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A Critical Examination of Herapath's Dynamical Theory of Gases

Published online by Cambridge University Press:  05 January 2009

Eric Mendoza
Affiliation:
Israel Science Teaching Centre, The Hebrew University of Jerusalem, Israel.

Extract

In recent years John Herapath has emerged as an important figure in the early history of the dynamical theory of gases. In a series of papers published in 1821 and 1822 he outlined an elaborate theory of the states of matter, specific and latent heats, vapours and gases, culminating in a theory of the gravitational ether. This work was based on the rejection of the caloric theory of heat and was founded instead on the idea that the particles of matter were in constant motion; the forces of caloric were replaced by the transfer of momentum. Herapath's is one of the earliest of dynamical theories of gases to be worked out in any mathematical detail.

Type
Research Article
Copyright
Copyright © British Society for the History of Science 1975

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References

A paper on Herapath's theories was presented in August 1970 at the Aarhus Symposium on the interplay between mathematics and physics in the nineteenth century; the present paper evolved from it. It has benefited from correspondence with Stephen Brush and from detailed criticism by Robert Fox, to whom I am much indebted.

1 Brush, S. G., ‘The Royal Society's first rejection of the kinetic theory of gases (1821), John Herapath versus Humphrey Davy’, Notes and records of the Royal Society of London, xvii (1963), 161–80CrossRefGoogle Scholar, and the same author's introduction to Herapath, John's Mathematical physics, facsimile edition published by Johnson Reprint Corporation (New York and London, 1972), p. xiv.Google Scholar

2 Herapath, J., ‘A mathematical inquiry into the causes, laws and principal phenomena of heat, gases, gravitation, etc.’, Annals of philosophy, 2nd ser. i (1821), 273–93, 340–51, 401–16Google Scholar; ‘Tables of temperature, and a mathematical development of the causes and laws of phenomena which have been adduced in support of the hypotheses of “Calorific Capacity”, “Latent Heat”, etc.,’ ibid., ii (1821), 50–6, 89–103, 201–11, 256–74, 363–88, 434–62; iii (1822), 16–28.

3 Herapath, J., Mathematical physics (London, 1847)Google Scholar, most readily available in the facsimile edition edited and with an introduction by Brush, S. G., op. cit. (1).Google Scholar

4 Truesdell, C., Essays in the history of mechanics (Berlin, etc., 1968), pp. 283–8.CrossRefGoogle Scholar

5 Quoted by S. G. Brush in his introduction to the facsimile edition of Mathematical physics, op. cit. (1), p. xix.Google Scholar

6 Dalton, J., A new system of chemical philosophy (Manchester, 1808), i, part 1.Google Scholar

7 An excellent account of this theory, together with all the relevant illustrations, is given by Fox, R., The caloric theory of gases from Lavoisier to Regnault (Oxford, 1971), chapter 4.Google Scholar

8 Dalton, , op. cit. (6), p. 57, equation 8.Google Scholar

9 Ibid., p. 53.

10 Fox, , op. cit. (7), p. 31.Google Scholar

11 Herapath, , op. cit. (2), ii. 450.Google Scholar

12 Ibid., ii. 443–62. The equations on p. 444 (and equation 1 of Mathematical physics, i. 330Google Scholar) imply that the latent heat of melting of ice is equal to (b-B)T per gram, where T is the ‘true’ temperature corresponding to the melting point of ice, b and B are the numbers of particles per unit mass (baromins), which are in turn equal to the specific heats in arbitrary units.

13 Herapath, , op. cit. (3), p. 182, para. 3d, and p. 221, para. 49.Google Scholar

14 Dalton, , op. cit. (6), p. 190.Google Scholar

15 Herapath, , op. cit. (2), i. 402.Google Scholar

16 Herapath, , op. cit. (3), i. 254.Google Scholar

17 Ibid., i. 217, paras. 42, 43.

18 They are most accessible in Fox, , op. cit. (7), plates 3 and 4.Google Scholar

19 Dalton, , op. cit. (6), p. 185.Google Scholar

20 Herapath, , op. cit. (3), ii. 8, 37.Google Scholar

21 Ibid., ii. 37.

22 Ibid., ii. 65.

23 Ibid., ii. 66.

24 Ibid., i. 237. Similar descriptions are given in Herapath, , op. cit. (2)Google Scholar, notably in Annals of philosophy, 2nd ser. i (1821), 278Google Scholar, but those in Mathematical physics are more detailed.

25 Herapath, , op. cit. (3), ii. 61.Google Scholar

26 Ibid., ii. 237. Similar cases are considered in ibid., ii. 86 and 144.

27 Ibid., ii. 63.

28 Ibid., i. 257. The word ‘revolution’ does not mean motion in a circle; see ibid., i. 217, para. 44.

29 Ibid., i. 16. In op. cit. (2), i. 344, the words ‘revolution’, ‘returns’, and ‘periods’ are similarly used.

30 Herapath, , op. cit. (3), i. 216.Google Scholar

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