RICHARDS AND ARCHIBALD. — GROWING CRYSTALS. 351 



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 = 3 are given 

 above, for comparison with the experimental curve. It is clear that the 

 curve with the latter value, n = 3, is the nearest, possessing the same gen- 

 eral curvature, and deviating from the average less than the individual 

 measurements do. This is equivalent to saying that equal increments of 

 lime 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 tendency of the curve is established. It 

 is probable that under the necessarily ill-defined conditions of our experi- 

 ments the growth follows no one law with precision ; supersaturatiou, 

 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 Figure 10; this crystal grew at first less rapidly than 

 usual, and finally came almost to a standstill. It is possible that an in- 

 creasing 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 sin- 

 gle cases which appear to have begun to crystallize very near the begin- 

 ning or end of the interval. In these cases, the first image of the crystal 

 will appear either almost as large as the second image, or very small 

 compared with it. It will appear almost as large as the second image 

 when the preceding exposure has just not caught the beginning of the 

 crystal, which has thus had a whole interval for growth ; or very much 

 smaller than the second image when the first impression has registered a 

 crystal only a very small fraction of a second old. Marked examples of 

 the former case are to be found in Figure 11, and of the latter in the largest 

 crystal in Figure 9, and the smallest crystal in Figure 15. The times of 

 revolution represented by Figures 9 and 11 are the same, 1.25 seconds, and 

 the other conditions also were identical, hence we may compare these with 

 accuracy. Careful measurements of the sizes in Figure 9 showed the first 

 large impression of the crystals to be about eighty per cent of the diam- 

 eter of the next impression, and approximately the same relationship ap- 

 pears in Figure 11. In order to find if this relationship corresponds with 

 the equation D 3 = Id, the larger diameter is assumed to be 0.93, the the- 

 oretical value corresponding to two intervals of time, if that corresponding 

 to two and one half intervals is taken as unity. Hence the smaller one 



