352 PROCEEDINGS OF THE AMERICAN ACADEMY, 



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^ = kt is confirmed. That the same curve holds 

 approximately for the further growth of the crystal is manifest by a 

 quantitative study of Figure 9 (Plate II.). 



In this connection 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 Figure 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 pro()orti()ns, being 0.035 mm. X 0.022 mm. After two or three 

 more seconds the form given in Figure 9 began to change slightly, the 

 crystal becoming slightly less elongated in shape ; but by this time the 

 neighboring crystals had grown so much as to apjjroach it, and hence 

 to alter the conditions. A similar constancy in proportion 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 suddenness 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 speedy growth alone is capa- 

 ble 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 very intense light. Whether or not we shall 

 be able to obtain more positive knowledge with the present apparatus, is 

 a questionable matter. The same phenomenon casts a measure of doubt 

 over some of the observations of Link and his followers. Is it not possi- 

 ble that the subjective effect of the rapidly growing crystal might be mis- 

 taken for that of a globule of liquid ? Even upon the photographic plate 

 there is a slight resemblance, and in one or two cases deliberate study is 

 needed to detect evidence of structure in the smallest crystals. 



In conclusion, the report of the foregoing pages may be summarized as 

 follows. It has been found possible to take very frequent photomicro- 

 graphs of crystals during their birth and growth. An enlargement of 

 over four thousand diameters was obtained, and both common and polar- 



