THE VARIATION OF ANGLES OBSERVED IN CRYSTALS. 
495 
emergence of the reflected light; i.e., the angle between the rays entering the 
telescope from the crystal and the normal to the face OB. 
If, then, A be the angle AOB, and n be the refractive index of the crystal, the 
refi’active index, p, of the liquid is given by the formula 
— 
n 
— cos ; where tan p = 
sin ( 45° + ^ 2 ^ ^ ^ 
A + 
o 
sin A 
A preliminary experiment was made on November 14, 1900, with a good crystal of 
potash-alum growing at a temperature of 18'6°. The refractive index of the alum 
crystal for sodium light was measured in two ways: (l) by minimum deviation, 
using tlie octahedron as refracting prism ; (2) by total internal reflection, making use 
of the natural faces of the crystal, and was found to be 
1'4598 by minimum deviation, 1'4605 by total reflection. 
The values previously found Ijy Stefan, Grailich, Mulheims, Soret, Took, and 
F. Kohlrausch vary between 1’4549 and 1'4565. 
The refractive index of a solution saturated at 18'G° was also determined in two 
vnys : (l) by minimum deviation, using a hollow glass prism filled with the solution ; 
(2) by total reflection, using a glass prism of refractive index 1'51704 immersed in 
the solution contained in the square trough, and pursuing the process described 
above. 
It was found to be 
1-34251 at 18° by total reflection, 1-34280 at 15° l.)y minimum deviation 
(the latter corresponding to 1-34250 at 18°). 
With a prism of 70° 31' formed Ijy two octahedron faces, and with 1-4598 for the 
index of the crystal, and 1-3425 for the index of the liquid, the angle of emergence 
should be 0 — 3° 57' 3G". 
Of coui-se one difficulty Introduced by the use of the alum crystal itself is that the 
angle is not exactly that of the regular octahedron, and is lialfle to small variations. 
The faces. A, B, of the crystal used in this experiment did not give multiple images, 
and were inclined to one another at the angle 70° 24'. For this prism the angle of 
emergence should be 9 = 3° 50' 0". 
The preliminary experiment gave a smaller angle of emergence, indicating a higher 
refi'active index for the liquid, and showing that the solution in contact with the 
gro wing crystal is, in fact, supersaturated. 
Before proceeding to determine the exact refractive index of the liquid, it was now 
necessary to ascertain (l) how the refractive index of strong solutions varies with 
their concentration; (2) whether there is any sudden change in the index in passing 
