in connexion with the Kinetic Theory of Gases. 65 



Also in 22R>*, R is the repulsive force, r the distance be- 

 tween any two particles, or between a particle and a point on 

 the surface, and the summation includes every pair of points 

 between which any force acts. 



Then 22R?' is a function of position of the particles, having 

 a definite value for each configuration, and 2)2Rr denotes the 

 mean value of 22R?' for any long time; and we might therefore 

 write 



fm. = .Cyf--(SSBr)i*' < to l dy 1 ... < fe A 



555' ••«^*»i<fr»w%** 



Now let 



P=P, + P 2 , 



and let 



I t^=|- • .....••... a) 



|P 2 «=iS2Kr (2) 



t follows from (1) that 



and 



i v > 



1 V 



Also from (2), 



P,-JS6B;. 



Vf,=ySSB%r 



Now for each configuration 



Therefore, taking mean values, 



dv 



p 2 s v =SSr^==-^« 



therefore 

 lerefore 



dv 



hF^v^-h^Xdv. 

 dv 



Phil. Mag. 8. 5. Vol. 1. No, 1. Jan, 1876. F 



