¹ Letter from Thomson, to Faraday, , 19 06 1849Google Scholar, in Thompson, S. P., The life of William Thomson Baron Kelvin of Largs, 2 vols., London, 1910, i, 214–6Google Scholar (hereafter, Lift of Thomson); Williams, L. P. (ed.), The selected correspondence of Michael Faraday, 2 vols., Cambridge, 1971, ii, 559–61Google Scholar (hereafter, Correspondene).

² Life of Thomson, op. cit. (1), p. 215.Google Scholar

³ ‘On the uniform motion of heat in homogeneous solid bodies, and its connection with the mathematical theory of electricity’, Cambridge mathematical journal, 1842, 3, 71–84Google Scholar; Thomson, William, Reprint of papers on electrostatics and magnetism, London, 1872, pp. 1–14Google Scholar, (hereafter, Reprint); cf. Thompson, , Life of Thomson, op. cit. (1), i, 141–4.Google Scholar

⁴ This appeared in the twenty-fifth and twenty-sixth series of Faraday, 's Experimental researches in electricity, 3 vols., London, 1839Google Scholar, 1844, 1855; reprinted New York, 1965, iii, 169–268, cited hereafter as Researches. Where possible hereafter I refer to Faraday's work by the paragraph numbers supplied by him; thus the preceding reference would be Researches, iii, paras. 2718–2968.Google Scholar

⁵ Ibid., paras, 2787–90, 2797–2846.

⁶ Ibid., paras. 2696–7, 2790.

⁷ Ibid., paras. 2782–90, 2832–5.

⁸ In addition to Thomson's letter, op. cit. (1), see his June 1849 paper ‘A mathematical theory of magnetism’, Philosophical transactions, 1851, 141, 243–68Google Scholar, continued June 1850, ibid., 269–85, reprinted in Reprint, op. cit. (3), pp. 340–405Google Scholar; Life of Thomson, op. cit. (1), i, 210–14Google Scholar; and below, section 5.1.

⁹ See Life of Thomson, op. cit. (1)Google Scholar; Smith, C., ‘Natural philosophy and thermodynamics: William Thomson and ‘The dynamical theory of heat’’, British journal for the history of science, 1976, 9, 293–319CrossRefGoogle Scholar; idem, ‘A new chart for British natural philosophy: the development of energy physics in the nineteenth century’, History of science, 1978, 16, 231–79Google Scholar; and Wise, M. Norton, ‘William Thomson's mathematical route to energy conservation: a case study of the role of mathematics in concept formation’, Historical studies in the physical sciences, 1979, 10, 49–83.CrossRefGoogle Scholar On Faraday, see Williams, L. P., Michael Faraday, London, 1965Google Scholar; Heimann, P. M., ‘Faraday's theories of matter and electricity’, British journal for the history of science, 1971, 5, 235–57CrossRefGoogle Scholar; and Gooding, D. C., ‘Metaphysics versus measurement: the conversion and conservation of force in Faraday's physics’, Annals of science, 1980, 37, 1–29.CrossRefGoogle Scholar

¹⁰ The two first met at the British Association meeting of June 1845 (Life of Thomson, op. cit. (1), i, 134).Google Scholar They met at the Royal Institution and at British Association meetings, in May and June 1846 (ibid., pp. 164, 165–6), June and July 1847 (ibid., 202–5), June 1848 (ibid., 207), and June 1849 (ibid., 214). Although I shall not discuss their interaction after 1850, correspondence at the Institution of Electrical Engineers (and elsewhere) suggests that the exchange of ideas continued into the 1860's.

¹¹ Life of Thomson, op. cit. (1), i, 144.Google Scholar The analogy was based on the similarity of the form of the mathematical expressions for the distribution of electricity and for the diffusion of heat, expressions for which Thomson provided no physical interpretation, ‘On the uniform motion of heat’, op. cit. (3); see also Wise, , op. cit. (9), pp. 58–62.Google Scholar

¹² Williams, , op. cit. (9), pp. 383–5Google Scholar; idem, The origins of field theory, New York, 1965, p. 93Google Scholar; and Thomson, 's letter to Faraday, , 6 08 1845Google Scholar, Correspondence, op. cit. (1), i, 458–60.Google Scholar

¹³ Doran, , ‘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, 1975, 6, 132–260CrossRefGoogle Scholar, especially pp. 162–79, (hereafter, ‘Field theory’).

¹⁴ Buchwald, J. Z., ‘William Thomson and the mathematization of Faraday's electrostatics’ Historical studies in the physical sciences, 1977, 8, 101–36 (107).CrossRefGoogle Scholar

¹⁵ For a similar treatment of the impact of Faraday's major magnetic discoveries of 1845, see Knudsen, O., ‘The Faraday effect and physical dieory, 1845–1873’, Archive for history of exact sciences, 1976, 15, 235–81.CrossRefGoogle Scholar

¹⁶ Agassi, J., Faraday as a natural philosopher, Chicago & London, 1971, pp. 111, 272–4.Google Scholar Thomson had established the mathematical equivalence of Faraday's and Coulomb's approaches in a paper read to the British Association in June 1845, ‘On the elementary laws of statical electricity’, Report of the fifteenth meeting of the British Association London, 1846, part II (sections), pp. 11–12Google Scholar; see also ‘On the mathematical theory of electricity in equilibrium I: on the elementary laws of statical electricity’, Cambridge and Dublin mathematical journal, 1846, 1, 75–95Google Scholar, reprinted in Reprint, op. cit. (3), pp. 15–37.Google Scholar

