Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T23:28:14.072Z Has data issue: false hasContentIssue false
  • English
  • Français

The uses of analogy: James Clerk Maxwell's ‘On Faraday's lines of force’ and early Victorian analogical argument

Published online by Cambridge University Press:  22 March 2010

KEVIN LAMBERT
KEVIN LAMBERT
Affiliation:
Department of Liberal Studies, H-223G, California State University, 800 N. State College Blvd., Fullerton, CA. 92831, USA. Email: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Early Victorian analogical arguments were used to order the natural and the social world by maintaining a coherent collective experience across cultural oppositions such as the ideal and material, the sacred and profane, theory and fact. Maxwell's use of analogical argument in ‘On Faraday's lines of force’ was a contribution to that broad nineteenth-century discussion which overlapped theology and natural philosophy. I argue here that Maxwell understood his theoretical work as both a technical and a socially meaningful practice and that embedding his use of analogy in the social and intellectual context of Victorian Britain provides a means of telling a sociocultural history of Maxwell's development of a new cognitive tool: a way of thinking on paper analogous to thinking with objects in the laboratory.

And analogy can do no more, immediately or directly, than shew such and such things to be true or credible considered only as matters of fact.

Bishop Butler, 17361

Type
Research Article
Information
The British Journal for the History of Science , Volume 44 , Issue 1 , March 2011 , pp. 61 - 88
Copyright
Copyright © British Society for the History of Science 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 Joseph Butler, The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature, in The Works of Bishop Butler (ed. David E. White), Rochester: University of Rochester Press, 2006, Chapter VII, §1, pp. 147–314, p. 214.

2 The literature on Maxwell's use of analogies is huge but the classic discussion is Mary Hesse, Models and Analogies in Science, London: Sheed & Ward, 1963. See also, more recently, Nancy Nersessian, Faraday to Einstein: Constructing Meaning in Scientific Theories, Dordrecht: Nijhoff, 1984, pp. 69–74. P.M. Harman, The Natural Philosophy of James Clerk Maxwell, Cambridge: Cambridge University Press, 1998, pp. 71–90. Also Cat, Jordi, ‘On understanding: Maxwell on the methods of illustration and scientific metaphor’, Studies in the History and Philosophy of Modern Physics (2001) 32, pp. 395–441.CrossRefGoogle Scholar

3 James Clerk Maxwell, ‘On Faraday's lines of force’, in The Scientific Papers of James Clerk Maxwell (ed. W.D. Niven) (hereafter SP), 2 vols., New York, 2005, vol. 1, p. 157.

4 The development of Maxwellian theoretical practice was a historical process that continued even after Maxwell's death. For the difficulties of making sense of Maxwell's Treatise on Electricity and Magnetism at Cambridge see Andrew Warwick, Masters of Theory: Cambridge and the Rise of Mathematical Physics, Chicago: University of Chicago Press, 2003, Chapter 6; and for the development of Maxwellian theory outside Cambridge see Bruce J. Hunt, The Maxwellians, Ithaca, NY: Cornell University Press, 1991.

5 I therefore see this paper as contributing to both sociocultural and cognitive history of science. There has been a tendency to see some conflict between these two domains, perhaps needlessly. See Nersessian, Nancy J., ‘Opening the black box: cognitive science and history of science’, Osiris (1995) 10, pp. 194–211.CrossRefGoogle Scholar Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History, Cambridge: Cambridge University Press, 1999, pp. 1–8.

6 Maxwell, ‘Are there real analogies in nature?’ in The Scientific Letters and Papers of James Clerk Maxwell (ed. P.M. Harman) (hereafter SLP), 3 vols., Cambridge: Cambridge University Press, 1990–2002, vol. 1, pp. 376–383. The essay is also reproduced in Lewis Campbell and William Garnett, Life of James Clerk Maxwell, London: Macmillan, 1882, pp. 235–244.

