268 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES, 



where 



A=vi"y*-yi'y*"> (582) 



T-l' T1 



//S -L 1 -L 2 



n\ y\ y* > (583) 



ft // // 



nv y\ 72 



^=r i (y 2 // -y 2 / ) + r 2 (y/-y 1 l. (584) 



It will be observed that A vanishes when the composition of the two 

 homogeneous masses is identical, while B and C do not, in general, 

 and that the value of A is negative or positive according as the mass 

 specified by ' contains the component specified by x in a greater or 

 less proportion than the other mass. Hence, the values both of 



(-T:} and of (-T-J become infinite when the difference in the com- 

 position of the masses vanishes, and change sign when the greater 

 proportion of a component passes from one mass to the other. This 

 might be inferred from the statements on page 99 respecting co- 

 existent phases which are identical in composition, from which it 

 appears that when two coexistent phases have nearly the same 

 composition, a small variation of the temperature or pressure of the 

 coexistent phases will cause a relatively very great variation in 

 the composition of the phases. The same relations are indicated by 

 the graphical method represented in figure 6 on page 125. 



With regard to gas-mixtures which conform to Dalton's law, we 

 shall only consider the fundamental equation for plane surfaces, and 

 shall suppose that there is not more than one component in the liquid 

 which does not appear in the gas-mixture. We have already seen 

 that in limiting the fundamental equation to plane surfaces we can 

 get rid of one potential by choosing such a dividing surface that the 

 superficial density of one of the components vanishes. Let this be 

 done with respect to the component peculiar to the liquid, if such 

 there is; if there is no such component, let it be done with respect 

 to one of the gaseous components. Let the remaining potentials be 

 eliminated by means of the fundamental equations of the simple gases. 

 We may thus obtain an equation between the superficial tension, the 

 temperature, and the several pressures of the simple gases in the 

 gas-mixture or all but one of these pressures. Now, if we eliminate 

 dfjL 2 , dfjL 3 , etc. from the equations 



dor = t] S (i)dt r 2(1) cfyz 2 r 3(1) cZ//3 etc., 



! = J/V2<^ + 72< 



etc., 



where the suffix 1 relates to the component of which the surface- 

 density has been made to vanish, and y 2 , y 3 , etc. denote the densities 



