¹Crowther, J. G., British scientists of the nineteenth century (Harmondsworth: Pelican Books, 1941). pp. 234–6.Google Scholar

²Crowther, J. G., pp. 290–1.Google Scholar

³Thompson, D'Arcy W., ‘Obituary of Joseph Larmor’, Year book of the Royal Society of Edinburgh (1941–1942), p. 12.Google Scholar

⁴Thomson, William, Mathematical and physical papers (6 vols., Cambridge, 1882–1911), i. 174–316.Google Scholar

⁵ See Meyerson, Émile, Identity and reality, trans, by Loewenberg, K. (London, 1930), pp. 189–214 and 259–90, for an analysis of the philosophical difficulties encountered with the two laws of thermodynamics. Meyerson argues that conservation principles, of which the first law of thermodynamics is an example, are anticipated by us to some extent and so are always readily accepted by the mind. The second law, however, with its feature of irreversible change, ‘in no way participates in this “plausibility”’ and depends entirely on our experience of the world as it is. In this paper I shall deal with these problems strictly in the historical context of William Thomson.Google Scholar

⁶Thompson, S. P., The life of William Thomson, Baron Kelvin of Largs (2 vols., London, 1910), i. 4–12. Meikleham held the Glasgow chair of natural philosophy from 1803 until 1846. The relevant notebooks areGoogle Scholar

Thomson, James (senior), ‘Exercises in natural philosophy 1811–12’ (Thomson Collection, Queen's University Library, Belfast), andGoogle Scholar

Thomson, William, ‘Notebook of natural philosophy class 1839–40’ (Kelvin Collection, Cambridge University Library). Both notebooks relate to Meikleham's lectures. My thanks are due to the librarians of the Belfast and Cambridge University Libraries for permission to quote from these papers.Google Scholar

⁷Thomson, James (senior), op. cit. (6).Google Scholar

¹³Thomson, William, op. cit. (6).Google Scholar

¹⁸Thompson, , op. cit. (6), p. 12.Google Scholar

¹⁹Thomson, William, op. cit. (6). The notes taken from Nichol's lectures are in the same notebook, preserved in Cambridge.Google Scholar

²⁰Thompson, , op. cit. (6), pp. 12, 23–160.Google Scholar

²¹Whewell, William, A treatise on dynamics (Cambridge, 1823), andGoogle Scholar

An elementary treatise on mechanics (5th edn., London, 1836);Google Scholar

Pratt, J. H., The mathematical principles of mechanical philosophy (Cambridge, 1836). These works were recommended byGoogle Scholar

Meikleham, in Thomson, W., op. cit. (6).Google Scholar

²²Thompson, , op. cit. (6), pp. 239–51.Google Scholar

Thomson, William's ‘Introductory lecture’ is there printed in its entirety.Google Scholar

²³Thomson, William's, p. 239.Google Scholar

²⁴Thomson, William's, p. 241.Google Scholar

²⁵Thomson, William's, pp. 241–2.Google Scholar

²⁶Thomson, William's, p. 242.Google Scholar

²⁷Thomson, William's, pp. 242–3.Google Scholar

²⁸Thomson, William's, p. 243.Google Scholar

²⁹Thomson, William's, p. 243.Google Scholar

³⁰Thomson, William's, p. 245.Google Scholar

³¹ Kelvin Collection, Cambridge University Library, Notebook c. 1862, relating to the early stages of the Thomson, W. and Tait, P. G. project, the famous Treatise on natural philosophy (Oxford, 1867). The notebook contains the following remarks by Thomson:Google Scholar

‘In fact I think that even now we may sometimes conveniently speak of books of descriptive science or books of dynamical science. Good books on geology are mixed descriptive & dynamical. In the best of them the dynamical part is very bad, Hopkins alone excepted.’ One object of the 1867 Treatise was ‘to give a tolerably complete account of what is now known of Natural Philosophy’, and dynamics was again given a central role, though the emphasis by this time was on the concept of energy. See Brush, S. G., ‘The development of the kinetic theory of gases. VIII. Randomness and irreversibility’, Archive for history of exact sciences, xiii (1974), 15–16, for a discussion of Hopkins.Google Scholar

