A New Chart for British Natural Philosophy: The Development of Energy Physics in the Nineteenth Century

Gillispie C. C. , The edge of objectivity. An essay in the history of scientific ideas (Princeton, 1960), 352. Remarks made at the beginning of his chapter on ‘energetics’.

See, for example, Smith Crosbie , “‘Mechanical philosophy’ and the emergence of physics in Britain: 1800–1850”, Annals of science, xxxiii (1976), 3–29. In that paper I traced out the conceptual demarcations which characterized natural philosophy for thinkers located in various British centres—the Scottish universities, Cambridge, and London—between 1800 and 1850.

For able discussions of such historiographical problems see Skinner Quentin , “The limits of historical explanation”. Philosophy, xli (1966), 199–215, and Dunn John , “The identity of the history of ideas”, Philosophy, xliii (1968), 85–104.

See McCormmach Russell , “Editor's foreword”, Historical studies in the physical sciences, iii (1971), ix–xxiv. McCormmach briefly illustrates the discipline approach by a discussion of nineteenth century German physics. A fascinating account of French physics from a similar point of view is to be found in Fox Robert , “The rise and fall of Laplacian physics”, Historical studies in the physical sciences, iv (1974), 89–136.

See respectively Hiebert E. N. , Historical roots of the principle of conservation of energy (Wisconsin, 1962); Kuhn T. S. , “Energy conservation as an example of simultaneous discovery”, in Clagett M. (ed.), Critical problems in the history of science (Wisconsin, 1957), 321–56; Elkana Y. , The discovery of the conservation of energy (London, 1974). Hiebert's book is a valuable account of mechanics prior to the full development of the energy principle. Kuhn's paper has become a classic analysis of the many and varied men who came near to, if they did not actually arrive at, a principle of energy conservation. Elkana's book, however, is a disappointing and weak effort, full of errors, contradictions and ambiguities, and adding little to previous analyses such as Kuhn's. An interesting reappraisal of Kuhn is given by Heimann P. M. , “Conversion of forces and the conservation of energy”, Centaurus, xviii (1974), 147–61.

See respectively Klein M. J. , “Gibbs on Clausius”, Historical studies in the physical sciences, i (1969), 127–49, for an account of thermodynamics in the period; Doran B. G. , “Origins and consolidation of field theory in nineteenth century Britain: From the mechanical to the electromagnetic view of nature”, Historical studies in the physical sciences, vi (1975), 133–260; Olson Richard , Scottish philosophy and British physics 1750–1880 (Princeton, 1975), 271–321 for an analysis of the methodology of Rankine W. J. M. Maxwell James Clerk ; Hesse Mary , “Maxwell's logic of analogy”. The structure of scientific inference (London, 1974), 259–81, for a penetrating discussion of Maxwell's employment of analogical reasoning from a philosophical point of view.

Clark Peter , “Atomism versus thermodynamics”, in Howson Colin (ed.), Method and appraisal in the physical sciences (Cambridge, 1976), 41–105.

See the remarks by Merz J. T. , A history of European thought in the nineteenth century (2 vols, Dover reprint of 1904–12 edition, New York, 1965), ii, 95–199, esp. pp. 135–51. Merz refers to the “revolutions in the domain of scientific thought” occasioned by the energy principle, and to the “task of rebuilding the edifice of the physical sciences, and establishing on a large scale that which I term the physical view of nature”. Men's comments suggest the need for a thorough analysis of the work of natural philosophers in the period after the establishment of the energy principles around 1850. The unpublished doctoral dissertation by Moyer D. F. , “The use of dynamics as the basis of physical theory by British theoretical physicists in the latter half of the nineteenth century” (University of Wisconsin, 1973), relates quite closely to the history of the energy concept in the post-1850 era. Unfortunately this work lacks adequate conceptual analysis and relies instead on very lengthy quotations from the primary sources, some of which quotations run to several pages.

See Moyer D. F. , “Energy, dynamics, hidden machinery: Rankine, Thomson and Tait, Maxwell”, Studies in the history and philosophy of science, viii (1977), 251–68. For my specific criticism of Moyer, see ref. 72 below.

For an account of some of these wider dimensions in the early thought of William Thomson, see my paper “Natural philosophy and thermodynamics; William Thomson and ‘the dynamical theory of heat’”, The British journal for the history of science, ix (1976), 293–319. See also Heimann P. M. , “The Unseen Universe: Physics and the philosophy of nature in Victorian Britain”, The British journal for the history of science, vi (1972), 73–79. I hope to deal further with these issues in a forthcoming article.

