L 459 j 



XLIL On the Theory of Osmotic Equilibrium. 



To the Editors of the Philosophical Magazine. 



Foxcombe, 

 nr. Oxford. 



Gentlemen,— Sept. 18th, 1917. 



MR. SHORTER'S letter as published in the July number 

 differs from that which I saw. In his original letter 

 he tailed to distinguish between the two cases mentioned on 

 p. 268 of my paper; his present communication is, however, 

 more precise and possibly it may be thought to need an 

 answer. 



Mr. Shorter says, " Suppose a mixture of two liquids A 

 and B to be in equilibrium with the mixed vapours through 

 a membrane permeable to A only, under conditions of pressure 

 and concentration such that they would also be in equilibrium, 

 if placed in communication through a membrane permeable 

 to B. Let p and ty be the pressures of the liquid and vapour 

 respectively. Let us increase p to p + 8p and ^jr to ty -+- Syfr, 

 adjusting the increments so tluit there is no disturbance of 

 equilibrium." He then goes on to say, "Suppose now that 

 this liquid and vapour are put into communication through a 

 membrane permeable to B. There will not in general be 

 equilibrium." It is here that we disagree. 



His conclusion is easily shown to be wrong ; for, assume 

 that, on altering the pressures as above, the original mixture 

 (of concentration a) is not in equilibrium when the " B " 

 membrane is opened, then there must be some other mixture 

 (of concentration a say) which will be in equilibrium. That 

 is to say, the vapour mixture a' under pressure ty-+8yjr is in 

 osmotic equilibrium with the liquid under pressure p + 8p 

 when both membranes are open. Now by proposition (a) on 

 p. 267 of my paper we may close the membrane permeable to 

 B without disturbing the equilibrium. Thus we have two 

 different mixtures a and a! in equilibrium with the same 

 liquid through membranes permeable only to A ; hence by 

 the equivalence theorem (and it is to be observed that this 

 theorem is here only concerned with membranes permeable 

 to one component) these two mixtures, each of which is 

 under the pressure ty-rS^, would be in equilibrium with 

 one another through an " A " membrane — clearly this is 

 impossible. 



The rest of Mr. Snorter's letter, doubtless, would not have 

 been written had he realized that I have imposed no restriction 

 on the magnitude of the individual partial pressures of the two 

 components except that their sum is to be equal to yjr. 