³² Kelvin Collection, Cambridge University Library: Thomson, William, ‘Notebook 21, c. 1839–40’.Google Scholar

See Wilson, D. B., ‘Kelvin's scientific realism: the theological context’, The philosophical journal, xi (1974), 55–8, for a transcript of ‘Essay xvi’, constituting part of this notebook.Google Scholar

See also Thompson, , op. cit. (6), i. 39, 53, 163 for comments on William Fleming, who was apparently known to his students as ‘Moral Will’ and was thought of by the Thomsons as a rather self-righteous and excessively pious gentleman. His views on morality apart, Fleming's ideas on the nature of God and His relation to the world are gleaned from a wealth of sources. In what follows I shall refer some passages in Thomson's notes to the subsequently published work ofGoogle Scholar

Fleming, , A manual of moral philosophy (London, 1867), Book III, ‘Theistic ethics or natural theology’.Google Scholar

³³ See Fleming, , op. cit. (32), pp. 323–40.Google Scholar

³⁴ See, for example, Wilson, , op. cit. (32), pp. 41–53.Google Scholar

³⁵ See Fleming, , op. cit. (32), pp. 346–7.Google Scholar

See also Paley, William, Natural theology: or, evidences of the existence and attributes of the deity, collected from the appearances of nature, ed. Brougham, Henry Lord and SirBell, Charles (4 vols., London, 1836), ii. 92–109.Google Scholar

³⁶ See Fleming, , op. cit. (32), pp. 347–8.Google Scholar

³⁷Fleming, , pp. 348–9.Google Scholar

³⁸Fleming, , pp. 349–65.Google Scholar

³⁹Fleming, , pp. 365–7. There Fleming states these views in full: ‘Were not His everlasting arms underneath, all things would sink back into their primitive non-existence … I. Whatever is created can have no necessary or independent existence; so that the same power which called it into being is requisite to preserve it in being; and if God be the Creator, He must also be the Preserver of the World. II. If the beauty and order which appear in the works of nature prove that they are not the products of chance, but of an intelligent designing cause, the continuance of that beauty and order argues the superintendance of the cause which at first produced them’.Google Scholar

⁴⁰Fleming, , pp. 365–7.Google Scholar

⁴¹ See the final section of this article.Google Scholar

⁴² See Oakley, Francis, ‘Christian theology and the Newtonian science: the rise of the concept of the laws of nature’, Church history, xxx (1961), 433–57, for an account of the origins and nature of the Voluntarist tradition.CrossRefGoogle Scholar

⁴³ The other phrases noted above are: ‘The same power requisite to create any thing is requisite to preserve it in being’ and ‘All created things must be sustained’.Google Scholar

⁴⁴Thomson, William, op. cit. (6).Google Scholar

⁴⁵Thompson, , op. cit. (6), i. 346–50.Google Scholar

⁴⁶Thomson, James, Collected papers in physics and engineering, ed. SirLarmor, Joseph and Thomson, J. (Cambridge, 1912), p. xxxvii. Letter dated 15 08 1846. The italics are mine.Google Scholar

⁴⁷Thomson, James, p. xl. According to his biographers, James Thomson had questioned the faith of his family prior to this letter dated 3 March 1849, and he then stated his creed as a Unitarian after much thought and heart-searching.Google Scholar

See Thomson, James, op. cit. (46), pp. xxxix–xl, andGoogle Scholar

Thompson, , op. cit. (6), ii. 1087–8. Denial of the Trinity, however, did not change his basic view of the relation between God and nature.Google Scholar

⁴⁸Playfair, John, ‘La Place, Traité de méchanique céleste’, Edinburgh review, xxii (1808), 277.Google Scholar

⁴⁹ Thomson Collection, Queen's University Library, Belfast: Thomson, James (senior), ‘Introductory lecture, Glasgow College, 6th November 1832’.Google Scholar

⁵⁰Thomson, William, op. cit. (6).Google Scholar

⁵¹Whewell, William, Astronomy and general physics considered with reference to natural theology (London, 1833), p. 193.Google Scholar

