76 The Law of Distribution [CH. v 



The analysis of 72 holds for the most general field of intermolecular 

 force. Hence it appears that in the present case, as before, the density of 

 fluid in the generalised space may be regarded as constant throughout all 

 time, and therefore we need only discuss the ratio of the volumes of this space 

 which are occupied by the different possible classes of systems. 



84. Let us agree to adopt the artifice explained in 56, to limit the 

 variation of the coordinates of the various types of molecules to a finite 

 range. Let us divide up the possible range of coordinates for a single- 

 molecule of type a into n a equal "cells," the possible range for a single 

 molecule of type /3 into np equal cells, and so on. The range for a compound 

 molecule of type a/3 will then be n a np cells, if for the moment we regard any 

 combination of an a molecule with a /3 molecule as a compound of the a/3 

 type. If we only regard these as forming a double molecule when the inter- 

 molecular force exceeds a certain amount, then it follows that double mole- 

 cules can only occur in certain of these n a np cells, and not in all it does not 

 at present matter in how many. 



Let us now consider a special class of system class A in which there 

 are 



cti, a 2 ... single molecules of type a in the respective n a cells, 

 &,&... ft n ft -(181), 



(a/3)i,(a/3) 2 ... double a/3 n a np 

 and so on. 



Each arrangement of molecules which form a system of class A will be 

 represented in an element of the generalised space which forms a fraction 



of the whole. Using equations (178) this becomes 



1 



.(182). 



Now the number of ways of distributing the rdles of the various con- 

 stituent molecules so that conditions (181) are satisfied is 



Here the factor yi a I is the number of ways in which the 9tf a permanent 

 constituent molecules of type a can be permuted inter se, ^ I is the number 

 of ways in which the molecules in the first of the n a cells can be permuted 

 inter se, and so on. Expression (183), then, gives the number of elements 

 which represent systems of class A. Multiplying expressions (183) and (182) 