¹⁷ Quoted in Williams, , op. cit. (9) p. 507.Google Scholar

¹⁸ Nor has Thomson's importance been recognized in other accounts, e.g. McGuire, J. E., ‘Forces, powers, aethers, and fields’, Boston studies in the philosophy of science, 1974, 14, 119–59CrossRefGoogle Scholar; Schaffner, K. F., Nineteenth-century aether theories, Oxford, 1972Google Scholar; Hesse, M. B., Forces and Fields, London, 1961Google Scholar; Whittaker, E. T., A history of the theories of aether and electricity, 2vols., London, 1951–1953.Google Scholar

¹⁹ Researches, op. cit. (4), iiiGoogle Scholar, paras. 2247, 2257, 2450, 2463–7, 2470, 2496, 2502–4, 2591, 2600. Faraday first used the term in his laboratory diary, see Martin, T. (ed.), Faraday's diary, 7 vols., London, 1932–1936, ivGoogle Scholar, paras. 7979, 8014, 8085, 8148, 8180, 8675, 8962 (hereafter, Diary).

²⁰ I argue this in ‘Final steps to the field theory: Faraday's empirical study of magnetic phenomena, 1845–1850’, forthcoming in Histarical studies in the physical sciences.

²¹ Faraday's concept is of a field (and not merely of a medium, as Buchwald, supposes; op. cit. (14), p. 107).Google Scholar This is shown by his references to the ‘force’ or ‘action’ of the field and his belief that ferromagnetics take power away from the field in which they have been magnetized, Researches, op. cit. (4), iiiGoogle Scholar, paras. 2466, 2502–4.

²² O Knudsen has argued that ‘for both Kelvin and Maxwell the homogeneous elastic substance served as a means of visualizing the abstract concept of a field, and as a tool for setting up differential equations for field quantities’, ‘From Lord Kelvin's notebook: ether speculations’, Centaurus, 1971, 16, 41–53 (44).Google Scholar

²³ Thomson, , ‘Remarks on the forces experienced by inductively magnetized ferromagnetic or diamagnetic non-crystalline substances’ (first published 10 1850)Google Scholar, reprinted in Reprint, op. cit. (3), pp. 500–14Google Scholar, especially pp. 510ff.

²⁴ See his ‘Report of an address on the attractions and repulsions due to vibrations, observed by Guthrie and Schellbach’ (12 1870)Google Scholar, Reprint, op. cit. (3), pp. 574–8 (575).Google Scholar

²⁵ In ‘Final steps’, op. cit. (20).Google Scholar

²⁶ Faraday had to combine the idea of a field as a region in which each point is characterized by a force of a certain strength, with the idea that the region has a certain conductivity for lines efforce.

²⁷ There are resonances between Faraday's conflating of static and dynamical conceptions (described in my ‘Metaphysics versus measurement’, op. cit. (9)Google Scholar, section 3) and the physical conceptions implied by Thomson's use of certain mathematical relationships (examined by Wise, Norton, op. cit. (9)Google Scholar, especially pp. 62–74). I touch on this below, in section 5. As Wise's study of Thomson appeared after the present article had been completed, I hope to consider its implications in greater detail elsewhere.

²⁸ Buchwald, , op. cit. (14), pp. 107, 122–4.Google Scholar

²⁹ ‘Field theory’, op. cit. (13).Google Scholar As her title implies, Doran is primarily concerned with nineteenthcentury developments up to Joseph Larmor. She argues that the dominance of British aether physics culminates in the modern concepts of the atom and the field, but that the intellectual heritage of this tradition was the eighteenth-century conflict between the rival metaphysics of atomism (action at a distance) and the continuum. Thus the problem of action at a distance derived from metaphysical dualism, in which matter and its forces are distinguished from empty space. For a different interpretation of eighteenth-century developments in which Newton's force-aether features as a third alternative, see Heimann, P. M. and McGuire, J. E., ‘Newtonian forces and Lockean powers: concepts of matter in eighteenth century thought’, Historical studies in the physical sciences, 1971, 3, 233–306.CrossRefGoogle Scholar

³⁰ ‘Field theory’, op. cit. (13), p. 178.Google Scholar

³¹ Ibid., pp. 165–74.

³² Ibid., pp. 174–78. Doran argues that Thomson had adopted the continuum hypothesis in 1846 because it was then that he explored the possibility of representing electric and other forces as distortions (strains) in an elastic solid, in ‘On a mechanical representation of electric, magnetic, and galvanic forces’, Cambridge and Dublin mathematical journal, 1842, 2, 61–4.Google Scholar See below, section 5.

³³ ‘Field theory’, op. cit. (13), pp. 138–62.Google Scholar

³⁴ But Thomson did draw upon more contemporary sources, including natural theology, to justify the arguments that led to the central concept of energy and its laws of conservation and dissipation: see Smith, , ‘Natural philosophy and diermodynamics’, op. cit. (9).Google Scholar

³⁵ For a different interpretation see Buchwald, , op. cit. (14).Google Scholar

³⁶ See also Gooding, D. C., ‘Conceptual and experimental bases of Faraday's denial of electrostauc action at a distance’, Studies in history and philosophy of science, 1978, 9, 117–49.CrossRefGoogle Scholar

³⁷ Doran ignores this changing experimental context, which was crucial to Faraday's published theoretical position. He eventually obtained part of the necessary confirming evidence in 1847 and what he regarded as a complete confirmation in 1850. For these developments see Gooding, , ‘Final steps’, op. cit. (20)Google Scholar; Faraday, 's Diary, op. cit. (19), vGoogle Scholar, paras. 9066 ff., 10712 ff., 10822 ff.; and below, section 3.

³⁸ ‘Field theory’, op. cit. ( 13), pp. 175–6.Google Scholar

³⁹ Ibid., pp. 167–8; cf. Thomson, op. cit. (3).