⁵²Whewell, William, pp. 194–9.Google Scholar

⁵³Whewell, William, pp. 199–200.Google Scholar

⁵⁴Whewell, William, p. 201.Google Scholar

⁵⁵Whewell, William, p. 202.Google Scholar

⁵⁶Whewell, William, p. 203.Google Scholar

⁵⁷ This argument has a distinctly Newtonian character. See Newton, Isaac, Opticks (4th edn., London, 1730), p. 399, where Newton claims: ‘Seeing therefore the variety of Motion which we find in the World is always decreasing, there is a necessity of conserving and recruiting it by active Principles.’ Unlike Newton, Whewell does not argue that active principles actually do recruit and conserve (in the sense of restore) motion in the world.Google Scholar

⁵⁸Newton, Isaac, pp. 203–4.Google Scholar

⁵⁹Newton, Isaac, pp. 206–7. Whewell is quoting Newton here.Google Scholar

See Newton, , op. cit. (57), p. 369.Google Scholar

⁶⁰Fourier, Joseph, The analytical theory of heat, trans, by Freeman, A. (Cambridge, 1878), p. 23. First published asGoogle Scholar

Théorie analytique de la chaleur (Paris, 1822).Google Scholar

⁶¹ See Herivel, J. W., Joseph Fourier. The man and the physicist (Oxford, 1975), pp. 224–8, for an account of Fourier's attitude to his theory of heat as an autonomous branch of physics. Herivel sees Fourier's attitude as a dogmatic one, being based on mathematical reasons and personal grounds. Conduction phenomena, however, have no conceptual link with dynamical science. They cannot be strictly reduced to dynamics on the one hand, and they lead to no dynamical effects on the other. Realization of these aspects of conduction gave rise to Thomson's subsequent worries about the foundations of thermodynamics.Google Scholar

See also Brush, , op. cit. (31), pp. 12–14.Google Scholar

⁶² See Thompson, , op. cit. (6), pp. 13–15.Google Scholar

See also Herivel, J. W., ‘The influence of Fourier on British mathematics’, Centaurus, xvii (1972), 51–2.Google Scholar

⁶³Fourier, , op. cit. (60), p. 26.Google Scholar

⁶⁴ See Herivel, J. W., ‘Aspects of French theoretical physics in the nineteenth century’, The British journal for the history of science, iii (1966–1967), 123–5. Herivel tends not to explicate the various degrees of positivism.Google Scholar

⁶⁵Fourier, , op. cit. (60), p. 2.Google Scholar

⁶⁶Fourier, , p. 1. See also pp. 7–8 for a reference by Fourier to ‘that unchangeable order which presides over all natural causes’.Google Scholar

⁶⁷Thomson, and Tait, , op. cit. (31), preface. For an account of the Common Sense position in relation to laws of nature,Google Scholar

see Heimann, P. M. and McGuire, J. E., ‘Newtonian forces and Lockean powers’, Historical studies in the physical sciences, iii (1971), 265–8;Google Scholar

Laudan, L. L., ‘Thomas Reid and the Newtonian turn of British methodological thought’, in Butts, R. E. and Davis, J. W. (eds.), The methodological heritage of Newton (Oxford, 1970), pp. 103–31. Common sense philosophers such as Thomas Reid or Dugald Stewart distinguished scientific or physical causes from efficient causes, the former being ‘only the rule according to which the efficient cause operates’, and the latter being related to God.CrossRefGoogle Scholar

See also Kargon, R. H., ‘Model and analogy in Victorian science: Maxwell's critique of the French physicists’, Journal of the history of ideas, xxx (1969), 430. Kargon there recognizes that the British physicists do not go all the way towards ‘positivism’, but he tends to see them as strongly influenced by engineering conceptions. With respect to Thomson, my analysis shows his framework grounded much more in traditions of natural philosophy and theology.Google Scholar

⁶⁸Thomson, , op. cit. (4), i. 10–47. The 1842 and 1844 papers are entitled ‘On the linear motion of heat’ and ‘Note on some points in the theory of heat’ respectively.Google Scholar

See Thompson, , op. cit. (6), pp. 41–2 and pp. 111–12;Google Scholar

Brush, , op. cit. (34), p. 17, for an account of these aspects.Google Scholar

⁶⁹ See Thompson, , op. cit. (6), pp. 184–9, where an account of William Thomson's 1846 inaugural dissertation ‘On the distribution of heat through the body of the earth’ is given.Google Scholar

