BIREFRINGENCE. 
107 
In Fig. 64 lines of equal birefringence 5 per cent less than the correct value 
(y a), are drawn for different optic axial angles and show that inclinations 
of 15 produce errors of 5 per cent and less of the true value (7 a), while 
inclinations of 20 (Fig. 65), produce errors of 10 per cent and less of the 
total birefringence. Similarly, for sections normal to a bisectrix, Fig. 66 
indicates that for an optic axial angle, 2 T' = 45, a plate cut at an angle of 
7 with the bisectrix may produce a positive or negative error of 10 per 
cent or less in the birefringence (7 /3) or (/3- a). But in this case the bire- 
fringence (7 ~/3) or (/3 a) is only about 14 per cent of the total birefringence 
and an error of 10 per cent therefore usually applies only to the fourth 
decimal place. In Fig. 67 the directions for which the birefringence is 
FIG. 67. FIG. 68. 
FIG. 67. Similar to Fig. 66, except that the center of the projection plat is the obtuse 
bisectrix (2^ = 45). As in Fig. 66, the directions whose birefringence is 10 per cent 
greater or less than that of the obtuse bisectrix are indicated. 
FIG. 68. Similar to Fig. 66, except that the optic axial angle is 2 K=9O. The dotted 
curves again represent the directions for which the birefringence is 10 per cent greater 
or less than that of the bisectrix at the center of the projection plat. In this stereo- 
graphic plat, as in all preceding, the concentric circles are 10 apart. 
10 per cent greater or less than (/3 a) or (7 j3) here about 85 per cent of 
(7 a) for 2 V = 45 (obtuse bisectrix) approach within 1 8 of the bisectrix. 
In this figure the curve indicating an increase of 10 per cent birefringence 
is 50 and over from the obtuse bisectrix. Plates making an angle of less 
than 20 with the bisectrix can, therefore, be safely assumed to furnish 
values of (j8 a) or (7 /3) which are not over 10 per cent in error. An 
inclination of 8 would produce an error of about 2 per cent in 03 a) or 
(7 /3). In Fig. 68, the rate of change of birefringence for sections at 
different angles with the bisectrix is indicated on the assumption that 
27 = 90; there an inclination of 12 and over is required to effect a nega- 
tive error of 10 per cent in the birefringence (7 /3) or (/3 a) and 18 or 
more to effect an equal positive error. Assembling these data, it may be 
assumed in general that the birefringence of a plate inclined at an angle 