⁴⁰ Reproduced in Williams, , op. cit. (9), p. 181.Google Scholar

⁴¹ Researches, op. cit. (4), iGoogle Scholar, para. 1331; see also paras. 1215 ff., especially 1224–31, 1562–6, and plate VIII, fig. 115. At para. 1316 Faraday suggests that ‘the specific inductive capacity of crystals will vary in different directions, according as the lines of inductive force (1304) are parallel to, or in other positions in relation to the axes of the crystals’. His general theory of 1850 developed the approach of 1837–38.

⁴² Faraday did not really believe that the ‘physical and chemical relations’ of bodies could be treated separately. This was a major source of his departure from the usual views: see Researches, op. cit. (4), iGoogle Scholar, paras. 1295–1305, 1320–79, 1406–12.

⁴³ Thus heat and light appear only when the rays or vibrations are intercepted and electricity gives rise to chemical change whose effects appear at surfaces between chemically different media. If the analogy does hold, dien poles (electrodes) should not be necessary for decomposition. Faraday proved this in series 5, Researches, op. cit. (4), iGoogle Scholar, paras. 450 ff., esp. 493–500.

⁴⁴ Ibid., paras. 1326–28, 1561, 1603–12.

⁴⁵ Ibid., series 4, paras. 380–394 and esp. paras. 412–16. I argue elsewhere that this was one source of Faraday's ‘wave-model’ for the conversion and transmission of electric and other forces; ‘Metaphysics versus measurement’, op. cit. (9), pp. 12–25.Google Scholar

⁴⁶ Conversely, the voltaic cell could be envisaged as a source of the force carried by the wave of current electricity, series 8, Researches, op. cit. (4), iGoogle Scholar, para. 875 ff. Although Faraday only hints at the analogies with heat in the published papers, references were common in his Royal Institution lectures on heat (see Gooding, , ‘Metaphysics versus measurement’, op. cit. (9)Google Scholar for references; and Brush, S. G., ‘The wave theory of heat: a forgotten stage in the transition from the caloric theory to thermodynamics’, British journal for the history of science, 1970, 5, 145–67CrossRefGoogle Scholar, for the background). Faraday was familiar with Melloni's theory of heat, in which both heat and light are transmitted as vibrations in an intermolecular aether, ‘Memoir on the free transmission of radiant heat through different solid and liquid bodies …’, Stientific memoirs, 1837, 1, 1–39.Google Scholar

⁴⁷ See nn. 43, 45, above. The background to Faraday's approach to electricity was therefore very different from Thomson's.

⁴⁸ Faraday often alluded to the current as an ‘axis of power’, to the possibility of its being a vibration (e.g., Researches, op. cit. (4), iGoogle Scholar, paras. 283, 257, 1110, 1115), and occasionally speaks of the lines of static induction as ‘rays’. Williams has noticed Faraday's view of electricity as a vibration, but he fails to recognize its importance as part of the analogy with light and heat, Michael Faraday, op. cit. (9), pp. 14–15, 138, 179, 199–200, 247–48, 268)Google Scholar, cf. Agassi, , Faraday, op. cit. (16), pp. 103–5.Google Scholar

⁴⁹ ‘An answer to Dr. Hare's letter on certain theoretical opinions’ (07 1840)Google Scholar, Researches, op. cit. (4), ii, 262–74(267).Google Scholar

⁵⁰ Faraday's 1837 theory was a step towards this general theory of conversion; see: Researches, op. cit. (4), iGoogle Scholar, paras. 1114–15, 1410–11, 1658–66, 1709–35.

⁵¹ Ibid., paras. 876, 959, 1161, 1292, 1305, 1320, 1338, 1358, 1410, 1523, 1623.

⁵² Thus he would not have denied electrostatic induction in vacuo; ibid., paras. 1615–16; and Faraday, to Hare, , loc. cit. (49).Google Scholar

⁵³ Ibid., iii, para. 2446, cf. 2443.

⁵⁴ ‘Thoughts on ray-vibrations’, ibid., pp. 447–52.

⁵⁵ Unity required not just that forces be inter-convertible but that each form of force would resemble others in important respects, such as polarity. See Gooding, , op. cit. (36).Google Scholar

⁵⁶ See below, section 5.

⁵⁷ See Heilbron, J. L., Electricity in the 17th and 18th century, a study of early modern physics, Berkeley, 1979.Google Scholar

⁵⁸ Although it may date from earlier discoveries of 1821 and 1831, Faraday's rejection of fluid explanations of dynamical phenomena is most clearly expressed in a letter to Whewell, of 09 1835Google Scholar; Correspondence, op. cit. (1), i, 294–6.Google Scholar His attitude had just been reinforced by the discovery of self-induction, Researches, op. cit. (4), i, paras. 1077–1100, ii, pp. 204–10.Google Scholar

⁵⁹ Faraday did not regard motion as an important quantity, even after he had recognized that relative motion is a necessary condition for the magnetic induction of a current; see Gooding, , op. cit. (9)Google Scholar, section 3.1.

⁶⁰ Researches, op. cit. (4), i, paras. 60–75, 242.Google Scholar

⁶¹ ‘Field theory’, op. cit. (13), pp. 165–73.Google Scholar

⁶² The problem was stated by Hare, Robert in ‘A letter to Prof. Faraday, on certain theoretical opinions’, printed in Researches, op. cit. (4), ii, pp. 251–61Google Scholar, to which Faraday, 's ‘Answer’, op. cit. (49)Google Scholar, is a reply. Williams, Levere, and Heimann argue that Faraday did face the problem of a regress of aethers; see Williams, , op. cit. (9), pp. 306 ff.Google Scholar; Levere, T. H., Affinity and matter, Oxford, 1971, pp. 96–101Google Scholar; Heimann, , op. cit. (9), pp. 241–4Google Scholar; see also McGuire, , op. cit. (18), p. 139.Google Scholar But whereas Heimann argues that Faraday had largely solved the problem (in his ‘Speculation touching electric conduction and the nature of matter’ (01 1844)Google Scholar, Researches, ii, pp. 284–93)Google Scholar, Doran maintains that Thomson was the source of Faraday's solution, after 1845.

