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



value and then diminish. Let the temperature at which the 

 velocity is a maximum be 1 . 



Suppose first that the supercooling of the liquid is less than 

 (0 O — dj). Then the heat produced by the solidification will raise 

 the temperature of the tip of the ray of solid which will make the 

 velocity smaller, consequently the ray will grow at a somewhat 

 smaller rate than it would if its tip were at the original tem- 

 perature of the liquid. The diminution of the velocity due to this 

 cause will probably be a larger fraction of the velocity when the 

 supercooling is small than when it is large, which perhaps is the 

 cause of the small rate of increase of the velocity with the super- 

 cooling when the supercooling is very small. 



Suppose now that the supercooling of the liquid is greater 

 than (# — 0,), then the heat produced by the solidification will 

 raise the temperature of the tip which will make the velocity 

 greater, consequently the velocity will continue to increase until 

 the temperature is reached at which the velocity is a maximum. 

 Hence when the supercooling of the liquid is greater than (6 — 6 t ) 

 the velocity will be independent of the supercooling because the 

 tip of the ray will always be maintained at the temperature 6 X . 



If the supercooling is very great the viscosity of the liquid 

 may be so great that practically no solidification can take place or 

 the initial velocity may be so small that the tip will not be heated 

 appreciably, so that the velocity will remain small. If when this 

 is the case the supercooling is gradually diminished, a point will 

 at length be reached at which the velocity will suddenly attain 

 the maximum value owing to the heat generated by the solidi- 

 fication taking place at the original temperature having become 

 sufficient to appreciably raise the temperature of the solid being 

 formed. The temperature at which this takes place corresponds 

 very closely to the temperature of ignition of an explosive gaseous 

 mixture. 



Thus the observed relation between the supercooling and the 

 velocity can be accounted for. 



I shall now consider certain cases of solidification in detail. 

 The general problem in solidification may be stated as follows : — 

 given the distribution of solid and liquid and the temperature 

 throughout a given space at any time and also the boundary 

 conditions, to find the distribution at any subsequent or previous 

 time. 



Consider a surface of separation between ice and water. The 

 rate of solidification at the surface depends on the supercooling of 

 the surface and for small supercoolings may be taken as pro- 

 portional to the supercooling. So that v— C (0 O — 6) where v is 

 the velocity of the surface, 6 the melting point, and 6 the tem- 

 perature of the surface and C a constant. 



