422 F. E. Wright — New Ocular for Use with the 



using sections inclined at low angles with the correct direc- 

 tions. For a given plate the birefringence can be calculated 

 approximately from the usual formula, 



y — < 



sin I' sin I 



y— a 



in which I and \! are the angles which the normal to the plate 

 makes with the two optic axes (or optic binormals) respectively. 

 In figs. 3-8 these relations are shown graphically in stereo- 

 graphic projection. In each figure the angular distance 

 between any two successive concentric circles is 10°. Thus in 

 fig. 3 are indicated the positions of the sections whose bire- 

 fringence is 2 per cent less than the true birefringence (y-a) 

 exhibited by a properly cut plate exactly perpendicular to 

 the optic normal. The position of these lines of equal bire- 

 fringence is different for different optic axial angles as indi- 

 cated by the lines for 2 Y=0°, 45° and 90°, but it is evident 

 from the figures that an inclination of 10° with the true 

 optic normal section will cause an error not over 2 per 

 cent less than the true value (y-a) and often much less. In 

 fig. 4 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 in the true value (y-a), while inclinations of 20° 

 (fig. 5) produce errors of 10 per cent and less of the total bire- 

 fringence. Similarly, for sections normal to a bisectrix, ~B.g. 6 

 indicates that for an optic axial angle 2 V=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 (y-fi) 

 or (/3-a). But in this case the birefringence (y-/3) or (fi-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. 7 the directions for which the bire- 

 fringence is 10 per cent greater or less than (/3-a) or (7-/5), here 

 about 8J per cent of (y-a) for 2 Y=145° (obtuse bisectrix), 

 approach within 18° 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 (fi-a) or (y—fi), which are not 

 over 10 per cent in error. An inclination of 8° would 

 produce an error of about 2 per cent in (fi-a) or (y-fi). In 

 fig. 8, the rate of change of birefringence for sections at differ- 

 ent angles with the bisectrix is indicated on the assumption 

 that 2 Y=90° ; there an inclination of 12° and over is required 

 to effect a negative error of 10 per cent in the birefringence 

 (y-fi) or (fi- a ), and 18° or more to effect an equal, positive 

 error. — Assembling these data, it may be assumed in general 



