Published online by Cambridge University Press: 05 January 2009
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.
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.Google Scholar
2 Thomson, William, Kelvin, Lord (1824–1907).Google Scholar 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, 1882–1911Google Scholar; 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, 1889–1894Google Scholar will be cited as Thomson Lectures.
5 For accounts of the development of the laws of thermodynamics see Truesdell, C., The Tragicomical History of Thermodynamics 1822–1854, New York, 1980CrossRefGoogle Scholar; Scott, W. L., The Conflict between Atomism and Conservation Theory 1644–1860, London, 1970Google Scholar; Elkana, Y., The Discovery of the Conservation of Energy, London, 1974Google Scholar; 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.Google Scholar
6 Newton, I., The Mathematical Principles of Natural Philosophy, (Motte-Cajori, translation), Berkeley, 1960, pp. 540–2.Google Scholar 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.CrossRefGoogle Scholar 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.Google Scholar
7 Euler, L., Lettres a une Princesse d'Allemagne, 2 volumes, St Petersburg, 1758Google Scholar, 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.
10 See McRae, R. J., ‘The Origin of the Conception of the Continuous Spectrum of Heat and Light’, University of Wisconsin, Ph.D. thesis, 1969Google Scholar 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.CrossRefGoogle Scholar
11 Pouillet, Claude-Servais-Mathias (1790–1868), ‘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, 24–65.Google Scholar 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, 44–90.Google Scholar J. F. W. Herschel had also done some work on determining the solar constant; see his Outlines of Astronomy, London, 1849Google Scholar, 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 Constant’ Ann. Sci., 1981, 38, 457–76.CrossRefGoogle Scholar
12 Pouillet, , Sci. Mem., Op. cit. (11), p. 50.Google Scholar The accepted present day value is 2°C.
16 Mayer, J. R., Die organische Bewegung in ihiem Zusammenhang mit dem Stoffwechsel. Ein Beitrag zur Naturkunde, Heilbronn, 1845.Google Scholar Translated into English as ‘The Motions of Organisms and their Relatio to Metabolism. An Essay in Natural Science’ in Lindsay, , Op. cit. (15), pp. 75–145, p. 99.Google Scholar
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.
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.Google Scholar 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’.
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.
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.
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, 475–82CrossRefGoogle Scholar; 1854, 21, 123–71; Papers I, 174–291.Google Scholar 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, 293–319.CrossRefGoogle Scholar
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, 41–60, pp. 58–9.Google Scholar
50 Stokes, G. G. (1819 1903).Google Scholar 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, CambridgeGoogle Scholar, forthcoming.
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, 108–13CrossRefGoogle Scholar; Papers I, 50510.Google Scholar He mentions Pouillet's work on p. 505, of which Stokes had, presumably, informed him.
59 Thomson, to Stokes, , 20 02 1854Google Scholar, ULC add MS 7656, K 62 and Thomson, to Helmholtz, H., 24 07 1855Google Scholar (in Thompson, S. P., The Life of William Thomson, Baron Kelvin of Largs, 2 volumes, London, 1910, 1, 309)Google Scholar, make it quite clear that Thomson was not at the Hull meeting.
61 Waterston, J. J., ‘On dynamical sequences in Kosmos’, Athenaeum, 1853, 1099–1100.Google Scholar 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.
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.Google Scholar The main source for the nebular hypothesisis the final book of Laplace, P. S., Exposition du Systeme du Monde, Paris, 1796Google Scholar; it went through several changes (see Jaki, S. L., ‘The Five Forms of Laplace's Cosmogony’, Am. J. Phys., 1976, 44, 411)CrossRefGoogle Scholar 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.
78 Thomson, to Stokes, , 2 03 1854Google Scholar, 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.
81 Stokes, to Thomson, , 28 03 1854Google Scholar, 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, 46–72.Google Scholar
83 Stokes, to Thomson, , 28 03 1854Google Scholar, ULC add MS 7342, S 369. The quotation is a misquote of Genesis 27. 1.
87 Thomson, to Stokes, , 21 03 and 29 04 1854Google Scholar, 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)Google Scholar which was read to the Royal Society of Edinburgh on 17 April 1854.
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.Google Scholar 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, 57–61Google Scholar; Papers II, 28–33.Google Scholar
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.
105 Stokes, to Thomson, , 24 02 1854Google Scholar, ULC add MS 7342, S 366. Foucault, L., ‘Lumière électrique’, L'Institut, 1849–1850, 17, 44–6.Google ScholarMiller, 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, 81–91.Google Scholar For a discussion of this work see M. Sutton, A., ‘Spectroscopy and the Chemists: A Neglected Opportunity?’, Ambix, 1976, 23, 16–26.CrossRefGoogle Scholar
108 Appendix no. 2, ‘Friction between vortices of meteoric vapour and the sun's atmosphere’ in Thomson, , Papers, Op. cit. (58), pp. 19–21.Google Scholar
111 Helmholtz, Hermann (1821–1894).Google Scholar He had not yet met Thomson, although he was to do so the following year, when they became close friends.
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.Google Scholar Translated into English by Hastie, W. as Universal Natural History and Theory of the Heavens, 1900, reprinted, Ann Arbor, 1969.Google Scholar 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.Google Scholar
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.
133 Thomson, , Rep. Brit. Ass., Op. cit. (131), p. 62.Google Scholar This passage appeared in a footnote that Thomson omitted from his Papers.
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.Google Scholar
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, 359–78Google Scholar, especially section 2.
138 Thomson, W., ‘Mémoire sur l'énergie mécanique du système solaire’, Camptes Rendus, 1854, 39, 6827.Google Scholar
139 For an account of how Neptune was discovered see Grosser, M., The Discovery of Neptune, Boston, 1962.Google Scholar
148 Thomson, W., ‘Physical Considerations regarding the Possible Age of the Sun's Heat’, Rep. Brit. Ass., 1861, part 2, 27–8Google Scholar; Papers V, 141–4.Google Scholar It is worth noting that Thomson's popular Macmillan's Magazine paper (Op. cit. (3))Google Scholar (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.
151 Appendix no. 4, ‘On the Age of the Sun’, in Thomson, , Papers, Op. cit. (58), pp. 23–5.Google Scholar
158 See DeVorkin, D. H., ‘An Astronomical Symbiosis: Stellar Evolution and Spectral Classification (1860–1910)’, Leicester University Ph.D. thesis, 1978Google Scholar, 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. 509–510.Google Scholar 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.Google Scholar 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, 5–77.Google Scholar 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.Google Scholar 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.Google Scholar It is not clear whether Helmholtz did this before or after he delivered his lecture.