¹ More properly, theories of the nature of air, because air was the only gaseous substance recognized in the seventeenth century.

² e.g. Galileo, , Il Saggiatore, 1623Google Scholar, quoted by Drake, Stillman, Discoveries and Opinions of Galileo, New York, 1957, pp. 276–278.Google Scholar

³ Principia Philosophiae, 1644, Book IV, xlv–xlvii.Google Scholar

⁴ The Works of the Honourable Robert Boyle, ed. Birch, Thomas, 2nd edition, London, 1772, volume (i), pp. 156–163.Google Scholar The law was really due to Towneley, as Boyle admitted (p. 160); see Webster, C., Nature, cxcvii (1963), 226–228.CrossRefGoogle Scholar

⁵ The Works of the Honourable Robert Boyle, i, p. 11.Google Scholar

⁶ Ibid., i, pp. 12, 19–20; v, p. 614.

⁷ Ibid., i, pp. 235–236. Boyle here gives Hobbes's criticisms in “An Examen of Mr. T. Hobbes his Dialogus Physicus de Natura Aēris”, which appeared as an appendix to the 1662 edition of New Experiments … touching the Air.

⁸ Ibid., i, p. 236.

⁹ Hooke, , Potentia Restitutiva, 1678, p. 16Google Scholar; in Gunther, R., Early Science at Oxford, viii (1931), 348.Google Scholar

¹⁰ Opticks, Query 31 (Dover reprint, New York, 1952, p. 376)Google Scholar; but compare the third rule of reasoning in Principia (ed. Cajori, 1934, p. 398).Google Scholar

¹¹ The role of attractive forces in chemical combination was discussed in Opticks, Query 31 (Dover reprint, see especially p. 395).

¹² Principia, proposition xxiii, theorem xviii (ed. Cajori, , 1934, pp. 300–302)Google Scholar. Newton's working is given in the scholium, and deals also with the general case where the repulsive force is as the nth power of the distance between particles.

¹³ Ibid., p. 302.

¹⁴ Opticks, Query 31, Dover reprint, p. 396.Google Scholar

¹⁵ Ibid., pp. 395–396.

¹⁶ De aēre et aethere; in Hall, A. R. and Hall, M. B., Unpublished Scientific Papers of Isaac Newton, Cambridge, 1952, p. 224.Google Scholar

¹⁷ Discours de la Nature de l'Air, 1676, new edition ed. Solovine, Maurice, Paris, 1923, p. 38.Google Scholar

¹⁸ Ibid., p. 47.

¹⁹ Amontons, , Mém, de l'Acad. Sci. Paris, 1703, p. 101Google Scholar. Guillaume Amontons (1663–1705) deserves to be better known for his work on the science of heat. His colleague in the Paris Academy, Antoine Parent (1666–1716) was very critical of the idea that particles of air were like sponges or coiled fibres, and apparently preferred a dynamical theory of air. (Parent, A., Essais et Recherches de Mathématique et de Physique, Paris, 1713, part ii, p. 174Google Scholar; also Mém. de l'Acad. Sci., Paris, 1708.)Google Scholar

²⁰ Ibid., p. 102.

²¹ His assumption that the height of the barometer fell approximately as an arithmetic progression with altitude would then be justified. But after Cassini, and Maraldi, (Hist. de l'Acad. Sci. Paris, 1703, p. 11Google Scholar; Mém., p. 229)Google Scholar had shown that neither his idea nor the simple application of Mariotte's law had applied in practice, it was suggested that the air at the top of a mountain differed fundamentally from air at sea level, perhaps in its homogeneity (Hist. de l'Acad. Sci. Paris, 1705, pp. 14–15).Google Scholar Kinetic theory discussions are often linked with calculations of the height of the atmosphere, e.g. by Bernoulli, Jacques (Opera, Geneva, 1744, vol. II, p. 1076)Google Scholar and by Bernoulli, Daniel (Hydrodynamica, Strasbourg, 1738, pp. 203 ff.).Google Scholar

²² Hist. de l'Acad. Sci. Paris, 1705, p. 12.Google Scholar

²³ De Gravitate Aetheris, Amsterdam, 1683Google Scholar: reprinted in Jacobi Bernoulli, Basileensis, Opera, Geneva, 1744, volume i, p. 93.Google Scholar

²⁴ Ibid., p. 94; the symbols have been altered and the expression written as a ratio of densities instead of a ratio of volumes.

