187 



than this sum. In tlie first instance, the temperature will 

 just reach the freezing point ; in the second, the tempera- 

 ture will rise to a maximum somewhat below the freezing- 

 point ; if the third were possible, the temperature would 

 rise above the freezing point ; but this cannot happen since 

 the heat produced by the advancing head of a crystal in 

 formation will first raise the temperature of the fluid im- 

 mediately in contact w^ith it, and when this local temper- 

 ature, precisely in the area where the crystal is to grow, 

 reaches the melting point, all crystal growth will stop. So, 

 after subcooling, the temperature never rises above the 

 freezing point, it reaches the freezing point in two of the 

 three cases given and remains below the freezing point 

 in the third. 



When the freezing point cannot be reached, it is almost 

 always because Q.. is too high, in other words because 

 cooling is too rapid. The following example gives an idea 

 of the order of magnitude of the cooling velocity required 

 to prevent the ascent of temperature to the freezing point. 

 Let us suppose that, out of a total mass of 10 grams of 

 water supercooled at -4°, 1 gram freezes out, and that one 

 half of the heat liberated, that is, 40 calories, are with- 

 drawn by the cooling bath during freezing (during the 

 time B"B'), there is still enough heat left (40 calories) 

 to bring all the water from -4° to 0°. To prevent the rise 

 of temperature to 0°, the cooling velocity should then be 

 such that more than 40 calories be withdrawn during the 

 time B"B' (a fraction of a minute). This is a very high 

 cooling velocity. 



Some investigators, having simply admitted (perhaps 

 from a too docile belief in classical statements) that, at 

 crystallization after subcooling, the temperature reaches 

 the freezing point, have made valueless determinations of 

 the latter. With such cooling velocities as 10 degrees per 

 minute, the temperature might not have the time to rise 

 from the subcooling point to a maximum and it will simply 

 be retarded in its drop (cf. Fig. 7, Curve 5) ; or if it 

 reaches a maximum, there is no evidence that this is the 

 freezing point. 



