on Osmotic Theory. 267" 



A general Method for connecting the several Osmotic Pressures 

 with the Physical Properties of the Fluids under con- 

 sideration. 



Before proceeding to the discussion o£ the osmotic pressures,, 

 it will be necessary to establish three propositions : — 



(a) When a solution is in osmotic equilibrium with its 

 mixed vapour through a membrane permeable to both com- 

 ponents, the closing of the membrane to one of the components 

 alters neither the equilibrium nor the concentrations. 



Consider compartments (1), (2), (5) of fig. 1; these are 

 already in osmotic equilibrium. Let the right-hand half of 

 the horizontal membrane between (2) and (5) (permeable to 

 B) be closed. It is easy to show by the equivalence theorem 

 that no disturbance takes place. Again, consider compart- 

 ments (2), (3), and (5), and close the left-hand half — the 

 equivalence theorem proves similarly that no disturbance 

 results. 



(6) It is possible to change the pressures on the solution 

 and its mixed vapours (separated from one another by a 

 membrane permeable to both components) in such a manner 

 as to keep osmotic equilibrium between them without any 

 change in concentration taking place. 



For consider compartments (I), (2), and (5) : — Close the 

 membranes between (2) and (5), and alter the pressures on 

 (1) and (2) from yfr p to yjr p , and ir &p to ir &p , in such a way as 

 to keep osmotic equilibrium through the membrane (l)/(2), 

 and, at the same time, alter the pressure on the solution to p' 

 so as to keep it in equilibrium with (1) through the mem- 

 brane (l)/(5) ; then, on opening the membrane (2)/(5), if 

 we apply the equivalence theorem, it can be shown that com- 

 partments (2) and (5) are still in equilibrium. Now, as (2) 

 and (5) were in equilibrium to begin with, and are so at the 

 end, we can state that the pressures on these two com- 

 partments could have been altered progressively and simul- 

 taneously without any disturbance of the osmotic equilibrium 

 through the membrane. 



(c) It is possible to change the pressures on the solution 

 and its mixed vapours, separated from one another by a 

 membrane permeable to either component only, in such 

 a manner as to keep osmotic equilibrium between them 

 without any change in concentration taking place. 



This proposition is at once self-evident, if we remember 

 that, at any stage in the alterations of the corresponding 



