454 MR. S. CHAPMAN ON THE KINETIC THEORY OF A GAS 



Hence 



Q' 1S (V ) = ^V^'-^ypdp = TrV (<r + a7, 



and 



Q"i2 (V ) = TrV P" 1 (^W) 2 sin 3 2 X sin x cos x d x = l^ u 



Jo 



Consequently we find that 



(44) F, S = ^w>- 



R',, = 



From these we obtain the equations 



(45) 71 ^, 



(46) k = |, ^ = f , k 2 = ft, 



so that in this case the constants k, k lt k 2 (defined by equations (27) and (37)) are 

 numerical constants ; in general, they are functions of the temperature (i.e., of h). 



14. Molecules which are Point Centres of Force. 



We next consider the hypothesis that the molecules are geometrical points 

 endowed with inertia and repelling or attracting one another with forces which are 

 functions only of the distance between their centres. 



Let 12 (r) be the mutual potential energy of two molecules m, m' at distance r, and 



let us write </>' l2 (r) in place of - r- 12 (r). The first two integrals of the equations 



mm 



of motion of the second molecule in terms of co-ordinates r, 6 with the first molecule 

 as origin are as usual 



where A and B are constants. Eliminating the time from these equations we get 



