EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 259 



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. (This case is not quite identical 

 with that considered on page 104, since the system in question con- 

 tains two different phases, but the principles involved are entirely 

 the same.) 



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

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

 venient to denote the pressures of the three phases by > A , p B , p c , and 

 to regard these quantities as functions of the temperature and 

 potentials. 



If - AB = <7 AC + a- BC for values of the temperature and potentials which 

 make PAPBPC) it w ^[ not be possible to alter the temperature and 

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

 PA~PB> an( i PC>PA> f r 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 + 0"Bc> we can vary the temperature and potentials 

 so that j9 A =_p B , and p c > p&, 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 

 o'Ac+o'Bc-'O'AB per 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. 

 The stability of the system in respect to such a change must therefore 

 extend beyond the point where the pressure of C commences to be 

 greater than that of A and B. We arrive at the same result if we use 

 the expression (520) as a test of stability. Since this expression has 

 a finite positive value when the pressures of the phases are all equal, 

 the ordinary surface of discontinuity must be stable, and it must 

 require a finite change in the circumstances of the case to make it 

 become unstable.* 



*It is true that such a case as we are now considering is formally excluded in the 

 discussion referred to, which relates to a plane surface, and in which the system is 

 supposed thoroughly stable with respect to the possible formation of any different 

 homogeneous masses. Yet the reader will easily convince himself that the criterion 

 (520) is perfectly valid in this case with respect to the possible formation of a thin sheet 

 of the phase C, which, as we have seen, may be treated simply as a different kind of 

 surface of discontinuity. 



