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The case of Brownian motion

  • Roberto Maiocchi (a1)

The explanation of the phenomenon of Brownian motion, given by Einstein in 1905 and based on the kinetic–molecular conception of matter, is considered one of the fundamental pillars (or even the main one) supporting atomism in its victorious struggle against phenomenological physics in the early years of this century. Despite the importance of the subject, there exists no specific study on it of sufficient depth. Generally speaking, most histories of physics repeat the following scheme: the discovery made by Robert Brown in 1827 (but only announced the following year), of the continuous movement of small particles suspended in a fluid did not arouse interest for a long time. Finally, at the close of the century, Gouy's research brought it to the attention of the physicists. Gouy was convinced that Brownian motion constituted a clear demonstration of the existence of molecules in continuous movement. Nevertheless, he did not work out any mathematized theory that could be subjected to quantitative confirmation. All nineteenth-century research remained at the qualitative level and yet it was able to clarify some general characteristics of the phenomenon: the completely irregular, unceasing, motion of the particles is not produced by external causes. It does not depend on the nature of the particles but only on their size. The first significant measurements, carried out by Felix Exner in 1900, appeared to deny the possibility of reconciling the kinetic theory with Brownian motion. The discovery of the ultra-microscope then allowed Zsigmondy to perceive the presence of movements, which were completely analogous to Brown's, in the particles of the colloids; these movements were rather smaller in size than those invesigated up to then. Thus Zsigmondy aroused interest in the phenomenon. Finally, in 1905, Einstein succeeded in stating the mathematical laws governing the movements of particles on the basis of the principles of the kinetic–molecular theory. The following year Smoluchowski arrived at conclusions which corresponded to Einstein's. These laws received a first, rough confirmation in the years immediately following by the work of The Svedberg, Seddig and, for some historians, Henri. Then in 1908 Jean Perrin gave it a definitive confirmation.

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1 The school inspired by Lakatos' ideas has, with Clark, P., Atomism versus thermodynamics, in Howson, C. (ed.) Method and Appraisal in the Physical Sciences, Cambridge, 1976, pp. 41105, made Brownian motion the corner-stone of its own rational reconstruction of the victory of atomism. According to this the ‘kinetic programme’ only became ‘progressive’ with Einstein's theory.

2 See, as an example, Gliozzi, M., Storia delle fisica, in Abbagnano, N. (ed.) Storia delle scienze, 4 vols, Torino, 1962, ii, p. 366.

3 See Kerker, M., ‘Brownian Movement and Molecular Reality prior to 1900’, Journal of Chemical Education, (1974), 51, pp. 764768.

4 Brown, R., ‘A Brief Account of Microscopical Observations made in the Months of June, July, August 1827, on the Particles contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies’, The Philosophical Magazine, (1828), 4, pp. 161173. On this subject see Goodman, D.C., ‘The Discovery of Brownian Motion’, Episteme, (1972), 6, pp. 1229; Powles, J.G., ‘Brownian Motion, June, 1827’, Physical Education, (1978), 13, pp. 310312.

5 On these aspects see Nye, M.J., Molecular reality. A perspective on the scientific work of Jean Perrin, London & New York, 1972, especially pp. 913.

6 Inductivist histories underestimate this fundamental aspect of nineteenth-century research and speak of a completely false unanimity of opinion. For example Gliozzi says: ‘The most careful observers of the phenomenon (Brown himself, Gouy, Cantoni, Exner, Wiener) ascertained that the movement of each particle is absolutely independent of the neighbouring particles, that it is truly infinite and that it takes place in the same way whatever the precautions taken to ensure the mechanical and thermal equilibrium of the liquid in suspension. They also confirmed that the nature or intensity of the light used to observe the phenomenon has no effect on the movement of the particles, that the nature of the particles in suspension does not influence the phenomenon: only their mass does so, the motion of the smaller particles proving to be faster’ (Gliozzi, , op. cit. (2), p. 366). Also Nye describes the empirical research before Einstein in a form too clean and too clear-cut: in her opinion it was Gouy who established the theory's empirical bases, having with his research ‘definitively established’ and ‘demonstrated’ the main characteristics of Brown's phenomenon (Nye, , op. cit. (5), p. 28).

