IN RARIFIED OASES 



f f, K denote what / becomes when in place of the velocity-com- 



gf jf before the encounter we put those of M, before the encounter, 



nd those of Jf, and M, after the encounter, respectively, and the integration 

 M fflrtflmfrH to all values of 4> and b and of , 17,, ,, the velocity-com- 

 ponents of the second molecule J/,. 



It M impossible, in general, to perform this integration without a know- 

 ledge, not only of the law of force between the molecules, but of the form 

 of the functions /, / /T, /.'. which have themselves to be found by means of 

 the equation. 



It is only for particular cases, therefore, that the equation has hitherto 

 been solved. 



If the medium is surrounded by a surface through which no communica- 

 tion of energy can take place, then one solution of the equation is given by 

 the conditions 



y dz 



which (rive 



f t mAfr****** (9) 



where ^, is the potential of the force whose components are X lt Y lt Z 1} and 

 At is a constant which may be different for each kind of molecules in the 

 medium,, but h is the same for all kinds of molecules. 



This is the complete solution of this problem, and is independent of any 

 hypothesis as to the manner in which the molecules act on each other during 

 an encounter. The quantity h which occurs in this expression may be deter- 

 mined by finding the mean value of f , which is _, . Now in the kinetic 



theory of gases, 



P e=p = R P 8 (10) 



where p is the pressure, /> the density, 6 the absolute temperature, and R a 

 constant for a given gas. Hence 



<) 