²⁵ Ibid., p. 95.

²⁶ The most eccentric case of a kinetic theory accompanying work on the explanation of gravity was with G. L. Le Sage's theory of gravity (1758) which involved “gravific” particles travelling through space at great speed (Berthold, G., Rumford und die Mecanische Warmthcorie, Heidelberg, 1875, pp. 16–17)Google Scholar. It is also interesting to find the two subjects linked together in Herapath's work (see below).

²⁷ Phoronomia sive de viribus et motibus corporum solidorum et fluidorum libri duo. Amsterdam, 1716, p. 376Google Scholar, translated by Middleton, W. E. Knowles, British J. Hist. Sci., ii (1965), 248.Google Scholar

²⁸ Grimel, P., Dictionnaire des Biographies, Paris, 1958.Google Scholar

²⁹ Truesdell, C. A., Leonhardi Euleri Opera Omnia, series II, vol. xii, pp. xxiii–xxx.Google Scholar

³⁰ Discours sur les loix de la communication du mouvement, 1727, pp. 92, 100Google Scholar (in Récueil des Pièces qui ont remporté les Prix de l'Académie Royale des Sciences, volume i, 1720–1727, Paris, 1758)Google Scholar. Bernoulli was here concerned primarily with the elasticity of solids.

³¹ Ibid., p. 103.

The circular motions of each particle were supposed to trace out a sphere. If air in a cylinder is compressed by a piston until it occupies an eighth part of its previous volume, the radius of each of these spheres is “reduced by half… and assuming that the degree of heat does not change, the circular motions … continue with the same velocity after the compression … Then each of the circular motions will give rise to twice the centrifugal force than before the compression, and each sphere will tend to expand with twice the force. The piston will have four times as many particles contiguous to it, each of which will exert twice as much force. The result will be a total pressure on the piston eight times as great” (ibid., p. 105). Thus, after the compression, the pressure has increased and the volume decreased by the same factor, which means that Boyle's law is obeyed.

³² Ibid., p. 92.

³³ Ibid., p. 100.

³⁴ Letter of 5 November 1727, quoted by Truesdell, , op. cit., p. xxii.Google Scholar

³⁵ Commentarii Acad. Sci. Petrop., 1727 (1729), pp. 347–368.Google Scholar

³⁶ Trans. Truesdell, , op. cit., p. xxii.Google Scholar

³⁷ Ibid., p. lxxvi.

³⁸ Hydrodynamica, Strasbourg, 1738, pp. 200–202.Google Scholar The working is somewhat simplified.

³⁹ Ibid., pp. 202–203; the symbols have been altered.

⁴⁰ Cf. Partington, J. R., History of Chemistry, vol. ii, p. 477Google Scholar; Thomson, Thomas, Arm. Phil., vol. xi, p. 241 (1818)Google Scholar; and Berthold, G., op. cit.Google Scholar One of Le Sage's papers on the subject was published by Pierre Prévost as the first part of Deux Traités de Physique Mécanique (Geneva and Paris, 1818)Google Scholar. In the second part of the work, Prévost developed some of Le Sage's ideas relating to gases and to light.

⁴¹ Lomonosov, M. V.. Commentarii Acad. Sci. Petrop., 1750, pp. 230–244Google Scholar; also Collected Works, Moscow, 1951, vol. ii (Physics and Chemistry), pp. 105–143Google Scholar; also in Ostwald's, Klassiker, no. 178, pp. 28–33.Google Scholar

⁴² Ibid., § 2–3.