7 Thirion, , see Appendix, p. 53.

8 Gouy, , Note…, see Appendix, p. 562.

9 Perrin, J., Les atomes, Paris, 1913, p. 172.

10 Jevons; Henri, V., ‘Influence du milieu sur les mouvements browniens’, Comptes Rendus, (1908), 147, pp. 6265.

11 Maltézos, see Appendix; Spring, see Appendix; Gouy, , ‘Le mouvement…’, see Appendix.

12 Muncke, see Appendix; Cantoni, see Appendix.

13 Jevons, , ‘On the movements…’, see Appendix; Gouy, , ‘Le mouvement…’, see Appendix; for Carbonnelle see Thirion, , see Appendix, p. 53.

14 Cantoni, see Appendix.

15 Quincke, see Appendix; Gouy, , ‘Le mouvement…’, see Appendix; S. Exner, see Appendix.

16 For Carbonnelle see Thirion, , see Appendix, p. 53; Maltézos, see Appendix; Ehrenhaft, F., ‘Ueber eine der Brown'schen Molekularbewegung in den Flüssigkeiten…’, Sitzungsberichte der Mathematisch-Naturwissenschaftlichen Klasse der Kaiserlichen Akademie der Wissenschaften, (1907), 116, pp. 11391149, for Zsigmondy and Svedberg see below.

17 Gouy, , ‘Note …’, see Appendix, p. 562.

18 Perrin, J., ‘Mouvement brownien et réalité moléculaire’, Annales de Chimie et de Physique, (1909), VIII, 18, p. 10.

19 Ibid., p. 30.

20 Gouy, , ‘Note …’, see Appendix, p. 563.

21 For an account of nineteenth-century theories of Brownian motion see Nye, , op. cit. (5), especially pp. 913; Kerker, , op. cit. (3); Brush, S.G., The Kind of Motion we call Heat; a History of the Kinetic Theory of Gases in the 19th Century, 2 vols, Amsterdam, Oxford and New York, 1976, chapter 15.

22 Maltézos, see Appendix.

23 Nägeli, see Appendix.

24 Gouy, , ‘Note …’, see Appendix, p. 563; Ramsay, , ‘Pedetic …’, see Appendix.

25 F. Exner, see Appendix.

26 Clark, , op. cit. (1), p. 96.

27 Kerker, , op. cit. (3), p. 768.

28 Exner, F., see Appendix, p. 846.

29 Ibid., p. 549.

30 Einstein, A., ‘Ueber die von der molekularkinetischen Theorie der Wärme Bewegungen von in ruhenden Flüssigkeiten suspendierten Teilchen’, Annalen der Physik, (1905), 17, pp. 549560.

31 Ibid., p. 549.

32 As is well known the law states that a spherically shaped body of radius P which moves with a velocity V in a fluid with a coefficient of viscosity μ experiences a braking force equal to 6πμP V.

33 Smoluchowski, M., ‘Essai d'une thérorie cinétique du mouvement brownien et des milieux troubles’, Krakau Anzeiger, (1906), 7, pp. 577602.

34 Ibid., pp. 585–586.

35 Svedberg, T., ‘Studien zur Lehre von den kolloiden Lösungen’, Nova Acta Regiae Societatis Scientiarum Uppsala, (1907), 2, pp. 1160.

36 The only mention of a numerical verification, contained in the article, is a brief one regarding the calculation of λx in one second for a spherical particle of 0·001 mm in diameter in water at 17°C, which gives a value of 0·8 μ. Einstein does not give any empirical value with which to compare this result. It is noticeable that F. Exner (see Appendix), for an analogous case, had measured a velocity of 3–2 μ a second, a value four times greater than that calculated by Einstein if we assume that Exner's values can be used as terms of comparison for λx.

37 Einstein, , op. cit. (30), p. 560.

38 This work was published the following year: Einstein, A., ‘Eine neue Bestimmung der Moleküldimensionen’, Annalen der Physik, (1906), 19, pp. 289306.

39 Ibid., p. 305.

40 It is to be stressed, however, that for Einstein there was no substantial difference between molecules in solution (sugar) and spherical particles of any substance whatsoever: ‘According to the kinetic-molecular conception there is no essential difference between a dissolved molecule and a suspended particle. We will therefore consider the equation [for λx] valid for all cases involving spherical suspended particles of any type’ (Einstein, A., ‘Elementare Theorie der Brownschen Bewegung’, Zeitschrift für Elektrochcmie (1908), quoted from Fürth, R. (ed.) Investigations on the Theory of the Brownian Movement, New York, 1973, p. 82).

