a letter to Savary of 13 Jan 1837. On the relation of his later hydrodynamics work to this paper, cf. Melucci (ref. 93), 54-90.
279. Saint-Venant, "Mémoire sur la dynamique des fluides," Archives de l'Académie des Sciences, pochette de séance of 14 Apr 1834. Saint-Venant mistakenly assumed that the sheer stress on a given surface element of the fluid was always in a plane perpendicular to this element and parallel to the fluid velocity. He renounced publication in a letter to Savary of 13 Jan 1837. On the relation of his later hydrodynamics work to this paper, cf. Melucci (ref. 93), 54-90.
280. Saint-Venant, "Commencement d'un traité de mécanique" (1835), FSV, carton 19, MS B5, p. 1 (page numbers are mine).
281. FSV, carton 19.
282. Saint-Venant (ref. 117), 3, 14-15, 5, 35.
283. Ibid., 10, 11, 15.
284. Ibid., 15, 4.
285. Ibid., 8, 35, 12, 13. See also MS B3, FSV, carton 19. Saint-Venant discussed the issue with Ampère, who disagreed: see Saint-Venant, Notice sur la vie et les ouvrages de Pierre-Louis-Georges Comte du Buat (Lille, 1866), 17. Moigno (ref. 63), xxii-xxvii, judged Saint-Venant's effort "contre-nature."
286. Ibid., 8, 35, 12, 13. See also MS B3, FSV, carton 19. Saint-Venant discussed the issue with Ampère, who disagreed: see Saint-Venant, Notice sur la vie et les ouvrages de Pierre-Louis-Georges Comte du Buat (Lille, 1866), 17. Moigno (ref. 63), xxii-xxvii, judged Saint-Venant's effort "contre-nature."
287. Ibid., 8, 35, 12, 13. See also MS B3, FSV, carton 19. Saint-Venant discussed the issue with Ampère, who disagreed: see Saint-Venant, Notice sur la vie et les ouvrages de Pierre-Louis-Georges Comte du Buat (Lille, 1866), 17. Moigno (ref. 63), xxii-xxvii, judged Saint-Venant's effort "contre-nature."
288. Saint-Venant (ref. 117), 5, 26, 29-30. Saint-Venant returned to the problem of free will after Boussinesq's contribution: cf. Saint-Venant, "Accord des lois de la mécanique avec la liberté de l'homme dans son action sur la matière," CR, 84 (1877), 419-423.
289. Saint-Venant (ref. 117), 5, 26, 29-30. Saint-Venant returned to the problem of free will after Boussinesq's contribution: cf. Saint-Venant, "Accord des lois de la mécanique avec la liberté de l'homme dans son action sur la matière," CR, 84 (1877), 419-423.
290. Saint-Venant (ref. 117), 20, 39, 35.
291. Saint-Venant, cahier 9 (1826) ref. 102; ref. 117, 9. On projective geometry and kinematics, cf. Daston (ref. 57), 282-283.
292. Saint-Venant, cahier 9 (1826) ref. 102; ref. 117, 9. On projective geometry and kinematics, cf. Daston (ref. 57), 282-283.
293. Saint-Venant (ref. 117), 12, 34.
294. Ibid., 6, 11, 38; MS on hydrodynamics (18-34), ref. 116, for Poisson's and Cauchy's arguments. In his "Historique," ref. 64, on clxi-clxv, Saint-Venant mentioned that Cauchy also pleaded for point-molecules in his Sept leçons de physique générale, delivered in 1833 during his exile in Turin and published by Moigno (Paris, 1868). Cauchy offered a different reason (Ibid., 36-37): extended molecules would be indefinitely divisible, against Cauchy's principle that "only God is infinite, everything is finite except him" (Ibid., 27).
295. Ibid., 6, 11, 38; MS on hydrodynamics (18-34), ref. 116, for Poisson's and Cauchy's arguments. In his "Historique," ref. 64, on clxi-clxv, Saint-Venant mentioned that Cauchy also pleaded for point-molecules in his Sept leçons de physique générale, delivered in 1833 during his exile in Turin and published by Moigno (Paris, 1868). Cauchy offered a different reason (Ibid., 36-37): extended molecules would be indefinitely divisible, against Cauchy's principle that "only God is infinite, everything is finite except him" (Ibid., 27).
296. Ibid., 6, 11, 38; MS on hydrodynamics (18-34), ref. 116, for Poisson's and Cauchy's arguments. In his "Historique," ref. 64, on clxi-clxv, Saint-Venant mentioned that Cauchy also pleaded for point-molecules in his Sept leçons de physique générale, delivered in 1833 during his exile in Turin and published by Moigno (Paris, 1868). Cauchy offered a different reason (Ibid., 36-37): extended molecules would be indefinitely divisible, against Cauchy's principle that "only God is infinite, everything is finite except him" (Ibid., 27).