⁴³ Ibid., § 18.

⁴⁴ Commentarii Acad. Sci. Petrop., 1750, pp. 305–312Google Scholar; also in Collected Works, vol. ii, pp. 145–166Google Scholar, and abbreviated, in Ostwald's, Klassiker, no. 178, pp. 34–36: see § 11.Google Scholar

⁴⁵ Ibid., § 2–10.

⁴⁶ e.g. Mendoza, E., Mem. Manchester Lit. Phil. Soc., cv (1962–1963), 15.Google Scholar

⁴⁷ e.g. Dalton, John, A New System of Chemical Philosophy, Part I, Manchester, 1808, p. 147.Google Scholar

⁴⁸ Crosland, M. P., “The Development of Chemistry in the Eighteenth Century”, Studies on Voltaire, xxiv (1963), pp. 382–390.Google Scholar

⁴⁹ A modern instance of several “speculative” theories (about magnetization processes) which all agree equally well with the empirical evidence has been discussed by Bates, L. F. and Pacey, A. J., Brit. J. Applied Physics, xv (1964), 1394.Google Scholar

⁵⁰ Important papers have been written about Herapath by Brush, S. G. (Ann. Sci., xiii, 1957 (1959), 188–198)CrossRefGoogle Scholar and by Mendoza, E. (Mem. Manchester Lit. Phil. Soc., cv (1962–1963), 15–28).Google Scholar

⁵¹ Ann. Phil., n.s., i (1821), 273 ff.Google Scholar; 340 ff.; being the text of a letter to Gilbert, Davies V.P.R.S., and continued in “Tables of Temperature, and on the Causes of Calorific Capacity, Latent Heat etc.”, Ann. Phil., n.s., ii (1821), 89–103; 201–211; 256–274, 363–388; 434–462; and iii (1822), 16–28.Google Scholar

⁵² It was quite generally accepted that Newton had proposed this, e.g. Leslie, J., An Experimental Enquiry into the Nature and Propagation of Heat, London, 1804, p. 136.Google Scholar

⁵³ Herapath, , Ann. Phil., n.s., i (1821), 278.Google Scholar

⁵⁴ Ibid., p. 279.

⁵⁵ The relevant papers are given in Alembic Club Reprints, no. 4, Foundations of the Molecular Theory, Edinburgh, 1893.Google Scholar

⁵⁶ Herapath, , op. cit., p. 273.Google Scholar

⁵⁷ Rumford's Essays, London, 1797, vol. ii, p. 493.Google Scholar

⁵⁸ Davy, , Elements of Chemical Philosophy, London, 1812, p. 95.CrossRefGoogle Scholar

⁵⁹ He thought the amplitude of the vibrations grew larger as the particles became smaller and he assumed that gases had the smallest particles, e.g. Herapath, , op. cit., p. 406.Google Scholar

⁶⁰ Davy also suggested rectilinear motion for the “imponderable” particles which he thought the probable cause of the phenomena of radiant heat and light. Thus his scheme encompassed all three types of motion possible in a kinetic theory.

⁶¹ As one example, Ure strongly supported Davy's claims on behalf of William Higgins as originator of the atomic theory.

⁶² Ure, , Chemical Dictionary, 1821Google Scholar, article “Caloric”. (This work has no page numbers.)

⁶³ Herapath, , Mathematical Physics, London, 1847, vol. i, p. 217.Google Scholar

⁶⁴ Ann. Phil., n.s., ii (1821), 305.Google Scholar

⁶⁵ Ibid., n.s., i (1821), 279.

⁶⁶ Phil. Mag., lvii (1821), 130–133, 260–262.Google Scholar

⁶⁷ See for example Ann. Phil., n.s., ii (1821), 223 ff., 303 ff., 390 ff., 418 ff., 462 if.Google Scholar; iii (1822), 29–34, 290 ff.; 357 ff.; iv (1822), 197–222, etc.

