150 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



For the sake of completeness the corresponding phenomena in the case 

 of other mixtures will next be considered. 



In Figure 3 let the tube CAB contain a homogene- 

 ous mixture of liquids and the outer vessel one of the 

 pure liquids, X, alone. A and B represent two mem- 

 branes permeable to X alone. If pressure is applied in 

 the tube so that X neither enters nor leaves the tube at 

 A, then there will be equilibrium at B also, for other- 

 wise a continuous cyclic process would be kept up, 

 contrary to the second law of thermodynamics. The 

 escaping tendency of X is the same outside and inside 

 at A and also at B, since there is equilibrium at both 

 points, but the changes in pressure between A and B 

 which determine the magnitude of that tendency are different inside and 

 outside the tube. If c?^is the height A B, and the specific gravity of 

 the mixture and the liquid X are Si and .^2 respectively, the changes in 

 pressure are 5'icf^inside the tube and S2 d H outside. If dP^ and f/Pp? 

 respectively, represent these changes in pressure, 



Figure 3. 



dPi 

 ~dP. 



Si 

 02 



or 



dPi 



JPo 



o-i 



This is the same as equation (2), and at first sight it seems that the 

 influence of pressure upon the equilibrium between two phases is as 

 simple in the case of mixtures as in the case of pure substances. It is 

 actually, however, much more complicated. In the above example there 

 is a change in the escaping tendency of X from the mixture, not only 

 because there is a change of pressure, but also because, in general, between 

 A and B there is a change in the relative amounts of the components of 

 the mixture. In other words, the concentration of X differs at A and B.* 

 Moreover if there is chemical equilibrium in the mixture the chemical 

 reaction will have run nearer to completion in A or in B according to 

 whether the total volume is increased or diminished by the reaction. On 

 account of this complexity the further study of mixtures, although of 

 much interest, must be deferred, since it is not essential to the present 

 paper. 



* See Gouy and Chaperon, Ann. Ch. Ph. (6), XII. .384 (1887). 