297. Ibid., 6, 11, 38; MS on hydrodynamics (18-34), ref. 116, for Poisson's and Cauchy's arguments. In his "Historique," ref. 64, on clxi-clxv, Saint-Venant mentioned that Cauchy also pleaded for point-molecules in his Sept leçons de physique générale, delivered in 1833 during his exile in Turin and published by Moigno (Paris, 1868). Cauchy offered a different reason (Ibid., 36-37): extended molecules would be indefinitely divisible, against Cauchy's principle that "only God is infinite, everything is finite except him" (Ibid., 27).
298. Ibid., 6, 11, 38; MS on hydrodynamics (18-34), ref. 116, for Poisson's and Cauchy's arguments. In his "Historique," ref. 64, on clxi-clxv, Saint-Venant mentioned that Cauchy also pleaded for point-molecules in his Sept leçons de physique générale, delivered in 1833 during his exile in Turin and published by Moigno (Paris, 1868). Cauchy offered a different reason (Ibid., 36-37): extended molecules would be indefinitely divisible, against Cauchy's principle that "only God is infinite, everything is finite except him" (Ibid., 27).
299. Saint-Venant (ref. 117), 11 (point-atoms), 16 (mechanics defined), 40 (the two principles, and God), 13 (velocities instead of accelei ations). Late in his life, Saint-Venant published some of his epistemological reflections, without the theological underpinning: cf. Konstantinos Chatzis, "Les conceptions de Saint-Venant en matière de théorie de la connaissance," MS of a talk given at the conference Entre mécanique et architecture (Université Catholique de Louvain, 28-29 Jul 1997).
300. Saint-Venant (ref. 117), 11 (point-atoms), 16 (mechanics defined), 40 (the two principles, and God), 13 (velocities instead of accelei ations). Late in his life, Saint-Venant published some of his epistemological reflections, without the theological underpinning: cf. Konstantinos Chatzis, "Les conceptions de Saint-Venant en matière de théorie de la connaissance," MS of a talk given at the conference Entre mécanique et architecture (Université Catholique de Louvain, 28-29 Jul 1997).
301. Saint-Venant, "Sur la question de savoir si la matière est continue ou discontinue" (20 Jan 1844), Société Philomatique, Procès verbaux, 12 (1844), 9-16; Saint-Venant (ref. 64), clxi-clxiii.
302. Saint-Venant, "Sur la question de savoir si la matière est continue ou discontinue" (20 Jan 1844), Société Philomatique, Procès verbaux, 12 (1844), 9-16; Saint-Venant (ref. 64), clxi-clxiii.
303. Saint-Venant (ref. 129), 6, 7, 15-16. Cf. Max Jammer, Concepts of force: a study in the foundations of dynamics (Cambridge, 1957), 183-184. Saint-Venant's kept returning to this issue since it determined his preference of the rari-constant theory of elasticity: cf. Isaac Todhunter and Karl Pearson, A history of the theory of elasticity and of the strength of materials from Galilei to the present time (2 vols., Cambridge, 1886, 1893), 1, 496-505.
304. Saint-Venant (ref. 129), 6, 7, 15-16. Cf. Max Jammer, Concepts of force: a study in the foundations of dynamics (Cambridge, 1957), 183-184. Saint-Venant's kept returning to this issue since it determined his preference of the rari-constant theory of elasticity: cf. Isaac Todhunter and Karl Pearson, A history of the theory of elasticity and of the strength of materials from Galilei to the present time (2 vols., Cambridge, 1886, 1893), 1, 496-505.
305. Saint-Venant (ref. 129), 6, 7, 15-16. Cf. Max Jammer, Concepts of force: a study in the foundations of dynamics (Cambridge, 1957), 183-184. Saint-Venant's kept returning to this issue since it determined his preference of the rari-constant theory of elasticity: cf. Isaac Todhunter and Karl Pearson, A history of the theory of elasticity and of the strength of materials from Galilei to the present time (2 vols., Cambridge, 1886, 1893), 1, 496-505.
306. Saint-Venant, "Mémoire sur les sommes et les différences géométriques et sur leur usage pour simplifier la mécanique," CR, 21 (1845), 620-625. Cf. Michael Crowe, A history of vector analysis (Notre Dame, 1967), 56 (exchange between Grassmann and Saint-Venant), 81-85 (Saint-Venant's approach).
307. Saint-Venant, "Mémoire sur les sommes et les différences géométriques et sur leur usage pour simplifier la mécanique," CR, 21 (1845), 620-625. Cf. Michael Crowe, A history of vector analysis (Notre Dame, 1967), 56 (exchange between Grassmann and Saint-Venant), 81-85 (Saint-Venant's approach).
308. Saint-Venant, MS of a talk delivered at the Société Philomatique on 12 Dec 1846, FSV, #1008, 1 (my page numbering), from which I have also inferred the contents of the talk of the previous week. On the reform, cf. Chatzis (ref. 57), 101-104.
