EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 159 



in equilibrium, and denote the densities of one of its components at 

 two different points by y l and y/, we shall have by (275) and (234) 



Ml -Ml' ff(h'-h) 



-0=e i =e i< . (284) 



7i 



From this equation, in which we may regard the quantities distin- 

 guished by accents as constant, it appears that the relation between 

 the density of any one of the components and the height is not 

 affected by the presence of the other components. 



The work obtained or expended in any reversible process of com- 

 bination or separation of ideal gas-mixtures at constant temperature, 

 or when the temperatures of the initial and final gas-masses and of the 

 only external source of heat or cold which is used are all the same, 

 will be found by taking the difference of the sums of the values of \{r 

 for the initial, and for the final gas-masses. (See pages 89, 90.) It 

 is evident from the form of equation (279) that this work is equal to 

 the sum of the quantities of work which would be obtained or 

 expended in producing in each different component existing separately 

 the same changes of density which that component experiences in the 

 actual process for which the work is sought.* 



We will now return to the consideration of the equilibrium of a 

 liquid with the gas which it emits as affected by the presence of 

 different gases, when the gaseous mass in contact with the liquid may 

 be regarded as an ideal gas-mixture. 



It may first be observed, that the density of the gas which is 

 emitted by the liquid will not be affected by the presence of other 

 gases which are not absorbed by the liquid, when the liquid is pro- 

 tected in any way from the pressure due to these additional gases. 

 This may be accomplished by separating the liquid and gaseous 

 masses by a diaphragm which is permeable to the liquid. It will 

 then be easy to maintain the liquid at any constant pressure which is 

 not greater than that in the gas. The potential in the liquid for the 

 substance which it yields as gas will then remain constant, and there- 

 fore the potential for the same substance in the gas and the density 

 of this substance in the gas and the part of the gaseous pressure due 

 to it will not be affected by the other components of the gas. 



But when the gas and liquid meet under ordinary circumstances, 

 i.e., in a free plane surface, the pressure in both is necessarily the 

 same, as also the value of the potential for any common component 

 $ r Let us suppose the density of an insoluble component of the gas 



* This result has been given by Lord Rayleigh (Phil. Mag., vol. xlix., 1875, p. 311). 

 It will be observed that equation (279) might be deduced immediately from this 

 principle in connection with equation (260) which expresses the properties ordinarily 

 assumed for perfect gases. 



