( - ? 51 ) 



XII. — On the Foundations of the Kinetic Theory of Gases. II. 



By Professor Tait. 



(Read December 6, 1S86, and January 7, 1887. Revised April 4, 1887.) 



PAGE 



Introductory and Preliminary, . . 251 



Part X. On the Definite Integrals, j vV r 



J T 



and J^. 2 ' §§33,34, . 256 



INDEX TO CONTENTS. 



PACE 



Part XI. Pressure in a Mixture of Two 



Sets of Spheres, § 35, . . 258 

 „ XII. Viscosity, §§ 36, 37, . . 259 

 „ XIII. Thermal Conductivity, §§38-44, 261 

 „ XIV. Diffusion, §§ 45-56, . .266 



Appendix. Table of Quadratures, . .277 



[Erratum in Part I., ante, p. 65. For 1676, read 1678, as the date of Hooke's Pamphlet.] 



In the present communication I have applied the results of my first paper 

 to the question of the transference of momentum, of energy, and of matter, in 

 a gas or gaseous mixture ; still, however, on the hypothesis of hard spherical 

 particles, exerting no mutual forces except those of impact. The conclusions 

 of §§ 23, 24 of that paper form the indispensable preliminary to the majority of 

 the following investigations. For, except in extreme cases, in which the causes 

 tending to disturb the " special " state are at least nearly as rapid and persistent 

 in their action as is the process of recovery, we are entitled to assume, from 

 the result of § 24, that in every part of a gas or gaseous mixture a local special 

 state is maintained. And it is to be observed that this may be accompanied 

 by a common translatory motion of the particles (or of each separate class of 

 particles) in that region ; a motion which, at each instant, may vary continuously 

 in rate and direction from region to region; and which, in any one region, may 

 vary continuously with time. This is a sort of generalisation of the special 

 state, and all that follows is based on the assumption that such is the most 

 general kind of motion which the parts of the system can have, at least in any 

 of the questions here treated. Of course this translational speed is not the 

 same for all particles in any small part of the system. It is merely an average, 

 which is maintained in the same roughly approximate manner as is the 



VOL. XXXIII. PART II. 2 