7 For reasons of space and organization I am unable to discuss other factors that informed Maxwell's use of analogies, perhaps most obviously his education at Edinburgh before he entered Cambridge. I especially do not wish to deny by omission the real importance of Maxwell's Scottish education, including the greater emphasis on experimental natural philosophy, as a resource for the development of his theoretical practice, although I would also point out that Maxwell's most important Edinburgh professors still sought to maintain a strong distinction between the higher power of the mind and the more banausic production of facts. For example J.D. Forbes, Maxwell's professor of natural philosophy at Edinburgh, dedicated two lectures in the opening of the 1848–1849 session to arguing against Whig historian Thomas Babington Macaulay and his claim that a little knowledge was not a dangerous thing. In that discussion Forbes's emphasis is on the ‘faculty of patient and concentrated thought’ (my emphasis) that distinguishes the ‘profound and practical student’ from the mere ‘empiric’. See John Campbell Shairp, Peter Guthrie Tait and Anthony Adams-Reilly, Life and Letters of James David Forbes (1873), London, 2005, pp. 190–195. For an account of the importance of Maxwell's education in Edinburgh see Harman, op. cit. (2), pp. 13–70. For what is still a classic account of the nineteenth-century Scottish universities see George Elder Davie, The Democratic Intellect: Scotland and Her Universities in the Nineteenth Century, Edinburgh: Edinburgh University Press, 1964.

8 David Gooding ‘“Magnetic curves”and the magnetic field: experimentation and representation in the history of a theory’, in David Gooding, Trevor Pinch and Simon Schaffer (eds.), The Uses of Experiment, Cambridge: Cambridge University Press, 1989, pp. 183–223, p. 209.

9 The terms ‘atonement’ and ‘incarnation’ theology used here and later are borrowed from Boyd Hilton, The Age of Atonement: The Influence of Evangelicalism on Social and Economic Thought, 1785–1865, Oxford: Clarendon Press, 2001. As Hilton has shown, they are general terms that incorporated a wide range of meanings in nineteenth-century Britain. Although atonement theology was strongest among the evangelicals, as the example of Whewell shows, it also had a presence among Broad Church Anglicans.

10 James Clerk Maxwell to William Thomson, 13 September 1855, SLP, op. cit. (6), vol. 1, p. 323.

11 See the series of letters Maxwell wrote to Thomson in the period from 20 February 1854 to 22 February 1856, which all refer to either geometry or electricity and magnetism, often both. Reproduced in SLP, op. cit. (6), vol. 1, nos. 45, 47, 51, 66, 71. For an example of how Maxwell changed the meaning of Thomson's mathematics see Wise, M. Norton, ‘Lecture sous influences’ (English title: ‘Creative misreading: Maxwell rewrites Thomson’), Les Cahiers de Science et Vie (2002), pp. 54–62.Google Scholar

12 The term ‘incarnation theology’ is also borrowed from Hilton, op. cit. (9).

13 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, p. 158.

14 The close relationship between Maxwell's work on the bending of surfaces and the mathematical approach taken in his ‘On Faraday's lines of force’ is discussed in M. Norton Wise, ‘The flow analogy to electricity and magnetism: Kelvin and Maxwell’, Ph.D. dissertation, Princeton University, 1977, No. AAT7714252, pp. 131–137. See also idem, ‘The mutual embrace of electricity and magnetism’, Science (1979) 203, pp. 1310–1318. Both have been immensely useful for this paper.

15 In her work on British mathematics Joan Richards has demonstrated the importance of understanding the meaning of mathematics. See, for example, Joan L. Richards, ‘The history of mathematics and L'esprit humain: a critical reappraisal’, Osiris (1995), 2nd Ser., 10, pp. 122–135. Another important resource for thinking about practices as having cultural meaning has also been Pierre Bourdieu, Outline of a Theory of Practice (tr. Richard Nice), Cambridge: Cambridge University Press, 1977.

16 Iwan Rhys Morus, ‘Currents from the underworld: electricity and the technology of display in early Victorian England’, Isis (1993) 84, pp. 50–69. Morus distinguishes between the ‘professoriat’, which included Sir Humphrey Davy, John Frederic Daniell, Charles Wheatsone and William Robert Grove, and the ‘electricians’, which included Peter Barlow and William Sturgeon. For Morus, the difference of approach between the groups was that the electricians considered the apparatus as constituting nature; the professariat saw the apparatus as tools for exploring an external nature.

17 After his discovery of electromagnetic induction in 1831 Faraday wrote, ‘It is quite comfortable to find that experiment needs not quail before mathematics but is quite competent to rival it in discovery.’ Faraday to Phillips, 29 November 1831, as cited in Olivier Darrigol, Electrodynamics from Ampère to Einstein, New York: Oxford University Press, 2000, p. 24. For an account of Faraday's experimental method see David Gooding, Experiment and the Making of Meaning: Human Agency in Scientific Observation and Experiment, Dordrecht: Kluwer Academic Publishers, 1990.