⁶⁸ For a list of those taking Leibniz's side in the dispute, see Hutton, Charles, Mathematical and Philosophical Dictionary, London, 1796, vol. i, p. 495 (article on force).Google Scholar

⁶⁹ Herapath, , Ann. Phil., xi (1818), 208 n.Google Scholar

⁷⁰ Ibid., n.s., i (1821), 282 ff. He accepted that the hard body theory was essential to his whole scheme; Ibid., n.s., ii (1821), 306.

⁷¹ Ibid., n.s., i (1821), 345, or Mathematical Physics, i, 221.Google Scholar

⁷² His latent heat theory required all sorts of curious assumptions to be made about shapes of particles in order to avoid the conclusion that phase changes could only take place at absolute zero. This was because Herapath's collision theory did not envisage any means by which particles could coalesce unless they had no relative velocity. (Ibid., n.s., ii ( 1821 ), 267.)

⁷³ For example, he pleaded quite justly that Newton had not specifically affirmed that air consisted of particles repelling one another inversely as their distances. (Ibid., n.s., ii (1821) 306 n.)

⁷⁴ Except for one critic who thought the question important but held the view that a purely mathematical demonstration as given by Herapath was not proof but only a strong argument. (Ibid., n.s., ii (1821), 418.)

⁷⁵ In a paper on heat and elastic fluids read October 1848. Mem. Manchester Lit. Phil. Soc., ix (1850), 107.Google Scholar

⁷⁶ P. 95.

⁷⁷ Thus repeating a previous assertion in a paper read to the Manchester society, Joule's Scientific Papers, London, 1887, vol. i, pp. 121–122.Google Scholar

⁷⁸ But see note 60.

⁷⁹ Cardwell, D. S. L., Mem. Manchester Lit. Phil. Soc., cvi (1963–1964), 118.Google Scholar

⁸⁰ E. Mendoza, ibid., cv (1962–63), 24.

⁸¹ Joule's Scientific Papers, i, 121 ff.Google Scholar

⁸² Ibid., pp. 51–52.

⁸³ Ibid., pp. 172 ff.

⁸⁴ Herapath, , Mathematical Physics, vol. i, p. xxx.Google Scholar

⁸⁵ In part of the second edition of his book on chemistry, which Herapath read in November 1846.

⁸⁶ Mathematical Physics, ii, 9Google Scholar. Herapath claimed here to have derived the law in March 1844, and to have only read of Graham's work in November 1846. But in August 1845 he discussed a diffusion formula produced by Pecqueur. The formula was closely similar to Graham's law, and was mentioned in the Railway Journal because of its possible relevance to a controversy about atmospheric railways in which Herapath was engaged (Herapath's, Railway and Commercial Journal, vii (1845), 1429).Google Scholar

⁸⁷ He had already decided in principle on this course in 1825, Ann. Phil., n.s. ix (1825), 353.Google Scholar

⁸⁸ Mathematical Physics, ii, 107, 123 f.Google Scholar

⁸⁹ Dalton, , Mem. Manchester Lit. Phil. Soc., v (1802), part 2.Google Scholar

⁹⁰ Mathematical Physics, ii, 122.Google Scholar

⁹¹ Phil. Mag. [3], xxiii (1845), 263 ff.Google Scholar

⁹² Mathematical Physics, ii, 136.Google Scholar

⁹³ Ibid., pp. 115–116.

⁹⁴ In the Joule collection, University of Manchester Institute of Science and Technology Library.

⁹⁵ Brockbank, E. M., John Dalton, Manchester, 1944, pp. 19–21.Google Scholar

⁹⁶ Joule's Scientific Papers, ii, 11–215.Google Scholar

⁹⁷ Ann. Phil., n.s. iii (1822), 18.Google Scholar

⁹⁸ Mathematical Physics, i, p. xviii.Google Scholar

⁹⁹ Hooykas, R., Arch. Int. Hist. Sci., 1948, pp. 180–184.Google Scholar

¹⁰⁰ Also in the Joule Collection (see note 94).