309. Saint-Venant (ref. 132), 3-4; Boussinesq to Saint-Venant, 21 April 1876, Bibliothèque de l'Institut. Bélanger's course (ref. 73) came out in 1847. On Poncelet's relevant course, cf. Konstantinos Chatzis, "Jean-Victor Poncelet (1788-1867) ou le Newton de la mécanique appliquée. Quelques réflexions à l'occasion de soi cours inédit à la Sorbonne," in Société des Amis de la Bibliothèque de l'Ecole Polytechnique, Bulletin, 19 (1998), 69-97. Poncelet's earlier texts did not include molecular derivations of the principles of mechanics.
310. Saint-Venant (ref. 132), 3-4; Boussinesq to Saint-Venant, 21 April 1876, Bibliothèque de l'Institut. Bélanger's course (ref. 73) came out in 1847. On Poncelet's relevant course, cf. Konstantinos Chatzis, "Jean-Victor Poncelet (1788-1867) ou le Newton de la mécanique appliquée. Quelques réflexions à l'occasion de soi cours inédit à la Sorbonne," in Société des Amis de la Bibliothèque de l'Ecole Polytechnique, Bulletin, 19 (1998), 69-97. Poncelet's earlier texts did not include molecular derivations of the principles of mechanics.
311. Saint-Venant, Principes de mécanique fondés sur la cinématique (Paris, 1851). Cf. H. Padé, "Barré de Saint-Venant et les principes de la mécanique," Revue générale des sciences pures et appliquées, 16 (1904), 761-767; Jammer (ref. 130), 215-216.
312. Saint-Venant, Principes de mécanique fondés sur la cinématique (Paris, 1851). Cf. H. Padé, "Barré de Saint-Venant et les principes de la mécanique," Revue générale des sciences pures et appliquées, 16 (1904), 761-767; Jammer (ref. 130), 215-216.
313. Saint-Venant, Principes de mécanique fondés sur la cinématique (Paris, 1851). Cf. H. Padé, "Barré de Saint-Venant et les principes de la mécanique," Revue générale des sciences pures et appliquées, 16 (1904), 761-767; Jammer (ref. 130), 215-216.
314. Saint-Venant (ref. 134), 119n-120n (on friction).
315. Saint-Venant to Reech, 16 Aug 1846, FSV, carton 19. Coriolis' citation of Saint-Venant's memoir was discreetly placed in a footnote (ref 82, 93n).
316. Hermann von Helmholtz, Über die Erhaltung der Kraft, eine physikalische Abhandlung (Berlin, 1847), also in Wissenschaftliche Abhandlungen (3 vols., Leipzig, 1882-1895), 1, 12-68, on 17 (Arbeit), 18 (live force), 22 (Spannkräfte), 27 (quote), 28 (machines). Cf. Fabio Bevilacqua, "Helmholtz's Übe r die Erhaltung der Kraft: The emergence of a theoretical physicist," in David Cahan, ed., Hermann von Helmholtz and the foundations of nineteenth-century science (Berkeley, 1993), 291-333.
317. Hermann von Helmholtz, Über die Erhaltung der Kraft, eine physikalische Abhandlung (Berlin, 1847), also in Wissenschaftliche Abhandlungen (3 vols., Leipzig, 1882-1895), 1, 12-68, on 17 (Arbeit), 18 (live force), 22 (Spannkräfte), 27 (quote), 28 (machines). Cf. Fabio Bevilacqua, "Helmholtz's Übe r die Erhaltung der Kraft: The emergence of a theoretical physicist," in David Cahan, ed., Hermann von Helmholtz and the foundations of nineteenth-century science (Berkeley, 1993), 291-333.
318. Hermann von Helmholtz, Über die Erhaltung der Kraft, eine physikalische Abhandlung (Berlin, 1847), also in Wissenschaftliche Abhandlungen (3 vols., Leipzig, 1882-1895), 1, 12-68, on 17 (Arbeit), 18 (live force), 22 (Spannkräfte), 27 (quote), 28 (machines). Cf. Fabio Bevilacqua, "Helmholtz's Übe r die Erhaltung der Kraft: The emergence of a theoretical physicist," in David Cahan, ed., Hermann von Helmholtz and the foundations of nineteenth-century science (Berkeley, 1993), 291-333.
319. Cf. Peter Heimann, "Helmholtz and Kant: The metaphysical foundations of Über die Erhaltung der Kraft," Studies in the history and philosophy of science, 5 (1974), 205-238; Norton Wise, "German concepts of force, energy, and electromagnetic ether," in Geoffrey Cantor and M.J.S. Hodge, Conceptions of ether: Studies in the history of ether theories, 1740-1900 (New York, 1981), 269-307.
