308 
The American Geologist. 
November, 1903 
Angles of refraction for 
Diff. 
Index 
Incidence of 
y n 
y m 
(n-m) 
45° 20° 
1.50 
28° 10' 
13° 10' 
1.87 
1.56 
.31 
1.54 
27° 20' 
12° 50' 
1.93 
1.60 
.33 
1.56 
27° 0' 
12° 40' 
1.96 
1.62 
.34 
1.60 
26° 10' 
12° 20' 
2.04 
1.66 
.38 
1.70 
24° 40' 
11° 40' 
2.18 
1.76 
.42 
2.00 
20° 40' 
9° 50' 
2.65 
2.10 
.55 
puted with this in mind. . In these yn for 1.54 is .03 less 
than for 1 . 56. If these figures are reduced so as to be com- 
parable with the thickness of microscope sections, the dif- 
ference in a section of .030 mm.' thick would be about 
.0005 mm. — a magnitude which, though hard to measure 
accurately, is easily observed. 
The difference between ym and yn bears a fairly con- 
stant ratio to yn for the common range of indices — being 
about one-sixth. This in a slide .030 mm. thick would be 
.005 if yn be taken as the thickness of the plate. This 
magnitude (.005) is about the average change in focus neces- 
sary to cause the bright band to shift from one side of the 
contact to the other. Within this distance the light coming 
from the side having the greater index is totally reflected, 
while from the other side the larger part is refracted at the 
contact. Therefore the focus must be changed through a 
distance of this order of magnitude in order to show the 
band on opposite sides. 
The application of this method of determining relative 
index of refraction is very simple. If the instrument used 
is not provided with a diaphragm below the condensing 
lense, the hand may be used to shade the mirror, thus cut- 
ting off part of the light. As a matter of experience it is 
found that the hand is used quite as frequently as the dia- 
phragm by one accustomed to the method. The fact that 
as the objective is raised the light band goes to the side of 
the higher index and vice versa provides a simple memory 
rule — focus high, band on side of higher index; focus low, 
band on side of lower index. 
Department of Geology, 
University of Wisconsin. 
