28 



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



agreement with the fact that at O the solid and liquid are in 

 equilibrium. It is, however, easy to obtain the formula 



P = sF 



0„ 



in another way which shows that s should refer to the solid state 

 in it. 



Imagine a cylinder fitted with a piston and provided with a 

 bottom permeable to water but not to ice. Let this be filled with 

 ice and immersed in water all at a temperature 6 below O . 



Then if the pressure on the piston is great enough the ice will 

 be melted and forced through the bottom as water. Let P be 

 the least pressure required for this which is evidently equal to 

 the difference between the internal pressures in the water and 

 ice at 0. Then if unit volume of ice is melted and squeezed 

 through, the work done by the piston is P, and the heat absorbed 

 is s s F, and since the operation is reversible, and P = when 

 = O , 



P = s x F 



%-0 

 n 



by the 2nd law of thermodynamics. 



This equation is closely analogous to that usually given for the 

 pressure required to lower the melting point of ice by a given 

 amount. In the case usually considered, however, both the ice 

 and the water are supposed compressed, whereas in the present 

 case the water is supposed unconstrained. It may be remarked 

 that in many of the cases usually cited as examples of the equation 

 for the case where both the water and the ice are subject to the 

 pressure the water is really unconstrained, so that the ordinary 

 equation is not applicable and should be replaced by the one just 

 obtained. Such cases are the melting of ice at the feet of glaciers 

 due partly to the pressure of the ice above, and the well-known 



