EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 263 



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

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

 potentials, it will be impossible for that having the greater tension to 

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

 sidered. Hence, when p c has the value determined by equation (571), 

 and consequently <r A o + o- BO * s one value of the tension for the surface 

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

 surface cr AB should be greater than this. If cr AB = o- AC -f or 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 would make p greater than the 

 second member 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 <r AB <<r A o+<rBc wnen equation (571) is satisfied, this equation 

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

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

 change before the film of phase C, or (as we shall see in the 

 following paragraph) a lentiform mass of that phase, can be formed. 



The work which must be expended in order to form on the surface 

 between indefinitely large masses of phases A and B a lentiform mass 

 of phase C in equilibrium, may evidently be represented by the 

 formula w 



"AC ^AC T O"BC ^BC 



B , (573) 



where $ AO , $ BO denote the areas of the surfaces formed between A and 

 C, and B and C ; $ AB the diminution of the area of the surface between 

 A and B; V G the volume formed of the phase C; and F A , F B the 

 diminution of the volumes of the phases A and B. Let us now 

 suppose cr A c, OBC> O"AB> PA> PE t remain constant and the external 

 boundary of the surface between A and B to remain fixed, while p 

 increases and the surfaces of tension receive such alterations as are 

 necessary for equilibrium. It is not necessary that this should be 

 physically possible in the actual system ; we may suppose the changes 

 to take place, for the sake of argument, although involving changes 

 in the fundamental equations of the masses and surfaces considered. 

 Then, regarding W simply as an abbreviation for the second member 

 of the preceding equation, we have 



d W= cr AC dS AC + o- BO dS EG o- AB dS AE 



-p c dV c +p A dV A +p E dV B - V c dp c . (574) 



But the conditions of equilibrium require that 



o- AC AC CT BC EO cr AB 



0. (575) 