⁶³ Researches, op. cit. (4), iGoogle Scholar, paras. 1164–8, 1615–6, 1628–9, 1665, 1680, and his ‘Answer’, op. cit. (49), pp. 265–6.Google Scholar

⁶⁴ Researches, op. cit. (4), i, para. 1680.Google Scholar

⁶⁵ Ibid., para. 1615; and loc. cit. (63). Since Faraday continued to defend this notion of contiguity he must have intended something that escaped his readers, as both Williams, (op. cit. (9), p. 306)Google Scholar, and Agassi, (op. cit. (16), p. 274)Google Scholar point out. See Gooding, , op. cit. (36), pp. 122–32.Google Scholar

⁶⁶ Faraday, regarded the vacuum as a ‘very hypothetical case’; ‘Answer’, op. cit. (49), p. 267.Google Scholar This was because ‘one cannot procure a space perfectly free from matter’, Researches, op. cit. (4), iiiGoogle Scholar, para. 2787. However, he had earlier considered that it ‘Would be strange it we could prove that no induction across a vacuum’, Diary, op. cit. ( 19), iii, paras. 3574–6.Google Scholar

⁶⁷ This strategy is discussed further in my ‘Faraday's atomism’, forthcoming.

⁶⁸ Patterns formed in iron filings or in lycopodium dust revealed that the lines do have a certain (but variable) distribution; Researches, op. cit. (4), i, paras. 114, 1350–1, 1369–70, 1449–50.Google Scholar

⁶⁹ Faraday's local or ‘contiguous’ actions are, of course, defined in terms of the nearest existing particle and not in terms of the nearest possible material point, as in Fourier, 's definition, Analytical theory of heat (tr. by Freeman, A.), Cambridge, 1878Google Scholar; facsimile reprint, New York, 1955, p. 460. This point is discussed below, in section 5.1.

⁷⁰ A prime task for the experimentaist was to ‘limit’ or ‘refine’ the meaning (reference) of theoretical terms. Faraday saw this as a gradual process in which our ‘conventional representations’ would approximate more closely to natural truth, as I hope to show in a future study of the uses of experiment.

⁷¹ I develop such an interpretation elsewhere (op. cit. (67)); here I deal only with Doran's claims that Faraday postulated an aether distinct from matter and that he held three different views of this aether between 1840 and 1849.

⁷² ‘Field theory’, op. cit. (13), pp. 165–73Google Scholar; Hare, , op. cit. (62).Google Scholar

⁷³ ‘Faraday, 's theories’, op. cit. (9), pp. 237, 243–6, 256–7.Google Scholar However, Heimann does notsuggest that this shift was occasioned by Thomson's influence.

⁷⁴ Doran, , op. cit. (13), p. 163Google Scholar, Doran's italics.

⁷⁵ Ibid.

⁷⁶ ‘A speculation’, op. cit. (62); and ‘Matter’, a lecture of February 1844, published in Levere, T. H., ‘Faraday, matter, and natural theology: reflections on an unpublished manuscript’, British journal for the history of science, 1968–1969, 4, 95–107 (105–7).CrossRefGoogle Scholar

⁷⁷ Agassi emphatically denies that Faraday was ever an aether theorist in this sense, op. cit. (16); see also ‘Field theory in De la Rive's Treatise on Electricity’, Organon, 1975, 11, 285–301 (298–9).Google Scholar

⁷⁸ See also section 5, below.

⁷⁹ ‘Field theory’, op. cit. (13), pp. 171–2, 174.Google Scholar

⁸⁰ Loc. cit. (49).

⁸¹ This idea may date back as far as his lectures to the City Philosophical Society of 1818–19. See my ‘Faraday's Atomism’, op. cit. (67); and Knight, D. M., The transcendental part of chemistry, Folkestone, 1978, pp. 91–123.Google Scholar

⁸² ‘Ray vibrations’, op. cit. (54), especially pp. 449–50. If all properties are the effects of active powers, then the aether differs from matter only in respect of the number of powers that it has.

⁸³ See n. 66, above.

⁸⁴ The relevance of these experiments on gases has been widely overlooked; see Researches, op. cit. (4), iiiGoogle Scholar, paras. 2400–16, and especially paras. 2432–47; ‘On the magnetic affection of light, and on the distinction between the ferromagnetic and diamagnetic conditions of Matter’ (09 1846)Google Scholar, ibid., iii, pp. 453–66; ‘On the diamagnetic conditions of flame and gases’ (12 1847)Google Scholar, ibid., pp. 467–90; series 25 (August 1850), ibid., paras. 2718–2796; and Faraday, 's Diary, op. cit. (19), vGoogle Scholar, paras. 10714–10843, 10860–75, 10896–11075.

⁸⁵ ‘Ray vibrations’, op. cit. (54).

⁸⁶ ‘On the magnetic affection of light’, op. cit. (84), especially pp. 455, 464–6; ‘On the diamagnetic conditions of flame and gases’, op. cit. (84), especially pp. 473, 487–9, and cf. paras. 2433, 2786–9.

