432 J. W. Gibhs — Equilibrium, of Heterogeneous ^hstauces. 



(A mass thus existing without any surface of discontinuity must of 

 course be entirely surrounded by matter of the same phase.)* 



The form in which the values of (-^) and (-^— ) are ffiven in 



\dt)i) \dp)t ^ 



equation (580) is adapted to give a clear idea of the relations of 



these qiiantities to the particular state of the system for which they 



are to be determined, but not to show how they vary with the state 



of the system. For this purpose it will be convenient to have the 



values of these diiferential coefficients expressed with reference to 



ordinary components. Let these be specified as usual by j and ^. 



If we eliminate r///, and d^^ from the equations 



— da ■=. 7/s dt -\- I \ (?//, -+- /'o dfi^, 

 dp = //v' dt + r^' diA^ + y.^' dfi^, 

 dp = jjy" dt + ri" c?/<i + r/, d/.i2, 



* If we set 



and in like manner 



E. = e, - -^ e/ - ~ e". (c) 



7' 7 " ^ ' 



we may easily obtain, by means of equations (93) and (507), 



K = tB, + G~pV. (d) 



Now equation (580) may be written 



da= -H.,dt + Vdp. (e) 



Differentiating (d), and comparing the result with (e), we obtain 



dE,= tdRs~pdV. (/) 



The quantities Es and Hj might be called the superficial densities of energy and 

 entropy quite as properly as those which we denote by e^ and r/^. In fact, wheu the 

 composition of both of the homogeneous masses is invariable, the quantities Es and 

 H are much more simple in their definition than e^ and ??s, and would probably be 

 more naturally suggested by the terms superficial density of energy and of entropy. It 

 would also be natural in this case to regard the quajitities of the homogeneous masses 

 as determined by the total quantities of matter, and not by the surface of tension or 

 any other dividing surface. But such a nomenclature and method could not readily 

 be extended so as to treat cases of more than two components witli entire generality. 



In the treatment of surfaces of discontinuity in this paper, the definitions and 

 nomenclature whicli have been adopted will be strictly adhered to. The object of 

 this note is to suggest to the reader how a different method might be used in some 

 cases with advantage, and to show the precise relations between the quantities which 

 are used in this paper and otliers wliich might be confounded with them, and which 

 may be made more prominent wlien tlie subject is treated differently. 