See Cardwell D. S. L. , From Watt to Clausius: The rise of thermodynamics in the early industrial age (London, 1971), esp. pp. 186–294.

Thomson William , “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” [read to the Royal Society of Edinburgh, 17 March, 1851], Mathematical and physical papers (6 vols, Cambridge, 1882–1911), i, 174–89; Stokes G. G. , “On the dynamical theory of diffraction” [read to the Cambridge Philosophical Society, 26 November, 1849], Mathematical and physical papers (5 vols, Cambridge, 1880–1905), ii, 243–328.

Stokes G. G. , “Notes on hydrodynamics, III. On the dynamical equations”, Cambridge and Dublin mathematical journal, iii (1848), 121–7, p. 121. Stokes and Thomson contributed a series of such notes on hydrodynamics to the Journal of which Thomson was the editor. The notes were aimed especially at Cambridge students of mathematics.

Cardwell , op. cit. (ref. 11), 239–44; Smith C. W. , “William Thomson and the creation of thermodynamics: 1840–1855”, Archive for history of exact sciences, xvi (1976), 231–88.

Joule J. P. , The scientific papers of James Prescott Joule (2 vols, Dawson's reprint, London), i, 123, 188–9.

Thomson William , “An account of Carnot's theory of the motive power of heat, with numerical results deduced from Regnault's experiments on steam” [read 2 January, 1849], op. cit. (ref. 12), i, 118n.

See Smith , op. cit. (ref. 14), 280–8, for a transcript of the early draft manuscript of the dynamical theory of heat from which these extracts are taken. The original manuscript of early 1851 is preserved in Cambridge University Library.

Thomson William , op. cit. (ref. 12), 174.

Ibid., 174–5.

See the transcript in Smith , op. cit. (ref. 14), 286. Thomson's actual words were: “Man cannot create matter. Heat may be created by man. ∴ Heat is not matter”.

Thomson , op. cit. (ref. 12), 175–6.

For a transcript of Michael Faraday's report, see Smith C. W. , “Faraday as referee of Joule's Royal Society paper ‘On the mechanical equivalent of heat’”, Isis, lxvii (1976), 444–9.

In the published version Joule did in fact drop the ‘inference’ from his main conclusions.

See Smith , op. cit. (ref. 22).

See Smith , op. cit. (ref. 10).

See, for example, the Cambridge textbooks by Whewell William Pratt J. H. on mechanics and dynamics. See especially, Whewell W. , A treatise on dynamics (Cambridge, 1823), 394–403; Pratt J. H. , The mathematical principles of mechanical philosophy (Cambridge, 1836), 201–2; Whewell W. , Mechanics of engineering (Cambridge, 1841), 145–57.

Larmor Joseph Sir , “The scientific environment of James Clerk Maxwell”, proof version of unpublished memoir, St John's College Library, Cambridge.

See Clausius R. , “On the motive power of heat, and on the laws which can be deduced from it for the theory of heat” [1850], in Mendoza E. (ed.), Reflections on the motive power of fire (Dover reprint, New York, 1960), 109–52.

Ibid., 112. Clausius there wrote: “We shall not consider here the kind of motion which can be conceived of as taking place within bodies, further than to assume in general that the particles of bodies are in motion, and that their heat is the measure of their vis viva, or rather still more generally, we shall only lay down a principle conditioned by that assumption as a fundamental principle”, viz., the mechanical equivalence of heat and work.

Ibid., 132–4.

See the interesting paper by Truesdell C. , “Early kinetic theories of gases”, Archive for history of exact sciences, xv (1975), 1–66, esp. pp. 18–20 for discussions by Joule and Thomson (among others) of molecular theories of gases around the mid-century. Thomson set for students at St Peter's College, Cambridge, in June 1852, an examination question which related to such theories. For a general history of nineteenth century kinetic theories of gases see Brush S. G. , The kind of motion we call heat (2 vols, Amsterdam, 1976).

Although no specific model had yet been constructed, Thomson's approach does suggest a cautious realism—in other words, that he believed that knowledge of unobservable entities was possible in principle. His so-called ‘dynamical illustrations’ employed in his work on the Faraday effect (the rotation of the plane of polarized light by a strong magnetic field) during the 1850s suggest an even more cautious approach to the unobservable realm. See Knudsen Ole , “The Faraday effect and physical theory, 1845–1873”, Archive for history of exact sciences, xv (1976), 235–81, esp. pp. 244–7.

