82 PHYSICAL DETERMINATIONS. 



known strength, the freezing point of which is calculated from 



18*72 P 

 the formula of Raoult, C = ~ _ Q.QQ p- ^ = freezing point, 



P = grammes of cane sugar per 100 grammes of water, by tapping 

 the thermometer continuously to prevent the mercury sticking, 

 and by correcting for the expansion of the emergent column, 

 and preferably by eliminating this by having a very short 

 emergent stem. 



(2) Those due to bath temperature, which may be eliminated 

 by choosing such a temperature of the freezing bath that the 

 heat withdrawn is balanced by the heat developed by the 

 stirring apparatus, which is obtained by actual trial with the 

 apparatus. 



(3) Those due to concentration of the solution owing to the 

 separation of ice, which may be very large, and which has been 

 most often neglected ; the figure observed is always slightly 

 too large, and may be corrected for by the formula 



C = true freezing point. 

 C* = observed freezing point. 

 K = a constant (0-017 for milk). 

 S = degree of supercooling. 



There is a special error which applies only to the determination 

 of the freezing point of distilled water, due to the formation of 

 a thin film of ice on the walls of the vessel, the effect of the 

 abstraction of heat being to increase the thickness of this, and 

 not to balance the heat developed by the stirrer, which thus 

 causes the reading of the thermometer to be too high. The 

 formation of ice films in distilled water (they do not occur in 

 milk) can be prevented by careful regulation of the bath tem- 

 perature with very efficient stirring. 



Monier- Williams' apparatus is far too complicated for use as 

 a practical test, but with it he has determined that the method 

 is capable of yielding very useful results in the case of milks 

 whose composition leads to uncertainty as to whether they 

 are genuine. 



The freezing points of 141 samples, many of them from 

 cows at the end of their lactation period, including a number 

 which were very abnormal in composition, were determined ; 

 the freezing point, however, showed approximate constancy 

 (Table XVI). 



