Freezing-Points and the Freezing-Point Methods. 463 



ice, therefore our equation is dt= 1 K. / (t — t)f(t)dz. I tried to 

 investigate the velocity of the melting of separated solid sol- 

 vends, e. g. of ice, in liquid solvents or solutions, of a tempe- 

 rature higher than the freezing-tempei'ature, as carefully as 

 possible. The experimental difficulties are here very much 

 greater than in delicate freezing-point determinations them- 

 selves, as will be shown in a future paper, "On the Velocity of 

 Reaction before Perfect Equilibrium takes place." This is the 

 reason why 1 was unable to obtain in this way even rough 

 experimental evidence for the above equation. Only by inves- 

 tigating cube-shaped pieces of ice in warmer water or solutions 

 could 1 succeed in this. This also furnishes a method for 

 accurate determination of the relative velocities with which 

 ice melts in water and aqueous solutions of different concen- 

 trations. Having proved the above equation to be correct, 

 we can approximately assume for the velocity of melting of 

 ice when separated from overcooled liquids the equation 



|=KA-0[(*„-O-fo-<)]; 



where t ov is the temperature to which the liquid was over- 

 cooled below the freezing-temperature t , and t h is the tempe- 

 rature of the taken warmer liquid, with which the separated ice 

 is brought in contact. If t h — t is very small, we may assume 



f z =KXt -t)(to-t ov ). 



4. The Process of Ice-separation. 



Careful measurements have shown that the velocity of the 

 formation of ice in overcooled liquids finds expression in the 



equation ( -j-C"[t — t)(t —t w ) ; in which t is the freezing- 

 temperature, t the read temperature of the overcooled liquid 

 at the time z, C" is a constant which is directly proportional 

 to the latent heat of fusion and inversely proportional to the 

 specific heat of the liquid, and t ov is the temperature to which 

 the liquid was overcooled, Since the rise of temperature of an 

 overcooled liquid is directly proportional to the quantity of 

 separated ice, the above equation means that the velocity of 

 ice separation from overcooled liquids is directly proportioned 

 to the remoteness from the freezing '-ten iperature and to the sur- 

 face of the ice in contact with the liquid. Here both parts of 

 the heterogeneous system are of the same, or nearly of the 

 same temperature during the formation of ice, and the above 

 equation represents the first case in which it is, in its form but 



2 M2 



