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A Historical Role for Dimensional Analysis in Maxwell’s Electromagnetic Theory of Light

  • Salvo D’Agostino
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 213)

Abstract

Maxwell’s contributions to physics have been extensively scrutinised by historians in the last decade, but certain aspects of his work, however, are still partially unexplored. Many of Maxwell’s historians have perhaps favoured those parts of Maxwell’s work which are, more or less, related to our modern theory. The consideration of some outmoded or controversial parts of his theories, such as the ones dealt with in this paper, will contribute, I hope, to a better understanding of the historical situation of Maxwell’s electromagnetism.

Keywords

Dimensional Analysis Electromagnetic Theory Historical Role Transitional Principle Dimensional Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.
    Weber, “Elektrodynamische Maasbestimmungen. Über ein allgemeines Grundgesetz der Elektrischen Wirkung” [1846] in: Weber [1893] 25–211.Google Scholar
  2. 2.
    Weber & Kohlrausch [1856] 597–608.Google Scholar
  3. 3.
    Among them Bromberg [1957]; Everitt [1975].Google Scholar
  4. 4.
    D’Agostino [1980].Google Scholar
  5. 5.
    Larmor [1973] 705.Google Scholar
  6. 6.
    Larmor [1973] 729.Google Scholar
  7. 7.
    Because of Weber’s choice of electrodynamic units the factor 1/2 appeare before the velocity c. However Weber adopted also electromagnetic units (D’Agostino [1980] 285).Google Scholar
  8. 8.
    Maxwell, “On Physical Lines of Force”, in: Maxwell [1861]; Maxwell [1854], Vol. I, 451–513.Google Scholar
  9. 9.
    Maxwell [1854] 500.Google Scholar
  10. 10.
    On this point: Bromberg [1957] 227; Heimann [1870] 193. Both authors agree on the fact that Maxwell did not know Weber’s numerical value when he discove red that the velocity of his magnetic waves was equal to Weber’s factor. In the fol lowing, he would have discovered that this factor was equal to the velocity of light. For the argument of my paper is irrelevant whether Maxwell’s identification of the velocity of electromagnetic waves with that of light was or was not a discovery.Google Scholar
  11. 11.
    Maxwell [1850].Google Scholar
  12. 12.
    Maxwell [1861] 495.Google Scholar
  13. 13.
    Maxwell [1861] 498.Google Scholar
  14. 14.
    Maxwell [1861] 500.Google Scholar
  15. 15.
    Niven [1980] xvi.Google Scholar
  16. 16.
    Niven [1980]xvi.Google Scholar
  17. 17.
    “Report of the Committee appointed by the British Association on Standards of Electrical Resistance”, in: Maxwell & Jenkin [1863] 111–176.Google Scholar
  18. 18.
    Although I do not deal in this work with Thomson’s program of precise measurements, I wish to call attention to this important section of Thomson’s research, one that was recently studied in great detail by Crosbie Smith and Northon Wise (Smith & Wise [1989]).Google Scholar
  19. 19.
    Maxwell & Fleming [1863] 130–163, 131.Google Scholar
  20. 20.
    Maxwell & Fleming [1863] 130–163, 132.Google Scholar
  21. 21.
    Maxwell & Fleming [1863] 130–163, 132–135.Google Scholar
  22. 22.
    The relevance of Fourier’s analysis for Maxwell and Thomson’s measurement program is duly underlined in Smith & Wise [1989] 125, 150, 161, passim.Google Scholar
  23. 23.
    “The Report of the Committee” [1893], 118.Google Scholar
  24. 25.
    Larmor [1907] 26.Google Scholar
  25. 26.
    C.W.F. Everitt valuates highly this unduly neglected paper by Maxwell because it “supplied a vital step” in the definition of a “dual system of electrical units” (Everitt [1975] 100). I agree with Everitt on this point. He continues by stating that “by 1863, then, Maxwell had found a new link of a purely phenomenological kind between electromagnetic quantities and the velocity of light” (ibid. 101). I think that the construction of the dual system, from which Maxwell’s new link was derived, is far from being phenomenological, although I admit that the new link requires a minor number of ad hoc hypotheses in comparison with physical lines. For other aspects of the 1863 “Report”: D’Agostino (1978).Google Scholar
  26. 27.
    Maxwell [1864].Google Scholar
  27. 28.
    Maxwell [1864] 536, 568.Google Scholar
  28. 29.
    Maxwell [1864] 569.Google Scholar
  29. 30.
    Maxwell [1864] 579.Google Scholar
  30. 31.
    Maxwell [1864] 563–564.Google Scholar
  31. 32.
    Maxwell [1864] 589–597.Google Scholar
  32. 33.
    Maxwell [1868].Google Scholar
  33. 34.
    Maxwell [1868] 128.Google Scholar
  34. 36.
