182 GUGGENHEIM art. e 



phases be in complete equilibrium or only in partial equilibrium, 

 that is, in equilibrium as regards this species but not as regards 

 all the species present. 



The general conditions that two phases, denoted respectively 

 by a single and by a double accent, shall be in complete equilib- 

 rium are the following. First, in order that the two phases 

 shall be in thermal equiUbrium the temperatures of the two 

 phases must be the same, that is, 



f ^ 



t". (1) [19] 



Second, in order that the two phases shall be in mechanical or 

 hydrostatic equilibrium the pressures of the two phases must 

 be equal, or 



P' = P". (2) [20] 



Third, in order that the two phases shall be in chemical equi- 

 librium as regards the various chemical species Si, S2, . . . Sn the 

 potential of each species must be the same in the two phases, or 



Ml = Ml , 



/ n 



M2 = M2 , 



/ // 



Mn = Mn . 



(3) [21] 



The essential feature of Gibbs' treatment of equiUbrium is that, 

 thanks to his invention of the potentials of the chemical species, 

 the conditions (3) [21] for chemical equilibrium are of a form 

 analogous to the condition (1) [19] for thermal equilibrium 

 and to the condition (2) [20] for hydrostatic equiHbrium. 



The importance and usefulness of Gibbs' method for the 

 treatment of membrane equihbria depend on the fact that, pro- 

 vided two phases are in thermal equilibrium, i.e., (1) [19] is 

 satisfied, the other equilibrium conditions, namely, (2) [20] for 

 hydrostatic equilibrium and the several equations of (3) [21] 

 for chemical equilibrium, are all independent of one another. 

 In other words, if two phases, denoted respectively by a single 

 and by a double accent, be separated by a membrane capable 



