266 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



r 



evident that , T , represents the distance from the surface of 



y-y 



tension to a dividing surface located so as to make the superficial 

 density of the single component vanish (being positive, when the 

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

 the coefficient of 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 t] 8(l) on page 235. 



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 differential coefficients of the tension with respect 

 to these variables may be represented in a simple form if we 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 



dp' = 77 v ' dt + y dp, , 



where the marks , and u are used instead of the usual l and 2 to indi- 

 cate the identity of the component specified with the substance of 

 the homogeneous masses specified by ' and ". Eliminating dp, and 



dfji a we obtain 



/ T 1 T \ T 1 T 



7 / J- i r -*- // ff\ 7j -*- / 7 / * - 7 /K*7C\\ 



dcr = { rjo ,t]y "i *7v ) dt , -, dp ", dp . (t> i v) 



\ y y / y y 



We may generally neglect the difference of p f and p", and write 



'L /+ Lt\d p . (580) 



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



r r 



for a plane surface. It is evident that > and -% represent the dis- 



y y 



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



r r 



would make IV vanish, and the other r , that ; + ", represents 



y y 



the distance between these two surfaces, or the diminution of volume 

 due to a unit of the surface of discontinuity, and that the coefficient 

 of dt (without the negative sign) represents the excess of entropy in 

 a system consisting of a unit of the surface of discontinuity 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 





