258 The Earl of Berkeley on Solubility and 



that any two liquid phases which are in equilibrium with one 

 another have the same osmotic pressure. 



Referring to fig. 2, let A represent the solute saturated 

 with solvent (this will be called the 2nd phase), and B the 

 solvent saturated with solute (the 1st phase), and ab the 

 surface of separation. A and B are in equilibrium with one 

 another, and this equilibrium will not be disturbed if ab 

 represents a membrane permeable to the solvent. If 

 represents a solution in osmotic equilibrium with B, it is easy 

 to show, by a similar process to that outlined in paragraph (5), 

 that A will also have the same osmotic pressure as (J, so that 

 C can be replaced by the solvent under pressure q x *. 



(9) On this system as now defined, perform the same cycle 

 as in paragraph (6) and designate the new quantities involved 

 thus : — 



C\ and c 2 are the number of grammes of solvent and 

 solute respectively in one gramme of the second 

 phase. 



Si and s 2 are the spaces occupied, in the second phase, 

 by one gramme of solvent and of solute respectively. 



x is the specific volume of the second phase. 



As before, we need only consider the terms in mSp, and 

 the 1st and 4th operations do not contribute any terms to the 

 final result. In the 2nd operation the work term on the left 

 is 



£ f c 2 dw c 2 dx x — wV c 2 dc 2 c 2 dc 2 ~\\ 



^ \c 2 ' — c 2 dp c 2 ' — c 2 dp c 2 —c 2 L c 2 —c 2 dp c 2 f — c 2 dp J J ' 



and that on the right is 



In the third operation the work term on the left is 



mhp f , , \~dc 2 f*-c 2 w + c 2 x , \ 



c 2 c 2 L r Ldp\ C 2 ~C 2 / 



dc 2 /C2 ! w — c 2 x \ c 2 'dw c 2 dx~\~\ 

 dp\ c 2 —c 2 J dp dp J J ' 



* Incidentally attention may be drawn to the fact that by a similar 

 process of reasoning it can be shown that if one liquid phase is in equili- 

 brium with a solid component, the other phase must also be in equilibrium 

 with it. Thus, two liquid phases in equilibrium with one another have 

 the same freezing-point. 



