EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 221 



any other (suitable) rule, the energy of the mass on the other side 

 must be less by the same amount when determined by the first rule 

 than when determined by the second, since the discontinuity relative 

 to the second mass is equal but opposite in character to the discon- 

 tinuity relative to the first. 



If the entropy of the mass which occupies any one of the spaces 

 considered is not in the nature of things determined without refer- 

 ence to the surrounding masses, we may suppose a similar method 

 to be applied to the estimation of entropy. 



With this understanding, let us return to the consideration of the 

 equilibrium of the three masses M, M', and M". We shall suppose 

 that there are no limitations to the possible variations of the system 

 due to any want of perfect mobility of the components by means of 

 which we express the composition of the masses, and that these com- 

 ponents are independent, i.e., that no one of them can be formed out 

 of the others. ^ 



With regard to the mass M, which includes the surface of discon- 

 tinuity, it is necessary for its internal equilibrium that when its 

 boundaries are considered constant, and when we consider only 

 reversible variations (i.e., those of which the opposite are also 

 possible), the variation of its energy should vanish with the variations 

 of its entropy and of the quantities of its various components. 

 For changes within this mass will not affect the energy or the entropy 

 of the surrounding masses (when these quantities are estimated on 

 the principle which we have adopted), and it may therefore be 

 treated as an isolated system. For fixed boundaries of the mass M, 

 and for reversible variations, we may therefore write 



Se^A^ri+A^m^+A^mz+Qtc., (476) 



where A Q , A lt A 2 , etc., are quantities determined by the initial 

 (unvaried) condition of the system. It is evident that A is the 

 temperature of the lamelliform mass to which the equation relates, 

 or the temperature at the surface of discontinuity. By comparison 

 of this equation with (12) it will be seen that the definition of A 19 

 A 2 , etc., is entirely analogous to that of the potentials in homo- 

 geneous masses, although the mass to which the former quantities 

 relate is not homogeneous, while in our previous definition of 

 potentials, only homogeneous masses were considered. By a natural 

 extension of the term potential, we may call the quantities A l ,A 2 , etc., 

 the potentials at the surface of discontinuity. This designation will 

 be farther justified by the fact, which will appear hereafter, that the 

 value of these quantities is independent of the thickness of the lamina 

 (M) to which they relate. If we employ our ordinary symbols for 

 temperature and potentials, we may write 



(477) 



