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



d?X _ d0 

 " dt 2 dt ' 



.*. -j-= oo , when t ■= 0. 

 dt- 



Consequently if a curve is drawn to represent the variation of 

 the temperature of the surface of the ice with the time it will 

 be of the following general form. 



When t = the curve touches the axis of 0, and when t = oo 



rt yjv n 



Since X = ~dt = G(0 n -0) 



J o dt Jo 



dt 



= C(0 o -0 1 )t-c( t (0-0 1 )dt, 



Jo 



the area between the above curve and the line = O is propor- 

 tional to X. Hence X at first increases rapidly but the rate of 

 increase falls off very quickly as the time increases. 



If a supercooled liquid is poured on to a plane layer of the 

 solid solidification does not take place uniformly all over the 

 solid but rays of solid grow out into the liquid. Any small 

 projection on the solid loses heat to the liquid more easily than 

 the rest and consequently grows quicker, so that a plane surface 

 of the solid is unstable when in contact with supercooled liquid. 



Since the rays of solid formed grow with a uniform velocity 

 they must lose heat by conduction at the same rate that it is 



Fig. 4. 



produced by the solidification. Hence round the point of the 

 ray there is a distribution of temperature of constant type 

 travelling through the liquid along with the point of the ray. 



