1898.] Mr Wilson, On Velocity of Solidification. 27 



Eliminating C and C by means of the equality of the vapour 

 pressures at 6 the melting point, these equations give 



log 



Pp = F(1 

 p s R\0 



Since p p —p s is small compared with p s this gives very approxi- 

 mately 



F(l ^ 



Pp Ps-Ps E \ e Q o 



Now, according to Van 't Hoff*, the osmotic pressure of a 

 solution can be calculated from its vapour pressure by multiplying 

 the difference between its vapour pressure and that of pure water 

 by the ratio of the density of water to the density of its vapour. 

 This gives the osmotic pressure of the salt in the solution, or what 

 is the same thing the diminution of the internal pressure due to 

 the presence of the salt. Assuming that the internal pressure 

 in the solid is diminished by an amount measured by the diminu- 

 tion of the vapour pressure in the same way as in the case of a 

 salt solution, we get for the difference between the internal 

 pressures in the liquid and solid 



P = (p P -p s ) S ~, 

 P 



where s and p are the densities of the liquid and its vapour 

 respectively. Substituting the above value of (p p —p b ) this gives, 



P 



since P = fy> 



P = sF.^. 



In getting this expression the change in density which takes 



place during solidification has been left out of account, so that it is 



not clear whether s should be the density of the liquid or that of 



the solid. It might be thought that the proper method of getting 



s s 



P would be to multiply p p by — , and p s by — , and subtract, so 



Pp Ps 



that 



{ Pp Ps 



but this expression is not zero at O (unless s p = s s ) which is not in 



* Studies in Chemical Dynamics, p. 232. 



