946 Dr. S. A. Shorter : Contribution to the 



This notation is convenient for many reasons, the chief of 

 which is that the ordinary differential notation is ambiguous 

 in cases where there is' a relation between the variables. 

 Thus if II is the vapour pressure of a solution of concen- 

 trations 5 X and s 2 at a temperature 0, the symbol 



^A ( Sl) s 2 , n, 0) 



may mean either the quantity 



r^-/iOi, s 2 ,p, 9)\ , 



which, according to the above system of notation, is denoted 

 by Sh (si, 5 2 , II, 6) , or the quantity 



&„(*!, *„ n, ^) + p x (^^n, 0)|3. 



The quantities Pi are connected with the specific volume 

 v ( 5l , s 2 , p, 0) of the mixture by the equations 



• ■ • (21) 

 ? 1 (s 1 ,s 2 ,p } 0)=v(s 1 ,s 2 ,p,0) + (l + s 1 + s 2 )^. . . {22} 



P 2 (s 1 ,s 2 ,p,6)=v(s 1 ,s 2 ,p,0)+(l + s 1 + s 2) ^. . . (23) 



It is easily proved that Pi is the increase of volume of a 

 large mass of the mixture when unit mass of C* is added 

 to it. 



3. The Variation of the Chemical Potentials with 

 the Composition of the Mixture. 



In the case of a binary mixture the further addition of 

 one of the components raises the chemical poteutial of that 

 component and lowers that of the other. From inequalities 

 (14), (15), and (16) we see that in the case of a ternary 

 mixture the further addition of one of the components raises 

 the chemical potential of that component. It does not follow 

 from this, however, that this addition necessarily lowers the 

 chemical potential of the other components. 



AVe will examine this point a little more closely. Suppose 



