THE VARIATION OF ANGLES OBSERVED IN CRYSTALS. 
5II 
experiments, then the light after emergence traverses a licpnd whose index changes 
from to IX ,; and, if it he assumed that it changes uniformly, then the index can 
be deduced from the angle of emergence 9 and the angle of the crystal a by the 
formula 
Uo sin 0 
,« ^ - - 
fx^ — jX cos 
cos' 
a 
Under the conditions described below, tliis formula is practically identical with that 
given on p. 495. 
(1.) Potash-alum. 
With alum either the acute or the obtuse angle of the octahedron may ])e 
employed, and, therefore, a theoretically ])erfect crystal would admit of four deter¬ 
minations without readjustment, using In turn the four octahedron faces as the 
totally reflecting surface. In general it was not possible to carry out more tlian one 
determination on eacli crystal in consetpience either of vicinal faces, or the difficulty 
of illumination owing to tlie shape of the crystal, or the imperfections of the faces. 
A very perfect crystal giving single reflections from two faces B and 0 was adjusted, 
and immersed in concentrated solution one evenina: and 
allowed to grow during the night; on the following day no 
reading could he obtained, hut on the second day a reading 
was obtained for total reflection at C, the light emerging 
through D (fig. 19). 
Assuming that the angle a is 109° 29', and calculating 
from the reading for which C was perpendicular to tlie tele¬ 
scope (I) itself being a somewhat unsatisfactory face), the 
angle of emergence, 6, was found to he — 4G° 54U. Taking 
the value 1’4598 for the Index of the alum, this leads to the 
value 1'3455 for the index of the liquid In contact with C, 
and, therefore, indicates that the liquid is only slightly 
supersaturated. 
If the index of the liquid had been 1-34232, the value found for the saturated 
solution, the angle of emergence would be — 47° 26', a difference lying far beyond the 
errors of observation. 
If the angle of the prism \vas 109° 23^', as deduced from the measured angle BC, 
instead of the theoretical angle 109° 29', the angle of emergence would have been 
— 46° 49', indicating tliat the difference observed caunot be attributed to a small 
error in the angle of the crystal. 
The crystal was re-examined in the evening, and, immediately after the reading 
for total reflection had been taken, the crystal was dried with a soft tongue of 
blotting paper and re-measured. The faces CD yielded (in addition to other 
