1198 



We shall presently consider the temperature function f {a) in the 

 quantity a somewhat more fully. 



It may only be remarked already here, that when we generally 

 put the integral of work : 



r« 



ƒ 



i(»f,l^-.p,^,_,„,|;/«>_„^j.^ ^ 1^1 



dr 

 f {a) may be represented by 



/(«) = - • . (4) 



a 



It is easy to see that (4) will hold generally, whatever be the 

 form of the factor of distribution, provided this be only such a 

 function of SPr, that it becomes = 1 for P,. = 0. a^, will then 

 always be =zv{hcj)^a. 



In the special case that the factor should be constant = 1,1^ 



becomes simply = {NP,)^'' = — {N x—M) z=MN=(i. f (a) then 

 also becomes =1, so that the quantity a becomes independent of 

 the temperature. 



XI. The Virial of Collision. 



^. 

 Here Pr will assume the value + oo for ?• = .? — tf — at least 

 when the molecule is supposed t obe incompressible — whereas P,. for 

 r =r 5 will evidently again have the value — M. This makes the 

 tirst integral indicated in the expression (a) for pv: 



{-■^) 





and we find for the virial of repulsion {n: N is again v): 



Let us then put 



then bg becomes : 



n = ^-^ftr//^^. 



(MooX/^'^^ = 6„ (d) 



^7 = (M«>x/^'^'' = (M«X/(6) (5) 



and 



Vk = RT^ • . (6) 



V 



