J. W. Gihhs — Equilihrium of Heterogeneous Substances. 423 



limit is reached at which the interior of the film ceases to have the 

 properties of matter in mass. Now if Cac+^bc is greater than (Tab, 

 the tension of the ordinary surface between A and B, such a film will 

 be at least practically unstable. (See page 403.) We cannot sup- 

 pose that o'ab^o'ac+ ^bc, foi' this would make the ordinary surface 

 between A and B unstable and difficult to realize. If (Tab=<5'ac+ o'bc, 

 we may assume, in general, that this relation is not accidental, and 

 that the ordinary surface of contact for A and B is of the kind which 

 we have described. 



Let us now suppose the phases A and B to vary, so as still to 

 satisfy the conditions of equilibrium at plane contact, but so that the 

 pressure of the phase C determined by the temperature and poten- 

 tials of A and B shall become less than the pressure of A and B. A 

 system consisting of the phases A and B will be entirely stable with 

 respect to the formation of any phase like C. (The case is not quite 

 identical with that considered on page 161, since the system in ques- 

 tion contains two dififerent phases, but the principles involved are 

 entirely the same.) 



With resjject to variations of the phases A and B in the opposite 

 direction we must consider two cases separately. It will be conven- 

 ient to denote the pressures of the three phases by p^^^ /)b, p^^ and to 

 regard these quantities as functions of the temperature and potentials. 



If o'ab=o'ac+<5'bc for values of the temperature and potentials which 

 make pi^z=2H'=^pc, it will not be possible to alter the temperature and 

 potentials at the surface of contact of the phases A and B so that 

 Pa=2H, aiit^ Pc^Pa, foi" the relation of the temperature and potentials 

 necessary for the equality of the three pressures will be preserved by 

 the increase of the mass of the phase C. Such variations of the phases 

 A and B might be brought about in separate masses, but if these 

 were brought into contact, there would be an immediate formation 

 of a mass of the phase C, with reduction of the phases of the adjacent 

 masses to such as satisfy the conditions of equilibrium with that 

 phase. 



But if o"ab<^0'ac+ Cbc, we can vary the temperature and potentials 

 so that 2^A=2'ii, and Pc^Pa, and it will not be possible for a sheet of 

 the phase of C to form immediately^ i. e., while the pressure of C is 

 sensibly equal to that of A and B ; for mechanical work equal to 

 <5'acH-<5'bc— o'ab pel' unit of surface might be obtained by bringing the 

 system into its original condition, and therefore produced without 

 any external expenditure, unless it be that of heat at the temperature 

 of the system, which is evidently incapable of producing the work. 



Trans. Conn. Acad., Yol. III. 54 Nov., 1877. 



