Spontaneous Crystallization of Supercooled Liquids. 83 



The experimental results show, however, that an abnormally 

 large number of: tubes tend to crystallize in the very early 

 stages, and that the later stages are always drawn out much 

 longer than the exponential relation given above allows (see 

 curves in fig. 1). In other words, the tendency to crystallize 

 is different in different tubes. For example, in the salol 

 experiments tube 9 almost invariably crystallized very early 

 while tube 18 was as frequently still unchanged at tbe con- 

 clusion of the experiment. As the phenomenon appears to 

 be catalytic this is not surprising, as the amount and activity 

 or the catalyst may vary from tube to tube. 



In this case we might assume that the exponential ex- 

 pression held, but that % instead of being constant had values 

 distributed about a most probable value — e.g., that the number 

 of tubes for which % lay within a certain range was given by 

 some such distribution law as 



so that 



Then 



so that 



dn = ax 2 e Fx ^%, 



ax 2 e- h2 x 2 dx. 



) 



n=J^«-*V(l-«-x')i X 



_ /,2 r 2 7 at 



/ a at 2 \ C 



2A2 



This gives a curve steeper initially than the raonomolecular 

 curve and reaching- its limiting value more slowly. 

 • The curves (e. g. those in fig. 1) cannot, however, be 

 represented even by an expression like this with distributed 

 values of %, being far too steep in the first short interval of 

 time. 



Experiments were made with p.-toluidine, diphenylamine, 

 and o.-nitrophenol in very thin small tubes, about 1 mm. by 

 20 mm., which very rapidly attained thermal equilibrium 

 when plunged in the thermostat. The results obtained with 

 these (Tables III. and IV.) show that at a given temperature 

 a certain proportion of the tubes crystallize almost instanta- 

 neously, and that among the remainder there is a distribution 

 of activities something like that suggested above. 



The probable explanation seems to be as follows : — Nucleus 

 formation occurs round the colloidal particles which the liquid 

 has derived from the air. An adsorbed layer is presumably 



G2 



