( 528 ) 
oi PAE: NE, 
Ny 
ie ae my 7 
2 @ 1 0 
S= N(2amO) e lS @. de) e oen VAE) 
1 fe 
§ 2. The properties of an observed system are identical with those 
in a vessel of the volume V. And let us imagine a canonical ensemble built up 
of N systems. 
In this ensemble the number of systems — having the coordinates of the 
centres of the molecules between x, and #, +dx)... 2n and zn + den and the 
components of the velocities of these points between a, anda, and Ly ie cat 
En and zn + den — amounts to 
We 
G ‘ 6 
N m3" e Ul ae den ADs a UB ken ge 
Here, the energy of the system is expressed by «, and ¥ is a constant for 
the ensemble depending on © and V. The value of ¥ can be found by integrat- 
ing (d) with respect to the coordinates and the velocities. The result of this 
integration must be N, which yields a relation for w. The number of the systems 
in which the velocities have any values, but whose coordinates are lying between 
the specified limits is obtained by integrating (a) over the velocity components 
from — ooto + oc. 
n 
| : : : 
The energy € is given by the relation € = @, + ) = m (a?,-+ y?, + 27,) 
1 
in which e, is the total potential energy and m the mass of a molecule. Therefore 
the result of the integration is 
—n 
2 g . 
N(2xOm) e dens dan. : (b) 
Let us now divide the volume V into k elements dV,.. dVy .. dVk. If nz 
molecules are situated in an element of volume dVx the 277 coordinates of their 
centres may still vary between certain limits; in other terms, a certain extension 
is left open to the point representing these coordinates in a 37,-dimensional space. 
l shall represent the magnitude of this extension by 
4 (n,, dV;). 
The repulsive forces between the molecules are accounted for by excluding 
from the 3n,-dimensional space (JV) all those parts in which there exists a 
relation of the form : 
(a, — ap)? + (yo yr) H (eve) <0 ... + (©) 
between the ordinary coordinates of the centres of two molecules. We can 
represent 7 (nx, dVz) by 
RENEE. dee eN 
where the integration has to be extended over the whole space (dV), with the 
exception of the parts determined by (c). By a simple reasoning we can show 
