350 F. E. Wright — Measurement of the Optic Axial Angle 



cal 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 determinations of the position 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 compara- 

 tively accurate method to accomplish this consists in first turn- 

 ing the stage about H 2 until the known optic axis comes to lie 

 in the plane normal to the axis V^OCD, fig. 22), and in deter- 

 mining the extinction angle (-jCEOD) when the stage is in hori- 

 zontal position and also at such an inclination about Y 1 that 

 the extinction angle is 45° ; this can be recognized most read- 

 ily by placing the nicols in the 45° position and then revolving 

 the preparation about Y t until darkness ensues. By thus 

 ascertaining the angle of revolution necessary to attain the 

 required 45° extinction angle, the great circle CA„M is fixed 

 with reference to the horizontal diameter, the plane in which 

 the unknown optic axis A/ 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 (<EOD)for the plate in the hori- 

 zontal position, fixes the position of the second optic axis in the 

 projection. This method, however, is not always applicable 

 owing to the indistinctness of extinction phenomena in 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 "V, as in 

 the above method, measure the extinction angles for different 

 inclinations of the stage about V, (the angles, as usual, to be 

 reduced to real angles within the crystal by means of its aver- 

 age refractive index), and plot these directions of extinction in 

 stereographic projection. (Fig. 23.) tinder these conditions 

 the radii, which make an angle with the vertical diameter 

 OMj equal to twice the extinction angles, 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 

 O A/, the small circle, whose arc A 2 A/ intercepted between the 

 radii is equal to the angle of revolution of the stage. In prac- 

 tice it is advisable to repeat the determinations of the extinc- 

 tion angles and to take as angles of inclination those equivalent 

 to 0°, 10°, 20°, 30°, 40° and 45° in the crystal on both sides of 

 the normal to the section. 



