in the Kinetic Theory of Gases. 307 



due to encounters, and by ^ — its time-variation due to ex- 

 J ^t 



ternal causes. In steady motion 



dK BH _~ 



lit ~dt ~ 



In like manner for any other function, as F, -=- shall be 



the time-variation due to encounters, ^- that due to exter- 



cK 



nal causes, and the condition for steady motion is 



d¥ BF 



dt T ^t 



13. Let us consider the case of two sets of molecules, each 

 subject to a small disturbance. 

 For the M set let 



F(a,)=N(™)V AM « a (l + X). 



For the m set let 



Here N and n are the numbers of molecules per unit volume 

 of the M and m sets respectively, and X and x represent the 

 disturbances. 



Let us form the spherical shells described about C, with 

 radii E, r as in (6). Let PCp be any common diameter, and 



©=OP, +=Op. 

 Let Xp, x p be the values of X and x at P and p respectively. 

 In that case 



Mo) 2 + m^= (M + m) V 2 + MR 2 + mr 2 



= (M+m) (V+ -R 2 ) 



and 



F/ — F/=Nn( J f— 1 e K M+m / {X + ,^-(Ap + 



where 



