the Osmotic Theory of Solutions. 605' 



therefore necessary to deduce a relation connecting r— ^ 



with the vapour-pressure, this is obtained as follows : — 



Prof. Porter*, assuming the validity of the partial pressure 

 law, has put forward an equation connecting the osmotic 

 pressure and the vapour-pressure of a mixture when both 

 components are volatile. This equation can be made exact, 

 whether the partial pressure law holds or notf, by defining 

 7T Q as the pressure of the pure solvent vapour which is in 

 osmotic equilibrium with the mixed vapours (ft) through a 

 membrane permeable to the solvent vapour only ; an exactly 

 complementary definition holding good for (f> Q . 



The equation in question, in its strict signification, may be 

 regarded as expressing the osmotic pressures of the volatile 

 mixture in terms of the pressure of the saturated mixed vapour, 

 and its osmotic pressures ft — ttq and ft — </>c2, measured with 

 respect to solvent and solute vapour respectively. 

 In the new notation the equation becomes 



\ Sl dp=\ udp+\ vdp .... (19) 



Differentiating (19) with respect to r 2 and keeping q t 

 constant, we get 



* c 2 JqOC 2 l dc 2 dc 2 



(This equation is exact and can be derived from first 

 principles without reference to the pure solvent.) 



But 



dc 2 S^2 "dj> ' dc 2 



and Prof. Porter J has shown that %— = — ; 



O/' v 

 therefore (20) becomes 





(21) 



* Proe. Roy. Soc. Series A, vol. lxxx. p. 460. 



t It would seem from the determinations of the osmotic pressures 

 derived from the vapour-pressures of solutions of calcium ferrocyanide 

 set forth in the Phil. Trans. Roy. Soc. Series A. vol. ccix. pp. 199-203, 

 that for water-vapour in air at 0° C, the assumption of the validity of 

 the partial pressure law may not be warranted. 



% Proc. Roy. Soc. A. vol. lxxix. p. 525. 