⁷⁰Thompson, , pp. 132–3.CrossRefGoogle Scholar

⁷¹ Kelvin Collection, Cambridge University Library: Letter T402, Thomson, James to Thomson, William, 4 08 1844.Google Scholar

See also Thompson, , op. cit. (6), i. 275n, where this letter is briefly referred to as ‘containing a curious piece of primitive thermodynamics’.Google Scholar

⁷²Carnot, S., Reflections on the motive power of fire, ed. Mendoza, E. (New York: Dover, 1960), p. 20.Google Scholar

⁷³Thompson, , op. cit. (6), pp. 132–3, and Kelvin Collection, Cambridge University Library: Letter T415,Google Scholar

Thomson, James to Thomson, William, 23 02 1846.Google Scholar

⁷⁴ See Thompson, , op. cit. (6), i. 263–6. I deal with the details of the debate between Joule and the Thomsons in a forthcoming paper in the Archive for history of exact sciences.Google Scholar

⁷⁵ Kelvin Collection, Cambridge University Library: Thomson, William to Joule, J. P. (copy), 27 10 1848.Google Scholar

See Heimann, P. M., ‘Conversion of forces and the conservation of energy’, Centaurus, xviii (1974), 147–61, for an account of Joule's theology. Thomson was responding here to what Joule had written in 1844: ‘Believing that the power to destroy belongs to the Creator alone, I entirely coincide with Roget and Faraday in the opinion that any theory which, when carried out, demands the annihilation of force, is necessarily erroneous’;CrossRefGoogle Scholar

Joule, J. P., ‘On the changes of temperature produced by the rarefaction and condensation of air’, in The scientific papers of James Prescott Joule (2 vols., London, 1887), i. 189.Google Scholar

⁷⁶ See, for example, Pratt, J. H., op. cit. (21), pp. 201–2;Google Scholar

Whewell, William, An elementary treatise on mechanics (5th edn., London, 1836), p. 161.Google Scholar

⁷⁷Thomson, , op. cit. (4), i. 118n. The full paper byGoogle Scholar

Thomson, was ‘An account of Carnot's theory of the motive power of heat, with numerical results, deduced from Regnault's experiments on steam’, Transactions of the Royal Society of Edinburgh, xvi (1849), 541–74; also in op. cit. (4), i. 113–64. Thomson had further empirical support for Carnot's theory by 1850 in the confirmation of his brother James's prediction of the lowering of the freezing point of ice with pressure.CrossRefGoogle Scholar

See, for example, Klein, Martin, ‘Carnot's contribution to thermodynamics’, Physics today, xxvii (1974), 23–8.CrossRefGoogle Scholar

⁷⁸Clausius, R. J. E., ‘On the motive power of heat, and on the laws which can be deduced from it for the theory of heat’, Annalen der Physik, ed. J. C. Poggendorf, lxxxix (1850), 368, 500. For a good account of Clausius,CrossRefGoogle Scholar

see Cardwell, D. S. L., From Watt to Clausius. The rise of thermodynamics in the early industrial age (London, 1971), pp. 244–76.Google Scholar

⁷⁹ It may be noted that in 1845 Waterston, J. J., responding to Clapeyron, 's paper translated for Taylor, 's Scientific memoirs in 1837, employed a mechanical theory of heat along with Carnot's principle for a reversible gas cycle of finite temperature range.Google Scholar

See Waterston, J. J., Collected scientific papers, ed. Haldane, J. S. (Edinburgh, 1928), pp. xl–xlii, 275–8.Google Scholar

⁸⁰Clausius, R. J. E., ‘On several convenient forms of fundamental equations of the mechanical theory of heat’, in his The mechanical theory of heat, with its applications to the steam engine and to the physical properties of bodies, ed. Hirst, T. A. (London, 1867), pp. 327–76.Google Scholar

See also Garber, E. W., ‘Clausius and Maxwell's kinetic theory of gases’, Historical studies in the physical sciences, ii (1970), 303 (‘Clausius motive for studying the properties of gases was to explore the nature of heat’);Google Scholar

