Growing Crystals by Instantaneous Photomicrography, 499 



crystal in fig. 15. The times o£ revolution represented by 

 figs. 9 and 11 are the same, 1*25 seconds, and the other con- 

 ditions also were identical, hence we may compare these with 

 accuracy. Careful measurements of the sizes in fig. 9 showed 

 the first large impression of the crystals to be about eighty 

 per cent, of the diameter of the next impression, and approxi- 

 mately the same relationship appears in fig. 11. In order to 

 find if this relationship corresponds with the equation D 3 = &£, 

 the larger diameter is assumed to be 0'93, the theoretical 

 value corresponding to two intervals of time, if that corre- 

 sponding to two and one half intervals is taken as unity. 

 Hence the smaller one becomes 0*75, corresponding to one 

 interval of time ; a value, marked in a circle on the diagram, 

 which is surprisingly near the cubic curve. Hence the 

 equation D d = kt is confirmed. That the same curve holds 

 approximately for the further growth of the crystal is mani- 

 fest by a quantitative study of fig. 9 (Plate VIII.). 



In this connexion it is interesting to note that the crystal 

 seems often to grow at first in the same proportion in all 

 directions. Even the very minute image in the centre of the 

 second exposure, given in fig. 9, shows itself under the 

 microscope to be elongated like the crystal which grows from 

 it. In the next exposure this crystal had the proportions 

 0*02 mm. x 0*0125 mm., and after four more exposures it 

 still had almost exactly the same proportions, being 0*035 mm. 

 x 0*022 mm. After two or three more seconds the form 

 given in fig. 9 began to change slightly, the crystal becoming 

 slightly less elongated in shape ; but by this time the neigh- 

 bouring crystals had grown so much as to approach it, and 

 hence to alter the conditions. A similar constancy in pro- 

 portion may be observed in many other series here given. 



The diagram shows how exceedingly fast the diametric 

 growth of the crystal must be in the first tenth of a second of 

 its existence. Hence we have an explanation for the sudden- 

 ness of its appearance to the eye of an observer, and for the 

 blurred edges of its photographic image. It is true that 

 another cause may contribute to the blurred effect ; namely, 

 the irregular refraction caused by the convection of the 

 lighter solution which has just deposited part of its load ; 

 but the speedv growth alone is capable of explaining the 

 observed indistinctness. 



Interesting as the rapid initial growth in diameter may be, 

 it places a serious bar in the way of more precise study of the 

 birth of crystals. One clearly needs not only high magnifying 

 power, but also great speed ; and these two together require 