320. Cf. Peter Heimann, "Helmholtz and Kant: The metaphysical foundations of Über die Erhaltung der Kraft," Studies in the history and philosophy of science, 5 (1974), 205-238; Norton Wise, "German concepts of force, energy, and electromagnetic ether," in Geoffrey Cantor and M.J.S. Hodge, Conceptions of ether: Studies in the history of ether theories, 1740-1900 (New York, 1981), 269-307.
321. S.D. Poisson, Traité de mécanique, 2nd edn. (Paris, 1833), par. 565, 682; F. Minding, "Über die Anwendung des Satzes der lebendigen Kräfte in der Maschinenlehre," in Heinrich Dove, ed., Repertorium der Physik, 8 vols. (1837-1849), vol. 5 (1844), 71-76; Julius Weisbach, Lehrbuch der Ingenieur-und Maschinen-Mechanik (Braunschweig, 1846), par. 67-70 (Mechanische Wirkung and Arbeit). Cf. Robert Brain and Norton Wise, "Muscles and engines: Indicator diagrams and Helmholtz's graphical methods," in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin, 1994), 124-148. Helmholtz discussed Clapeyron's "Sur la puissance motrice du feu," JEP, 14 (1834), 153-190, in which the motive power of heat was measured by Navier's "quantité d'action." Kuhn's statement (ref. 1, 66) that Helmholtz was not aware of the French engineering tradition must be rejected.
322. S.D. Poisson, Traité de mécanique, 2nd edn. (Paris, 1833), par. 565, 682; F. Minding, "Über die Anwendung des Satzes der lebendigen Kräfte in der Maschinenlehre," in Heinrich Dove, ed., Repertorium der Physik, 8 vols. (1837-1849), vol. 5 (1844), 71-76; Julius Weisbach, Lehrbuch der Ingenieur-und Maschinen-Mechanik (Braunschweig, 1846), par. 67-70 (Mechanische Wirkung and Arbeit). Cf. Robert Brain and Norton Wise, "Muscles and engines: Indicator diagrams and Helmholtz's graphical methods," in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin, 1994), 124-148. Helmholtz discussed Clapeyron's "Sur la puissance motrice du feu," JEP, 14 (1834), 153-190, in which the motive power of heat was measured by Navier's "quantité d'action." Kuhn's statement (ref. 1, 66) that Helmholtz was not aware of the French engineering tradition must be rejected.
323. S.D. Poisson, Traité de mécanique, 2nd edn. (Paris, 1833), par. 565, 682; F. Minding, "Über die Anwendung des Satzes der lebendigen Kräfte in der Maschinenlehre," in Heinrich Dove, ed., Repertorium der Physik, 8 vols. (1837-1849), vol. 5 (1844), 71-76; Julius Weisbach, Lehrbuch der Ingenieur-und Maschinen-Mechanik (Braunschweig, 1846), par. 67-70 (Mechanische Wirkung and Arbeit). Cf. Robert Brain and Norton Wise, "Muscles and engines: Indicator diagrams and Helmholtz's graphical methods," in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin, 1994), 124-148. Helmholtz discussed Clapeyron's "Sur la puissance motrice du feu," JEP, 14 (1834), 153-190, in which the motive power of heat was measured by Navier's "quantité d'action." Kuhn's statement (ref. 1, 66) that Helmholtz was not aware of the French engineering tradition must be rejected.
324. S.D. Poisson, Traité de mécanique, 2nd edn. (Paris, 1833), par. 565, 682; F. Minding, "Über die Anwendung des Satzes der lebendigen Kräfte in der Maschinenlehre," in Heinrich Dove, ed., Repertorium der Physik, 8 vols. (1837-1849), vol. 5 (1844), 71-76; Julius Weisbach, Lehrbuch der Ingenieur-und Maschinen-Mechanik (Braunschweig, 1846), par. 67-70 (Mechanische Wirkung and Arbeit). Cf. Robert Brain and Norton Wise, "Muscles and engines: Indicator diagrams and Helmholtz's graphical methods," in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin, 1994), 124-148. Helmholtz discussed Clapeyron's "Sur la puissance motrice du feu," JEP, 14 (1834), 153-190, in which the motive power of heat was measured by Navier's "quantité d'action." Kuhn's statement (ref. 1, 66) that Helmholtz was not aware of the French engineering tradition must be rejected.
325. S.D. Poisson, Traité de mécanique, 2nd edn. (Paris, 1833), par. 565, 682; F. Minding, "Über die Anwendung des Satzes der lebendigen Kräfte in der Maschinenlehre," in Heinrich Dove, ed., Repertorium der Physik, 8 vols. (1837-1849), vol. 5 (1844), 71-76; Julius Weisbach, Lehrbuch der Ingenieur-und Maschinen-Mechanik (Braunschweig, 1846), par. 67-70 (Mechanische Wirkung and Arbeit). Cf. Robert Brain and Norton Wise, "Muscles and engines: Indicator diagrams and Helmholtz's graphical methods," in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin, 1994), 124-148. Helmholtz discussed Clapeyron's "Sur la puissance motrice du feu," JEP, 14 (1834), 153-190, in which the motive power of heat was measured by Navier's "quantité d'action." Kuhn's statement (ref. 1, 66) that Helmholtz was not aware of the French engineering tradition must be rejected.
