250 On Solidification and Viscosity of Supercooled Liquids. 



s 



It thus appears that the formula y = 0== represents the 



variation of v with s sufficiently well to justify the conclusion 



that the velocity is largely determined by the viscosity in the 



way indicated by the formula. 



Two main causes, to which I have already referred, probably 



s 

 account for the discrepancies between the values of C -rr an( i 



the velocities observed. The first cause, namely, the rise of 

 temperature due to the production of heat accompanying the 

 solidification, does not affect the comparison of the calculated 

 and observed velocities in the case of salol, for in this case 

 it was measured and allowed for ; but wiih the other three 

 bodies investigated the temperatures at which the velocities 

 are measured are too low, owing to this effect. If the cor- 

 rection for this effect were made, it would probably raise the 

 point at which the straight part of the velocity-curve when 

 produced cuts the temperature-axis, so that measuring s from 

 this point probably partly eliminates the error due to this cause. 

 The other cause, namely, the presence of impurities in the 

 substance, probably accounts for the small velocities observed 

 near the melting-point, which I have not attempted to repre- 

 sent by the formula, and which occur with three out of the 

 four substances investigated. When impurities are present, 

 solidification near the melting-point is more correctly de- 

 scribed as cry>tallization from a strong solution, and must 

 evidently depend on the rates of diffusion of the substance and 

 impurities in each other, for as the pure substance separates 

 out the impurities collect round it; and so it is easy to see 

 that the rate of solidification may be greatly affected by small 

 amounts of impurities quite insufficient to have a corre- 

 sponding influence on the viscosity of the substance. That 

 purifying the material is able to diminish greatly the range of 

 temperature over which the velocity increases very slowly 

 with the supercooling has been shown by Friedlander and 

 Tammann (loc.cit.), so that it seems reasonable to suppose that 

 with pure substances the velocity would be at first propor- 



tional to the supercooling, as the formula C^ indicates, and 



as is approximately the case with the benzoic anhydride I used. 

 I think, therefore, that the above results render it probable 

 that the velocity of solidification of a pure substance varies 

 directly as the actual supercooling at which the solidification 

 occurs, and inversely as the viscosity of the liquid* 

 Wilmersdorf, Berlin, 

 Feb. 15, 1900. 



