EQUILIBEIUM OF HETEROGENEOUS SUBSTANCES. 253 



Again, the surfaces of discontinuity have been regarded as separating 

 homogeneous masses. But we may easily conceive that a globular 

 mass (surrounded by a large homogeneous mass of different nature) 

 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. This, however, will cause no difficulty, if 

 we regard the phase of the interior mass as determined by the same 

 relations to the exterior mass as in other cases. Beside the phase of 

 the exterior mass, there will always be another phase having the 

 same temperature and potentials, but of the general nature of the 

 small globule which is surrounded by that mass and in equilibrium 

 with it. This phase is completely determined by the system con- 

 sidered, and in general entirely stable and perfectly capable of realiza- 

 tion in mass, although not such that the exterior mass could exist 

 in contact with it at a plane surface. This is the phase which we 

 are to attribute to the mass which we conceive as existing within the 

 dividing surface.* 



With this understanding with regard to the phase of the fictitious 

 interior mass, there will be no ambiguity in the meaning of any of 

 the symbols which we have employed, when applied to cases in which 

 the surface of discontinuity is spherical, however small the radius 

 may be. Nor will the demonstration of the general theorems require 

 any material modification. The dividing surface which determines 

 the value of e 9 , if, mf, mf , etc. is as in other cases to be placed so as 

 to make the term K^i + ^2)^( c i+ c 2) i n equation (494) vanish, i.e., so 

 as to make equation (497) valid. It has been shown on pages 225-227 

 that when thus placed it will sensibly coincide with the physical 

 surface of discontinuity, when this consists of a non-homogeneous 

 film separating homogeneous masses, and having radii of curvature 

 which are large compared with its thickness. But in regard to 

 globular masses too small for this theorem to have any application, it 

 will be worth while to examine how far we may be certain that the 

 radius of the dividing surface will have a real and positive value, 

 since it is only then that our method will have any natural application. 



The value of the radius of the dividing surface, supposed spherical, 

 of any globule in equilibrium with a surrounding homogeneous fluid 

 may be most easily obtained by eliminating a- from equations (500) 

 and (502), which have been derived from (497), and contain the radius 

 implicitly. If we write r for this radius, equation (500) may be written 



2(r = (p'-p")r, (550) 



* For example, in applying our formulae to a microscopic globule of water in steam, 

 by the density or pressure of the interior mass we should understand, not the actual 

 density or pressure at the center of the globule, but the density of liquid water (in 

 large quantities) which has the temperature and potential of the steam. 