Letter from Stokes G. G. to Thomson W. , 23 May, 1854, Kelvin collection, Cambridge University Library. My italics.

See Newton Isaac Sir , Mathematical principles of natural philosophy, translated by Motte Andrew Cajori Florian (reprinted Berkeley, Los Angeles, and London, 1971), xvii–xviii, for Newton's own programme and framework of natural philosophy.

See Fox , op. cit. (ref. 4).

See Smith , op. cit. (ref. 2), 6–16.

Hesse , op. cit. (ref. 6), 265.

Robison John , Elements of mechanical philosophy (Edinburgh, 1804), 99, 108–14; Laplace P. S. , The system of the world, translated by Pond J. (2 vols, London, 1809), ii, 375–9. The best known Cambridge texts were Whewell William , An elementary treatise on mechanics (Cambridge, 1819); A treatise on dynamics (Cambridge, 1823) and Pratt J. H. , The mathematical principles of mechanical philosophy (Cambridge, 1836). See also Smith , op. cit. (ref. 2), 22.

Pratt , op. cit. (ref. 38), 201–2.

Ibid., 485–7.

Thomson William , “Introductory lecture to the course of natural philosophy”, published in Thompson S. P. , Life of Lord Kelvin (2 vols, London, 1910), i, 239–51. See also Smith , op. cit. (ref. 10), 294–8.

Thomson W. , “On the elementary laws of statical electricity”, part I of “On the mathematical theory of electricity in equilibrium”, Cambridge and Dublin mathematical journal, i (1845), 75–95. Also published in Thomson's Reprint of papers on electrostatics and magnetism (London, 1872), 15–37. References below are to this volume. Compare the article by Buchwald J. Z. , “Sir William Thomson (Baron Kelvin of Largs)”, in Gillispie C. C. (ed.), Dictionary of scientific biography (15 vols, New York, 1970–76), xiii, 374–88. Buchwald's account contains several quite serious errors of a factual nature—Thomson's father was professor of mathematics, not engineering, at Belfast, for example, and Thomson read Fourier during his 1840 visit to Germany and not during his 1839 visit to Paris—but his analysis is worth careful study. Unfortunately, however, Buchwald seems to have ignored one of the best analyses of Thomson William , viz., Larmor Joseph Sir , “William Thomson, Baron Kelvin of Largs, 1824–1907”, Proceedings of the Royal Society [series A], lxxxi (1908), iii–lxxvi.

Thomson W. , op. cit. (ref. 42), 26.

Ibid., 29.

Compare Olson, op. cit. (ref. 6). It might be argued that Thomson's approach was due to the influence of the Scottish Common Sense philosophers. Given that there appears to be no direct evidence to support the possibility of this claim, that Thomson's sources were very diverse not least because of his familiarity with French physics, and that Common Sense philosophy could accommodate a wide range of methodologies, I would suggest that no such claim can as yet be sub-substantiated. Olson himself (p. 7) evades the issue, and in so doing undermines his claim to understand “the Victorian scientific style”.

Thomson W. , “A mathematical theory of magnetism”, Philosophical transactions of the Royal Society (1851), 243–85; Reprint of papers on electrostatics and magnetism, 340–425, esp. pp. 340–1.

Ibid. (Reprint of papers …), 341–405.

Ibid., 406.

Ibid., 419–20. My emphasis.

See Buchwald , op. cit. (ref. 42), 383–4, for a recognition of Thomson's move to unobservable entities. Buchwald, however, does not analyze this move in terms of Thomson's key energy principles, especially that of energy dissipation.

Reprint of papers on electrostatics and magnetism, 37. My emphasis.

Rankine W. J. M. , “On the reconcentration of the mechanical energy of the universe” [read before the British Association at Belfast, 2 September, 1852], in Millar W. J. (ed.), Miscellaneous scientific papers (London, 1881), 200–2, p. 200.

For the correspondence between Rankine Thomson William around 1850, see Smith , op. cit. (ref. 14), 253–61.

See Olson , op. cit. (ref. 6), 271–86, for a discussion of Rankine's Common Sense methodology especially as set forth in 1855. My contention that Thomson directly influenced Rankine clearly modifies Olson's interpretation.

