628 RICE ART. L 



that of a system in which the second phase occupies the whole 

 space, is 



[e] - t[r]] - ni[mi] - )U2[W2] - . . . , 



which is denoted by W (Equation [552]). This is a function of 

 the temperature and potentials and is independent of any 

 selected situation for the dividing surface; so we write it W{t, ju). 

 Now, as Gibbs himself notes at the outset of this subsection, 

 the method of selecting the surface of tension in former cases 

 is hardly applicable here, and it is not at all clear just how 

 he proposes to select it since his remarks concerning the 

 Ci8ci + C25C2 terms do not appear very convincing. As he says, 

 the |(Ci — C2) 5(ci — C2) term does not concern us for spheri- 

 cal surfaces. But what of the ^(Ci + C2) 5(ci + C2) term? 

 However, on closer investigation it becomes clear what he 

 does. In the earlier parts he showed that the special choice 

 which got rid of the Ci8ci + €2602 terms placed the dividing 

 surface so that it satisfied the condition 



p' - v" = o-(ci + C2), 



so here he takes the dividing spherical surface to have a radius 

 given by 



2 a{t, ix) 



r = 



v'{t, n) - p"{t, m) 



This is tantamount to assuming that the ideal system which 

 replaces the heterogenous globule and exterior mass, supposed 

 to be in equilibrium, is a homogeneous sphere of the first phase, 

 an ideal surface with the tension ait, ju) and the exterior mass of 

 the second phase, which is in equilibrium mechanically, as well as 

 with regard to temperature and potentials. The radius of this 

 surface then becomes a definite function of the temperature and 

 potentials; for as is shown on page 254 



as = e^ — tt]^ — nirrii^ — ^2^2^ — . . . 



= TF + v'{v' - V"), 



