Spontaneous Crystallization of Supercooled Liquids. 85 



increase in the size of the colloidal particles present, and 

 the decrease to the subsequent destruction of their activity 

 owing to coagulation or some other cause. The loss 

 of activity is the general rule, and may be so serious as 

 to make one experiment incomparable quantitatively with 

 the next. This was unfortunately the case with diphenyl- 

 amine. o.-nitrophenol was more satisfactory, while a set 

 of tubes filled with p.-toluidine was sufficiently " stable " J or 

 a whole series of experiments to be carried out under approxi- 

 mately constant internal conditions. The details of these are 

 now given. 



The procedure is as follows : — 



(a) To calculate the variation with temperature of the 



radius of p.-toluidine particles in equilibrium with 

 the liquid. 



(b) To determine the number of tubes of p.-toluidine 



which crystallize instantaneously at a given 

 temperature. 



By combining (a) and (h), we find how many 

 tubes contain active dust particles whose radius is 

 greater than a certain value. 



(c) From the n, t curves at different temperatures to find 



the average life of tubes containing particles of 

 radius between certain limits. 



(a) Ostwald * showed that this could be calculated from 

 the surface energy of the solid. Jones and Partington f 

 have made a similar calculation. 



The following is a modification of Ostwald' s calculation, 

 introducing Nernst's Heat Theorem : — 



Let A be the free energy of the process of crystallization 

 of a supercooled liquid with respect to a plane surface of the 

 solid. Then, by Nernst's Heat Theorem J, 



A = U -/3T 2 , 



where U and j3 have the conventional meanings. 



Let r be the radius of small particles of the solid which 

 would be in equilibrium with the liquid at the temperature T; 

 then, if a be the surface energy of the solid and p its density, 

 the work done when one gram of the solid is changed 

 from particles of radius r to radius go (i. e. a plane surface) 



. 2(7 



is — . 

 pr 



* Zeitschr. phys. Chem. xxxiv. p. 495 (1900). 



t Phil. Mag. xxix. p. 35 (1915). 



t Nernst, Theor. Chem. 4th Eng. ed., p. 750. 