326. Helmholtz (ref. 137), 35-36.
327. James Joule, "Matter, living force, and heat" (May 1847), in Scientific papers, 2 vols. (London, 1884, 1887), 1, 268, 271, 269. Cf. Cardwell (ref. 1); Smith (ref. 2), 52-76.
328. James Joule, "Matter, living force, and heat" (May 1847), in Scientific papers, 2 vols. (London, 1884, 1887), 1, 268, 271, 269. Cf. Cardwell (ref. 1); Smith (ref. 2), 52-76.
329. James Joule, "On the caloric effect of magneto-electricity, and on the mechanical value of heat" (1843), in Papers (ref. 141), 1, 123-159, on 158.
330. James Joule, "Investigations in magnetism and electro-magnetism" (1839), in Papers (ref. 141), 1, 10-14, on 14. On Joule qua chemist, cf. John Forrester, "Chemistry and the conservation of energy: The work of James Prescott Joule," Studies in the history and philosophy of science, 6 (1975), 273-313. On Joule qua brewer, cf. Otto Sibum, "Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England," in ibid., 26 (1995), 73-106.
331. James Joule, "Investigations in magnetism and electro-magnetism" (1839), in Papers (ref. 141), 1, 10-14, on 14. On Joule qua chemist, cf. John Forrester, "Chemistry and the conservation of energy: The work of James Prescott Joule," Studies in the history and philosophy of science, 6 (1975), 273-313. On Joule qua brewer, cf. Otto Sibum, "Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England," in ibid., 26 (1995), 73-106.
332. James Joule, "Investigations in magnetism and electro-magnetism" (1839), in Papers (ref. 141), 1, 10-14, on 14. On Joule qua chemist, cf. John Forrester, "Chemistry and the conservation of energy: The work of James Prescott Joule," Studies in the history and philosophy of science, 6 (1975), 273-313. On Joule qua brewer, cf. Otto Sibum, "Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England," in ibid., 26 (1995), 73-106.
333. Peter Ewart, "On the measure of moving force" (read in Nov 1808), Literary and Philosophical Society of Manchester, Memoirs, 2 (1813), 105-158. Cf. Scott (ref. 4), 138-141.
334. Peter Ewart, "On the measure of moving force" (read in Nov 1808), Literary and Philosophical Society of Manchester, Memoirs, 2 (1813), 105-158. Cf. Scott (ref. 4), 138-141.
335. William Wollaston, "The Bakerian lecture on the force of percussion," Royal Society of London, Philosophical transactions, 96 (1806), 13-22, on 22, 17, 20. Wollaston's connection between Newton's scholium and energetic reasoning had a future: see Crosbie Smith and Norton Wise, Energy and empire: A biographical study of Lord Kelvin (Cambridge, 1989), 382-383.
336. William Wollaston, "The Bakerian lecture on the force of percussion," Royal Society of London, Philosophical transactions, 96 (1806), 13-22, on 22, 17, 20. Wollaston's connection between Newton's scholium and energetic reasoning had a future: see Crosbie Smith and Norton Wise, Energy and empire: A biographical study of Lord Kelvin (Cambridge, 1989), 382-383.
337. Thomas Young, A course of lectures on natural philosophy and the mechanical arts (London, 1807), 78, 79. In a letter to Pierre Varignon of 26 Jan 1717, Jean Bernoulli called "énergie" the virtual moment of a force: cf. Hiebert (ref. 7), 82.
338. Thomas Young, A course of lectures on natural philosophy and the mechanical arts (London, 1807), 78, 79. In a letter to Pierre Varignon of 26 Jan 1717, Jean Bernoulli called "énergie" the virtual moment of a force: cf. Hiebert (ref. 7), 82.
339. Henry Moseley, The mechanical principles of engineering and architecture (London, 1843), vi (work), xviii (praising Poncelet), 67 (vis viva = "accumulated work"), 160 ("transmission of work" by machines), 586-592 (impact theory à la Poncelet); Eaton Hodgkinson, "Some account of the late Mr. Ewart's paper on the meaning of moving force; and on the recent applications of the principle of living forces to estimate the effects of machines and movers" (30 Apr 1844). Literary and Philosophical Society of Manchester, Memoirs, 7 (1846), 137-156, on 146; Davies Gilbert, "On the expediency of assigning specific names to all such functions of simple elements as represent definite physical properties with the suggestion of a new term in mechanics; illustrated by an investigation of the machine moved by recoil, and also by some observations on the steam engine," Royal Society of London, Philosophical transactions (1827), 25-38. On Hodgkinson, cf. Smith (ref. 2), 72.