18 Michael Faraday, ‘On some new electro-magnetical rotations, and on the theory of magnetism’, in Quarterly Journal of Science (1821) 12, pp. 74–96. Reproduced in idem, Experimental Researches in Electricity (3 vols.) New York: Dover, 1965, vol. 2, pp. 127–147.

19 Interestingly, Faraday's originality was called into question at the time. See L. Pearce Williams, Michael Faraday, New York: Simon & Schuster, 1971, pp. 157–161; and the discussion in Darrigol, op. cit. (17), p. 22.

20 André-Marie Ampère, ‘Notes relatives au mémoire de M. Faraday’, Annales de chimie et de physique (1821) 18, pp. 370–379, as cited by L. Pearce Williams, ‘Faraday and Ampère: a critical dialogue’, in David Gooding and Frank A.J.L. James (eds.), Faraday Rediscovered: Essays on the Life and Work of Michael Faraday, 1791–1867, New York: Macmillan, 1985, p. 95.

21 James R. Hofmann, André-Marie Ampère: Enlightenment and Electrodynamics, Cambridge: Cambridge University Press, 1996, pp. 123–143. As both Darrigol and Hofmann have noticed, different theoretical approaches also imply different experimental styles. Ampère failed to find new electromagnetic effects such as rotations and, most famously, electromagnetic induction because his devices were designed to prove the consequences of his theory. Darrigol, op. cit. (17), p. 21. Hofmann, , ‘Ampère, electrodynamics and experimental evidence’, Osiris (1987) 3, pp. 45–76.CrossRefGoogle Scholar

22 T.R. Birks, ‘The analogy of mathematical and moral certainty’, in idem, First Principles of Moral Science: A Course of Lectures Delivered in the University of Cambridge, London: Macmillan, 1873, pp. 291–320.

23 Birks, op. cit. (22), p. 311. For short discussions of Birks and his analogy see Thomas L. Hankins, ‘A “large and graceful sinuosity”: John Herschel's graphical method’, Isis (2006) 97, pp. 631–632. Hilton, op. cit. (9), pp. 365–367.

24 Birks, op. cit. (22), p. 306. The citation is from Samuel Taylor Coleridge, Elements of Religious Philosophy, in The Complete Works of Samuel Taylor Coleridge with an Introductory Essay upon His Philosophical and Theological Opinions (ed. William G.T. Shedd), 7 vols., New York, 1853, vol. 1, p. 193. ‘We have begun, as in geometry, with defining our terms; and we proceed, like the geometricians, with stating our postulates; the difference being, that the postulates of geometry no man can deny, those of moral science are such as no good man will deny.’

25 Maxwell, ‘Analogies’, SLP, op. cit. (6), vol. 1, p. 378, original emphasis. Harman, op. cit. (2), p. 33.

26 William Whewell, The Philosophy of the Inductive Sciences Founded upon Their History, 2 vols., London, 1967, vol. 1, pp. 16–51; vol. 2, pp. 647–668.

27 Whewell, op. cit. (26), vol. 1, p. 23.

28 Whewell, op. cit. (26), vol. 1, pp. 23–24.

29 James Clerk Maxwell, ‘Inaugural lecture at Marischal College Aberdeen, 3 November 1856’, SLP, op. cit. (6), vol. 1, p. 430.

30 For a discussion of the highly technical training provided by coaches at Cambridge see Warwick, op. cit. (4). Warwick discusses the tension between the ideal of public teaching and research and private tutoring for the tripos on pp. 94–109.

31 Becher, Harvey W., ‘William Whewell and Cambridge mathematics’, Historical Studies in the Physical Sciences (1980) 11, pp. 1–48.CrossRefGoogle Scholar

32 For a good short account of Butler's theology see David E. White, ‘Introduction’, in Butler, op. cit. (1), pp. 1–9.

33 G.M. Young argued that the foundational texts of atonement theology were Wilberforce, A Practical View of Christianity and Malthus, Essay on the Principle of Population. G.M. Young, Victorian England: Portrait of an Age, London: Oxford University Press, 1977, p. 29. Hilton, op. cit. (9), pp. 3–4.

