﻿578 On the Virial of a Mixture of Ions. 



virial on A of all the remaining ions in the volume the value 



\J=-whx 'Q6= -0*198 w, for A=0'3. 



The figure also contains the curves which correspond to two 

 other values of A, and in the following table the values of 

 (f>(h) obtained are gathered together, in order to show the 

 course of the function. 



h. 



0(70. 











0109 



-042 



03 



-0-66 



0-867* 



-1-03 



* This value of h is so large that the expression for the virial obtained in 

 this paper would no longer be valid ; cp(h) was calculated only because it was 

 of interest to trace the course of the function. 



As h increases from 0, <f>(K) increases very rapidly at first, 

 afterwards more slowly, and it tends to become practically 

 constant as h continues to increase. It is easy to show that 

 when h=co <j)(h) has the limiting value of — u x or —1*354. 



The average virial E of all the ions is obtained by multi- 

 plying U by N, the number of + or of — ions in the volume 

 V. We can therefore express it finally as 



where iv( = UT/v, eq. 2) is the most probable kinetic energy 

 of an ion, 



(q being the ionic charge), and cj)(Ji) is a function of ^, the 

 course of which is shown in the preceding table f . In a 

 subsequent paper I hope to deal with some of the applications 

 of this result to the osmotic pressure of electrolytes. 



t This result is only strictly applicable when h is small. 



