J. W. Glbbs — Equilibrium of Heterogeneous Substances. 431 



latter surface is on the side specified by the double accents,) and that 

 the coefficient oi dt (without the negative sign) represents the super- 

 ficial density of entropy as determined by the latter dividing surface, 

 i. e., the quantity denoted by //g, ,^ on page 397. 



When there are two components, neither of which is confined to 

 the surface of discontinuity, we may regard the tension as a function 

 of the temperature and the pressures in the two homogeneous masses. 

 The values of the diflerential coefiicients of the tension with respect 

 to these variables may be represented in a simple form if w^e choose 

 such substances for the components that in the particular state con- 

 sidered each mass shall consist of a single component. This will 

 always be possible when the composition of the two masses is not 

 identical, and will evidently not affect the values of the differential 

 coefficients. We then have 



da= — //s dt — / ; d)-i^ — I ; djA^, , 

 <r^>' =r ?/v' dt -j- y' d}x^ , 

 dp"=i^,"dt^y"df.i,,, 



where the marks ^ and. ^^ are used instead of the usual , and g to indi- 

 cate the identity of the component specified with the substance of 

 the homogeneous masses specified by ' and ". Eliminating dfx^ and 

 d}.i^^ we obtain 



da = ~ (ih - -; Vy^- ^ vA dt - ^ dp' - ^ dp". (579) 



\ Y y I y r 



We may generally neglect the difference of/)' and p'\ and write 



da = - ^/s - -^ 7v' '^ W) di - (-, + -i\ dp. (580) 



The equation thus modified is strictly to be regarded as the equation 

 for a plane surfiice. It is evident that —7 and — ' represent the dis- 



y y 



tances from the surface of tension of the two surfaces of which one 



would make 1\ vanish, and the other /"^^, that — ^, + —, represents 



the distance between these two surfaces, or the diminution of vol- 

 ume due to a unit of the surface of discontinuity, and that the coeffi- 

 cient of dt (without the negative sign) represents the excess of 

 entropy in a system consisting of a unit of the surface of discon- 

 tinuity with a part of each of the adjacent masses above that 

 which the same matter would have if it existed in two homogeneous 

 masses of the same phases but without any sui-face of discontinuity. 

 Trans. Conn. Acad., Vol. III. 55 Nov., \%V,. 



