( 120 ) 



intersections, which have been subtracted too much from V. These 

 parts are equal for by far the majority of the possible combinations 

 of elements in the spaces from the first up to the (n 1 -\- n t — l) th . 

 We may suppose that the distribution of the points corresponding 

 to the centres of molecules from 1 tot n 1 -\- n t — 1 is uniform in 

 the (n^ -\- n,)*' 1 space. 



1. The number of pairs of points (corresponding to molecules of 

 the first kind) with mutual distance lying between x and x -j- dx 

 amounts to 



x* dx 



2.1V -y~ (10) 



The common part of two spheres of radius o having a central 

 distance x is given by 



/4 x l \ 



*{f- a '* + n) <"> 



Hence, the total part subtracted too much on account of these 

 intersections is equal to 



2jtV 



V 



*C(± . x \ *XY8 8 1 a'\ 



J ^3 ^ 12J V \9 9 l ^2 ' 36y v ' 



2. The number of pairs of points (corresponding to the centres 

 of molecules of the second kind) with a mutual distance between 

 x and x -\- dx is 



2* (», - 1) (« f - 2) ^p- (13) 



The common part of the spheres is found for this case, if in (11) 

 we replace o by <>,, so that we find for the part subtracted too 

 much from V 



(n — 1)(» — 2)/Y4 , , x*\ 17(n t -l)(n 1 -2)/2 V 



3. The number of pairs of points such that one point corresponds 

 to the centre of a molecule of the first kind and one to that of a 

 molecule of the second kind, the mutual distance lying between 

 x and x -J- dx, amounts to 



x*dx 

 4^r n 1 (n, — 1)— — (15) 



