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Thermodynamics and Sources of Solar Heat, 1846–1862

  • Frank A. J. L. James (a1)


In 1859 Charles Darwin in chapter nine of the Origin of Species showed how he had calculated that the age of the Weald was three hundred million years and that consequently the age of the earth was considerably greater than that. Darwin of course needed such a long period of time for the process of evolution by natural selection to occur. Arguments which showed that the earth could not be that old would therefore cast serious doubt on his theory. Such views were advanced in 1862 by William Thomson, later Lord Kelvin, professor of Natural Philosophy at Glasgow. He specifically challenged the result of Darwin's calculation of the age of the Weald by arguing that the sun could not have emitted its heat and light for that length of time. The consequences of this assertion for the biological and geological sciences for the remainder of the nineteenth century have already been delineated by Burchfield. What I wish to do in this paper is to show that the theoretical basis of Thomson's 1862 assertion had not been specifically developed as a response to Darwin, but that it was a consequence of the formulation of the first two laws of thermodynamics. I shall also show that Thomson's work was not done in isolation but that the question of the maintenance of solar energy was a serious concern of a number of physicists who had formulated the laws of thermodynamics.

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I wish to thank Dr M. B. Hall, Dr J. D.Burchfield, and Prof. G.J. Whitrow for their comments on earlier versions of this paper. I also thank the University Library Cambridge for permitting me to study the correspondence of G. G. Stokes and William Thomson. A shorter version of this paper was presented to the History of Astronomy and Physics section of the XVIth International Conference of the History of Science in Bucharest in August 1981.

1 Darwin, C., On the Origin of Species by Means of Natural Selection, London, 1859, pp. 286–7.

2 Thomson, William, Kelvin, Lord (18241907). The main collection of his MSS is in the University Library Cambridge (ULC add MS 7342); there is also a smaller collection in the University of Glasgow Library. Most of Thomson's scientific papers were collected in his Mathematical and Physical Papers, 6 volumes, Cambridge, 18821911; volumes 1–3 were edited by Thomson and volumes 4–6 were edited by J. Larmor. These will be cited as Thomson Papers. Thomson, 's Popular Lectures and Addresses, 3 volumes, London, 18891894 will be cited as Thomson Lectures.

3 Thomson, W., ‘On the Age of the Sun's Heat’, Macmillan's Magazine, 1862, 5, 388–93; Lectures I, 356–75. The explicit reference to the Weald occurs on p. 368.

4 Burchfield, J. D., Lord Kelvin and the Age of the Earth, New York, 1975.

5 For accounts of the development of the laws of thermodynamics see Truesdell, C., The Tragicomical History of Thermodynamics 1822–1854, New York, 1980; Scott, W. L., The Conflict between Atomism and Conservation Theory 1644–1860, London, 1970; Elkana, Y., The Discovery of the Conservation of Energy, London, 1974; Kuhn, T., ‘Energy Conservation as an Example of Simultaneous Discovery’ in Claggett, M. (ed.), Critical Problems in the History of Science, Madison, 1969, pp. 321–56.

6 Newton, I., The Mathematical Principles of Natural Philosophy, (Motte-Cajori, translation), Berkeley, 1960, pp. 540–2. This aspect of Newton's work is discussed by Kubrin, D., ‘Newton and the Cyclical Cosmos: Providence and the Mechanical Philosophy’, J. Hist. Ideas, 1967, 28, 325–46. In this passage in the Principia Newton only discussed novae. However Newton does seem to have been deliberately ambiguous as to what he thought was the source of solar heat. This is apparent from his conversation with Conduit printed in Brewster, D., The Life of Sir Isaac Newton, London, 1831, pp. 363–6.

7 Euler, L., Lettres a une Princesse d'Allemagne, 2 volumes, St Petersburg, 1758, Reprinted in Leonhardi Euleri Opera Omnia, 3 series, Berlin, Göttingen, Leipzig, Heidelberg, Zürich, 1911-, 3rd series, volumes 11 and 12 (edited by A. Spieser), Zürich, 1960. Letter 17.