Rankine W. J. M. , “On the general law of the transformation of energy”, Philosophical magazine [4th series], v (1853), 106–17, p. 106. This passage did not appear in the reprint of the paper in Rankine's Miscellaneous scientific papers, op. cit. (ref. 52), 203–8.

Rankine , op. cit. (ref. 52), 203.

Rankine W. J. M. , “On the phrase ‘potential energy’, and on the definitions of physical quantities”, op. cit. (ref. 52), 229–33, p. 230.

Letter from Joule J. P. to Thomson W. , 3 February, 1853 (Kelvin Papers, Cambridge University Library).

Rankine W. J. M. , “On the conservation of energy, and Note to a letter ‘On the conservation of energy’”, Philosophical magazine [4th series], xvii (1859), 250–3 and 347–8.

Ibid., 250.

Ibid., 251–2.

Ibid., 252–3.

Ibid., 347. By the rather ambiguous phrase “an unknown secondary cause”, Rankine probably meant that not only was the source or primary cause unknown but that the secondary cause was itself only known by its effects, viz., visible motion.

Ibid., 348.

Ibid., 253.

Maxwell James Clerk , “On the mathematical classification of physical quantities”, in Niven W. D. (ed.), The scientific papers of James Clerk Maxwell (2 vols, Dover reprint of 1890 edition, 1965), ii, 256–66, p. 259.

Ibid., 260.

Ibid., 261.

Ibid., 262.

Herschel J. F. W. , “On the origin of force”. Fortnightly review, i (1865), 435–42. For an account of Herschel's views on the nature of science, see Cannon W. F. , “John Herschel and the idea of science”, Journal of the history of ideas, xxii (1961), 215–39. The concept of force is also described there as it was discussed by Herschel in his famous and influential Preliminary discourse on the study of natural philosophy (London, 1831). For Herschel's philosophy of scientific method, see Ducasse C. J. , “John F. W. Herschel's methods of experimental inquiry”, in Madden E. H. (ed.), Theories of scientific method: The Renaissance through the nineteenth century (Seattle, 1960), 153–82.

Herschel , op. cit. (ref. 71), 439. Rankine's counter-attack appeared in his 1867 paper “On the phrase ‘potential energy’ and on the definitions of physical quantities”, op. cit. (ref. 52), 229–33. He argued that definitions were by themselves neither true nor false but may be real or fantastic according as the description contained in them “corresponds, or not, to real objects and phenomena”. Such was the case with the energy principles. See Moyer , op. cit. (ref. 9), 253–5. Moyer claims that Rankine in this paper expressed the laws of motion as laws of conservation specifying the attributes of systems which are independent of hidden details, a claim which seems to read too much into Rankine's work. Furthermore, Moyer states, “this broader form of Rankine's program was developed in Thomson and Tait's Treatise on natural philosophy and from there entered theoretical physics”. Such a claim for influence from Rankine to Thomson and Tait has no direct evidence as support, and, more importantly, suffers from the fact that both Rankine's paper and the Treatise were published in the same year (1867). In other words, given that the Treatise was being written throughout the 1860s, might it not have been Rankine who read the Treatise in proof and was under its influence rather than vice versa? In the absence of other evidence, such an explanation seems at least as plausible’ as that of Moyer, and indicates the pitfalls of the notion of ‘influence’ in history of science.

Ibid., 440. For a relevant discussion of Boscovich, see Scott W. L. , The conflict between atomism and conservation theory 1644 to 1860 (London, 1970), esp. 65–67.

Ibid., 441. Herschel probably had in mind a system such as Rankine's hypothesis of molecular vortices. See Rankine , op. cit. (ref. 52), 234–84.

Herschel , op. cit. (ref. 71), 435.

See Smith , op. cit. (ref. 2), 29. Whewell, for example, saw mathematization as the feature which distinguished the various branches of ‘mathematical physics’ from all the other inductive sciences.

Clausius R. J. E. , “On several convenient forms of fundamental equations of the mechanical theory of heat”, in Hirst T. A. (ed.), The mechanical theory of heat (London, 1867), 327–76.

