./. W. Gibbs — Equilibrium of Heterogeneous Substances. 223 



The properties of an ideal gas-mixture (according to the definition 

 which we have assumed) when in equilibrium with liquids or solids 

 have been developed at length, because it is only in respect to these 

 properties that there is any variation from the properties usually 

 attributed to perfect gases. As the pressure of a gas saturated with 

 vaporis usually given as a little less than the sum of the pressure of the 

 gas calculated from its density and that of saturated vapor in a space 

 otherwise empty, while oxir formulae would make it a little more, when 

 the gas is insoluble, it would appear that in this respect our formulae 

 are less accurate than the rule which would make the pressure of the 

 gas saturated with vapor equal to the sum of the two pressures 

 mentioned. Yet the reader will observe that the magnitude of the 

 quantities concerned is not such that any stress can be laid upon 

 this circumstance. 



It will also be observed that the statement of Dalton's law which we 

 have adopted, while it serves to complete the theory of gas-mixtui-es 

 (with respect to a certain class of properties), asserts nothing 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 

 aS'j denote the common component of the gaseous and liquid or solid 

 masses, and /Sg 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 ^'2 receive the increment dm^., its volume and the 

 quantity which it contains of the other component, as well as the 

 temperature, remaining constant. The potential for S^ in the gaseous 

 mass will receive the increment 



\ani2l t, V, m 

 and the pressure will receive the increment 



\dm. 



I dnic 



[dm 2 ft, V, m 



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

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



\ dpJt,m \dmjt,j>, 



