THERMODYNAMIC AL SYSTEM OF GIBBS 119 



i.e., 



•> 



(jT^^) = ^'- (115) [214] 



\d log W2/t. p. m, 



The integral of this equation may be put in the form 



Bm-2 



M2 = A'log ' (116) [215] 



mi 



where B, like A', is independent of W2 and Wi. This equation 

 holds for such small values of rrii/mi that d\L\ldmi in (111) has 

 the same value as in the limiting case when m2 = 0. In such 

 cases mi/y may be regarded as constant and we may write 



/i2 = A' log ' 



or 



M2 = C + A' log T/iaA, (117) 



where 



Cwi/y = 5, and C = A' log C. 



Suppose that the independently variable components of a 

 homogeneous body are Sa,--. Sg and Sh, and that the quantity 

 of Sk is very small compared with the quantities of Sa,- ■ . S, 

 and is incapable of negative values. Then, by an extension of 

 the argument, it can be shown that 



a 



M. = A,' log ^\ (118) 



but Ah and Ch may be fimctions not only of the temperature 

 and pressure but also of the composition of the "solvent" 

 (composed oi Sa,. . .Sg) in which Sh is dissolved. If another 

 component Si is also present in very small amount, it is reason- 

 able to assume that the value oi nh and therefore those of Ah and 

 Ch are nearly the same as if it were absent. Thus the potentials 

 of components Sh,. . • Sk, the quantities of which are very small 



