Growing Crystals by Instantaneous Photomicrography . 497 



evidently started immediately after the previous exposure, 

 while in fig. 9 they were registered while still very young. 

 The averaging o£ a much larger number of observed diameters 

 led to the slightly different values given below, corresponding 

 to the accompanying times : — 



Time=*. 



Diameter— D. 



interval 

 0*50 interval 

 1-50 intervals 

 2 - 50 intervals 



Diameter 

 Diameter 057 

 Diameter 0*87 

 Diameter 1*00 



These data are plotted in fig. 16 (see p. 498). 



The inspection of the figure shows at once that the curve- 

 is similar in general shape to one represented by the equation 

 T) n = kt, where D is the diameter of the crystal, t the time from 

 the birth of the crystal, and k a constant. The only question 

 is as to the magnitude of n. The curves which result from 

 the assumptions n=2 and n = o are given in the figure, for 

 comparison with the experimental curve. It is clear that the 

 curve with the latter value, w = 3, is the nearest, possessing 

 the same general curvature, and deviating from the average 

 less than the individual measurements do. This is equivalent 

 to saying that equal increments of time correspond to equal 

 increments of volume, instead of equal increments of surface, 

 as one might have supposed. Of course a law based upon 

 such merely approximate data cannot be considered as 

 definitely settled; but clearly the general character or ten- 

 dency of the curve is established. It is probable that under 

 the necessarily ill-defined conditions of our experiments the 

 growth follows no one law with precision ; supersaturation, 

 convection, diffusion, and evaporation must all influence the 

 result. The crystal which seems to have deviated most 

 widely from the average is that depicted in fig. 10 ; this 

 crystal grew at first less rapidly than usual, and finally came 

 almost to a standstill. It is possible that an increasing 

 solubility due to increasing temperature may have caused 

 this delaying tendency. 



It is interesting to compare this average, calculated on the 

 assumption that the crystal starts in the middle of the dark 

 interval, with a few single cases which appear to have begun 

 to crystallize very near the beginning or end of the interval. 

 In these cases, the first image of the crystal will appear 