⁸⁷ Between 1847 and 1849 Plücker published a number of papers on diamagnetism and performed experiments with Faraday at the Royal Institution in August 1848. Weber also published his theory in 1848. Faraday's response is analysed in Gooding, , ‘Final Steps’, op. cit. (20).Google Scholar

⁸⁸ ‘Field theory’, op. cit. (13), p. 169.Google Scholar

⁸⁹ ‘Ray vibrations’, op. cit. (54), p. 450Google Scholar; and ‘On the diamagnetic condition’, op. cit. (84), p. 465.Google Scholar

⁹⁰ Researches, op. cit. (4), iiiGoogle Scholar, paras. 2438–40; cf. Williams, , op. cit. (9), pp. 394–9.Google Scholar

⁹¹ He had already rejected one possibility, that diamagnetic action is just a differential effect of a single magnetic force acting on all matter; Researches, op. cit. (4), iiiGoogle Scholar, para. 2438; and loc. cit. (89), pp. 457 ff.

⁹² His discussion of E. Becquerel's theory shows that Faraday had never really accepted that space is non-magnetic: loc. cit. (84); and Researchts, op. cit. (4), iiiGoogle Scholar, paras. 2787–90 and 2847, footnote dated November 1850.

⁹³ Ibid., para. 2591; compare Doran, , ‘Field theory’, op. cit. (13), pp. 173–4Google Scholar; and Williams, , op. cit. (9), pp. 437–8.Google Scholar

⁹⁴ See section 2.1, above.

⁹⁵ Loc. cit. (52).

⁹⁶ Loc. cit. (5), 51), see also ‘On the physical character of the lines of magnetic force’, Researches, op. cit. (4), iiiGoogle Scholar, paras. 3243–99, especially paras. 3264–9.

⁹⁷ Ibid., para. 2787.

⁹⁸ Heimann, , op. cit. (9), pp. 256–7Google Scholar; Doran, , op. cit. (13), pp. 175–6.Google Scholar

⁹⁹ Researches, op. cit. (4), iiiGoogle Scholar, paras. 2787–90, 2832–5, and ‘Ray vibrations’, op. cit. (54), pp. 448–50.Google Scholar

¹⁰⁰ These assumptions are summarized in my ‘Metaphysics versus measurement’, op. cit. (9), pp. 7–11.Google Scholar Faraday's belief that muscular and ‘will force’ could be related to electricity suggests that living things also belonged in this hierarchy.

¹⁰¹ This is reproduced in Williams, , op. cit. (9), pp. 455–6.Google Scholar Doran inverts Williams's interpretation of this manuscript in order to interpret it as evidence of Faraday's supposed new belief in the continuum, ‘Field theory’, op. cit. (13), pp. 176–7.Google Scholar

¹⁰² Ibid., p. 177, footnote 123.

¹⁰³ Doran draws attention to Faraday's monism (ibid., pp. 165, 169) but she misinterprets this because she overlooks die strategy behind it: Faraday postulates active, discoverable powers, not the incompressible, inertial fluid of continuum-mechanics and Thomson's later vortex-atom theory.

¹⁰⁴ Researches, op. cit. (4), iiiGoogle Scholar, paras. 2454–2639; see also Williams, , op. cit. (9), p. 419 ff.Google Scholar

¹⁰⁵ Ibid., pp. 429–33.

¹⁰⁶ ‘Field theory’, op. cit. (13), p. 172Google Scholar; see Researches, op. cit. (4), iiiGoogle Scholar, paras. 2562, especially 2579–2604; and cf. paras. 2417–31, 2472–9.

¹⁰⁷ Ibid., para. 2591; cf. Diary, op. cit. (19), vGoogle Scholar, paras. 9910–19, especially para. 9912.

¹⁰⁸ Michael faraday, op. cit. (9), p. 416–9.Google Scholar

¹⁰⁹ ‘Field theory’, op. cit. (13), pp. 173–4.Google Scholar

¹¹⁰ For a similar view of the increasing importance of lines of force, see Heimann, , op. cit. (9), pp. 254 ff.Google Scholar

¹¹¹ Researches, op. cit. (4)Google Scholar, paras. 2221, 2236–40, 2420, and loc. cit. (84).

¹¹² Faraday, to Ampère, , 02 1822 and 09 1822Google Scholar, in Correspondence, op. cit. (1), i, 130–2, 134–5Google Scholar; cf. Faraday, to Whewell, William, 09 1835Google Scholar, ibid., pp. 294–6; Faraday, to Ward, F. O., 06 1834Google Scholar, ibid., p. 274; Researches, op. cit. (4), iGoogle Scholar, note on p. 321; cf. ibid., para. 1163, and the ‘Speculation’, op. cit. (62).

¹¹³ Weber, W., ‘On the excitation of diamagnetism according to the laws of induced currents’ (01 1848)Google Scholar, Scientific memoirs, 1852, 5, 477–88.Google ScholarFaraday, disproved Weber's theory in series 23 (01 1850)Google Scholar, Researches, op. cit. (4), iiiGoogle Scholar, paras. 2640–2701 (see also series 26, ibid., para. 2820). But Thomson showed that Weber's assumption of an induced reverse polarity was also a consequence of Faraday's law of diamagnetic action (ibid, iii, paras. 2269, 2418). See Thomson, 's papers ‘On the forces experienced by small spheres under magnetic influence …’, Cambridge and Dublin mathematical journal, 1847, 2, 230–35Google Scholar, and ‘Remarks on the forces experienced by inductively magnetized ferromagnetic or diamagnetic noncrystalline substances’, Philosophical magazine, 1850, 37, 241–53.Google Scholar

¹¹⁴ Faraday objected to the hypothetico-deductive approach which characterized the mathematical work of Weber, Plücker, , and others; Researches, op. cit. (4), iii, para. 2641.Google Scholar

¹¹⁵ Ibid., paras. 2591, 2626–8, 2797 and ff., especially 2818, and 3154 ff., 3293, 3307 ff.

