( 527) 
each other up to distances which are large in comparison with the 
diameter o and with the distance of neighbouring molecules. I shall 
denote by —g(/) the potential energy of this attraction for a pair 
of molecules whose centres are at a distance fand I shall suppose that 
- g(f)=0 for values of f which are large compared with o (and the 
distance between neighbouring molecules) but small compared with 
finite lengths, the same being also true of the function yw (/) determined 
by the equation 
NN =d Gale ite ar ots Dau GD 
Let us now consider a canonical ensemble with modulus @ built 
up of N systems of the above kind. 
We divide the volume of the cylinder by horizontal planes into 
a great number & of elements of a height dz, this height being large 
compared with o and small compared with the distance at which 
the molecules sensibly attract each other. I shall further suppose 
that the potential energy of attraction changes but little over a dis- 
tance of the order of magnitude dz, *). 
We shall determine the number, or, let us say, the “frequency” 
5 of those systems in the ensemble in which there aren, ... 7, ... Np 
molecules respectively in the elements dz,... dz, ... der. I shall 
suppose that the numbers », are very large; their sum being 72 we 
have the relation 
k 
ym ar at eee Pr Rie ree sce HT 
1 
The number of molecules per unit of volume in the element dz, 
(the molecular density) will be represented by nz,. 
I shall consider the mutual energy of a pair of molecules as 
belonging for one half to the first and for the other half to the 
second of the molecules. The energy determined in this way is the 
same for all the particles of the layer dz,. I shall represent this 
energy per molecule by €,. 
The total potential energy can therefore be represented by 
Kk 
> Ny Be. 
1 
The frequency ?) in question is given by the formula 
1) For the sake of simplicity I shall take the elements dz, of equal magnitude ; 
. Ny : ; F : 
our result will be that —~ => n, (the molecular density) is a function of 2, showing 
dz, 
that we do not lose in generality by this simplification. 
2) In explanation of the formula (II) the following may be observed, Let us 
consider a system constituted of 2 molecules of the kind above described enclosed. 
