146 PROCEEDINGS OP THE AMERICAN ACADEMY. 



In order to introduce a general discussion of this problem, which leads to 

 very notable and instructive results, let us consider first a simple, special 

 case, namely, the question of the effect upon the vapor pressure of a liquid 

 caused by a change in the total pressure on the surface of the liquid. 



Figure I represents a ring-shaped enclos- 

 ure containing a liquid X in the part BCD, 

 and the vapor of X throughout the remain- 

 ing space. The space D E contains also an 

 infinitesimal layer of some inert and insoluble 

 gas, which is prevented from diffusing into 

 the space B A E by a membrane at E, 

 which is permeable only to the vapor of X. 

 The foreign gas thus enclosed exerts a 

 pressure upon the liquid at D and maintains 

 a difference of level, dU, between B and 

 D *. This pressure, moreover, must have 

 an effect upon the vapor pressure of the liquid, for, on account of its 

 weight, the pressure of the vapor is greater at D than at B, but the 

 liquid is in equilibrium with the vapor at both points, therefore the 

 vapor pressure of the liquid is greater at D than at B. If dP^ represent 

 the difference in vapor pressure between B and D, and Si the specific 

 gravity of the vapor, then we may write, 



dP^ = SidH. 



If d Po represent the difference in the total pressure upon the liquid at 

 B and D, and $2 the specific gravity of the liquid, then 



dP2 = S2dH. 



From these two equations, 



dP^_Si 

 d P2 So ' 



or if o"! and 0-2 represent the specific volumes of vapor and liquid respec- 

 tively, then 



d Pi 0-2 ,js 



dP, 



2 o-i 



* Objection has been raised to proofs of this kind ; thus, in this case, it would 

 be argued that in reality the liquid will distil from B to the space above E. That 

 this may liappen in no way invalidates the proof, for it is not necessary that it 

 should liappen. By keeping E A free from drops of tlie liquid the system is in 

 perfect equilibrium, the equilibrium of supcrsaturation. That tliere is another 

 more stable equilibrium possible is of no concern. 