8 Ibid., letter 19.

9 Herschel, J. F. W., A Treatise on Astronomy, London, 1834, art. 337.

10 See McRae, R. J., ‘The Origin of the Conception of the Continuous Spectrum of Heat and Light’, University of Wisconsin, Ph.D. thesis, 1969 and Brush, S. G., ‘The Wave Theory of Heat: A Forgotton Stage in the Transition from the Caloric Theory to Thermodynamics’, B.J.H.S. 1970, 5, 145–67.

11 Pouillet, Claude-Servais-Mathias (17901868), ‘Mémoire sur le chaleur solaire, sur les pouvoirs rayonnants et absorbants de l'air atmosphérique, et sur la température de l'espace’, Comptes Rendus, 1838, 7, 2465. Translated into English as ‘Memoir on the solar heat, on the radiating and absorbing powers of atmospheric air, and on the temperature of space’, Taylor, 's Sci. Mem., 1846, 4, 4490. J. F. W. Herschel had also done some work on determining the solar constant; see his Outlines of Astronomy, London, 1849, art. 397. Pouillet's figure was, as we shall see, that generally adopted since in his paper he gave his data and listed his assumptions concerning the transfer of heat through the terrestrial atmosphere. He also provided the value for the rate of emission in easily utilisable forms. For a detailed account of this work see Kidwell, P. A., ‘Prelude to Solar Energy: Pouillet, Herschel, Forbes and the Solar ConstantAnn. Sci., 1981, 38, 457–76.

12 Pouillet, , Sci. Mem., Op. cit. (11), p. 50. The accepted present day value is 2°C.

13 Ibid., p. 53.

14 Ibid., p. 54.

15 Mayer, Julius Robert (18141878). For an account of his life and English translations of most of his papers see Lindsay, R. B., Julius Robert Mayer: Prophet of Energy, Oxford, 1973.

16 Mayer, J. R., Die organische Bewegung in ihiem Zusammenhang mit dem Stoffwechsel. Ein Beitrag zur Naturkunde, Heilbronn, 1845. Translated into English as ‘The Motions of Organisms and their Relatio to Metabolism. An Essay in Natural Science’ in Lindsay, , Op. cit. (15), pp. 75145, p. 99.

17 Mayer, J. R., Beiträge zur Dynamik des Himmels, in populärer Darstallung, Heilbronn, 1848. Translated into English by Dubus, H. as ‘On Celestial Mechanics’, Phil. Mag., 1863, IV, 25, 241–8, 387409417–28; p. 241.

18 Ibid., 244–5.

19 Ibid., 245. In performing this calculation Mayer assumed that the material of the sun had the same specific heat as water and that the sun emitted its heat uniformly from its whole mass. In his paper he did not specify the solar radius which he used, but from my calculation he appears to have assumed the radius to be 712200 kilometres. This agrees (approximately) with his statement (Ibid., 246) that the sun's diameter is nearly 112 times larger than the earth's.

20 Ibid., 245.

21 Mayer, , ‘The Motions …’, in Lindsay, , Op. cit. (15), p. 99.

22 The part of the paper which was published was entitled ‘Sur la transformation de la force vive en chaleur, et reciproquement’, Comptes Rendus, 1848, 27, 385–7. This makes clear, on p. 385, that the title of Mayer's paper, presented on 27 July 1846, was ‘Sur le production de lumière et de la chaleur du soleil’.

23 Mayer, , Phil. Mag., Op. cit. (17), pp. 241–2.

24 Ibid., 245.

25 Ibid., 246.

26 Ibid., 387.

27 Mayer, , ‘The Motions …’, in Lindsay, , Op. cit. (15), p. 88.

28 Mayer, , Phil. Mag., Op. cit. (17), p. 397.

29 Ibid., 388–9.

30 Ibid., 387.

31 Ibid., 389.

32 Ibid. Mayer did not have the problem of dealing with the asteroids since by 1848 only eight had been discovered. These being comparatively large bodies they would not fall towards the sun particularly quickly.

33 Ibid., 392.

34 Ibid., 395.

35 Ibid., 399.

37 Ibid., 397. In a footnote to this passage Mayer suggested that this was the reason why comet's tails pointed away from the sun.

