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



We now transform the variable in the integrals Q', S2" from p to a so tlmt 



4 



p dp = K', 2 V "-' a da. 

 where 



(47) K' 12 = 



Thus we have 



\ 3 ( V ) = K'uV,, 1 "- 4,r sin 2 x . a da, 



Jo 



" 12 ( V ) = K'^V,, 1 '^ P TT sin 2 2 X . a da. 



The definite integrals in the last two expressions are pure numbers depending on 

 n ia alone.* We shall denote them by X' (n 12 ) and X"(n 12 ) respectively. We thus 

 havet 



so that, as in the case of molecules which are elastic spheres, Q" is merely a constant 

 multiple of 0' If we substitute the last expressions in the integrals for P, R, S (see 

 equations (42)) and remember that 



C x hmm' ., 



.l v "'"'~= 



we find that 



2 



(48) 



. 12 i - 7- -- - 



\hmm'J \ HU 1 



- J-K' \'^ W ^ ^"""^T'/Q 2 \ p// xrr/ ,// v/ 2 V""^ 



- i^K) 8 -' lii = ^ KiiX{Wii) 



where 



* And on whether the molecules repel or attract, there being one value for each case, corresponding to 

 each value of n. 



t These formulae are true whether the forces are repulsive or attractive. The only difference occurs in 

 the value of the numerical constants X' and X". 



