264 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



Hence ' dW=-V dp . (576) 



Now it is evident that V G will diminish as p increases. Let us 

 integrate the last equation supposing p to increase from its original 

 value until V c vanishes. This will give 



W " - W = a negative quantity, (577) 



where W and W" denote the initial and final values of W. But 

 W" = 0. Hence W is positive. But this is the value of W in the 

 original system containing the lentiform mass, and expresses the 

 work necessary to form the mass between the phases A and B. It 

 is therefore impossible that such a mass should form on a surface 

 between these phases. We must however observe the same limitation 

 as in the less general case already discussed, that Pcp, PQPR 

 must not be so great that the dimensions of the lentiform mass are 

 of insensible magnitude. It may also be observed that the value of 

 these differences may be so small that there will not be room on the 

 surface between the masses of phases A and B for a mass of phase C 

 sufficiently large for equilibrium. In this case we may consider a 

 mass of phase C which is in equilibrium upon the surface between A 

 and B in virtue of a constraint applied to the line in which the three 

 surfaces of discontinuity intersect, which will not allow this line to 

 become longer, although not preventing it from becoming shorter. 

 We may prove that the value of W is positive by such an integration 

 as we have used before. 



Substitution of Pressures for Potentials in Fundamental Equations 



for Surfaces. 



The fundamental equation of a surface which gives the value of 

 the tension in terms of the temperature and potentials seems best 

 adapted to the purposes of theoretical discussion, especially when the 

 number of components is large or undetermined. But the experi- 

 mental determination of the fundamental equations, or the application 

 of any result indicated by theory to actual cases, will be facilitated 

 by the use of other quantities in place of the potentials, which shall 

 be capable of more direct measurement, and of which the numerical 

 expression (when the necessary measurements have been made) shall 

 depend upon less complex considerations. The numerical value of a 

 potential depends not only upon the system of units employed, but 

 also upon the arbitrary constants involved in the definition of the 

 energy and entropy of the substance to which the potential relates, 

 or, it may be, of the elementary substances of which that substance 

 is formed. (See page 96.) This fact and the want of means of 

 direct measurement may give a certain vagueness to the idea of the 