For a recent analysis of Helmholtz's famous 1847 memoir, see Heimann P. M. , “Helmholtz and Kant: The metaphysical foundations of Ueber die Erhaltung der Kraft”, Studies in the history and philosophy of science, v (1974), 205–38. Clausius, for his part, criticized Helmholtz for the assumption of central forces (pp. 234–5). We know that Thomson read Helmholtz's memoir in 1852 (p. 206), and that Thomson approved of its contents, but the available sources do not suggest any definite development of this interaction in the context of the energy view. Certainly Thomson saw Helmholtz's work as strengthening his own views of a conservation principle. See Thomson , op. cit. (ref. 12), i, 182–3n.

See, for example, Merz , op. cit. (ref. 8), ii, 143–4; Moyer , op. cit. (ref. 9), 255.

The paper by Moyer , op. cit. (ref. 9), claims that Duhem, in his Aim and structure of physical theory, was essentially mistaken in his criticism of British physicists for their mechanical model building. Rather, Moyer argues that “the basic ideas of their program were that observable phenomena can be reckoned as transformations of energy and that laws of these phenomena can be calculated by applying the generalized equations of motion, all of this without recourse to any hypotheses about hidden machinery” (p. 267). Olson , op. cit. (ref. 6), 323–35, also discusses Duhem and links British model building with a Scottish Common Sense tradition of emphasis on the usefulness or fruitfulness (the heuristic value) of such hypotheses rather than on their truth. I shall implicitly suggest in the present and in the final section that such interpretations are not wholly adequate to characterize British energy physics as there was a clear interest on the part of the physicists in unobservable entities, an interest which derived largely from successful kinetic theories of heat.

Thomson W. , “On a universal tendency in nature to the dissipation of mechanical energy”, Philosophical magazine [4th series], vi (1852), 304–6, p. 304.

Thomson W. , “The kinetic theory of the dissipation of energy”, Proceedings of the Royal Society of Edinburgh, viii (1874), 325–34, p. 325.

See, for instance, the article by Heimann P. M. , “Molecular forces, statistical representation and Maxwell's demon”, Studies in the history and philosophy of science, i (1970), 189–211.

Thomson W. , “Presidential address at Edinburgh to the British Association for the Advancement of Science”, British Association report, xli (1871), lxxiv–cv, p. xviii. Maxwell had apparently corresponded with Thomson on the history of the kinetic theory. See Bernstein H. T. , “J. Clerk Maxwell on the history of the kinetic theory of gases, 1871”, Isis, liv (1963), 206–16, esp. pp. 210–13. In addition, Thomson was the referee of Maxwell's “On the dynamical theory of gases”, Philosophical transactions, clvii (1866), 49–88. See manuscript RR6. 179 in the library of the Royal Society.

For further details see Larmor , op. cit. (ref. 42), xxxix–xliii.

See Klein M. J. , “Mechanical explanation at the end of the nineteenth century”, Centaurus, xvii (1972–73), 58–82, for an important analysis of the work of Helmholtz, Boltzmann and others in the context of problems raised for “mechanical explanation” by the second law of thermodynamics. The statistical interpretation, deriving from Maxwell and Thomson, was, of course, developed by Boltzmann, a devoted reader of Maxwell's work.

Larmor , op. cit. (ref. 42), xxxviii.

The older branches of mathematical physics, viz., gravitational theory, electrostatics, and magnetostatics, were easily integrated into the energy perspective via the concept of ‘potential’, due originally to George Green. Another extension of the energy view in an area outside thermodynamics was exemplified by Thomson's paper “On the mechanical values of distributions of electricity, magnetism, and galvanism” [read January, 1853], op. cit. (ref. 12), i, 521–33. See Larmor , op. cit. (ref. 42), xxii–xxix; Doran , op. cit. (ref. 6), 167.

Thomson W. , op. cit. (ref. 12), i, 174–232. Parts I and II of “On the dynamical theory of heat” dealt with the motive power of heat. Part in was entitled “Applications of the dynamical theory to establish relations between the physical properties of all substances”. Part IV treated of the compression and rarefaction of gases, and Part V was entitled “On the quantities of mechanical energy contained in a fluid in different states, as to temperature and density”. All these memoirs were read in 1851, and published in the early 1850s.

See, for example, Thomson W. Joule J. P. , “On the thermal effects of air rushing through small apertures”, Philosophical magazine [4th series], iv (1852), 481–91; “On the thermal effects of elastic fluids”, Philosophical transactions (1853), 357–65.

Thomson W. , “On the thermo-elastic and thermomagnetic properties of matter”, Quarterly journal of mathematics, i (1857), 55–77. [Memoir dated 10 March, 1855.] Reprinted, with subsequent additions, in Thomson W. , op. cit. (ref. 12), i, 291–316. For a more detailed analysis, see Larmor , op. cit. (ref. 42), xliv–xlix.