39 Ibid., 400.

40 Ibid., 388.

41 Ibid., 402.

43 Thomson, W., ‘On the dynamical theory of heat with numerical results deduced from Mr. Joule's equivalence of a thermal unit, and M. Regnault's observations on steam’, Trans. Roy. Soc. Edinb., 1851, 20, 261–98, 475–82; 1854, 21, 123–71; Papers I, 174291. For a discussion of this paper see Smith, C. W., ‘Natural Philosophy and Thermodynamics: William Thomson and the “Dynamical Theory of Heat”’, B.J.H.S., 1976, 9, 293319.

44 Thomson, , Op. cit. (43), art. 12. Thomson's emphasis.

45 ULC add MS 7342, PA 128. This is printed in Wilson, D. B., ‘Kelvin's Scientific Realism: The Theological Context’, Phil. J., 1974, 11, 4160, pp. 58–9.

46 Ibid., 58.

47 See Thomson, W. to Stokes, G. G., 26 04 1854, ULC add MS 7656, K 69.

48 Wilson, , Op. cit. (45), p. 58.

49 Ibid., 59. The quotation is from Isaiah 51. 6.

50 Stokes, G. G. (1819 1903). The main collection of Stokes's MSS is kept in the University Library Cambridge (ULC add MS 7656). The correspondence between Stokes and Thomson will shortly be published in Wilson, D. B., The Correspondence between Sir George Gabriel Stokes and Sir William Thomson, Baron Kelvin of Largs, Cambridge, forthcoming.

51 Thomson, to Stokes, , 13 01 1852, ULC add MS 7656, K 53.

52 Indeed almost the last problem which Thomson worked on was the theory of the sun, ‘The Problem of a Spherical Gaseous Nebula’, Phil. Mag., 1908, VI, 15, 687711; 16, 1–23; Papers V, 254–83.

53 Thomson, W., ‘On the mechanical action of radiant heat or light: on the power of animated creatures over matter: on the sources available to man for the production of mechanical effect’, Proc. Roy. Sac. Edinb., 1852, 3, 108–13; Papers I, 50510. He mentions Pouillet's work on p. 505, of which Stokes had, presumably, informed him.

54 Ibid., 510.

55 Thomson, W., ‘On a universal tendency in nature to the dissipation of mechanical energyProc. Roy. Sac. Edinb., 1852, 3, 13942; Papers I, 511–14.

56 Ibid., 514.

57 Thomson, to Stokes, , 26 04 1854, ULC add MS 7656, K 69.

58 Thomson, W., ‘On the mechanical energies of the solar system’, Trans. Roy. Soc. Edinb., 1854, 21, 6380; Papers II, 125. p. 4 where Thomson makes this point.

59 Thomson, to Stokes, , 20 02 1854, ULC add MS 7656, K 62 and Thomson, to Helmholtz, H., 24 07 1855 (in Thompson, S. P., The Life of William Thomson, Baron Kelvin of Largs, 2 volumes, London, 1910, 1, 309), make it quite clear that Thomson was not at the Hull meeting.

60 Waterston, John James (1811 1883).Haldane, J. S., The Collected Scientific Papers of J. J. Waterston, Edinburgh, 1928, contains a biographical sketch by Haldane of Waterston.

61 Waterston, J. J., ‘On dynamical sequences in Kosmos’, Athenaeum, 1853, 10991100. This was not published in Waterston's collected papers.

62 Waterston made an elementary error in his calculation since he used an escape velocity from the sun of 545 miles per second which is a factor too large. Therefore his calculation concerning the amount of meteoric matter needed was half the amount required according to his hypothesis. He also assumed that the meteoric material had the specific heat of iron and the density of water.

63 Waterston, , Op. cit. (61), 1099.

64 Ibid., 1100.

65 It is not clear how Waterston derived this figure.

66 He appears to have done this by simply considering the amount of heat produced by a body falling this distance.

67 Waterston, , Op. cit. (61), 1099. The main source for the nebular hypothesisis the final book of Laplace, P. S., Exposition du Systeme du Monde, Paris, 1796; it went through several changes (see Jaki, S. L., ‘The Five Forms of Laplace's Cosmogony’, Am. J. Phys., 1976, 44, 411) before the final version was published. The hypothesis became very well known and received a good deal of attention in the nineteenth century.

