626 RICE 



ART. L 



stance we have two phases of the same components whose pres- 

 sures are the functions p'(t, mi, M2, . . .) and p"(t, ni, m, . . .) of 

 temperature and potentials (written p'(t, ju) and p"(t, ju) for 

 brevity). A surface of discontinuity between two such phases 

 would have a surface tension which is the function a{t, mi, M2 . ■ . )> 

 or (T{t, ju), of the same temperature and potentials. For 

 the purposes of the argument we are assuming that these 

 functional forms are known. Now if the surface were plane, 

 the condition would not be one of equilibrium; the phase for 

 which the pressure function has the larger value at given values 

 of t, Hi, H2, ... would grow at the expense of the other. Actu- 

 ally, if the phase of greater pressure, say the single-accent phase, 

 were confined in a sphere whose radius is equal to 



2 (Tjt, m) 

 p'(t, m) - p"it, /x) 



there would be equilibrium when surrounded by the phase of 

 smaller pressure. However, as we know, if the second mass is 

 indefinitely extended the equilibrium is unstable (provided 

 there are no components in the internal phase which are not in 

 the external), and the first mass if just a little larger will tend to 

 increase indefinitely; while one a little smaller would tend to 

 decrease, leaving the field to the second mass. So under cer- 

 tain circumstances the mass of smaller pressure, if indefinitely 

 extended around the mass of larger pressure would be the one to 

 grow, thus somewhat qualifying the conclusion from the earlier 

 part of Gibbs' discussion. However, since the possibility of 

 this qualification depends on the smallness of the internal mass 

 of the higher pressure phase, it becomes necessary to take into 

 account the case where this mass "may be so small that no part 

 of it will be homogeneous, and that even at its center the matter 

 cannot be regarded as having any phase of matter in mass." 

 Pages 253-257 of Gibbs treat this problem. The reader is to 

 keep in mind that the phase which might be conceived to grow 

 out of this non-homogeneous nucleus under favorable circum- 

 stances is supposed to be known, with its fundamental equa- 

 tions, as well as, of course, the second phase inside which it may 

 grow; i.e., p'(t, /x), p"{t, /x) and ait, m) are to be regarded as 



