dD 
the moments belonging to the coordinates (the internal ones and 
those of the centres of gravity) mentioned above. Now, suppose dà; 
to represent an element of the extension in phase of the internal 
coordinates and moments. Consider the integral 
fru, vedan Arg 
where « is the total energy ¢ diminished by the energy of the 
progressive motion of the centres of gravity. The integration with 
respect to the coordinates of the centres of gravity must be extended 
over the 3(n, +..n.-+ nz)-dimensional space v32n, , whereas all 
values that are possible without dissociation of the molecules are to 
be ascribed to the internal coordinates and moments. 
If, in the case considered, there exists a sphere of repulsion such 
as there is with rigid, perfectly elastic molecules, then the conse- 
quence will be that «' takes an infinite value for certain configu- 
rations, and therefore the parts of the integral corresponding with 
these configurations will not contribute to it. Just as in the case of 
a simple substance and in that of a binary mixture’), one can show 
in this case that the integral may be put into the form 
k 
= Ny 
OPS eek ar DE). vt 
My ; 
where n‚=—, i. e. the number of molecules of the kind « pro 
Uv 
unit of volume. 
The function w may be determined if the structure of the mole- 
cules is given; but for our purpose it is sufficient for us to know 
that the integral can be reduced to the form mentioned above. 
2. We now imagine the volume V to be divided into a great 
number of equal elements of volume ,.. V;.. Vi, and we want 
to know the number of systems in a canonical ensemble for which 
the element V; contains respectively m.. na.. nx of the diffe- 
rent molecules. We have for the numbers n,) 
l 
SF i= 1 
l 
the total number of molecules of each kind being given. 
This number of systems 6, which I shall call the frequency of the 
systems mentioned, is represented by the formula 
Nx) 
¥ k ee l 
OF VD ii enters s By Vy as 
alee 0 Et \ by NIN. ij jat = (Piz. Dex» « Apo) =| (1) 
N 1 
Ny) ! 
1) Comp. my dissertation and these Comm. 1908, p. 107. 
