151 



which considerably disturbs tlic process of withdrawal of 

 heat from a freezing mass and which I'enders partially 

 inai)i)licable the laws established under ideal conditions, is 

 the gi-adually increasing inetficacy of stirring during the 

 progress of crystallization. 



The area BCC'B' is sometimes used as a measure of the 

 quantity of ice produced during the time interval B'C. If 

 the heat Q produced by freezing is entirely transmitted to 

 the bath, one can write that it is equal to the heat Q' dis- 

 sipated : 



Q = Q' (A) 



But the number Q of calories produced by crystallization 

 is equal to 80 times the number I of grams of ice formed : 



Q = 80I (B) 



On the other hand, the heat dissipated Q' (see, above, the 

 "Problem of the wall") is proportional to the difference 

 y of temperature between the freezing water and the cool- 

 ing bath, to the thickness d of the material separating 

 them, to the heat conductivity c of that material and to the 

 time t 



Q' = kytcd (C) 



where k is a constant of proportionality. From the equa- 

 tions (A), (B) and (0) one deduces 



l=^ytcd (D) 



that is, the amount of ice I is proportional to the area yt of 

 the rectangle BBT'C (when the heat conductivity c and 

 the thickness d are constant). 



The numerical value of the product kycd, that is, the 

 number of calories lost by water in one unit of time, in the 

 conditions of the experiment, can be determined by measur- 

 ing, on the cooling curve, at the point B, the nnml)er of 

 degrees by which the temperature drops in one nnit of time 

 and multiplying that value by the number of grams of 

 water present (each gram requiring 1 calorie to lower the 

 temperature by one degree). 



As we said, the formula D is established on the assump- 

 tion that the factors c and d are constant. But c, the heat 



