( 117 ) 



We suppose that the molecules «ire perfectly rigid and elastic and 

 that they attract each other with forces acting at distances so great 

 that we may consider the sphere of action as uniformly filled with 

 matter. 



For this case the value of W is given by the equation 



e 6 —{2nd m,) 2 "' (2 .t d to,) 2 " 2 J e 6 dx^.. dz 2 „^ . . (2) 



I shall represent the coordinates of the molecule .k of the first kind 

 by x ik, y\k and z { j : , and those of the molecule / of the second kind 

 by x-iu y-2i and z 2l . 



The integration has to be extended to a 3 (n 1 -J- n,)-dimensional 

 space, the notion of which is obtained if we take the 3 (w, -J- ?i s ) 

 coordinates of the centres of the molecules as cartesian coordinates 

 of a single point, and give all possible positions to the molecules of 

 the gas. 



We must exclude from the space all those points at which a con- 

 dition of one of the forms 



(«life — xuY + {y\k — yuY + (*i* — z\iY < <V , 



(«ifc - *2/) a + (yi* - yaY + (*ut - *a/)' <° i • • ( 3 ) 



(#24 — #2/)* -h (#24 — y-2lY + («24 — «**)' < «V 1 



is fulfilled. 



I have proved J ) in my dissertation that the large majority of the 

 systems of a canonical ensemble may be considered as identical in 

 all properties that are accessible to our means of observation. Por 

 all these equivalent or identical systems the value of the potential 

 energy of the attractive forces is equal. 



The sphere of action being uniformly filled, this quantity (e 9o ) can 

 be represented by 



«, n x s -f" 2 « n x n, -\- a t n, 1 

 TV 



6 ?o = 7T^ ( 4 ) 



As to the potential energy of the repulsive forces, we need not 

 speak of it when we take into account the conditions (3). 



We shall obtain a good approximation, if, in the equation (2), we 

 write e qo instead of e 7 (which differs from f Vo only in a small part 

 of the systems). By this, the exponential factor becomes a constant 

 and we may put it before the sign of integration. 



The quantity V is thus expressed by the equation 



l ) 1. c. p. 14 



