Lacroix 1 A xiul Goniometer. — Winchell. 
si 
Fig. 2. 
Suppose that on trial with a thin section of muscovite it is 
found that tin- distance 2sinE is divided by tin- revolution 
of the graduated rim B, tig. 1, into 1,430 parts. As these part- 
have no known value it is necessary to compare them with a 
standard. Such a standard is found in a mineral whose optic 
angle has been previously determined by other means. For 
instance, if the optic angle 2E in another specimen of musco- 
vite is known to he 71°, then E in the same is 35° .'!<»'. 
Let the unknown distance between the loci of the optic axes 
in this' muscovite he represented by 2d, and let the unknown 
ratio between its units and those of the number 1,430 he rep- 
resented by M. Then 
d „ '1 
bxdE ^r: M== • ., 
M sinE. 
On measuring 2d in this muscovite it may he found to be 
1,525. Hence 
" si„ *v :«»• : '°g M 
og 35° 30' 
Mil tJ*J i)\J 
log M 3.12085. 
Therefore, in the original specimen. 
logsinE log 71.") 3.12085 1.73346. 
E 32°46 r 3l" 
2E w.v. v %" 
The optic angle in muscovite may vary 30°. 
In making such measurements it is necessarry to use always 
the same objective, and to employ the same constant M ascer- 
tained for tin- microscope in use, which may he kept in its 
logarithmic form. 
4s the apparent size of the interference figure depends on 
the position of the Bertram! lens, it is necessary also to have 
