32 On the Theory of Osmotic Equilibrium. 



while the increment &yjr will increase that in the vapour by 

 <r a B\jr. Hence we must have 



s a 8p = * a 8yfr (1) 



Suppose now that the liquid and vapour are put into 

 communication through a membrane permeable to B. 

 There will not in general be equilibrium, since the incre- 

 ments of pressure which augment equally the values of the 

 chemical potential of A in the two portions of the system, 

 do not necessarily augment equally those of B. Let s b and 

 <r h denote the " apparent specific volumes w of B in the 

 liquid and vapour respectively. The respective increments 

 of the values of the chemical potential of B, will be sbBp and 

 o-bSyjr, and the relation 



SbSp = <T b h^ (2) 



will not in general be verified. Only when by accident the 

 relation * 



^ = - a (3) 



Sb CFb 



holds, will it happen that increments of the two pressures 

 which do not disturb equilibrium through a membrane 

 permeable to A, also do not disturb it through a membrane 

 permeable to B. 



If we assume the truth of the proposition, the simultaneous 

 fulfilment of equations (1) and (2) at once follows, as does 

 the universal validity of equation (3). This is essentially 

 the method adopted by the Earl of Berkeley in establishing 

 this relation. Equations (3) and (4) of his paper f corre- 

 spond respectively to equations (1) and (2) above, and lead 

 at once to equation (3) above {. 



In conclusion it may be pointed out that the fallacy in the 

 Earl of Berkeley's attempt to establish the proposition, lies 

 in applying his "Equivalence Theorem "§ to a system 

 containing membranes which differ with regard to the 

 components to which they are permeable. 



I am, 



Yours faithfully, 



S. A. Shorter. 

 The University, Leeds, 



March 8th, 1917. 



* If this relation were generally true, it would lead to the rule that 

 the densities of liquids were approximately proportional to their mole- 

 cular weights ! 



t P. 269. X Equation (6) on p. 270. § P. 265. 



