J. W. Gihhs — Eq^iilibrmni of Heterogeneous Substances. 417 



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 suri'ounded 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 divid- 

 ing 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 tlie 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 t^, if, ni], m%, etc., is as in other cases to be 

 placed so as to make the term ^(C^ -f 6\)^(Ci +(•„) in equation (494) 

 vanish, i. e., so as to make equation (497) valid. It has been shown 

 on pages 387-389 that when thus placed it will sensibly coincide 

 with the physical surface of discontiiuiity, 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 retrard to ulobular 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 wall have any 

 natural a})plication. 



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 o" 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 ff = (y - p")r, (550) 



the single and double accents referring respectively to the interior 

 and exterior masses. If we w^ite [e], [//], [m^], [/Wg], etc. for the 



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

 steam, by the density or pressure of tlie 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 lias the temperature and potential of the steam. 



