; ,> METHODS oi- PBYROGRAPHie-mCROSCOPIC KI:M:.\KCH. 
Alter reduction to corresponding crystal angles, the position of .li in 
projection was found to be 
//! 180, 7/ 2 90, 7/ 3 22 5 . 5 , V l 6 and F 2 i 
The 7/3 ellipsoidal plane was located by 
77, 180, 77 2 o, 77 3 315, I', -, 1' 2 26 
while for the ay ellipsoidal plane, the readings were 
77, iSo, II, 90, 77 3 22 5 . 5 , T r , -, To -1 
The optic axial angle thus determined in projection plat is 2!' = 64. In 
such cases, where the section is nearly normal to an optic axis, the method 
of extinction curves is not of practical value, owing to the difficulty of 
determining extinction angles with the requisite accuracy. 
Topaz. Section nearly normal to the obtuse bisectrix. 
The optic axial angle was found by first locating the principal ellipsoidal 
plane aft and ay and then measuring the extinction angle of the section when 
a coincided with the microscope axis and after rotation of the section from 
that position through known angles about Vi and V->. 
For the ellipsoidal planes the readings were : 
77 1 7/2 77r< I i I 2 
a/3 plane 180 90 236. 5 .. o 
ay plane 180 90 326 .. 17.5 
For a in coincidence with the microscope axis, the readings were found 
from the projection to be 
77: 185, 77 2 90, 77 3 326, T, 30, T' 2 22. 5 
After the rotation about l'i and I' 2 the angles recorded were 
77, i8 9 . 5 , 77 2 90, 77 3 326, ]\ 40, I', -15 
From these angles 2 V was measured in projection and found to be 66. 
By direct observation of the optic axis, the same angle was also obtained. 
This method may, in favorable instances, give reliable results, but in general 
it can not be considered accurate, owing to the undue influence in projec- 
tion of slight deviations of the extinction angle on the value of the optic axial 
angle. 
For the second section the readings were: 
77, 77 2 77, 1', r, 
o^plane 180 90 140 .. -fo.5 
07 plane 180 90 234 .. 32.5 
Opticaxis.li 180 90 140 4 +0.5 
The optic axis .1 1 was determined by direct readings. After proper reduc- 
tion to true crystal angles the value 2!' = 63 was obtained from the pro- 
jection plat. 
Topaz. Section about perpendicular to the optic normal. 
In this instance the principal ellipsoidal planes were first determined and 
ellipsoidal axis ft brought to coincide with the microscope axis and the cxtinc- 