34 William Whewell, Astronomy and General Physics: Considered with Reference to Natural Philosophy, London: Bohn, 1852, pp. 174–175.

35 Hilton describes Whewell's Elements of Morality (1845) as ‘pure Butler with touches of Kant’, although he also claims that Whewell's ‘boast that Butler was now accepted as the official moral philosophy of Cambridge (as well as Trinity) was mere bravado’. Hilton, op. cit. (9), p. 171.

36 Mary Douglas, Purity and Danger: An Analysis of Concepts of Pollution and Taboo, New York: Routledge, 2002.

37 Whewell to Jones, 17 October 1825, Trinity College Library, Cambridge University, Add. MS. c/51/23.

38 Thomson, William, ‘On the uniform motion of heat in homogenous solid bodies, and its connection with the mathematical theory of electricity’, Cambridge Mathematical Journal (1843) 3, pp. 71–84.Google Scholar

39 An important resource for Thomson whilst in Glasgow was John Pringle Nichol, who instructed William Thomson at Glasgow University before Thomson went to Cambridge. Nichol taught that ‘the quality of form is the simplest of all the qualities of matter, and hence geometry, which treats of it, stands at the head of Natural Philosophy’. It was Nichol who first introduced Thomson to Fourier's paper on the theory of heat. William Thomson, ‘Notebook of natural philosophy class’, quoted in Crosbie Smith and M. Norton Wise, Energy and Empire: A Biographical Study of Lord Kelvin, Cambridge: Cambridge University Press, 1989, p. 210.

40 David B. Wilson, ‘The educational matrix’, in P.M. Harman (ed.), Wranglers and Physicists: Studies on Cambridge Physics in the Nineteenth Century, Manchester: Manchester University Press, 1985, p. 30.

41 William Thomson, 16–17 March 1843, Diary, NB29, Kelvin Collection, Add. MS 7342, University Library, Cambridge original emphasis. As quoted in Smith and Wise, op. cit. (39), p. 213.

42 Crosbie Smith and Norton Wise have mapped the Glasgow culturescape in some detail in a number of places. See, for example, Smith and Wise, op. cit. (39). M. Norton Wise, ‘Work and waste: political economy and natural philosophy in nineteenth century Britain (III)’, History of Science (1990) 28, pp. 220–261. Crosbie Smith, ‘“Nowhere but in a great town”: William Thomson's spiral of classroom credibility’, in Crosbie Smith and Jon Agar (eds.), Making Space for Science: Territorial Themes in the Shaping of Knowledge, New York: Macmillan, 1998, pp. 118–146. And in the same volume, Ben Marsden's account of work to make space for the new discipline of engineering at Glasgow University: ‘“A most important trespass”: Lewis Gordon and the Glasgow chair of civil engineering and mechanics, 1840–55’, pp. 87–117.

43 Smith and Wise, op. cit. (39), Chapter 4; Crosbie Smith, The Science of Energy: A Cultural History of Energy Physics in Victorian Britain, London: Athlone, 1998, pp. 17–22. Chalmers, like Whewell, was a great admirer of Birks's essay. See Chalmers to Whewell, 4 March 1832, Trinity College Library, Cambridge University, Add. MS. a./202/25. Also Hilton, op. cit. (9), p. 365.

44 My use of the term ‘latitudinarian’ is borrowed from Smith and Wise, op. cit. (39), pp. 228–230.

45 See Thomson's paper, which appeared in what was now called the Cambridge and Dublin Mathematical Journal in 1847. ‘On a mechanical representation of electric, magnetic, and galvanic forces’, reproduced in William Thomson Kelvin Mathematical and Physical Papers, vol. 1, Boston, 2006, 76–80. A letter Thomson wrote to Faraday on the paper remained cautious – ‘What I have written is merely a sketch of the mathematical analogy’ – but he made clear that he was looking forward to a future physical theory which, ‘when taken in connection with the undulatory theory of light, in all probability [would] explain the effect of magnetism on polarized light’. William Thomson to Michael Faraday, 11 June 1847, quoted in Smith and Wise, op. cit. (39), p. 260. Ole Knudsen, ‘William Thomson's electromagnetic theory’, in Harman, op. cit. (40), p. 158.