¹¹⁶ At this time (1847–8) Thomson was reaching the conclusion that energy is the central, unifying concept of mathematical physics; see Smith, , ‘Natural philosophy and thermodynamics’, op. cit. (9)Google Scholar; Wise, , op. cit. (9)Google Scholar; and section 5, below.

¹¹⁷ Faraday had at first assumed that only those forces which are polar (inductive) at ail orders of magnitude do not act at a distance. Thus, in 1831, even electrostatic forces had appeared to be non-contiguous actions (Researches, op. cit. (4), iGoogle Scholar, para. 73). Non-polar forces of cohesion, crystallization, and gravitation remained ‘distance’ forces in this sense (ibid., i, paras. 523, 1231; iii, paras. 2568, 2578); see also ‘Ray vibrations’, op. cit. (54), p. 450.Google Scholar

¹¹⁸ ‘Ray vibrations’, op. cit. (54), pp. 450–1.Google Scholar

¹¹⁹ The aether remained a possibly useful concept: ‘Physical lines’. op. cit. (96)Google Scholar, para. 3263, and ‘On some points of magnetic philosophy’ (12 1854), Researches, iiiGoogle Scholar, paras. 3300–3362, especially para. 3302.

¹²⁰ ‘Field theory’, op. cit. (13), pp. 175–6.Google Scholar

¹²¹ This is argued in Gooding, , op. cit. (9).Google Scholar See also Faraday, 's ‘Points of magnetic philosophy’, op. cit. (118)Google Scholar; and ‘On the conservation of force’ (02 1857)Google Scholar, Experimental researches in chemistry and physics, London, 1859, pp. 443–63.Google Scholar

¹²² See, for example, Researches, op. cit. (4), i, paras. 1304, 1224–31.Google Scholar

¹²³ Ibid., iii, para. 3175, Faraday's italics.

¹²⁴ ‘Physical lines’, op. cit. (96)Google Scholar, paras. 3243–56; and ‘Points of magnetic philosophy’, op. cit. (118)Google Scholar, paras. 3300–06.

¹²⁵ ‘Physical lines’, op. cit. (96)Google Scholar, paras. 3277–9.

¹²⁶ This is why a soft iron bar is merely the ‘habitation’ of thepower in the lines of force; ibid., para. 3295, cp. 2591.

¹²⁷ Ibid., paras. 3305, 3361, 3276–7.

¹²⁸ Magnetism (and, by implication, any active power) is not inherent in things. It exists only in relation to other things. A ‘tonic’ or static state of tension underlies the possibility of ail action (ibid., paras. 3323 ff., and ‘On some points of magnetic philosophy’ (01 1855)Google Scholar, ibid., pp. 566–74).

¹²⁹ Faraday regarded weight and inertia as converted forms of the universal, ‘parent’ force: see Gooding, , op. cit. (9).Google Scholar

¹³⁰ ‘On some new electro-magnetical motions, and on the theory of magnetism’ (10 1821)Google Scholar, Researches, op. cit. (4), ii, pp. 127–47Google Scholar, especially p. 131; Diary, op. cit. (19), i, p. 93Google Scholar; and Researches, iii, para. 2591.Google Scholar

¹³¹ Ibid., i, para. 1 ff., especially paras. 60 ff., 193 ff.

¹³² Loc. cit. (58).

¹³³ Researches, op. cit. (4), iGoogle Scholar, paras. 217–30; iii, paras. 3084–3115, especially para. 3090.

¹³⁴ ‘Field theory’, op. cit. (13), p. 176.Google Scholar

¹³⁵ Loc. cit. (130); and Researches, op. cit. (4), i, para. 220.Google Scholar

¹³⁶ According to Maxwell, , Faraday, 's idea that ‘the moving conductor, as it cuts the lines of force, sums up the action due to an area or section of the lines of force … appears no new view of the case after the investigations of the second series have been taken into account’, Treatise on electricity and magnetism, 3rd edn., 2 vols., Cambridge, 1891, ii, 189.Google Scholar

¹³⁷ The analysis of self-induction ruled out an interpretation based on momentum or the kinetic energy of electric fluids; loc. cit. (58). Maxwell subsequently argued that the current is the seat of kinetic energy, but that this is energy of motion ‘going on in the space outside the wire’, Treatise, op. cit. (136), ii, 195 ff.Google Scholar

¹³⁸ Researches, op. cit. (4), iiiGoogle Scholar, para. 3263. Faraday continued to believe that ‘mathematical considerations cannot at present decide which of the three views [of the physical basis of magnetism] is either above or inferior to its co-rivals’, therefore ‘physical reasoning should be brought to bear upon the subject as largely as possible’, ibid., para. 3305. His reticence had been overcome by the ‘appreciation by mathematicians of the mode of figuring to one's self the magnetic forces by lines’.

¹³⁹ Ibid., paras. 3172–3; cf. paras. 3336–8.

¹⁴⁰ This had survived Faraday's earlier experimental refutation, loc. cit. (113). In 1857 Faraday again attacked central-force physics by criticizing die inverse square law as the basis of a complete theory of gravitation, in ‘On the conservation of force’, op. cit. (121).

