EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 233 



not the saine 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 

 pressures shall remain equal. 



Accordingly, we cannot in general expect to determine the 



/d<r\ * 

 superficial density I\ from its value ( -j ) by measurements of 



**thf*, /* 



superficial tensions. The case will be the same with F 2 , r s , etc., and 



also with TJ S , the superficial density of entropy. 



The quantities e s , */ s , I\, F 2 , etc., are 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 <r in terms of t, fa, fa, etc., with considerable 

 accuracy for plane surfaces, and extremely difficult or impossible to 

 determine the fundamental equation more completely. 



Fundamental Equations for Plane Surfaces of Discontinuity 



between Fluid Masses. 



An equation giving <r in terms of t, fa, fa, etc., 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 and the quantities of the component substances in the 

 vicinity of the surface of discontinuity. 



These results can be exhibited in a more simple form, if we deviate 

 to a certain extent from the method which we have been following. 

 The particular position adopted for the dividing surface (which 

 determines the superficial densities) was chosen in order to make the 

 term ^(G l -{-C 2 )8(c 1 -\-c 2 ) in (494) vanish. But when the curvature 

 of the surface is not supposed to vary, such a position of the dividing 

 surface is not necessary for the simplification of the formula. It is 

 evident that equation (501) will hold true for plane surfaces (supposed 

 to remain such) without reference to the position of the dividing 

 surface, except that it shall be parallel to the surface of discontinuity. 

 We are therefore at liberty to choose such a position for the dividing 

 surface as may for any purpose be convenient. 



None of the equations (502)-(513), which are either derived from 

 (501), or serve to define new symbols, will be affected by such a 



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

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



