[Footnotes]

[Footnotes]
*
CA, Clausius, Abhandlungen Über die mechanische Wärmetheorie (2 parts, Braunschweig, 1864)
CMT, Clausius, The mechanical theory of heat (London, 1867)
1
Clifford Truesdell, The tragicomical history of thermodynamics, 1822–1854 (New York, 1980)
2
Eri Yagi, "Analytical approach to Clausius's first memoir on the mechanical theory of heat (1850)," JSHS, 20 (1981), 77–94.
3
Rudolf Clausius, "Über die bewegende Kraft der Warme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen," AP, 79 (1850), 368–397, 500–524, in CA, 1, 16–78
"On the moving force of heat and the laws of heat which may be de- duced therefrom," PM, 2 (1851), 1–21, 102–121, in CMT, 14–69.
W. F. Magic, occurs in Eric Mendoza, ed., Reflection on the motive power of fire by Sadi Carnot (New York, 1960), 117–152.
4
Clausius, "Über ein veränderte Form des Zweiten Haupt-satzes der mechanischen Warmetheorie," AP, 93 (1854), 481–506, on 506, in CA, 1, 127–154, on 154
"On a modified form of the second fundamental theorem in the mechanical theory of heat," PM, 12 (1856), 81–98, on 98, in CMT, 111–135, on 135.
5
Clausius, CMT, 17, 19.
6
Clausius, "Über verschiedene fur Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie," AP, 125 (1865), 353–400, in CA, 2, 1–44
"Ninth memoir, on several convenient forms of the fundamental equations of the mechanical theory of heat," CMT, 327–365.
7
Clausius, "Ober die mechanische Warmetheorie," Dinglers Polytechnisches Journal, 150 (1858), 29–40, in CA, 1, 1–15
"Mathematical introduction," in CMT, 1–13.
8
Sadi Carnot, Réflexions sur la puissance motrice du feu (1834) (London, 1966)
R. H. Thurston, in E. Mendoza, ed., Reflection (ref. 3), 1–59
Emile Clapeyron, "Memoire sur la puissance motrice de la chaleur," Journal de l'école polytechnique, 14 (1834), 153–190
"Ü"ber die bewegende Kraft der Warme," AP, 59 (1843), 44–451, 566–586
"Memoir on the motive power of heat," tr. E. Mendoza, in Mendoza, ed., Reflection (ref. 3), 71–105.
9
G. Decher, "Über das Wesen der Wärme," Dinglers Polytechnisches Journal, 148 (1858), 1–10, 81–93, 161–173, 241–257
Clausius, CMT, 1.
10
Clausius (ref. 7).
11
CMT, 2, 26, CA, 2.
12
CMT, vii
Gaspard Monge, Application de Vanalyse à la géométrie (Paris, 1795), ed. Joseph Liouville (Paris, 18505), 105–114, 547–638.
13
Ibid., 617–619
I. Todhunter, A history of the progress of the calculus of variation (London, 1861), 505–507
J. d'Alembert, Traité de dynamique (Paris, 17582), 116–117.
14
Akira Kobori, 18seiki no sügaku (Mathematics in the 18th century) (Tokyo, 1979), 68–72
René Dugas, A history of mechanics, tr. J. R. Maddox (London, 1955), 282–283
S. S. Demidov, "The study of partial differential equations of the first order in the 18th and 19th centuries," AHES, 26 (1982), 325–350.
15
CMT, 20–21.
16
Clausius, "Warmetheorie" (ref. 7), 35.
17
Clausius, "Über den Zusammenhang des zweiten Hauptsatzes der mechanischen Warmetheorie mit dem hamilton'sche Prinzip," AP, 146 (1872), 585–591
"On the con- nection of the second proposition of the mechanical theory of heat with Hamilton's prin- ciple," PM, 44 (1872), 365–369
L. Boltzmann, "Ober die mechanische Bedeutung des zweiten Hauptsatzes der Warmetheorie," Wiener Berichte, 53 (1866), 195–220
C. Szily, "On Hamilton's principle and the second proposition of the mechanical theory," PM, 43 (1872), 339–343.
18
Clausius, "Ober die Zurückführung des zweiten Hauptsatzes der mechanischen Warmetheorie auf allgemeine mechanischen Prinzipien," AP, 142 (1871), 433–461
"On the reduction of the second axiom of the mechanical theory of heat to general mechanical principles," PM, 42 (1871), 161–181
Gilnter Bierhalter, "Das Virialtheorem in seiner Beziehung zu den mechanischen Grundlegungen des zweiten Hauptsatzes der Warmelehre," AHES, 27 (1982), 199–211.
19
CMT, 24–25.
20
Ibid., 26
CA, 1, 80
CMT, 70.
21
CA, 1, 86, 32
CMT, 76, 29.
22
CMT, 28–29.
23
CMT, 41 (an adiabatic process)
Siméon-Denis Poisson, "De la force élastique et la chaleur des gas," Traité de mécanique, 2nd ed. (2 vols., Paris, 1833), 2, 637–662.
24
CMT, 27.
25
CMT, 69–75.
26
Ibid., 71.
27
G. G. Stokes, Mathematical and physical papers, 5 (Cambridge, 1905), 320
Yagi (ref. 2), 92–93.
Truesdell (ref. 1), 206–207
28
Clausius, "A contribution to the history of the mechanical theory of heat," PM, 43 (18762), 106–115, on 107
Clausius, Die mechanische W&rmetheorie (Braunschweig, 1872)
The mechanical theory of heat, tr. Walter R. Brown (London, 1879), 339–340.
29
Clapeyron (ref. 8), 84–85.
30
CA, 1, 31.
31
W. 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 on steam," Royal Society of Edinburgh, Transactions, 20:2 (1851)
PM, 4 (1852), 8–21
Mathematical and physical papers (3 vols., Cambridge, 1882), 1, 174–189.
32
CMT, 355.
33
CMT, 46–47.
34
Clausius (ref. 4), in CMT, 116.
35
CMT, 69–75, on 70–71.
36
Ibid., 73.
37
CMT, 75–78.
38
Ibid., 28, 77.
39
Hashitsume, Netsutokei rikigaku nyumon (Introduction to thermodynamics statistical mechanics) (Tokyo, 1981), 77–79.
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