Freezing- Points and the Freezing -Point Methods. 461 



rogeneous system, at the freezing-temperature, will be con- 

 tinuously warmed by the arrangements of the experiment (by 

 the air- or liquid-bath, stirring &c), and the ice-melting 

 process must take place. On the other hand, if the conver- 

 gence-temperature be below the freezing- temperature the 

 heterogeneous system is continuously cooled, at the freezing- 

 temperature, by the arrangements of the experiment, and the 

 process of ice-separation takes place. 



In order to know better the processes which take place at 

 equilibrium and to get the chief conditions for a good freezing- 

 point method, as far as it concerns the heterogeneous system at 

 equilibrium, let us now consider the following processes : — 



(1) The cooling of the liquid by the air-bath (in Lewis's 

 and my method, and in the methods of Jones and Abegg) or 

 by the liquid-bath (Loomis, Raoult, Pickering, Eyckman) 

 when the liquid is not stirred, i. e. is not otherwise warmed. 



(2) The warming of the liquid by stirring (i. e. by the 

 stirrer and the air drawn in). 



(3) The process of melting of ice or of solid solvends in 

 liquid solvents or solutions. 



(4) The process of separation of ice or of solid solvends from 

 overcooled liquids. 



2. As regards (1) and (2) if the temperature of the air-bath be 

 T A , of the ice-bath Ti, the temperature read off at a given time 

 z be t, we ought to have, for the rate of cooling of the liquid, 



Newton's equation ( -r- \ = C (T A — 4), if no warming through 



stirring is taking place. 



Here C is inversely proportional to the mass and to the 

 heat-capacity, and directly proportional to the total surface of 

 the liquid. If at the same time the liquid is warmed by 

 regular stirring, the same amount of heat will be conveyed to 

 it in the unit of time, and we have for this single effect 



\-r) =K'> where K' is inversely proportional to the heat- 

 capacity and to the mass of the liquid. The actual rate of 

 warming or cooling the liquid is therefore 



dt 



^=C(T A -0+K' (I.) 



rtt 



The point at which y =0 is the convergence-temperature (t g ) 



in the given arrangement of the experiment. It follows from 

 Phil. Mag. S. 5. Vol. 44. No. 271. Dec. 1 897. 2 M 