See Thomson W. , “Thermo-electric currents” [read 1 May, 1854], op. cit. (ref. 12), i, 232–91, 324–5.

Ibid., 238–41. See Finn B. S. , “Thomson's dilemma”, Physics today, xx (1967), 54–59, for an analysis of this aspect of Thomson's work.

Thomson W. Tait P. G. , Treatise on natural philosophy, i (Oxford, 1867). For historical accounts of the writing of the Treatise, see Knott C. G. , The life and scientific work of P. G. Tait (Cambridge, 1911), 176–204, and Thompson S. P. , op. cit. (ref. 41), i, 447–80. Although rather dated, these accounts contain useful transcripts of correspondence between Tait and Thomson, and between Tait and Thomas Andrews. See also Moyer , op. cit. (ref. 9), 255–9, and ref. 72 for my criticisms of Moyer's thesis concerning the influence of Rankine on the Treatise.

Letter from Tait P. G. to Thomson W. , 12 December, 1861 (Kelvin papers, University Library, Cambridge). Published in Thompson, op. cit. (ref. 41), i, 453.

Young Thomas , A course of lectures on natural philosophy and the mechanical parts (2 vols, London, 1807), the second edition of which was edited by Kelland Philip and published as late as 1845; Robison John , op. cit. (ref. 38) and A system of mechanical philosophy, ed. by Brewster David (4 vols, Edinburgh, 1822). For Whewell Pratt , see ref. 38. In 1856 there appeared Tait P. G. Steele's W. J. Dynamics of a particle for use largely as a Cambridge textbook following closely on Pratt's text. The second chapter of the second edition (1865) was completely recast to bring it into line with the new viewpoint as set out in Thomson and Tait's Treatise. See Knott , op. cit. (ref. 95), 205.

Letter from Tait P. G. to Thomson W. , 28 December, 1861 (Kelvin papers, University Library, Cambridge).

See Thompson , op. cit. (ref. 41), i, 454.

Letter from Tait P. G. to Thomson W. , 20 January, 1862 (Kelvin papers, University Library, Cambridge). Published in Thompson , op. cit. (ref. 41), i, 459–60.

Letter from Tait P. G. to Thomson W. , 27 March, 1862 (University Library, Glasgow).

Thomson Tait , op. cit. (ref. 95), vi.

See Thompson , op. cit. (ref. 41), i, 473.

As Thompson (op. cit. (ref. 41), i, 470) points out, the section on kinematics enabled the authors to introduce Fourier's analysis of periodic functions, the use of generalized co-ordinates, and the spherical harmonic expansion of arbitrary functions as tools to be used in the subsequent sections on dynamics.

Thomson Tait , op. cit. (ref. 95), vi.

Ibid., 189.

Ibid., 190–1.

Ibid., 194–5.

Ibid., 195.

Letter from Tait P. G. to Andrews Thomas , 20 January, 1862. Published in Knott , op. cit. (ref. 95), 178–9.

See Smith , op. cit. (ref. 10), for a detailed account of these aspects of Thomson's work.

See Thomson Tait , op. cit. (ref. 95), 337.

Ibid., 200.

Lagrange's analytical methods were not widely discussed and employed in early to mid-nineteenth century Britain with the exceptions of men such as William Rowan Hamilton. See, for example, the important memoir by Cayley A. , “Report on the recent progress of theoretical dynamics”, British Association report, xxvii (1857), 1–42. After Thomson Tait's Treatise, however, the methods became quite widespread. See Maxwell's James Clerk Treatise on electricity and magnetism (2 vols, Oxford, 1873), a work which I shall consider briefly below.

See also Moyer , op. cit. (ref. 9), 257–9. Moyer tends to view Thomson Tait's Treatise from the vantage point of Maxwell.

Tait P. G. , The position and prospects of physical science. A public inaugural lecture delivered on November 7, 1860 (Edinburgh, 1860), 24–34.

Tait P. G. , “The dynamical theory of heat”, and “Energy”, North British review, xl (1864), 40–69, 337–68. Herschel , op. cit. (ref. 71), 436, strongly denounced Tait's speculation (p. 41) that the ultimate nature of force “depends upon the diffusion of highly attenuated matter throughout space”.

