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XLYI. On the Foundations of the Kinetic Theory of Gases. 

 By Prof. Tait *. 



THE attempt to account for the behaviour of gases by at- 

 tributing continuous pressure to exceedingly numerous, 

 but nearly infinitesimal, impacts on the containing vessel is 

 probably very old. It certainly occurs, with some little deve- 

 lopment, in Hooke's tract of 1676, "Lectures de potentid 

 restitntivd, or of Spring " ; and, a little more fully developed, 

 in the Hydrodynamica of D. Bernouilli, 1738. It was re- 

 called to notice in 1847 by Herapath in his Mathematical 

 Physics, and applied, in 1848, by Joule to the calculation of 

 the average speed of the particles in a mass of hydrogen at 



In and after 1857 Clausius greatly improved the theoretical 

 treatment of the problem by taking account of the mutual 

 impacts of the particles and the rotations which they com- 

 municate to one another, at the same time introducing (but 

 only to a limited extent) the statistical method. In this series 

 of papers we find the first hint of the length of the mean free 

 path of a particle, and the explanation of the comparative 

 slowness of the process of diffusion of one gas into another. 

 But throughout it is assumed, so far as the calculations are 

 concerned, that the particles of a gas are all moving with 

 equal speeds. 



In this Magazine for 1860 Clerk- Maxwell published his 

 papers on the u Collision of Elastic Spheres/'' which had been 

 read to the British Association in the previous year. In this 

 very remarkable investigation we have the first attempts at a 

 numerical determination of the length of the mean free path. 

 These are founded on the observed rate of diffusion of gases 

 into one another ; and on the viscosity of gases, which here 

 first received a physical explanation. The statistical method 

 is allowed free play, and consequently the law of distribution of 

 speed among the impinging particles is investigated, whether 

 these be all of one kind or a mixture of two or more kinds. In 

 the ardour of his research, Maxwell here and there contented 

 himself with very incomplete proofs (we can scarcely call 

 them more than illustrations) of some of the most important 

 of his results. This is specially the case with the investigation 

 of the law of ultimate partition of energy in a mixture of 

 smooth spherical particles of two different kinds. He obtained, 



* Abstract of Papers read to the Royal Society of Edinburgh, Dec. 7th, 

 1885, and subsequently : communicated (by permission of the Council) 

 at the request of Sir W. Thomson. 



