83-85] Intermolecular Forces 77 



together, we find that the fraction of the whole generalised space which is 

 occupied by systems of class A is 



e - J _ 9U9V... 



"X.Vfc... ai !a 2 !..; ..................... < 1{ 



85. The value of a just found is a generalised form of that given by 

 expression (60). If we proceed as in 40, using Stirling's Theorem [equation 

 (61)] in the form 



Lt 



we obtain log a = G- 2 (a, + )log ^- 2 (& + ) log^- 8 - ... 



n a 6 n p 6 



- 2 ((#). + *) fog <?>-... 



where (7 is a constant depending on the constants 91 , 910... n a , W0 ____ 

 From this equation it follows that the normal state is obtained by making > 

 a minimum, where 



The variation of ) is subject to the energy equation (177) and to equa- 

 tions of the type (180) expressing the permanency of the separate types of 

 permanent molecules. If we vary equation (185) and add the variation of 

 equation (177) multiplied by an undetermined multiplier \, and that of the 

 equations of the type (180) multiplied by ytt , ftp ... we obtain 



=/(log 0. 

 / 



L a + pp) Bfa + ... 



and the condition that j shall be a minimum is given by the systems of 

 equations 



log (f> a + \E a + p a = 0, etc., 



log fa + \E a p + fjb a + ftp = 0, etc., 

 log fa + \E aa + 2/i a = 0, etc., 



etc. 



Changing the constants X, /u, a , //, ...,and substituting for ^ a 0, E aa ... these 

 equations lead at once to the equations 



(186), 



etc. 