41 Smoluchowski, , op. cit. (39), p. 597.

42 Einstein, A., ‘Zur Theorie der Brownschen Bewegung’, Annalen der Physik, (1906), 19, pp. 371381.

43 Ibid., p. 371.

46 Smoluchowski, , op. cit. (33), p. 597 ff.

47 Ibid., p. 591.

48 Ibid., p. 597.

49 Kerker, , op. cit. (3), is essential on Svedberg's experiments regarding Brownian motion.

50 Nobel Lectures, including Presentation Speeches and Laureates's Biographies, Chemistry,1 922–1941, Amsterdam, London and New York, 1966, pp. 63.

51 Nobel Lectures, including Presentation Speeches and Laureates's Biographies, Physics, 1922–1941, Amsterdam, London and New York, 1965, p. 136.

52 Perrin, , op. cit. (18), 73.

53 Svedberg, T., ‘Ueber die Eigenbewegung der Teilchen in kolloidalen Lösungen’, Zeitschrift für Elektrochemie und Angewandte Physikalische Chemie, (1906), 12, pp. 853860.

54 Zsigmondy, , see Appendix, p. 134 of English translation.

55 Ramsay, see Appendix.

56 Svedberg, , op. cit. (53), p. 859.

57 Cotton, A. and Mouton, M.H., Les ultramicroscopes et les objets ultramicroscopiques, Paris, 1906.

58 Ibid., p. 910.

60 Svedberg, T., ‘Einige Bemerkungen über die Brownsche Bewegung’, Zeitschrift für Physiklalische Chemie (1910), 71, pp. 571576; also Die Existenz der Moleküle, Leipzig, 1912; also ‘Neurere Untersuchungen über die Brownsche Bewegung’, Jahrbuch der Radioaktivität und Elektronik, (1913), 10, pp. 467515.

61 Einstein's reply to Svedberg is in a brief note (‘Theoretische Bemerkungen über die Brownschen Bewegung’, Zeitschrift für Elektrochemie, (1907), 13, pp. 4142, quotations are from Fürt, (ed.), op. cit. (40)) in which, with a calculation which uses the kinetic theory of gases, the actual velocity of the particles is demonstrated to be unperceivable (if the validity of the theory is accepted): ‘Since an observer working with definite means of observation in a given way can never perceive the actual path traced in an arbitrarily small time interval, any mean velocity will always appear to the observer as an instantaneous velocity. But it is clear that the velocity thus determined does not correspond to any objective property of the motion under examination—at least if the theory corresponds to the facts’ (p. 67).

62 Langevin, P., ‘Sur la théorie du mouvement brownien’, Comptes Rendus, (1908), 146, p. 533.

63 Perrin, , op. cit. (18), pp. 7374 (Perrin's italics).

64 Ibid., p. 73.

65 Seddig, M., ‘Ueber Abhängigkeit der Brownschen Molekularbewegung von der Temperature’, Marburg Sitzungsberichte, (1907), 18, pp. 182188; also ‘Ueber die Messung der Temperaturabhängigkeit der Brownschen Molekularbewegung’, Physikalische Zeitschrift (1908), 9, pp. 465468.

66 Perrin, , op. cit. (9), p. 119.

67 Kerker, , op. cit. (3), p. 207. Kerker attributes a similar opinion even to Cotton, A., ‘Recherches récentes sur les mouvements browniens’, Revue du Mois, (1908), 5, pp. 737741, but Seddig is not even cited in Cotton's work.

68 Seddig, see Appendix.

69 Ibid., p. 365 (italics mine).

70 Ibid., pp. 365–366 (Seddig's italics).

71 Seddig, of course, realized this experimental imperfection thanks to the theory: when he found data in disagreement with Einstein's formula he looked for the flaws in the experimental procedure. The formula thus provided him with indications regarding the correctness or not of experimental procedure.

