io6 
METHODS OF PETROGRAPHIC-MICROSCOPIC RESEARCH. 
but it is evident from the figure that, in general, it is safe to assume that an 
inclination of 10 with the true optic normal section will cause an error of 
not over 2 per cent less than the correct value (7 a) and often much less. 
FIG. 63. FIG. 64. 
FIG. 63. In this stereographic projection plat (circles 10 apart) the positions of the 
directions in a biaxial crystal whose birefringence (y' a') is 2 per cent less than that 
of the optic normal (y a) are indicated for the optic axial angles 2 7=o, 45, and 90. 
The optic normal coincides with the central point of the figure. 
FIG. 64. Stereographic projection plat showing positions of the directions for which 
the birefringence (y' a') is 5 per cent less than that of the optic normal (y a), which 
coincides with the center of the concentric 10 circles. These curves are drawn corre- 
sponding to the optic axial angles 2 V = o, 45, and 90. 
FIG. 65. FIG. 66. 
FIG. 65. Like Fig. 64, except that the directions are indicated whose birefringence 
is 10 per cent less than that of the optic normal located at the center of the projection 
plat. The positions of the curves corresponding to optic axial angles 2 V = o, 15, 45, 
60, 75, 90 , are indicated in this figure. 
FIG. 66. In this figure the directions whose birefringence is 10 per cent less or greater 
than that of the acute bisectrix (optic axial angle 2^ = 45) are shown by the dotted 
curves. The dotted curve which passes through the center point (acute bisectrix) marks 
the directions whose birefringence is equal to that of the acute bisectrix (y ft) or (/3 a), 
as the case may be. 