    Maxwell [1868] 134–135.Google Scholar
  35. 37.
    Maxwell [1868] 143.Google Scholar
  36. 38.
    Maxwell [186]) 134–135.Google Scholar
  37. 40.
    Maxwell [1891); Maxwell [(1954].Google Scholar
  38. 41.
    Entitled “Preliminary”.Google Scholar
  39. 42.
    Maxwell [1954] §.2.Google Scholar
  40. 43.
    Maxwell [1954] § 625.Google Scholar
  41. 44.
    Maxwell [1954] § 624.Google Scholar
  42. 45.
    Maxwell [1954] §§ 625, 686.Google Scholar
  43. 46.
    Maxwell [1954] §526.Google Scholar
  44. 47.
    Maxwell [1954] §§ 620–629Google Scholar
  45. 48.
    Maxwell [1954] §622.Google Scholar
  46. 49.
    Maxwell [1954] § 624Google Scholar
  47. 50.
    Maxwell [1954] §626.Google Scholar
  48. 51.
    Maxwell [1954] § 627.Google Scholar
  49. 52.
    Maxwell [1954] §627.Google Scholar
  50. 53.
    Maxwell [1954] § 628.Google Scholar
  51. 54.
    Maxwell [1954] § 768.Google Scholar
  52. 55.
    Maxwell [1954] §§ 768–770.Google Scholar
  53. 56.
    This system Maxwell had analysed in detail in § 653 ff.Google Scholar
  54. 57.
    Maxwell [1954] § 769.Google Scholar
  55. 58.
    A note added by J.J. Thomson informs us that the effect was discovered by Rowland in 1876.Google Scholar
  56. 59.
    I think that Maxwell’s above distinction between a classification of v as a real quantity in the first conceptual experiment and as a physical quantity in the second may be deepened by analysing Maxwell’s ideas on a physical classification of quantities as distinct from their mathematical classification, a point that he makes in his Lecture “On the Mathematical Classification of Physical Quantities” (Maxwell [1954] a) Vol. 2, 257–266.Google Scholar
  57. 60.
    See Smith & Wise [1989].Google Scholar
  58. 61.
    Maxwell [1954] §§ 781–805.Google Scholar
  59. 62.
    Maxwell [1954] §786.Google Scholar
  60. 63.
    Eight experiments of various types to measure the ratio of units, some of them performed by Kelvin, others proposed or performed by Maxwell himself (Maxwell [1954] §§772–80)Google Scholar
  61. 64.
    Maxwell [1954] §787.Google Scholar
  62. 65.
    Maxwell [1954] §786.Google Scholar
  63. 66.
    Smith & Wise [1989].Google Scholar
  64. 67.
    Schaffer [1994].Google Scholar
  65. 68.
    I comment on this matter in D’Agostino [1986] 194–198.Google Scholar
  66. 69.
    Schaffer [1994] 139.Google Scholar
  67. 70.
    Schaffer [1994] 146 ff. Also in: Smith & Wise [1989] 455.Google Scholar
  68. 71.
    Raleigh [1915]. Other remarks in: Carneiro [1993].Google Scholar
  69. 72.
    Buckingham 19XX. Carneiro [1993].Google Scholar
  70. 74.
    D’Agostino [1996] 46–49.Google Scholar
  71. 76.
    Let me express my agreement on this point with Smith and Wise. In commenting on Kelvin’s statement that, in order to meet a scientific test, any quantity was to be measurable, they keenly remark that “Maxwell’s displacement current...had never been observed, let alone measured in the sense direct sense Thomson intended” (Smith & Wise [1989] 455).Google Scholar
  72. 77.
    Maxwell [1954] §526.Google Scholar
  73. 78.
    D’Agostino [1996] 47. In my paper I gave evidence of the fact that Maxwell never quoted or utilized Weber and Koholraush’s velocity c, but in his research he limited his approach to Weber’s ratio of units (see above Gauss’s and Weber’s metrology). On this point, see also Siegel [1991] 130.Google Scholar
  74. 79.
    Sommerfeld 1935], [1964] 53–54.Google Scholar
  75. 80.
    Panofsky & Phillips [1955] 375–378.Google Scholar
  76. 81.
    However, the authors add that Maxwell’s choice of only three fundamental mechanical units does not allow a numerical determination of the absolute values for the ethereal constants. This determination is possible if a fourth non mechanical unit is arbitrarily determined Panofsky & Phillips [1955] 376.Google Scholar
  77. 82.
    Panofsky & Phillips [1955] 375.Google Scholar
  78. 83.
    Panofsky and Phillips mantain (Panofsky & Phillips [1955] 376) that c in the expression above was first determined by Weber and Koholrausch by measuring the discharge of a condenser whose electrostatic capacity was known. In my study I proved that this velocity was not Maxwell’s velocity c (v in Maxwell’s and my notation).See D’Agostino [1996] 47.Google Scholar
  79. 84.
    As it can be also argued by referring to Buchwald’s very detailed analysis in: Buchwald [1985] 27–33, 37–40, 47.Google Scholar
  80. 85.
    Buchwald [1985] 23 ff.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Salvo D’Agostino
    • 1
  1. 1.Università “La Sapienza”RomaItaly

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