﻿484 Mr. S. A. Shorter : Application of the Theory 



the existence of an insoluble gas. We will therefore confine 

 ourselves to the consideration of the effect of capillary pres- 

 sure on the vapour-pressure of a solution. 



We will also consider the thermodynamical theory of the 

 equilibrum between the solution and solid solvent, and estab- 

 lish exact formulae connecting the freezing-point with the 

 osmotic pressure and vapour - pressure. These formulae, 

 which are obviously of fundamental importance in the 

 theory of solutions, appear never to have been previously 

 established. 



Some new Symbols used in this Communication. 



The following new symbols will be used in the part of the 

 paper dealing with the freezing of solutions. The new sym- 

 bols used in the earlier parts of the paper will be defined as 

 they occur in the text. 



T the freezing-point of the pure solvent under a 



pressure p ; 

 T the freezing - point of the solution under a 



pressure p ; 

 L the latent heat of fusion of the solid solvent, 

 when in equilibrium with the pure liquid 

 solvent under a pressure p * ; 

 7(5, p, t) the specific heat of the solution under a constant 

 pressure p, and at a temperature t ; 

 7o(Pj t ) the specific heat (under constant pressure) of the 

 , pure liquid solvent ; 



y s (p, t) the specific heat (under constant pressure) of the 



solid solvent ; 

 7d(P> T ) =7oO, T)—y£p, t) ; 



l Q (s, p, 0) the heat of dilution at a pressure p and tempera- 

 ture e t- 



</>o(p> 0) ^ ne chemical potential of the solid solvent at a 

 pressure jo and temperature 6; 

 AoO, p, 0) =/o(0, p, 0)-Ms, p, 6) ; 



r„o, ff) = —Up, Q-.&ti- ' P' ff) ' 



o {^p 9 0)^^A Q (s,p,e). 



* It is unnecessary to adopt the more precise notation T (p), T(s,p), 

 L (p), as we shall not consider variations of s and/?. 



t The hsat evolved when an infinitesimal mass 5M of the solvent is 

 added to the solution (pressure and temperature being' maintained 

 constant) is l e {s,p, 0)8U Q . 



