516 
PROFESSOR HENRY A. HIERS: AN ENQUIRY INTO 
It must be remarked that owino’ to the use of cleavao^e frao-ments in these 
experiments it is not absolutely certain in every case that the crystal was actually 
growing, and it is possible that the higher values are the most correct. 
It will he noticed that the refractive index of a saturated solution of sodium nitrate 
is greater than the extraordinary index, 1'33608, of the crystallised substance, and 
less than the ordinary index, 1'58739, so that only the ordinary index comes into 
operation in these experiments, and with regard to the index of the crystal no 
account need be taken of the direction in which the light is travelling in the crvstal. 
With all the three STdjstances examined the result is the same : the liquid in 
contact with a growing crystal is slightly, and only slightly, supersaturated. 
PART III. 
The Action op the Concentration Streams (Cra^stallisation in Motion). 
Interpretation of the Foregoing Results. A Possible Cause for the Vo.riation of 
Angle in Alum and other Crystals. 
In the preceding pages we have seen that, in the case of alum, the apparent 
variation of the octahedron angle is certainly due to the production of vicinal faces, 
and that the same cause is probably sufficient to account for tlie variations of angles 
in the forms of other substances. The variati<ms are small, l)ut they lead to the 
following important results : — 
The faces uHch actually occur upon a crystal are, in general, not those U'ith simple 
rational indices, hut are vicinal faces. 
It is true that these probably possess rational indices, l)ut such as can only be 
expressed by liigh numbers. 
To what are these faces to lie attrihuted ? 
There is little in crystallographic literature which throws light upon the subject, 
and, so far as I am aware, alisolutely no experimental work. 
Only in the recent remarkable and original investigations of G. Wulff, upon the 
velocity of crystal growth, is a definite exiilanation of the vicinal faces proposed. 
WuLFF finds that the velocity of outward growth of a crystal is different for 
different faces, and he supposes that it is probaldy inversely proportional to their 
reticidar density; the actual velocity of growth is, however, largely influenced by the 
intensity and direction of the concentration streams Avhich flow upwards round the 
crystal. Experiments upon these led him to the conclusion that the crystals grow 
* “ Zur Frage der Geschwindigkeit des Wachsthums und dcr AuHosuiig der I\ryst;dlflachen,” ‘ Zeitsch. 
f. Kryst.,’ 1901, vol. 34, p. 449. 
