288 PHYSICAL PROPERTIES 



and in alcohol-water mixtures which contain less than 4.5 mol. or 

 more than 7 mol. of alcohol. The formula most decidedly fails 

 to apply, however, to the rate of solution of casein in dilute alkali 

 containing between 4 and 8 mol. of alcohol, for in these mix- 

 tures the extremely curious phenomenon is observed of partial re- 

 precipitation, on continued stirring, of the casein which is initially 

 dissolved, so that after 2 hours of stirring, the casein dissolved 

 in these mixtures may actually be considerably less than after 

 only I hour of stirring. The penetration-formula obviously im- 

 plies a continuous and irreversible process, while in the presence 

 of the above-mentioned concentrations of alcohol the process of 

 solution is evidently partially reversible. Above and below this 

 critical zone of concentrations the relation between the time of 

 stirring and the concentration of casein dissolved is adequately 

 expressed by the penetration-formula. 



On examining the effect of alcohol upon the magnitude of the 

 coefficient of penetration it becomes evident that in the zone of 



Coefficient of Penetration 



0.3 



0.2 



\ 



Concentration of 

 Alcohol 



0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 M. 



concentrations lying between 4 and 8 mol. the character of the 

 relationship between the concentration of alcohol and the mag- 

 nitude of the coefficient of penetration is undergoing a transition. 

 For concentrations of alcohol lying below 4.5 mol., the coefficient 

 of penetration decreases with negative acceleration as the con- 

 centration of alcohol increases. In mixtures containing over 

 7 mol. alcohol, however, the coefficient of penetration decreases 

 with positive acceleration, as the concentration of alcohol in- 