¹⁴¹ See Wise, , op. cit. (9), pp. 71–6Google Scholar; Smith, , ‘Natural philosophy and thermodynamics’, op. cit. (9)Google Scholar; and idem., ‘William Thomson and the creation of thermodynamics: 1840–1855’, Archive for history of exact sciences, 1976, 16, 231–88.Google Scholar

¹⁴² Wise, , op. cit. (9), pp. 74–7.Google Scholar

¹⁴³ Thomson, , ‘On the mathematical theory of electricity in equilibrium’, op. cit. (16).Google Scholar

¹⁴⁴ Buchwald argues that Thomson, extended Faraday's idea of ‘mediated’ action by adding the idea that force is propagated, i.e. proceeds from point to point in a finite time; op. cit. (14), pp. 107, 122ff.Google Scholar

¹⁴⁵ Life of Thomson, op. cit. (1), i, 19–20.Google Scholar David Thomson was a cousin of Faraday and an acquaintance of William Thomson at Glasgow.

¹⁴⁶ For a discussion of Fourier in relation to Thomson, see Smidi, , ‘Natural philosophy and thermodynamics’, op. cit. (9), p. 305 ffGoogle Scholar; Wise, , op. cit. (9), pp. 51–8Google Scholar; and idem, ‘The flow analogy to electricity and magnetism, pan I: William Thomson's reformulation of action at a distance’, forthcoming in Archive for history of exact sciences.

¹⁴⁷ Loc. cit. (41) and Researches, op. cit. (4), iGoogle Scholar, paras. 1166, 1215 ff., 1305, 1449–50.

¹⁴⁸ For example, Buchwald states that Faraday, 's picture of induction led him to conclude that it is exerted in curved lines (op. cit. (14), p. 122).Google Scholar

¹⁴⁹ Life of Thomson, op. cit. ( 1), i, 20, 112.Google Scholar

¹⁵⁰ I would like to thank a referee for making this point. See Life of Thomson, op. cit. (1), i, 50.Google Scholar

¹⁵¹ Buchwald, , op. cit. (14), pp. 105–7.Google Scholar Buchwald also points out that Thomson did not mention Faraday in his 1841 paper on neat and electricity (op. cit. (3)). But this is not surprising. Thomson was exploring a purely formal analogy, not a physical one, and (as Buchwald himself argues) he was until 1845 primarily concerned with problems in the mathematical theory of heat.

¹⁵² Thomson, William to Thomson, James, 30 03 1845Google Scholar, in Life of Thomson, op. cit. (1), i, 128–9.Google Scholar Liouville's interest was shared by Arago, whose theory of electricity had been withdrawn as the subject for the mathematical prize essay of the Institute of France because of the doubt cast on it by Faraday's experiments. But Faraday had not presented his discoveries as refutations of the mathematical theories; see Researches, op. cit. (4), iGoogle Scholar, especially paras. 1305, 1320. Throughout his career he argued that the inverse-square force function is an incomplete description of what takes place when two bodies approach under eleccric, magnetic, or gravitational attraction.

¹⁵³ Loc. cit. (152).

¹⁵⁴ Op. cit. (4), the first volume of which appeared in 1839.

¹⁵⁵ Ibid., p. 129.

¹⁵⁶ Thomson published two versions: Nôte sur les lois élémentaires de l'électricité statique,' Journal de mathématiques pures et appliquées, 1845, 10, 209–21Google Scholar (compare his ‘On the elementary laws’, op. cit. (16)); and ‘On the mathematical dieory of electricity in equilibrium’, op. cit. (16). The latter was completed in November 1845, about 6 months after the former.

¹⁵⁷ Op.cit.(16), pp.271–4.

¹⁵⁸ See Thomson, 's ‘On the mathematical theory’, op. cit. (16)Google Scholar, especially pp. 83, 86; his ‘Mathematical theory of magnetism’, op. cit. (8), pp. 244, 247Google Scholar; and Faraday, 's Researches, op. cit. (4), iGoogle Scholar, paras. 1161, 1667.

¹⁵⁹ Wise argues that ‘from Fourier and the continuity equation Thomson learned … that [mathematical theory] need not be complex and it need not rely on a detailed physical picture …’; op. cit. (9), p. 56.Google Scholar

¹⁶⁰ Gooding, , ‘Metaphysics versus measurernent’, op. cit. (9), pp. 5–6.Google Scholar Faraday's theology ruled out knowledge of primary causes (of which we perceive only the effects).

¹⁶¹ Faraday, to SirLemen, C., 25 04 1834Google Scholar, in Correspondence, op. cit. (1), i, 267–8Google Scholar; Faraday, 's Diary, op. cit. (19), i, 425.Google Scholar

¹⁶² See Faraday, 's ‘Ray vibrations’, op. cit. (54).Google ScholarThomson, 's interest in aether models dates from early in 1846Google Scholar, see his ‘Mechanical representation’, op. cit. (32); Life of Thomson, op. cit. (1), i, 159, 197–8Google Scholar; and Wise, , op. cit. (9), pp. 69–70.Google Scholar

¹⁶³ Fourier, , Analytical theory, op. cit. (6), p. 460.Google Scholar Fourier assumed conservation of heat during transmission between points; Faraday insisted that contiguous actions are ‘limited’ and ‘definite’, i.e., conserved.

¹⁶⁴ Life of Thomson, op. cit. (1), i. 14Google Scholar, and passim.

