548 RICE 



ART. L 



repeat it once more, cr is a function of t, m,, y.^, etc., quantities 

 whose values in the bulk of the solution are meant, and any 

 approximations make <r still a function of physical variables as 

 measured in the homogeneous mass. The writer is not aware 

 that anyone has attempted to use Thomson's formula (16) or 

 (18) in numerical calculation. The feature of it just men- 

 tioned would render it difficult; but if it were possible it would 

 probably produce some improvement on the results calculated 

 by the approximate form of Gibbs' relation. To show this 

 suppose we write x for {—\/Rt) (da/dK); x will be positive 

 when there is actually a surface excess, i.e., when {dd/dK) is 

 negative. Equation (18) would then be 



P X?' X? 



The approximation would be 



- = \ -\- X. 

 P 



Clearly, since x is positive, the values of p obtained from the 

 first of these would be markedly larger than those obtained 

 from the second if x were not entirely negligible compared to 

 unity, and it is well-known that even in those experimental 

 results which show the best accord between observation and 

 calculation the tendency is for the observed concentration to be 

 above that calculated by the approximate form of Gibbs' 

 equation, which the second of the above equations most re- 

 sembles. 



It also merits attention that Thomson's equation can be 

 readily obtained by the present-day methods of statistical 

 mechanics in a very direct way. If the reader will look once 

 more at section IV of this article (Article L) under the heading 

 "Statistical Considerations" he will observe in equation (10) 

 how the concentrations in two phases are related in simple cases 

 to the work required to extract a molecule from one phase and 

 introduce it into another. Now in the present instance the 

 solution in bulk may be regarded as the second phase and the 



