p 



on Osmotic Theory. 265 



and & bb are those of the pure liquids in contact with 

 their pure vapours respectively. 



(F> =p - 



aa -t a 



and \?^=p b — 



i,h' 



[P aa and lF> are those of the pure liquids in contact with 

 the mixed vapours through a membrane permeable to 

 the vapour o£ A or B respectively. 



It will be noticed that throughout this notation the 

 suffixes a, b, a, and ft indicate, as far as possible, which 

 membranes are supposed to be operative ; and they also 

 specify the concentrations o£ the mixture, whether liquid or 

 vapour. In working with the notation it will be found that 

 this double use of the suffix leads to no ambiguity ; indeed, 

 it helps very materially in forming a mental picture of the 

 various operations. 



Theory. 



The Equivalence Theorem. — I will, in the subsequent 

 pages, use this locution to denote the following theorem. 

 " If we have any sets of molecules A, B, C, etc., each in 

 osmotic equilibrium with a set X, then the original sets are 

 in osmotic equilibrium with one another/' 



Before proving this for any state of matter (it is generally 

 accepted for solutions), we must postulate that, in general, 

 the osmotic pressure of any mixture increases with increase 

 of concentration ; should it diminish, instability would 

 set in. 



Now consider the system shown in fig. 2, where the dotted 

 lines are membranes permeable to A only. Under the 



Fie. 2. 



(1) 

 Mixture 

 A + C. 



(2) 



Mixture A+B. 



^^\Xn\\\^\^^\XS\^ 



^J» a 



pressures indicated, (l)/(3) and (2)/(3) are postulated to be 

 in osmotic equilibrium. It is required to prove that (l)/(2) 

 are also in equilibrium. • 