SirLarmor, Joseph, ‘William Thomson, Baron Kelvin of Largs, 1824–1907’, Proceedings of the Royal Society, Series A, lxxxi (1908), p. xxxv (‘In their parallel developments of the subject, while Clausius kept mainly to the theory of heat engines, applications over the whole domain of physical science crowded on Thomson’).Google Scholar

⁸¹ Kelvin Collection, Cambridge University Library: Thomson, William, ‘Draft of the dynamical theory of heat’ (1851), manuscript PA128. The theological parts of this draft are published inGoogle Scholar

Wilson, , op. cit. (32), pp. 58–9.Google Scholar

⁸⁴ Psalm 102, verses 25–7. For a commentary on this Psalm, see Pool, Matthew, Annotations upon the Holy Bible (3 vols., London, 1841), ii. 157. Concerning verse 25, the commentary notes that the eternity of God is both without beginning and without end: ‘Thou hadst a being before the creation of the world, when there was nothing but eternity, but the earth and heavens had a beginning given them by thy almighty power.’ ‘Like a garment’, Pool states, implies that the present frame of heaven and earth becomes worn out and laid aside, to be eventually exchanged for another: ‘The heavens and the earth, although they be the most permanent of all visible beings, and their continuance is oft mentioned to signify the stability and immutability of things, yet if compared with thee are as nothing; they had a beginning and had an end.’ The alternative verse in Isaiah, chapter 51, verse 6, reads: ‘for the heavens shall vanish away like smoke, and the earth shall wax old like a garment’. The reference to smoke, Pool remarks, may imply dissolution in regard to present state, properties, and use, although the substance of it be not destroyed. Alternatively, straightforward annihilation of all the material world could occur. See also note 88.Google Scholar

⁸⁵Thomson, , op. cit. (81).Google Scholar

⁸⁶ Second epistle of Peter, chapter 3, verses 5–7.Google Scholar

⁸⁷Thomson, op. cit. (4), i. 189. The full paper byGoogle Scholar

Thomson, is ‘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”’, Transactions of the Royal Society of Edinburgh, xx (1853), 261–88; also in op. cit. (4), i. 174–210 (read on 17 March 1851).CrossRefGoogle Scholar

See Cardwell, , op. cit. (78), p. 255, where it is pointed out that this statement of Thomson's ‘would hardly please a logician: if the energy is “irrevocably lost” how can one possibly know that it is not “annihilated”?’ That Thomson himself recognized this weakness is shown by his remarks that the dynamical theory could only assert that energy was not lost. It is precisely at the point of recognition of this ‘logical’ weakness that Thomson's theology comes into full play to strengthen the scientific arguments.Google Scholar

⁸⁸Thomson, , op. cit. (6), p. 284. Maxwell's later view of the second law of thermodynamics throws further light on what William Thomson meant by the second law being a law of natural history and not of natural philosophy. Maxwell saw the second law as having only statistical certainty, and he illustrated his arguments with the famous demon (Thomson's term). The second law was not wholly a dynamical one; it required a statistical mechanical interpretation at the micro-level.Google Scholar

See Heimann, P. M., ‘Molecular forces, statistical representation and Maxwell's demon’, Studies in history and philosophy of science, i (1970–1971), 189–211. With respect to Thomson's theology, it may be noted that these later developments pose fresh problems for a view of the second law as an expression of the will of God. The second law can clearly now be neither a direct expression of divine will nor a dynamical law.CrossRefGoogle Scholar

⁸⁹Thomson, W., ‘On a universal tendency in nature to the dissipation of mechanical energy’, Proceedings of the Royal Society of Edinburgh, iii (1852), 139–42; also in op. cit. (4), i. 511–14 (read 19 04 1852).Google Scholar

⁹⁰ See Brush, , op. cit. (31); pp. 25–6, where the author remarks on the obscurity and incompleteness of Thomson's ‘deduction’. Brush also stresses here the geological context of Thomson's thermodynamics.Google Scholar

⁹¹Thomson, W., ‘On the mechanical antecedents of motion, heat, and light’, Report of the British Association for the Advancement of Science (1854) (London, 1855), part II, 59–63; also in op. cit. (4), i. 34–40.Google Scholar

⁹³Thomson, W., ‘On the mechanical energies of the solar system’, Philosophical magazine, 4th ser. viii (1854), 409–30.Google Scholar