68 There is no evidence to indicate whether or not Thomson attempted to contact Waterston.

69 Thomson, , Papers, Op. cit. (58), p. 4.

70 Athenaeum, 1853, 1100.

72 Thomson, , Papers, Op. cit. (58), p. 3.

73 Ibid., 4.

74 Ibid., 10.

75 Ibid., 3.

76 Joule, J. P., ‘On Shooting Stars’, Phil. Mag., 1848, III, 32, 349–51; in The Scientific Papers of James Prescott Joule, 2 volumes, London, 18841887, 1, pp. 286–8. Thomson cited this paper in Thomson, , Papers, Op. cit. (58), p. 5.

78 Thomson, to Stokes, , 2 03 1854, ULC add MS 7656, K 64, Thomson's emphasis. This also shows that Thomson had already spotted Waterston's arithemetical error (see note 62) since 2000 pounds is just twice the amount that Waterston required.

79 Thomson, , Papers, Op. cit. (58), pp. 1013.

80 Thomson, to Stokes, , 9 03 1854, ULC add MS 7656, K 66.

81 Stokes, to Thomson, , 28 03 1854, ULC add MS 7342, S 369. It should be pointed out that Stokes did not reply at once because he had been ill.

82 Herschel, W., ‘On the Nature and Construction of the Sun and Fixed Stars’, Phil. Trans., 1795, 4672.

83 Stokes, to Thomson, , 28 03 1854, ULC add MS 7342, S 369. The quotation is a misquote of Genesis 27. 1.

84 Stokes, to Thomson, , 24 02 1854, ULC add MS 7342, S 366.

85 Thomson, to Stokes, , 2 and 9 03 1854, ULC add MS 7656, K 64 and 66 respectively.

86 Stokes, to Thomson, , 28 03 1854, ULC add MS 7342, S 369.

87 Thomson, to Stokes, , 21 03 and 29 04 1854, ULC add MS 7656, K 68. This presumably refers to Herschel, Op. cit. (11), art. 897 where he discussed the zodiacal light.

89 This Thomson, argued for in Op. cit. (58) which was read to the Royal Society of Edinburgh on 17 April 1854.

90 Thomson, to Stokes, , 9 03 1854, ULC add MS 7656, K 66.

91 Thomson, , Papers, Op. cit. (58) p. 7.

92 Ibid., 8.

94 Thomson, to Stokes, , 2 03 1854, ULC add MS 7656, K 64.

95 Thomson, W., ‘On the Mechanical Value of a Cubic Mile of Sunlight, and on the possible density of the Luminferous Medium’, Proc. Roy. Soc. Edinb. 1854, 2, 253–5. This was later published as ‘Note on the Possible Density of the Luminferous Medium and on the Mechanical Value of a Cubic Mile of Sunlight’, Trans. Roy. Soc. Edinb., 1852, 21, 5761; Papers II, 2833.

96 Ibid., 28, and Thomson, to Stokes, , 21 03 and 20 04 1854, ULC add MS 7656, K. 68.

97 Thomson, , Papers, Op. cit. (58), p. 9.

99 Ibid., 24.

100 Ibid., 20.

101 Ibid., 24–5.

102 Thomson, , Proc. Roy. Soc. Edinb., Op. cit. (95), p. 254.

103 For a detailed discussion of Stokes's spectral work see chapter 5 of my Ph.D. thesis, ‘The Early Development of Spectroscopy and Astrophysics’, University of London (Imperial College), 1981.

104 Thomson, to Stokes, , 2 03 1854, ULC add MS 7656, K 64.

105 Stokes, to Thomson, , 24 02 1854, ULC add MS 7342, S 366. Foucault, L., ‘Lumière électrique’, L'Institut, 18491850, 17, 44–6.Miller, W. A., ‘Experiments and observations on some cases of lines in the prismatic spectrum produced by the passage of light through coloured vapours and gases, and from certain coloured flames’, Phil. Mag., 1845, III, 27, 8191. For a discussion of this work see M. Sutton, A., ‘Spectroscopy and the Chemists: A Neglected Opportunity?’, Ambix, 1976, 23, 1626.