Tait P. G. , “Force”, in Lectures on some recent advances in physical science (2nd ed., London, 1876), 338–63, p. 347.

Merz , op. cit. (ref. 8), ii, 140n.

Tait , op. cit. (ref. 118), 347.

Ibid., 347–56.

Ibid., 341. Tait (p. 362) speculated that all kinds of energy might ultimately be kinetic. For a contrast to Tait's view, see Tyndall John , Faraday as a discoverer (London, 1868), 156–69. Tyndall retained the ontological primacy of force after the manner of Faraday and Helmholtz.

On Maxwell's theories of electricity and magnetism, and especially their relation to Faraday's ideas, see Heimann P. M. , “Maxwell and the modes of consistent representation”, Archive for history of exact sciences, vi (1970), 171–213. Hesse , op. cit. (ref. 6), 259–69, gives a penetrating analysis of Maxwell's method of analogy and its relation to other methodologies. Olson (op. cit. (ref. 6), 287–321) and Simpson T. K. (“Some observations on Maxwell's treatise on electricity and magnetism. On the role of the ‘dynamical theory of the electromagnetic field’ in Part iv of the treatise”, Studies in the history and philosophy of science, i (1970), 249–63) attempt to place aspects of Maxwell's work within a philosophical and metaphysical context. Chalmers A. F. , “Maxwell's methodology and his application of it to electromagnetism”, Studies in history and philosophy of science, iv (1973), 107–64, is a major treatment of Maxwell's scientific method. Only Moyer , op. cit. (ref. 9), 262–7, deals with Maxwell's work specifically from the energy point of view, and I am broadly in agreement with his sketch. See also above, Section in, for Maxwell's discussion of energy as a scalar quantity.

Maxwell's three major papers on electromagnetism were “On Faraday's lines of force” [1855–56], “On physical lines of force” [1861–62] and “A dynamical theory of the electromagnetic field” [1864], reprinted in op. cit. (ref. 66), 155–229, 451–513, 526–97, respectively.

Ibid., 528.

Maxwell J. C. , Matter and motion (Dover reprint (New York) or 1925 ed., edited by Larmor Joseph Sir ), 89–90. This text first appeared in 1877.

Maxwell , op. cit. (ref. 66), 564.

Maxwell J. C. , A treatise on electricity and magnetism (2nd ed., 2 vols, Oxford, 1881), v, 183.

Ibid., 184.

Ibid., 185–6.

Ibid., 186.

Maxwell , op. cit. (ref. 126), 91. Maxwell's views on thermodynamics and the kinetic theory of gases may be found in his Theory of heat (8th ed., London, 1885) where the energy view is again emphasized. See especially pp. 92–94 for his caution over the central force assumptions of Helmholtz .

See Hesse , op. cit. (ref. 6), 259–69, and Section in above. This summary analysis is not claiming, of course, that natural philosophers, during and prior to the 1840s, never employed physical hypotheses about unobservable entities. I am concerned here with the conceptual moves and reinterpretations which made energy physics possible, rather than with a survey of all previous approaches.

Thomson W. , “On the uniform motion of heat in homogeneous solid bodies, and its connexion with the mathematical theory of electricity” [1842], op. cit. (ref. 42), 1–14. See also Larmor , op. cit. (ref. 42), ix. Buchwald , op. cit. (ref. 42), 374, sees this analogy as purely a formal mathematical one, whereas it does in fact possess the characteristics of a physical analogy through the common geometrical interpretation.

Thomson W. , op. cit. (ref. 85), xciii–xciv.

See Thompson , op. cit. (ref. 41), ii, 1012–85; Knudsen , op. cit. (ref. 82), 244–7; Hesse Mary , “Models in physics”, The British journal for the philosophy of science, iv (1952), 198–214.

Thomson W. , “Steps towards a kinetic theory of matter” [opening address to the Montreal meeting of the British Association, 1884], Popular lectures and addresses (3 vols, London, 1889–94), i, 218–52, p. 218.

Doran , op. cit. (ref. 6), 133–260.

Ibid., 179–190, esp. 185. Thomson's vortex-atom theory, first set out in 1867, was an important attempt in his exploration of the unobservable level.

Tait P. G. , “Thermoelectricity” [Rede lecture, 1873], Scientific papers (2 vols, Cambridge, 1898), i, 206–17.

See Klein , op. cit. (ref. 87), 58–82.

Maxwell J. C. , op. cit. (ref. 126), 55.