THERMODYNAMICAL SYSTEM OF GIBBS 129 



in this volume. We shall only attempt to give in a concise form 

 the significant extensions of Gibbs' method, with examples 

 from solutions of non-electrolytes. 



The exact treatment of cases of equilibrium involving actual 

 solutions is greatly facilitated by the use of some additional 

 quantities, which we must first introduce. Consider a solution 

 containing Wi, . . . 7n„ grams of the independently variable com- 

 ponents /Si, . . . Sn, and let e, tj and v be the values of its energy, 

 entropy and volume. 

 Then, differentiating the equation 



^ = e - tr] + pv 

 with respect to mi, we have 



\dmi/t, p. m^, etc. \dmi/t. p. m., etc. \dmi/t, p, 



\dini/t. p. 



m^, etc. 



+ P[ 



mj, etc. 



or 



where 



m = h - tm + pvi, (151) 



.. = (r-) . (152) 



\ami/t, p, mj. etc. 



\dmi)t, p. ' 



"ni - \ j^ ] » 



WTj* etc. 



and 



Vi = 



\aWi/ I, p, mj, etc. 



(154) 



which represent the ratios of the increments of the energy, 

 entropy and volume of the solution to the increase of mi, when 

 the temperature, pressure and quantities of Si,. . . Sn remain 

 constant, are called the partial values of the energy, entropy and 