340. Henry Moseley, The mechanical principles of engineering and architecture (London, 1843), vi (work), xviii (praising Poncelet), 67 (vis viva = "accumulated work"), 160 ("transmission of work" by machines), 586-592 (impact theory à la Poncelet); Eaton Hodgkinson, "Some account of the late Mr. Ewart's paper on the meaning of moving force; and on the recent applications of the principle of living forces to estimate the effects of machines and movers" (30 Apr 1844). Literary and Philosophical Society of Manchester, Memoirs, 7 (1846), 137-156, on 146; Davies Gilbert, "On the expediency of assigning specific names to all such functions of simple elements as represent definite physical properties with the suggestion of a new term in mechanics; illustrated by an investigation of the machine moved by recoil, and also by some observations on the steam engine," Royal Society of London, Philosophical transactions (1827), 25-38. On Hodgkinson, cf. Smith (ref. 2), 72.
341. Henry Moseley, The mechanical principles of engineering and architecture (London, 1843), vi (work), xviii (praising Poncelet), 67 (vis viva = "accumulated work"), 160 ("transmission of work" by machines), 586-592 (impact theory à la Poncelet); Eaton Hodgkinson, "Some account of the late Mr. Ewart's paper on the meaning of moving force; and on the recent applications of the principle of living forces to estimate the effects of machines and movers" (30 Apr 1844). Literary and Philosophical Society of Manchester, Memoirs, 7 (1846), 137-156, on 146; Davies Gilbert, "On the expediency of assigning specific names to all such functions of simple elements as represent definite physical properties with the suggestion of a new term in mechanics; illustrated by an investigation of the machine moved by recoil, and also by some observations on the steam engine," Royal Society of London, Philosophical transactions (1827), 25-38. On Hodgkinson, cf. Smith (ref. 2), 72.
342. Henry Moseley, The mechanical principles of engineering and architecture
343. Cf. Scott (ref. 4), 137-141.
344. Cf. Harman (ref. 1), 19-21.
345. James Joule, "On a new class of magnetic forces" (16 Feb 1841), Papers (ref. 141), 46-53, on 52-53; "On the heat evolved in the electrolysis of water" (1843, and 1844 for the appendix), ibid., 109-123, on 122-123; "Some remarks on heat and on the constitution of elastic fluids" (1848), ibid., 290-297, on 293-294; John Dalton, A new system of chemical philosophy, 1 (1808), reprint (New York, 1964), 1, 57, 112-114. Cf. Forrester (ref. 142).
346. James Joule, "On a new class of magnetic forces" (16 Feb 1841), Papers (ref. 141), 46-53, on 52-53; "On the heat evolved in the electrolysis of water" (1843, and 1844 for the appendix), ibid., 109-123, on 122-123; "Some remarks on heat and on the constitution of elastic fluids" (1848), ibid., 290-297, on 293-294; John Dalton, A new system of chemical philosophy, 1 (1808), reprint (New York, 1964), 1, 57, 112-114. Cf. Forrester (ref. 142).
347. James Joule, "On a new class of magnetic forces" (16 Feb 1841), Papers (ref. 141), 46-53, on 52-53; "On the heat evolved in the electrolysis of water" (1843, and 1844 for the appendix), ibid., 109-123, on 122-123; "Some remarks on heat and on the constitution of elastic fluids" (1848), ibid., 290-297, on 293-294; John Dalton, A new system of chemical philosophy, 1 (1808), reprint (New York, 1964), 1, 57, 112-114. Cf. Forrester (ref. 142).
348. James Joule, "On a new class of magnetic forces" (16 Feb 1841), Papers (ref. 141), 46-53, on 52-53; "On the heat evolved in the electrolysis of water" (1843, and 1844 for the appendix), ibid., 109-123, on 122-123; "Some remarks on heat and on the constitution of elastic fluids" (1848), ibid., 290-297, on 293-294; John Dalton, A new system of chemical philosophy, 1 (1808), reprint (New York, 1964), 1, 57, 112-114. Cf. Forrester (ref. 142).
349. Joule (ref. 142), 159(1843); Joule, draft of ref. 141, discussed in Forrester (ref. 143,) 296-298; sketch re-drawn in Henry John Steffens, James Prescott Joule and the concept of energy (New York, 1979), 121.
350. Joule (ref. 142), 159(1843); Joule, draft of ref. 141, discussed in Forrester (ref. 143,) 296-298; sketch re-drawn in Henry John Steffens, James Prescott Joule and the concept of energy (New York, 1979), 121.
351. Joule (ref. 142), 159(1843); Joule, draft of ref. 141, discussed in Forrester (ref. 143,) 296-298; sketch re-drawn in Henry John Steffens, James Prescott Joule and the concept of energy (New York, 1979), 121.