72 Seddig, , see Appendix, pp. 377379.

73 Perrin, J., ‘L'agitation moleculaire et le mouvement brownien’, Comptes Rendus, (1908), 146, p. 968.

74 Ibid., p. 969.

75 Perrin, , op. cit. (18), note 32.

76 On Perrin see Nye, , op. cit. (5); Randriamasy, F., ‘Les grandes expériences de Jean Perrin. Les preuves expérimentales de la réalité moléculaire’, Revue du Palais de la Découverte, (1977), 5, n. 45, pp. 1833.

77 Einstein, A., op. cit. (42), p. 376.

78 Smoluchowski, , op. cit. (33), p. 585.

79 Langevin, , op. cit. (62).

80 Henri, V., ‘Etude cinématographique des mouvements browniens’, Comptes Rendus, (1908), 146, pp. 10241026.

81 Fürth, , op. cit. (40), pp. 102103; Kerker, , op. cit. (3), p. 203.

82 Svedberg, , ‘Einige …’, op. cit. (62).

83 Clark, , op. cit. (1), p. 97.

84 Henri, , op. cit. (80), p. 1026.

85 Henri, , op. cit. (10).

86 The slowing down measured by Henri is quite considerable: the addition of 1/32 of HCI to neutral water caused a slowing down of Brownian motion by a factor of about nine times!

87 Duclaux, J., ‘Pression osmotique et mouvement brownien’, Comptes Rendus, (1908), 147, pp. 131134.

88 Perrin, J., ‘L'origine du mouvement brownien’, Comptes Rendus, (1908), 147, pp. 530532.

89 Langevin, , op. cit. (62), p. 533.

90 Henri, , op. cit. (80), p. 1026.

91 Duclaux, , op. cit. (87), p. 132.

92 Perrin, J., ‘La loi de Stokes et le mouvement brownien’, Comptes Rendus, (1908), 147, pp. 475476.

93 Ibid., p. 476.

94 Perrin, , op. cit. (18), p. 69.

95 Perrin's measures raised the problem of reconsidering Stokes' law in the light of the kinetic theory of the gases. Various authors dealt with the topic: Cunningham, Zerner, McKeehan, Arnold, etc. A detailed analysis of the modifications of Stokes' law on the basis of the kinetic theory of gases can be found in Weyssenhoff, J., ‘Betrachtungen über de Gültigkeitsbereich der Stokes-Cunninghamschen Formel. I Hydrodynamischer Teil’, Annalen der Physik, (1920), 62, pp. 145. Duclaux was never convinced by Perrin's ‘reply’ and continued to criticize the use of Stokes' law; see Duclaux, J., Mouvement brownien. I: Partie expérimentale, Paris, 1937, especially pp. 1718.

96 Perrin, , op. cit. (9), 138 and 144.

97 See Perrin's explanation of his method of preparation of the emulsions in Perrin, J., ‘Les preuves de la réalité moléculairé, in Langevin, P. and De Broglie, M. (eds) La théorie du rayonnement et les quanta. Rapports et discussions de la réunion tenue à Bruxelles due 30 octobre au 3 novembre 1911, sous les auspices de M.E. Solvay, Paris, 1912, pp. 171172, and in Perrin, , op. cit. (9), note on p. 94. Perrin stopped the centrifuge, after a time interval that he had previously calculated (and tabulated) using Stokes’ law, in order to obtain granules of the size he wanted.

98 Cotton, , op. cit. (67).

99 Perrin, , op. cit. (9), pp. 119120.

100 Clark states: ‘When Perrin undertook to re-do Henri's experiments he failed to get the same results’ (Clark, , op. cit. (1), note 97). Thus the affair appears extremely unclear, even incomprehensible and the fact that Henri's experiments were allowed to sink into oblivion appears as a mean plot orchestrated by Perrin's group.

101 Chaudesaigues, M., ‘Le mouvement brownien et la formule d'Einstein’, Comptes Rendus, (1908), 147, pp. 10441046.

102 For the references to this ‘triumphal march’ see Perrin's account in Perrin, , op. cit. (9).

103 Perrin, J., ‘Le mouvement brownien de rotation’, Comptes Rendus, (1909), 149, pp. 549551.

104 Perrin, , op. cit. (18), p. 76.

105 Perrin, , op. cit. (9), note 119.

106 Chaudesaigues, , op. cit. (101), p. 1045.

107 Perrin, , op. cit. (18), p. 111.

108 Gouy, , ‘Note…’, see Appendix, p. 563.

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