J. W. Glhhs — ll]qi<llihriuin of Ileteroyeneous Siihutajices. 395 



Now I\ (Cj + C2) will generally be very small compared with 

 y i" — Xi'. Neglecting the former term, we have 



dff r. ^, ^ 



To integrate this equation, we may regard /'j, ;/,', y ^" as constant. 

 This will give, as an approximate value, 



a' denoting the value of ff when the surface is plane. From this it 

 appears that when the radii of curvature have any sensible magni- 

 tude, the value of o' will l)e sensil)ly the same as when the surface is 

 plane and the temperature and all the potentials except one have 

 the same values, unless the component for which the potential has 

 not the same value has very nearly the same density in the two 

 homogeneous masses, in which case, the condition under which the 

 variations take place is nearly equivalent to the condition that the 

 |»ressures shall remain equal. 



Accordingly, we cannot in general expect to determine the sixperfi- 



/ d(}\ * 

 cial density I\ from its value — ( -: — ) by measurements of super- 



ticial tensions. The case will be the same with F.^, F^, etc., and also 

 with ;/s, the superficial density of entropy. 



The quantities fgj Vs» ^u ^21 ^^^- ^''® evidently too small in general 

 to admit of direct measurement. When one of the components, 

 however, is found only at the surface of discontinuity, it may be 

 more easy to measure its superficial density than its potential. But 

 except in this case, which is of secondary interest, it will generally 

 be easy to determine G in terms of ^, /^j, //g, etc., with considerable 

 accuracy for plane surfaces, and extremely difiicult or impossible to 

 determine the fundamental equation more completely. 



Fundainental Equations for Plane Surfaces of Discontinuity. 

 An equation giving G in terms of t, //j, //g? ^tc, which will hold 

 true only so long as the surface of discontinuity is plane, may be 

 called a fundamental equation for a plane surface of discontinuity. 

 It will be interesting to see precisely what results can be obtained from 

 such an equation, especially with respect to the energy and entropy 



* The suffixed fi is used to denote that all the potentials except that occurring in 

 the denominator of the differential coefficient are to be regarded as constant. 