352. On a possible Scottish origin of Joule's theological conviction (through John Playfair), cf. Smith (ref. 2), 72.
353. James to William Thomson, 4 Aug 1844, discussed in Smith and Wise (ref. 145), 242-243; Notebook entry of 8 Apr 1845, quoted ibid., 245; William Thomson, "On the mutual attraction or repulsion between two electrified spherical conductors" (1853), in Thomson, Reprint of papers on electrostatics and magnetism (London, 1872), 86-97, on 92-93.
354. James to William Thomson, 4 Aug 1844, discussed in Smith and Wise (ref. 145), 242-243; Notebook entry of 8 Apr 1845, quoted ibid., 245; William Thomson, "On the mutual attraction or repulsion between two electrified spherical conductors" (1853), in Thomson, Reprint of papers on electrostatics and magnetism (London, 1872), 86-97, on 92-93.
355. James to William Thomson, 4 Aug 1844, discussed in Smith and Wise (ref. 145), 242-243; Notebook entry of 8 Apr 1845, quoted ibid., 245; William Thomson, "On the mutual attraction or repulsion between two electrified spherical conductors" (1853), in Thomson, Reprint of papers on electrostatics and magnetism (London, 1872), 86-97, on 92-93.
356. William Thomson, "On the theory of electromagnetic induction" (1848), in Reprint (ref. 153), 91-92, on 91; "Applications of the principle of mechanical effect to the measurement of electromotive forces, and of galvanic resistances, in absolute units" (1851), in Mathematical and physical papers (6 vols., Cambridge, 1882-1911), 1, 490-502. Cf. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000), 122-123.
357. William Thomson, "On the theory of electromagnetic induction" (1848), in Reprint (ref. 153), 91-92, on 91; "Applications of the principle of mechanical effect to the measurement of electromotive forces, and of galvanic resistances, in absolute units" (1851), in Mathematical and physical papers (6 vols., Cambridge, 1882-1911), 1, 490-502. Cf. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000), 122-123.
358. William Thomson, "On the theory of electromagnetic induction" (1848), in Reprint (ref. 153), 91-92, on 91; "Applications of the principle of mechanical effect to the measurement of electromotive forces, and of galvanic resistances, in absolute units" (1851), in Mathematical and physical papers (6 vols., Cambridge, 1882-1911), 1, 490-502. Cf. Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford, 2000), 122-123.
359. Cf. Smith and Wise (ref. 145), 242-245.
360. James to William Thomson, 13 Aug 1863, quoted in Smith and Wise (ref. 145), 286.
361. William Thomson, "An account of Carnot's theory of the motive force of heat; with numerical results from Regnault's experiments on steam" (1849), in Papers (ref. 154), 1, 113-155, on 118n-119n.
362. Cf. Smith and Wise (ref. 145), 302-332.
363. William Thomson, "On the dynamical theory of heat, with numerical results deduced from Mr. Joule's equivalent of a thermal unit, and M. Regnault's observations of steam" (1851), in Papers (ref. 145), 1, 174-332, on 178-179.
364. William Thomson, draft of ref. 159, quoted in Smith and Wise (ref. 145), 329. Cf. also Thomson's notes of 1839-40, quoted ibid., 306-307: "All created things must be sustained," or "The continual presence of God is necessary to preserve as to create."
365. Lewis Gordon, "A synopsis of lectures on civil engineering and mechanics" (London, 1849), 1-2, 5. Cf. Smith and Wise (ref. 145), 291; Smith (ref. 2), 37 (James on waterwheels); Ben Marsden, "Engineering science in Glasgow: Economy, efficiency and measurement as prime movers in the differentiation of academic disciplines," British journal for the history of science, 25 (1992), 319-346, and "'A most important trespass': Lewis Gordon and the Glasgow chair of civil Engineering and mechanics, 1840-55," in Jon Agar and Crosbie Smith, eds., Making space for science: Territorial themes in the shaping of knowledge (Houndmills, 1998), 87-117, on 110-112 (for "mechanical effect" in Gordon's course since 1840). In his synopsis, p. 5, Gordon ascribed the paternity of "mechanical effect" (mechanische Wirkung) to Weisbach, whose lectures he had attended. Although Weisbach (ref. 139), did not cite his sources, he borrowed much from Poncelet and Smeaton.
366. Lewis Gordon, "A synopsis of lectures on civil engineering and mechanics" (London, 1849), 1-2, 5. Cf. Smith and Wise (ref. 145), 291; Smith (ref. 2), 37 (James on waterwheels); Ben Marsden, "Engineering science in Glasgow: Economy, efficiency and measurement as prime movers in the differentiation of academic disciplines," British journal for the history of science, 25 (1992), 319-346, and "'A most important trespass': Lewis Gordon and the Glasgow chair of civil Engineering and mechanics, 1840-55," in Jon Agar and Crosbie Smith, eds., Making space for science: Territorial themes in the shaping of knowledge (Houndmills, 1998), 87-117, on 110-112 (for "mechanical effect" in Gordon's course since 1840). In his synopsis, p. 5, Gordon ascribed the paternity of "mechanical effect" (mechanische Wirkung) to Weisbach, whose lectures he had attended. Although Weisbach (ref. 139), did not cite his sources, he borrowed much from Poncelet and Smeaton.
