160 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



to vary, while the composition of the liquid and the temperature 

 remain unchanged. If we denote the increments of pressure and of 

 the potential for 8 l by dp and dfa, we shall have by (2*72) 



| dp = ( -=- J dp, 



t t m VCtTTZ/j/ t t p t m 



the index (L) denoting that the expressions to which it is affixed 

 refer to the liquid. (Expressions without such an index will refer 

 to the gas alone or to the gas and liquid in common.) Again, since 

 the gas is an ideal gas-mixture, the relation between p l and fa is 

 the same as if the component S l existed by itself at the same 

 temperature, and therefore by (268) 



Therefore a i^^Pi = \j) dp. (285) 



This may be integrated at once if we regard the differential co- 

 efficient in the second member as constant, which will be a very 

 close approximation. We may obtain a result more simple, but not 

 quite so accurate, if we write the equation in the form 



(L> dp, (286) 



where y x denotes the density of the component /S^ in the gas, and 

 integrate regarding this quantity also as constant. This will give 



(L) 



(P-P'), ; (287) 



where p^ and p' denote the values of p l and p when the insoluble 

 component of the gas is entirely wanting. It will be observed that 

 pp' is nearly equal to the pressure of the insoluble component, 

 in the phase of the gas-mixture to which p relates. S 1 is not 

 necessarily the only common component of the gas and liquid. 

 If there are others, we may find the increase of the part of the 

 pressure in the gas-mixture belonging to any one of them by 

 equations differing from the last only in the subscript numerals. 



Let us next consider the effect of a gas which is absorbed to some 

 extent, and which must therefore in strictness be regarded as a com- 

 ponent of the liquid. We may commence by considering in general 

 the equilibrium of a gas-mixture of two components 8 1 and $ 2 with 

 a liquid formed of the same components. Using a notation like the 

 previous, we shall have by (98) for constant temperature, 



whence (y< L > - -yjdfa = (y g - y< L) )dfi 