46 Smith, op. cit. (42), p. 122–123; Smith and Wise, op. cit. (39), pp. 104–108.

47 Smith and Wise, op. cit. (39), p. 190.

48 Smith and Wise, op. cit. (39), p. 342. There were, of course, many other factors involved in Thomson's struggles to develop a new direction in his natural philosophy. Smith and Wise give a detailed account on pp. 282–347.

49 Smith and Wise, op. cit. (39), p. 347.

50 Smith, op. cit. (43), pp. 213–214.

51 Hamish F.G. Swanston, Ideas of Order: Anglicans and the Renewal of Theological Method in the Middle Years of the Nineteenth Century, Assen: Gorcum, 1974, p. 100.

52 Frederick Denison Maurice, ‘Essay XI: on the ascension of Christ’, in idem, Theological Essays (4th edn.), London: Macmillan, 1881, p. 225.

53 An example of the unifying principle of Maurice's Christ is his inclusion of women. Thus although ‘Truth is a manly virtue’, in Christ ‘Truth is wedded to Obedience, the characteristic of woman’; therefore ‘Christ, the Head of humanity, exhibits the perfect type of that nature which belongs to man and woman. Neither the woman is without the man, nor the man without the woman in Him.’ Maurice, Gospel of John, quoted in Swanston, op. cit. (51), p. 105.

54 Frederick Denison Maurice, Kingdom of Christ: Or Hints on The principles, Ordinances, and Constitution of the Catholic Church in Letters to a Member of the Society of Friends, 3 vols., London, 1842, vol. 1, p. 336. Swanston, op. cit. (51), p. 107.

55 For a cultural history of the concept of work see M. Norton Wise with Smith, Crosbie W., ‘Work and waste: political economy and natural philosophy in nineteenth-century Britain’, History of Science (3 parts, 1989–1990) 27, pp. 221–261Google Scholar; 27 pp. 263–301; 28, pp. 220–261. I am arguing here that what Wise calls the new ‘discourse of work and waste’ which emerged in the 1830s and 1840s continued to develop through the middle of the century as Britain entered the period W.L. Burn once called the ‘age of equipoise’.

56 Frederick Denison Maurice, ‘On Mechanics’ Institutes', manuscript of a lecture among the Frederick Denison Maurice Papers (Add 8566), Cambridge University Library.

57 Letters covering the controversy have been published in Frederick Denison Maurice, The Life of Frederick Denison Maurice Chiefly Told in His Own Letters, 2 vols., London: Macmillan, 1884, vol. 2, Chapters 5 and 6.

58 Maurice, op. cit. (52), pp. 397, 409. David Young, F.D. Maurice and Unitarianism, Oxford: Clarendon Press, 1992, p. 245.

59 Henry Longueville Mansel, Man's Conception of Eternity: An Examination of Mr. Maurice's Theory of a Fixed State out of Time, Oxford, 1854. Young, op. cit. (58), p. 244.

60 William Hamilton, ‘Philosophy of the Unconditioned. In reference to Cousin's Doctrine of the Infinito-Absolute’, in idem, Discussions on Philosophy and Literature , Education and University Reform. Chiefly from the Edinburgh Review, New York: Harper and Brothers, 1861, pp. 20–21.

61 Bernard Lightman has argued that Mansel's theology was a source of T.H. Huxley's agnostic position and so was not a simple defence of an outmoded ‘atonement theology’ but was also an important resource for alternative responses to the religious and scientific challenges of the mid-nineteenth century. See Bernard Lightman, The Origins of Agnosticism: Victorian Unbelief and the Limits of Knowledge, Baltimore: Johns Hopkins University Press, 1987. The Broad Church movement represented only one response to the mid-century challenges to the Anglican Church. For a good short account of some of the issues and responses see Victor Shea and William Whitla, ‘From clerical culture to secularized Anglicanism: positioning Essays and Reviews in Victorian transformation’, in Victor Shea and William Whitla (eds.), Essays and Reviews: The 1860 Text and Its Reading, Charlottesville: University Press of Virginia, 2000, pp. 3–10.

62 Theerman, Paul, ‘James Clerk Maxwell and religion’, American Journal of Physics (1986) 54, p. 312CrossRefGoogle Scholar.

