SURFACES OF DISCONTINUITY 507 



referred to. The energy e^ associated with the dividing surface 

 is of course a function of these variables. (Actually Gibbs 

 introduces the curvatures of the element of the surface as 

 further variables, but disposes of them as of negligible impor- 

 tance, a point which we shall consider at a later stage, but 

 shall ignore for the present.) The partial differential coefficient 

 of e^ with regard to r?^ is of course the temperature of the dis- 

 continuous region, and those with regard to rrii^, mi^, etc., are the 

 chemical potentials of the various components in this region. 

 In the first few pages of this section we are provided with a proof 

 on exactly the same lines as that in Gibbs, I, 62 ei seq. that the 

 temperature and potentials in the discontinuous region are equal 

 to those in the homogeneous masses separated by this region, 

 provided of course that the usual condition is satisfied, viz., that 

 the components in the surface are actual components of the 

 homogeneous masses; if some of them are not, the usual in- 

 equalities hold. All this proceeds on familiar lines. There 

 remains the partial differential coefficient of e^ with regard to the 

 variable s; this is denoted by o-. It is clearly the analogue of 

 the partial differential coefficient of the energy of an ordinary 

 homogeneous mass with respect to its volume, i.e., the negative 

 pressure, — p, which exists in that phase. Equation [493] 

 (with the last two terms omitted for the present as explained 

 above) or equation [497] gives the formulation of the ideas just 

 outlined. The paragraphs between equations [493] and [497] 

 may well be omitted at this stage. The reader will then find 

 that the succeeding two paragraphs lead in a direct and simple 

 manner to the extremely important result expressed in equations 

 [499] or [500]. 



2. The Mechanical Significance of the Quantity Denoted by a 



If the reader pauses to reflect he will observe that in the earher 

 portion of Gibbs' treatment the quantity — p makes its appear- 

 ance strictly as the partial differential coefficient of the energy 

 with respect to the variable v. To be sure p has a mechanical 

 significance which is always more or less consciously kept before 

 us, but nevertheless in its original significance it is concerned 

 with the quantity of energy which is passed into or out of a 



