J. W. Gibbs — Equilibrium of Heterogeneous Substances. 427 



Essentially the same principles applj' to the more general problem 

 in which the phases A anrl B have modeiately diflferent pressures, so 

 that their surfaces of contact must be curved, but the radii of curva- 

 ture have a sensible magnitude. 



In order that a thin film of the phase C may be in equilibrium 

 between masses of the phases A and B, the following equations must 

 be satisfied — 



<?Ac(Cl + C2)=Pk- Pc, 

 (>Bc(Ci + ^2) = Pc ~ Pb, 



where c, and c^ denote the principal curvatures of the film, the 

 centers of positive curvature lying in the mass having the phase A. 

 Eliminating Ci-[-C2, we have 



O'bc (Pa ~ Pc) = O'ac (Pc - Pb), 



/'c=^i^±^'A (5?,) 



It is evident that if pc has a value greater than that determined by 

 this equation, such a film will develop into a larger mass; if jOc has a 

 less value, such a film will tend to diminish. Hence, when 



Pc< ff~^ff ' ^^^^^ 



l^BC T^ "AC 



the phases A and B have a stable surface of contact. 



Again, if more than one kind of surface of discontinuity is possible 

 between A and B, for any given values of the temperature and poten- 

 tials, it will be impossible for that having the greater tension to dis- 

 place the other, at the temperature and with the potentials con- 

 sidered. Hence, when p^ has the value determined by equation 

 (571), and consequently G'ac-\-<^bc is one value of the tension for the 

 surface between A and B, it is impossible that the ordinary tension 

 of the surface o'ab should be greater than this. If a'AB=<5'AcH-(''Bc? 

 when equation (571) is satisfied, we may presume that a thin film of 

 the phase C actually exists at the surface between A and B, and that 

 a variation of the phases such as woidd make p^ greater than the 

 second number of (571) cannot be brought about at that surface, as 

 it would be prevented by the formation of a larger mass of the phase 

 C. But if o'ab<0'ac+o'8c when equation (571) is satisfied, this equa- 

 tion does not mark the limit of the stability of the surface between 

 A and B, for the temperature or potentials must receive a finite 



