168 Dr. Harry 0. Jones on the 



thoroughly mixed. The amount of cooling below the freezing- 

 point was determined for all the substances employed. This 

 was accomplished at first by means of an ordinary Beckmann's 

 thermometer divided into hundredths of a degree, but it 

 could also be done with the large thermometer which ex- 

 tended only over 0*6° 0. by determining the time required 

 by the solution to cool 06°, and the time between the moment 

 when the mercury thread passed the zero of the thermometer 

 and the moment when the ice separation began. During this 

 entire time the stirring must be continued as uniformly as 

 possible. Since the undercooling was in general only a little 

 more than a degree, this was found to be quite accurate 

 enough. Indeed, with the organic compounds this under- 

 cooling was usually less than a degree. Whenever it amounted 

 to more than 1*2°, the solution was made to freeze by the 

 addition of a minute fragment of pure ice. 



The readings as made on the thermometer were in every 

 case corrected for the change in concentration produced by 

 the separation of the ice. This correction was based on the 

 latent heat of water = 80 cal. The separation of one gram of 

 ice would liberate enough heat to warm 80 cub. centiin. of 

 water 1°. Since the volume of the solution is known (1 litre) 

 and the amount of undercooling determined, the calculation of 

 the amount of ice is as follows : — Let S = specific heat of the 

 liquid; U=the amount of undercooling in degrees Celsius; 

 W= heat of solidification of unit weight of the liquid; T = 

 fraction of the liquid which solidifies : 



su 

 w 





In all u the solutions thus far investigated, water was the 

 solvent, where S = l and W = 80. For every degree of 

 undercooling 12*5 grs. ice separated from the litre of liquid. 

 The original solution was thus concentrated a given amount 

 by the separation of the ice, and the freezing-point as read 

 from the thermometer is that of the solution thus concentrated. 

 The lowering of the freezing-point of the water by the salt 

 is thus too great, and must be diminished in proportion as 

 the original solution was concentrated. This would then 

 give the correct lowering of the freezing-point for the original 

 solution. The correction is, however, not absolutely exact, 

 since the lowering of the freezing-point does not change in 

 exactly the same relation as the concentration, owing to an 

 increase in dissociation with increase in dilution. But the 

 amount of dissociation for very dilute solutions which have 