63 Campbell and Garnett, op. cit. (6), pp. 93–103.

64 The best source for Maxwell's religious beliefs is still Campbell and Garnett, op. cit. (6), pp. 169–172, 321–323, 338–340, 393–395. As Campbell and Garnett warn in a lengthy footnote (p. 170, n. 2), Maxwell was never completely identified with a particular school of religious opinion. For an example of Maxwell's natural theology see his lecture ‘Molecules’, SP, op. cit. (3), vol. 2, p. 378. Although its psycho-historical method now seems dated, C.W.F. Everitt's wonderful essay on Maxwell's scientific creativity also has some valuable insights into Maxwell's character that include discussions of Maxwell's religious background. See C.W.F. Everitt, ‘Maxwell's scientific creativity’, in Rutherford Aris, H. Ted Davis and Roger H. Stuewer (eds.), Springs of Scientific Creativity: Essays on the Founders of Modern Science, Minneapolis: University of Minnesota Press, 1983, pp. 71–141.

65 Maxwell to Lewis Campbell, 17 October 1855. Reproduced in Campbell and Garnett, op. cit. (6), p. 219. The Yezidi are a community found in Kurdistan, Armenia and the Caucasus that worship not only a supreme God but also seven angels, including the Devil, whom they believe has repented.

66 For example, ‘that we are to serve God because we are ignorant of his nature and character’, or that we are to serve Him ‘because the opposite course will involve us in ruin’. Maurice, op. cit. (52), p. 18.

67 Maxwell, ‘Solutions of Problems’, SP, op. cit. (3), vol. 1, pp. 74–79 (extracted from the Cambridge and Dublin Mathematical Journal (1854) 8, p. 188). See also SLP, op. cit. (6), vol. 1, pp. 230–236.

68 Mary Everest Boole, Collected Works (ed. E.M Cobham), 4 vols., London: Daniel, 1931, vol. 1, p. 16. For Boole's religious beliefs see Kevin Lambert, ‘Victorian stained glass as memorial: an image of George Boole’, in Minsoo Kang and Amy Woodson Boulton (eds.), Visions of the Industrial Age, 1830–1914: Modernity and the Anxiety of Representation in Europe, Aldershot: Ashgate, 2008, pp. 205–228.

69 Campbell and Garnett, op. cit. (6), p. 113, describe Boole's attempt at giving logic a mathematical expression as having ‘naturally strong attractions for Clerk Maxwell’.

70 James Clerk Maxwell, ‘Address to the Mathematical and Physical Sections of the British Association’, SP, op. cit. (3), vol. 2, p. 229. Maxwell's quotation is from George Boole, An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities (1854), New York: Dover, 1958, p. 408.

71 Boole, op. cit. (70), p. 419.

72 There are hints of the importance of Boole for Maxwell in the literature but the connection has never been fully articulated. See, for example, Cat, op. cit. (2), p. 431, n. 61. Harman, op. cit. (2), 125.

73 Boole, op. cit. (70), p. 406. Boole cites Whewell as the reference.

74 Boole, op. cit. (70), p. 405.

75 Peacock's law of equivalent forms: ‘Whatever algebraical forms are equivalent, when the symbols are general in form but specific in value, will be equivalent likewise when the symbols are general in value as well as in form.’ George Peacock, A Treatise on Algebra, 2 vols., New York, 1940, vol. 2, p. 59. For Peacock's historical approach to mathematics see George Peacock, Encyclopaedia Metropolitana (ed. Edward Smedley, Hugh James Rose and Henry John Rose), vol. 1: Pure Sciences, London, 1845, s.v. Arithmetic. See also Durand, Marie-José, ‘Genèse de l'algèbre symbolique en Angleterre: Une Influence possible de John Locke’, Revue d'histoire des sciences (1990) 43, pp. 129–180.CrossRefGoogle Scholar

76 For Boole, as for Gregory, the laws of combination that governed the algebra of quantity were the commutative law, which in terms of symbols can be written as ab=ba; the distributive law or a(b+c)=ab+ac; and the index law or a ba c=a b+c. The laws of combination that governed syllogistic reasoning differed only in the form of the index law, which Boole would give in 1847 as x n=x, and in 1854 as x 2=x.

77 As Maxwell's Victorian biographers Campbell and Garnett explain, Maxwell's Apostles essays are not ‘upon his oath’, a rule intended to encourage free speculation.

