Manchester Memoirs, Vol. Hi. (1908), No. 10. 51 



perature, any slight reactive change that can occur in the 

 phase must leave A sensibly unaltered, provided equili- 

 brium has arrived. Thus the thermodynamic potentials 

 /ij, ^,, ^,„,... 



in the phase must satisfy a number of relations indicating 

 the equilibrium of each possible partial reaction that can 

 occur in it, e.g., as there is a reaction possible of type 



we must have 



/ii + ^, = ^1, . 



The thermodynamic potentials of all compound substances 

 in the phase are thus found in terms of those of the 

 simple (or other) independent constituents 



1)1^, w,„ 1)1,. ; 



that is, the system will settle down to an equilibrium in 

 which they have the values thus determined. 



If two phases coexist in contact, jUj, /u„, ju,., must 



moreover have the same values in both of them. 



If P phases can coexist, there are' thus r{P - i) 

 conditions to be satisfied : and each phase has a char- 

 acteristic equation of state connecting in, v, and the tem- 

 perature T, — thus making up in all P conditions. Now 

 there are independent variables rP in number, together 

 with T, and the total volume v, — the portions of the 

 volume occupied by the various phases being determined 

 by their characteristic equations. The system will be 

 wholly determined if P = r+2. 



This is, in fact, Willard Gibbs' theory limiting the 

 number of phases that can coexist in given material, and 

 conversely. The thermodynamic potentials that are here 

 involved must be functions of the velocities of interaction 

 of the previous analysis. But are they always consistent 

 with the previous statistical view, without restriction? 



