83] Intermolecular Forces 75 



in the form in which the law of distribution is expressed. We shall suppose 

 that the number of single molecules of type a for which the 2n a coordinates 



, ,...&. .............................. (173), 



lie within the range d^dj;^ ... d 2 n a is 



so that by comparison with (137) we see that </> a replaces the old N a f a . The 

 point of this change is to absorb the variable quantity N a into the variable 

 function f a . In the former case, N a was constant and this absorption was 

 unnecessary : in the present case it reduces the apparent number of variables 

 from two to one. 



A double molecule of type a/3 will be a molecule composed of a molecule 

 of type a and a molecule of type /3 in encounter. The coordinates specifying 

 such a double molecule will be the coordinates, 



of its components, and the number of double molecules for which these co- 

 ordinates lie within the usual range will be taken to be 



^wdri, %2> '%!> 2 ) d^id^ 2 ... di d 2 f (176). 



Let E a be the energy of a single molecule of type a, expressed as a 

 function of the coordinates (173), E a p the energy of a double molecule of 

 type a/3 expressed as a function of the coordinates (175), and so on. Then 

 the total energy as expressed by equation (172) may be put in the form 



IE* + (177), 



in which the differentials are omitted to save printing, and the single thick 

 integral denotes integration over all values of these differentials. 



There will be a constituent molecule of type a, (i) in each single molecule 

 of type (a), (ii) in each double molecule of the types a/3, o/y . . . , and (iii) there 

 will be two such molecules in each double molecule of type aa ; and so on 

 for more complex molecules. Let N ai Np, N a p ... be the number of molecules 

 of types a, /3, a/3..., and let 9? a , 9?/3, ... be the numbers of the permanent 

 constituent molecules of types a, /3 ____ Then we have 



W a = N a +2N aa + N ali + N ay + .................. (178), 



and since we have equations of the form 



this may be written 



9?a 



There are similar equations for each of the types /3, 7 