106 Stokes, to Thomson, , 24 02 1854, ULC add MS 7342, S 366. Brewster, D., ‘On the luminous lines in certain flames corresponding to the defective lines in the sun's light’, Rep. Brit. Ass., 1842, part 2, p. 15.

107 Stokes, to Thomson, , 24 02 1854, ULC add MS 7342, S 366. Brewster, D., ‘Observations sur le spectra solaire’, Camptes Rendus, 1850, 30, 578–81.

108 Appendix no. 2, ‘Friction between vortices of meteoric vapour and the sun's atmosphere’ in Thomson, , Papers, Op. cit. (58), pp. 1921.

109 Thomson, , Papers, Op. cit. (95).

110 Smyth, C. P., ‘Account of experiments to ascertain the amount of Prof. Wm. Thomson's “Solar Refraction”’, Proc. Roy. Soc. Edinb., 1855, 3, 302–3.

111 Helmholtz, Hermann (18211894). He had not yet met Thomson, although he was to do so the following year, when they became close friends.

112 Helmholtz, H., Ueber die Wechselwirkung der Naturkräfte und die darauf be züglichen neuesten Ermittelungen der Physik, Königsberg 1854. Translated into English by Tyndall, John as ‘On the interaction of natural forces’, Phil. Mag. 1856, IV, 11, 489518.

113 Athenaeum, 1853, 1097.

114 Helmholtz, , Phil. Mag., Op. cit. (112), p. 512 refers to Mayer's work on tidal friction which is in Mayer, , Phil. Mag., Op. cit. (17), pp. 403–9.

115 Helmholtz, , Phil. Mag., Op. cit. (112), p. 503.

116 Thomson, , Op. cit. (55).

117 Helmholtz, , Phil. Mag., Op. cit. (112), p. 503.

118 See for example Herschel, , Op. cit. (9), art. 336.

119 Helmholtz, being German, and lecturing in Königsberg, maintained that Kant had devised a nebular hypothesis similar to Laplace's which he had devised independently. Kant had made a much more speculative suggestion than Laplace in his Allgemeine Naturgeschichte und Tkeorie des Himmels, Königsberg, 1755. Translated into English by Hastie, W. as Universal Natural History and Theory of the Heavens, 1900, reprinted, Ann Arbor, 1969. For a discussion of the differences between the hypotheses of Kant and Laplace see Whitrow, G. J., ‘The nebular hypotheses of Kant and Laplace’, Actes. XIIe Cong. Int. Hist. Sci., 1968, IIIB, 175–80.

120 Helmholtz, , Phil. Mag., Op. cit. (112), p. 505.

121 Ibid., 507.

122 Ibid., 506 and 516–8.

123 Ibid., 506.

124 Ibid., 517.

125 Helmholtz here assumed that the sun emitted its energy uniformly over its whole mass and that its specific heat was the same as water (Ibid., 517). He seems to have used a solar radius of 717600 kilometres. He appears to have used Pouillet's 4/3c formula with c = 1 (the specific heat of water) to obtain this figure.

126 Ibid.

127 Ibid., 514.

128 Ibid., 507.

129 Ibid., 506.

130 Thomson, to King, David, 3 02 1862, in King, A. G., Kelvin the Man, London, 1925, pp. 1012.

131 Thomson, W., ‘On the mechanical antecedents of motion, heat, and light’, Rep. Brit. Ass. 1854, part 2, 5963; Papers II, 34 40, p. 38.

132 Ibid.

133 Thomson, , Rep. Brit. Ass., Op. cit. (131), p. 62. This passage appeared in a footnote that Thomson omitted from his Papers.

134 Thomson, , Papers, Op. cit. (131), pp. 3940.

135 Apart from ULC add MS 7342, NB 34, pp. 204–5 where he attempted to examine on 6 and 15 August, and 27 October 1855, the effect on the excentricity of the planets due to meteorites falling onto the sun. These calculations were not published.

136 Leverrier, U. J. J., ‘Sur la théorié de Mercure et sur le mouvement du périhélie de cette planète’, Camptes Rendus, 1859, 49, 379–83.

137 For a discussion of how Leverrier made his discovery see Hanson, N. R., ‘Leverrier: The Zenith and Nadir of Newtonian Mechanics’, Isis, 1962, 53, 359–78, especially section 2.

