OPTIC AXIAL ANGLE. l8l 
The method of measuring the optic axial angle by means of optical curves 
can be used only when both optic axes appear within the field of vision. 
In other cases other methods are to be employed, which involve either the 
measurement of extinction angles in zones or the determination of the 
positions of the principal planes of the ellipsoid, these latter to be plotted 
in appropriate projection. In most cases, however, one optic axis can be 
determined directly by optical curves, while the second optic axis makes a 
large angle with the normal to the section and must be determined indirectly. 
A simple but comparatively accurate method to accomplish this consists in 
first turning the stage about H 2 until the known optic axis comes to lie in 
the plane normal to the axis V\ (OCD, Fig. no), and in determining the 
angle of the position of extinction ( < ROD} when the stage is in the hori- 
zontal position and also at such an inclination about V\ that the extinction 
angle is 45; this can be recognized most readily by placing the nicols in 
the 45 position and then rotating the preparation about V\ until darkness 
ensues. By thus ascertaining the angle of rotation necessary to attain the 
required 45 extinction angle, the great circle CA 2 M is fixed with reference 
to the horizontal diameter, which in turn represents the plane in which the 
unknown optic axis A 2 must rest when the extinction angle is 45. The 
intersection A 2 of the great circle CA 2 M with the radius OB drawn at an 
angle, with the vertical line, of twice the angle of extinction (<EOZ?) for 
the plate in the horizontal position, fixes the position of the second optic 
axis in the projection. 
This method, however, is not always applicable, owing to the indistinct- 
ness of extinction phenomena on steeply inclined sections (effect of elliptical 
polarization), and a second method of extinction curves, of which the above 
is only a special case, can be used to advantage. Having first placed the 
known optic axis in the plane normal to the axis Vi as in the above method, 
measure the extinction angles for different inclinations of the stage about 
Vi (the angles, as usual, to be reduced to real angles within the crystal by 
means of the average refractive index), and plot these directions of extinc- 
tion in stereographic or angle pt ejection (Fig. 1 1 1). Under these conditions 
the radii, which make an angle with the vertical diameter OM equal to twice 
the extinction angle, are evidently the planes containing the second optic 
axis A 2 , whose exact location can be readily found by noting (for two given 
radii, as OA 2 and OA 2 ') the small circle, whose arcA 2 A 2 intercepted between 
the radii is equal to the angle of rotation of the stage. In practice it is 
advisable to repeat the determinations of the extinction angles and to take 
as angles of inclination those equivalent to o, 10, 20, 30, 40, and 45 in 
the crystal on both sides of the normal to the section. 
In actual work with this method it happens occasionally that the deter- 
mination of the location of A 2 is not accurate because of the acute angle 
between the radius and the small circle A 2 A 2 . In such cases the writer has 
been able to apply with favorable results one of the two following methods,* 
which, like the preceding method, are based on the measurement of extinc- 
tion angles for different angles of inclination about one of the horizontal 
axes of rotation of the universal stage. The new circle V* renders hereby 
valuable assistance. 
*Amer Jour. Sci. (4), 24, 351, 1007 
