SURFACES OF DISCONTINUITY 529 



may help to visualize the situation; nevertheless it cannot be 

 too strongly emphasized here in view of the references later to 

 experimental work that e^, rj^, nii^, etc. do not refer to the actual 

 quantities of energy, entropy, etc. in the discontinuous region, 

 but to the excesses of these over those quantities which would be 

 present under the arrangement postulated in the text with ref- 

 erence to the surface S. The actual quantities present are of 

 course precisely determined by the physical circumstances of 

 the system; the quantities e^, rj^, mf, etc. are, however, partly 

 determined by the position chosen for the surface S. (This is 

 a point more fully elaborated later by Gibbs on page 234.) 

 That being so, there is something arbitrary about their values 

 unless we can select a position for S by means of some definite 

 physical criterion. Such a criterion Gibbs suggests and deals 

 with in pages 225-229. He calls this special position the 

 surface of tension. 



11. An Amplification of Gihhs' Treatment 



The criterion is based on the formal development of the 

 fundamental differential equation for the dividing surface 

 regarded as if it were a homogeneous phase of the whole system. 

 As usual the energy e^ of the portion 5 of the surface is regarded 

 as a function of the variables, rj^, mi^, m2^, etc. Among these 

 variables must of course be included the area s of s; but in 

 addition there exist two other geometric quantities; these 

 measure the curvature of s (regarded as sufficiently small to 

 be of uniform curvature throughout), viz., the principal curva- 

 tures Ci and C2. It is a possibility that a variation of the 

 curvature of s, which would obviously involve an alteration in 

 form of the actual region of discontinuity, would cause a change 

 in the value of e^ and in consequence we must regard e« as 

 dependent to some extent on ci and C2. The partial differential 

 coefficients de^/dci and de^/dCi are denoted by Ci and C2. 

 Now we know that e^ is dependent in value on the position which 

 we assign to s; also it appears that the values of the differential 

 coefficients just mentioned depend to some extent on the posi- 

 tion and form of s. Gibbs chooses that position of s, which 



