J. W. Gibhs — Equilibrium of Heterogeneous Sahntances. 433 



we obtain 



do- = -. dt ^ -^ dp, (581) 



where 



A = r,"r,'-r,'r,% (582) 



B= ;/v' ri' Vz , (583) 



c=i\ ir," - r,') + n (r/- r.")- (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 ^ in a greater or 

 less }»roportion than the other mass. Hence, the values both of 



(-^r I and of ( -r- \ become infinite when the diiference in the com- 

 dtjp \d2)/t 



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 155 respecting coex- 

 istent 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 184. 



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

 shall only consider the fuiidamental 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 elim- 

 inated 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 

 djU2, d/x^, etc. from the equations 