¹⁶⁵ ‘Mathematical theory of electricity in equilibrium’, op. cit. (16), pp. 92–3.Google Scholar

¹⁶⁶ Ibid., p. 96. Wise points out that Thomson was not yet willing to accept Faraday's view of propagation as a physical theory simply on the strength of the mathematical analogy between inductive capacity and thermal conductivity; op. cit. (9), p. 69.Google Scholar

¹⁶⁷ Loc. cit. (62); see also Gooding, , op. cit. (36), pp. 120–6.Google Scholar

¹⁶⁸ Loc. cit. (156). In comparing me two versions, Buchwald shows that by November 1845 Thomson had introduced an operational definition of electricity to complement his earlier rejection of fluid conceptions, and had correspondingly altered both his description of the function of Coulomb's proof plane and his view of the status of Coulomb, 's theory (which was now put in operational terms); op. cit. (14), pp. 127 and ff.Google Scholar

¹⁶⁹ Researches, op. cit. (4), iGoogle Scholar, paras. 1169ff.; Diary, op. cit. (19), iiGoogle Scholar, paras. 2808–74; and Gooding, , op. cit. (36), pp. 139–42.Google Scholar

¹⁷⁰ Life of Thomson, op. cit. (1), i, 130.Google Scholar

¹⁷² But this time Thomson was aware of what his earlier treatments had implied; see Wise, , op. cit. (9), p. 58 ff.Google Scholar, especially pp. 67–74.

¹⁷³ In fact he even excluded the consideration of other phenomena (such as the Faraday effect) which might suggest a physical interpretation; ‘Mathematical theory of magnetism’, op. cit. (8), pp. 243–4.Google Scholar

¹⁷⁴ Ibid., pp. 257–9. Thus the problem of determining me resultant force could be solved using methods developed by Laplace and Green. Thomson had shown this for electrostatic forces in 1845.

¹⁷⁵ For the separation of mathematical and physical assumptions in these studies see Wise, , op. cit. (9)Google Scholar; and Smith, , ‘A new chart for British natural philosophy’, op. cit. (9), pp. 241 ff.Google Scholar, especially p. 246.

¹⁷⁶ Agassi, , op. cit. (16), p. 272Google Scholar; for Faraday's view see loc. cit. (152).

¹⁷⁷ Agassi, , loc. cit. (176).Google Scholar Agassi rightly draws attention to the problem of molecular polarization, but he overlooks the fact that even after 1850 Faraday was cautious about his own solution to this problem (Researches, op. cit. (4), iii, p. 503).Google Scholar

¹⁷⁸ Treatise, op. cit. (136), i, p. ixGoogle Scholar, and ‘Action at a distance’, in Niven, W. D. (ed.), The scientific papers of James Clerk Maxwell, 2 vols., Cambridge, 1890, ii, 311–23 (319).Google Scholar

¹⁷⁹ By 1846 Faraday had discovered not only the magneto-optic effect but also the general suscept-ibility of matter to magnetism. Given the heuristic potential of the vibratory theory, this sanctioned his speculation of 1846, (op. cit. (54)). Thomson had realized the unifying potential of an electrical, optical, and magnetic aether by June 1847.

¹⁸⁰ ‘Points of magnetic philosophy’, op. cit. (118), para. 3304.Google Scholar

¹⁸¹ Ibid., paras. 3302–3.

¹⁸² Thomson, , loc. cit. (162).Google Scholar It had been argued that the theological context of Thomson's conception of natural science entailed a realist position on which man could have knowledge of unobservable entities, Wilson, D. B., ‘Kelvin's scientific realism: the theological context’, The philosophical journal, 1974, 11, 41–60.Google Scholar But there is no evidence that Thomson adopted a physical interpretation of the aether models he began to investigate in 1846. Until then Thomson had not shared his Cambridge contemporaries' interest in the application of aether theory to optics. Thus it would appear that he kept his realism at bay, at least until the late 1850s, when he began to identify phenomenal forces with motion of the aether; see ‘Dynamical illustrations of the magnetic and the helicoidal rotatory effects of transparent bodies on polarized light’, Proceedings of the Royal Society, 1856–1857, 8, 150–8Google Scholar; and the report of his Friday evening lecture at the Royal Institution, 18 May 1860, in Reprint, op. cit. (3), 208–25 (224).Google Scholar

¹⁸³ Loc. cit. (82).

¹⁸⁴ Researches, op. cit. (4), i, paras. 1320–31.Google Scholar

¹⁸⁵ Wise, , op. cit. (9), pp. 71–2.Google Scholar

¹⁸⁶ ‘Field theory’, op. cit. ( 13), p. 175.Google Scholar

¹⁸⁷ Researches, op. cit. (4), iGoogle Scholar, paras. 114, 1215 ff., plate VIII; iii, paras. 3070–74, plate III (especially figures 23, 24), and plate IV. Faraday's Diary shows that he had applied the conduction idea to ferromagnelism from the outset; see Gooding, , ‘Final steps’, op. cit. (20)Google Scholar; and Diary, op. cit. (19), ivGoogle Scholar, paras. 8144, 8260; v, paras. 9504, 9617, 9736 ff.

¹⁸⁸ Researches, op. cit. (4), iii, para. 2247.Google Scholar

¹⁸⁹ Loc. cit. (19).

¹⁹⁰ Researches, op. cit. (4), iii, paras. 2269, 2418Google Scholar; Diary, op. cit. (19), v, para. 9138.Google Scholar See also Thomson, , loc. cit. (23, 24).Google Scholar

¹⁹¹ As I show in ‘Final steps’, op. cit. (20).

¹⁹² See also my ‘Teleology and economy in Faraday's later physics’, read to the summer meeting of the British Society for the History of Science at Oxford, 11–13 September 1979.

¹⁹³ Wise, , op. cit. (9), p. 72.Google Scholar

¹⁹⁴ Researches, op. cit. (4), iii, paras. 2576 ff., 2624 ff.Google Scholar especially paras. 2626–8.

¹⁹⁵ ‘Field theory’, op. cit. ( 13), p. 172.Google Scholar

¹⁹⁶ Loc. cit. (40, 89).