( 118 ) 



3 3 8 q 



J dx xl . . 



e d = {2 7i 6 my (2jr<9m,)2 e J ^ . . dz^ . . (5) 



and its determination is reduced to the calculation of the integral 

 on the right-hand side. Let the function / {n x , «,) represent this integral. 



In my dissertation I have determined this function to the degree 

 of exactitude indicated above. Before proceeding to the determination 

 of the terms of higher order I shall repeat the former calculation 

 which now only wants further extension. 



The 3 (Wj -j- ??,)-dimensional space of integration can be decomposed 

 into n ï -J- n t threedimensional spaces, each corresponding to one of 

 the molecules. We shall divide these spaces into elements which 

 are small in comparison with the volume of a molecule. 



In order to determine the integral defining the function / (w, , n t ) 

 we decompose it into a sum of products of n l -f- n t elements chosen 

 in the spaces in question, each space being represented in the product 

 by one and only one element. 



In order clearly to see the way in which the products are formed 

 with the restrictions imposed by (3), we proceed as follows : We 

 number the spaces corresponding to the molecules of the first kind 

 from 1 to n lt those corresponding to the molecules of the second 

 kind from n x -f- 1 to n x -\- n t , and we choose the elements in the 

 order indicated by these numbers. 



We have to consider that, if we have chosen for the centre of the 

 k th molecule {k < n x ) an element lying at a point X\k> j/\k, Z\k, we 

 must exclude from the k -f 1 th up to the ?? 1 th space those elements 

 which are situated in spheres described with the radius o 1 around 

 the points of these spaces whose coordinates are equal to x xk , y\k 

 and z\] c . Similarly we must exclude those elements from the spaces 

 from Hj-j-1 up to n 1 -\-n,, which lie within the spheres of radius 

 a described around the points of the spaces having for coordinates 

 x lk , y lk and Z\u- If, further, in the space n x -\-\\ an element 

 has been chosen at a point with the coordinates x Vx + H , y sth +v a , 

 z in i Vl we must exclude in all following spaces the elements of 

 spheres with radius ^ described around the points of those spaces 

 having their coordinates equal to «, ni -|-,„ ?/ 3 > (1 +v 2 , ^,^+v,- 



The elements in the spaces 1 to n x -\- n, — 1 having been chosen, 

 there remains in the last space n x -\- ?i, a region g, h +n^ for the 

 choice of the (n x -\- n 3 ) ,h element. 



In determining the sum we can first take together all those cases 

 in which the elements of the spaces 1 to n x -\- n t — 1 are the same. 



Considering that n x and ?i 3 are very great numbers, and that the 



