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III. — On the Foundations of the Kinetic Theory of Gases. By Professor Tait. 



(Kevised May 14, 1886.) 



INDEX TO CONTENTS. 



Introductory, . 



Part I. OneSetof Equal Spheres, §§ 1-5, . 

 ,, II. Mean Free Path among Equal 



Spheres, §§6-11, 

 ,, III. Number of Collisions per Particle 

 per Second, §§ 12-14, . 

 Clerk-Maxwell's Theorem,§§ 15-22, 

 Rate of Equalisation of Average 

 Energy per Particle in two 

 Mixed Systems, §§ 23, 24, 



IV. 

 V. 



PAGE 



65 

 67 



71 



75 



77 



82 



Part VI. On some Definite Integrals, 



§§ 25-27, . . .84 



,, VII. Mean Path in a Mixture of 



two Systems, § 28, . .86 



,, VIII. Pressure in a System of 

 Colliding Particles, §§ 29, 

 30, . . . .86 



,, IX. Effect of External Potential, 



§§31,32, . . .91 



Appendix, . . . .95 



The attempt to account for the behaviour of gases by attributing their 

 apparently continuous pressure to exceedingly numerous, but nearly infinitesi- 

 mal, impacts on the containing vessel is probably very old. It certainly occurs, 

 with some little development, in Hooke's tract of 1676, Lectures de potentid resti- 

 tutivd, or of Spring ; and, somewhat more fully developed, in the Hydrodynamica 

 of D. Bernoulli, 1738. Traces of it are to be found in the writings of Le Sage 

 and Prevost some 80 or 90 years ago. It was recalled 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 

 various temperatures. Joule expressly states 4 ' r that his results are independent 

 of the number of the particles, and of their directions of motion, as also of their 

 mutual collisions. 



In and after 1857 Clausius greatly improved the treatment of the problem 

 by taking account not only of the mutual impacts of the particles but also of the 

 rotations and internal vibrations which they communicate to one another, with 

 the bearing of this on the values of the specific heats ; at the same time intro- 

 ducing (though 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 



* The paper is reprinted Phil. Mag. 1857, II. See especially p. 215. 

 VOL. XXXIII. PART I. I 



