162 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



with reference to any solid or liquid bodies. But the common rule 

 that the density of a gas necessary for equilibrium with a solid or 

 liquid is not altered by the presence of a different gas which is not 

 absorbed by the solid or liquid, if construed strictly, will involve 

 consequences in regard to solids and liquids which are entirely 

 inadmissible. To show this, we will assume, the correctness of the 

 rule mentioned. Let 8 l denote the common component of the gaseous 

 and liquid or solid masses, and $ 2 the insoluble gas, and let quantities 

 relating to the gaseous mass be distinguished when necessary by the 

 index (G), and those relating to the liquid or solid by the index (L). 

 Now while the gas is in equilibrium with the liquid or solid, let 

 the quantity which it contains of 8 2 receive the increment dm 2 , its 

 volume and the quantity which it contains of the other component, 

 as well as the temperature, remaining constant. The potential for S 1 

 in the gaseous mass will receive the increment 



) ,7 

 dm 9 



v ,m 

 and the pressure will receive the increment 



( d P Y G) A 

 *- dm. 



Now the liquid or solid remaining in equilibrium with the gas must 

 experience the same variations in the values of // x and p. But by (272) 



= 

 t>m ~ \drn t ,p,m 



\dm 2t)V , m 



It will be observed that the first member of this equation relates 

 solely to the liquid or solid, and the second member solely to the 

 gas. Now we may suppose the same gaseous mass to be capable of 

 equilibrium with several different liquids or solids, and the first 

 member of this equation must therefore have the same value for all 

 such liquids or solids ; which is quite inadmissible. In the simplest 

 case, in which the liquid or solid is identical in substance with the 

 vapor which it yields, it is evident that the expression in question 

 denotes the reciprocal of the density of the solid or liquid. Hence, 

 when the gas is in equilibrium with one of its components both in the 

 solid and liquid states (as when a moist gas is in equilibrium with 

 ice and water), it would be necessary that the solid and liquid should 

 have the same density. 



