i8o 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
racy of the determination of the positions of the optic axes, their approxi- 
mate positions being known from the preliminary determination, it is neces- 
sary, in actual practice, to take readings of # 2 only 5 or 10 on either side 
of the approximately correct position of the optic axis, as determined by 
the preliminary direct observations. Convenient positions of the nicols for 
optical curves are at o, 45, 15, and 30 from the V\ axis of revolution. If 
FIG. 1 10. In the method illustrated by this figure, the visible optic axis A t is brought 
to coincide with the plane DCO and the angle of the position of 'extinction DOE 
measured while the stage is in the horizontal position. A- must lie then in the plane 
OB, the angle BOE having been made by construction equal to DOE. The section 
is then rotated about OM (axis V t ) until the extinction angle becomes 45, in which 
case the plane OM contains A t , since .1 1 has remained during this rotation in the plane 
DCO; on turning the specimen back to its original position, the line OM becomes the 
great circle CA t M and the intersection of this great circle with the plane OB fixes A t 
definitely in the projection. In practice, the great circle CA t M need not be drawn, 
since on placing the tracing over the projection plat it is only necessary to find that 
small circle A t A ' f , the arc of which intercepted between OB and M is equal to the 
angle of rotation. 
both optic axes appear within the microscopic field of vision, the most 
satisfactory method for measuring the optic axial angle by means of the uni- 
versal stage is to determine the exact position of each axis by the above 
method and to plot the same (after proper reduction to corresponding angles 
within the crystal) in suitable projection, in which the angle can be measured 
directly by graphical methods rather than by calculation. 
The results obtained by the use of optical curves can be checked and 
verified by several of the methods described below, which are of general 
application and can readily be applied to this special case. 
Fedorow has shown that in actual practice with minerals of weak to 
medium birefringence the errors can be disregarded which are due to the 
reduction of all observed angles by means of the average refractive index 
of the crystal in place of the true refractive indices for each given direction. 