367. Lewis Gordon, "A synopsis of lectures on civil engineering and mechanics" (London, 1849), 1-2, 5. Cf. Smith and Wise (ref. 145), 291; Smith (ref. 2), 37 (James on waterwheels); Ben Marsden, "Engineering science in Glasgow: Economy, efficiency and measurement as prime movers in the differentiation of academic disciplines," British journal for the history of science, 25 (1992), 319-346, and "'A most important trespass': Lewis Gordon and the Glasgow chair of civil Engineering and mechanics, 1840-55," in Jon Agar and Crosbie Smith, eds., Making space for science: Territorial themes in the shaping of knowledge (Houndmills, 1998), 87-117, on 110-112 (for "mechanical effect" in Gordon's course since 1840). In his synopsis, p. 5, Gordon ascribed the paternity of "mechanical effect" (mechanische Wirkung) to Weisbach, whose lectures he had attended. Although Weisbach (ref. 139), did not cite his sources, he borrowed much from Poncelet and Smeaton.
368. Lewis Gordon, "A synopsis of lectures on civil engineering and mechanics" (London, 1849), 1-2, 5. Cf. Smith and Wise (ref. 145), 291; Smith (ref. 2), 37 (James on waterwheels); Ben Marsden, "Engineering science in Glasgow: Economy, efficiency and measurement as prime movers in the differentiation of academic disciplines," British journal for the history of science, 25 (1992), 319-346, and "'A most important trespass': Lewis Gordon and the Glasgow chair of civil Engineering and mechanics, 1840-55," in Jon Agar and Crosbie Smith, eds., Making space for science: Territorial themes in the shaping of knowledge (Houndmills, 1998), 87-117, on 110-112 (for "mechanical effect" in Gordon's course since 1840). In his synopsis, p. 5, Gordon ascribed the paternity of "mechanical effect" (mechanische Wirkung) to Weisbach, whose lectures he had attended. Although Weisbach (ref. 139), did not cite his sources, he borrowed much from Poncelet and Smeaton.
369. Lewis Gordon, "A synopsis of lectures on civil engineering and mechanics" (London, 1849), 1-2, 5. Cf. Smith and Wise (ref. 145), 291; Smith (ref. 2), 37 (James on waterwheels); Ben Marsden, "Engineering science in Glasgow: Economy, efficiency and measurement as prime movers in the differentiation of academic disciplines," British journal for the history of science, 25 (1992), 319-346, and "'A most important trespass': Lewis Gordon and the Glasgow chair of civil Engineering and mechanics, 1840-55," in Jon Agar and Crosbie Smith, eds., Making space for science: Territorial themes in the shaping of knowledge (Houndmills, 1998), 87-117, on 110-112 (for "mechanical effect" in Gordon's course since 1840). In his synopsis, p. 5, Gordon ascribed the paternity of "mechanical effect" (mechanische Wirkung) to Weisbach, whose lectures he had attended. Although Weisbach (ref. 139), did not cite his sources, he borrowed much from Poncelet and Smeaton.
370. Gordon (ref. 161), 33-37, on 33-34; Smith and Wise (ref. 145), 293.
371. Gordon (ref. 161), 33-37, on 33-34; Smith and Wise (ref. 145), 293.
372. William Whewell, Elementary treatise on mechanics, 4th ed. (Cambridge, 1833), xi (lower aim), 156 (collisions), 85 (friction), 239 (work), 240 (principle).
373. William Whewell, The mechanics of engineering (Cambridge, 1841), vii, 148, 156. Cf. Smith and Wise (ref. 145), 286-287.
374. William Whewell, The mechanics of engineering (Cambridge, 1841), vii, 148, 156. Cf. Smith and Wise (ref. 145), 286-287.
375. Whewell (ref. 164), 181, 216. Contra Smith and Wise (ref. 145), 288. Whewell did not suppose the annihilation of work. For Poncelet and Whewell, "lost" or "consumed" work did not vanish, it only became inaccessible. Their view was quite similar to Thomson's later notion of dissipation.
376. Whewell (ref. 164), 181, 216. Contra Smith and Wise (ref. 145), 288. Whewell did not suppose the annihilation of work. For Poncelet and Whewell, "lost" or "consumed" work did not vanish, it only became inaccessible. Their view was quite similar to Thomson's later notion of dissipation.
377. Cf. Crosbie Smith, "Mechanical philosophy and the emergence of physics in Britain: 1800-1850," Annals of science, 33 (1976), 3-29; Smith and Wise (ref. 145), 85-87.
378. Cf. Crosbie Smith, "Mechanical philosophy and the emergence of physics in Britain: 1800-1850," Annals of science, 33 (1976), 3-29; Smith and Wise (ref. 145), 85-87.