138 Thomson, W., ‘Mémoire sur l'énergie mécanique du système solaire’, Camptes Rendus, 1854, 39, 6827.

139 For an account of how Neptune was discovered see Grosser, M., The Discovery of Neptune, Boston, 1962.

140 Thomson, W., ‘Recent investigations of M. Leverrier on the motion of Mercury’, Proc. Glasg. Phil. Soc., 1859, 4, 263–66; Papers V, 134–7. Read 14 December 1859, p. 137.

141 Ibid.

142 Ibid., 134.

143 Thomson, W., ‘On the variation of the periodic times of the earth and inferior planets, produced by matter falling into the sun’, Proc. Glasg. Phil. Soc., 1860, 4, 272–4; Papers V, 138–40. Read 4 January 1860, p. 140.

144 Ibid.

145 Thomson, , Lectures, Op. cit. (3), p. 360.

146 Ibid.

147 Ibid., 360–1.

148 Thomson, W., ‘Physical Considerations regarding the Possible Age of the Sun's Heat’, Rep. Brit. Ass., 1861, part 2, 27–8; Papers V, 141–4. It is worth noting that Thomson's popular Macmillan's Magazine paper (Op. cit. (3)) (which can be regarded as an expanded version of this British Association paper) was the only place, at this time, where Thomson explicitly repudiated his meteoric hypothesis. In his British Association paper it is only by accepting Helmholtz's theory that he implicitly rejects the meteoric hypothesis. The other major difference between the two papers is that in the British Association paper Thomson did not explicitly attack Darwin's estimate of the age of the earth, whereas in the Macmillan's Magazine paper he did.

149 This he did later in the century with the knowledge of J. H. Lane's work. Thomson, W., ‘On the equilibrium of a gas under its own gravitation only’, Proc. Roy. Soc. Edinb., 1887, 14, 111–18; Papers V, 184–90.

150 Thomson, , Papers, Op. cit. (148), p. 143.

151 Appendix no. 4, ‘On the Age of the Sun’, in Thomson, , Papers, Op. cit. (58), pp. 23–5.

152 Thomson, , Papers, Op. cit. (148), pp. 143–4.

153 Thomson, , Lectures, Op. cit. (3), p. 368.

154 Ibid., 375.

155 Clerke, A. M., A Popular History of Astronomy during the Nineteenth Century, 3rd edition, London, 1893, p. 378. See also Merz, J. T., A History of European Thought in the Nineteenth Century, 4 volumes, Edinburgh, 19041912, II, 358–9.

156 See for example, Meadows, A. J., Science and Controversy: A Biography of Sir Normam Lockyer, London, 1972 and Early Solar Physics, Oxford, 1970.

157 See Burchfield, , Op. cit. (4) for an account of this debate.

158 See DeVorkin, D. H., ‘An Astronomical Symbiosis: Stellar Evolution and Spectral Classification (1860–1910)’, Leicester University Ph.D. thesis, 1978, for an account of the development of the theory after this period.

159 A point made quite explicitly by Thomson in Papers, Op. cit. (53), pp. 509510. In addition to what was said at footnote 61, we note that in 1846, Waterston, in a paper read to the Royal Society, had anticipated part of the kinetic theory of gases. In this paper he had also briefly speculated on the quantity of energy produced by the sun and on possible ways in which it might sustain itself. This was not published at this time apart from a short abstract: ‘On the Physics of Media that are Composed of Free and Perfectly Elastic Molecules in a State of Motion’, Proc. Roy. Soc. 1846, no. 65, p. 604. In 1891 the paper was discoverd in the archives of the Royal Society by Lord Rayleigh who had it published in full in Phil. Trans. 1892, 183, 577. Waterston's discussion of the sun occurs on pp. 54–5. For an account of the history of this paper see Brush, S. G., ‘J. J. Waterston’, D.S.B., XIV, 184–6. And in addition to footnote 113, note that Helmholtz abstracted Waterston's paper in Die Fortschritte der Physik im Jahre 1853, vol. 10, Berlin, 1856. It is not clear whether Helmholtz did this before or after he delivered his lecture.


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