78 Maxwell, ‘Analogies’, SLP, op. cit. (6), vol. 1, p. 377. Compare Boole, op. cit. (70), p. 411.

79 Maxwell, ‘Analogies’, SLP, op. cit. (6), vol. 1, p. 378.

80 See Harman's useful footnotes to Maxwell's ‘Analogies’, SLP, op. cit. (6), vol. 1, pp. 376–383.

81 Maxwell, ‘Analogies’, SLP, cit. op. (6), vol. 1, p. 381, original emphases.

82 See especially Boole, op. cit. (70), pp. 399–424; and George Boole, The Claims of Science Especially as Founded in Its Relations to Human Nature, London: Taylor, Walton and Maberly, 1851. The Claims of Science is also reproduced in George Boole, Studies in Logic and Probability (ed. R. Rhees), London: Watts, 1952, pp. 187–211.

83 Maxwell, ‘Analogies’, SLP, op. cit. (6), vol. 1, p. 383.

84 Boole, op. cit. (70), p. 4. I must point out that Boole did not consider the Aristotelian syllogism a fundamental law of thought. I have used the syllogism here because it is familiar, but Boole would insist that although it expressed a truth about the laws of reasoning it could be derived from his mathematical laws of thought.

85 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, p. 157.

86 Gooding, op. cit. (8), p. 209.

87 The concepts of intensity and quantity, we should also note, were used by electrical practitioners such as William Groves as measures of the efficacy of voltaic piles. For example, at a lecture at the Royal Institution in 1840 William Groves demonstrated the efficacy of his nitric acid battery in terms of a ‘quantity’ arrangement and an ‘intensity’ arrangement. The two classes of effect were measured by decomposition of water and heating of wires (quantity) and by the generation of sparks and flames (intensity). See Iwan Morus, ‘The sociology of sparks: an episode in the history and meaning of electricity’, Social Studies of Science (1988) 18, pp. 387–417.

88 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, p. 160.

89 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, p. 184, original emphasis.

90 Faraday, Experimental Researches, op. cit. (18), paras. 60–80. Maxwell admits that Faraday had rejected the idea of the electro-tonic state as unnecessary in the second series of his Experimental Researches, but also that ‘he still seems to think that there may be some physical truth in his conjecture’. Maxwell cites paras. 3172 (he may have meant 3173) and 3269 as evidence for that claim.

91 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, pp. 187–88.

92 Wise, ‘The mutual embrace’, op. cit. (14), pp. 1310–1318. Darrigol, op. cit. (17), pp. 139–147.

93 Wise, ‘The mutual embrace’, op. cit. (14), p. 1313. Maxwell first formulated an attempt at capturing this mathematical relation in a letter to Thomson. Maxwell, letter to William Thomson, 13 November 1854, SLP, op. cit. (6), vol. 1, pp. 254–263, especially p. 256. As Norton Wise has noted, there were serious problems with this rather loose formulation; ‘however, as a means for visualizing a complex physical situation, it suggested creative new ways of treating the … problem’. Wise, ‘The mutual embrace’, op. cit. (14), p. 1314. Darrigol, op. cit. (17), pp. 144–147.

94 Maxwell, ‘On Faraday's lines’, SP, op. cit. (3), vol. 1, p. 207, original emphasis.

95 Whewell, op. cit. (26), vol. 1, p. 17, original emphasis.

96 Mary Hesse once wrote that ‘it is not often noticed that Maxwell himself claimed that his method is the authentic Newtonian one of “deduction from experiments”’. Hesse, The Structure of Scientific Inference, Berkeley: Macmillan, 1974, p. 159.

97 William Thomson, ‘On a mechanical representation of electric, magnetic, and galvanic forces’, reproduced in William Thomson Kelvin Mathematical and Physical Papers, Cambridge: Cambridge University Press, 1882, vol. 1, pp. 76–80. Idem, ‘A mathematical theory of magnetism’, Philosophical Transactions of the Royal Society of London (1851) 141, pp. 243–268.

98 William Thomson, Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, founded on Mr A.S. Hathaway's stenographic report of twenty lectures delivered in Johns Hopkins University, Baltimore, in October 1884: followed by twelve appendices on allied subjects by Lord Kelvin, London: C.J. Clay and Sons and Baltimore: Publication Agency of the Johns Hopkins University, 1904, pp. 270–71, quoted in Smith and Wise, op. cit. (39), p. 464.

99 Maxwell, op. cit. (29).