J. W. Gihhs—Eqvilihrinm of Heterogeneous Substances. 487 



Q=-t?^. W=-p^. (596) 



where A, i?, and C represent the expressions mdicated by (582)- 

 (584). It will be observed that the values of Q and TFare in general 

 infinite for the surface of discontinuity between coexistent phases 

 which differ infinitesimally in composition, and change sign with 

 the quantity A. When the phases are absolutely identical in 

 composition, it is not in general possible to counteract the effect of 

 extension of the surface of discontinuity by any supply of heat. For 

 the matter at the surface will not in general have the same composi- 

 tion as the homogeneous masses, and the matter required for the 

 increased surface cannot be obtained from these masses without 

 altering their phase. The infinite values of Q and W are explained 

 by the fact that when the phases are nearly identical in composition, 

 the extension of the surface of discontinuity is accompanied by the 

 vaporization or condensation of a very large mass, according as the 

 liquid or the vapor is the richer in that component which is necessary 

 for the formation of the surface of discontinuity. 



If, instead of considering the amount of heat necessary to keep the 

 phases from altering while the surface of discontinuity is extended, 

 we consider the variation of temperature caused by the extension of 

 the surface while the pressures remain constant, it appears that this 

 variation of temperature changes sign with y i"y2' ~yi'y2'\ ^^^ 

 vanishes with this quantity, i. e., vanishes when the composition of 

 the phases becomes the same. This may be inferred from the state- 

 ments on page 155, or from a consideration of the figure on page 184, 

 When the composition of the homogeneous masses is initially abso- 

 lutely identical, the effect on the temperature of a finite extension or 

 contraction of the surface of discontinuity will be the same, — either 

 of the two will lower or raise the temperature according as the tem- 

 pei-ature is a maximum or minimum for constant pressure. 



The effect of the extension of a surface of discontinuity which is 

 most easily verified by experiment is the effect upon the tension 

 before complete equilibrium has been reestablished throughout the 

 adjacent masses. A fresh surface between coexistent phases may be 

 regarded in this connection as an extreme case of a recently extended 

 surface. When sufficient time has elapsed after the extension of a 

 surface originally in equilibrium between coexistent phases, the 

 superficial tension will evidently have sensibly its original value, 

 unless there are substances at the surface which are either not found 



