26 Mr Wilson, On Velocity of Solidification. [Oct. 31, 



No very satisfactory explanation of the relation between the 

 velocity and supercooling has as yet been given. Tammann (loc. 

 cit.) has suggested that if the substance were quite pure the 

 velocity would be the same whatever the supercooling, and has 

 pointed out that when the substance is purified the constant value 

 of the velocity is attained at a smaller supercooling than before. 



To explain so many of the phenomena observed by the presence 

 of supposed impurities is evidently unsatisfactory and the object 

 of this paper is to explain the observed relation between the 

 velocity and supercooling without the aid of supposed impurities 

 in the material used. 



At the melting point the solid and liquid exist together in 

 equilibrium and their vapour pressures are equal. Below the 

 melting point the vapour pressure of the liquid is greater than 

 that of the solid. The internal pressure corresponding to the 

 difference between the vapour pressures of the solid and liquid 

 can be obtained by multiplying the difference of the vapour 

 pressures by the ratio of the density of the liquid to that of the 

 vapour. For water and ice at — 1° C. it amounts, as I shall show 

 below, to about 12 atmospheres. When ice and water are in 

 contact at — 1° C. therefore the internal pressure in the water is 

 greater than that in the ice by 12 atmospheres, so that the layer 

 of molecules at the surface of separation is urged by this pressure 

 into the solid. It seems reasonable to suppose that the rate at 

 which solidification takes place at the surface of separation will 

 depend on the difference between the two internal pressures. 



An expression for the difference between the two vapour 

 pressures can be easily obtained by means of the equation 



L = (v 2 -v 1 )0% p , 



where L is the latent heat of evaporation of unit mass, v 2 the specific 

 volume of the vapour and v 1 that of the liquid, 6 the absolute 

 temperature and p p the vapour pressure of the liquid. 



Integrating and neglecting v x as being small compared with 



v 2 , this gives, putting v. 2 = — , 



Pp 



d + j / \ogp p +G = 0. 



For the solid in the same way 

 1 R 



where F is the latent heat of fusion. 



