Wright — Optical Character of Birefr acting Minerals. 293 



the equation of an equilateral hyperbola passing through the 

 zero coordinate point with asymptotes parallel to the X and Y 

 axes. For the special case under consideration where x = y , the 

 formula becomes 



J 1_2 (3) 



From (3) the curves of fig. 3 were plotted in gnomonic pro- 

 jection. 



For x : = oo , equation 3 becomes 



x = y 



the equation of a straight line passing through the zero point at 

 an angle of 45° with the coordinate axes. If the formula of 

 Mallard were exact, x 1 could not assume a value greater than 1 

 (sine 90°) ; since it is approximately correct only for small angles, 

 the above remark does not obtain. The gnomonic projection 

 was, therefore used in fig. 3 instead of the orthographic. 



In such limiting cases the graphic method gives more satisfac- 

 tory results and is in general better suited to the study of optical 

 phenomena. In fig. 4, the stereographic plat with curves for 

 optic axial angles 0°, 15°, 45°, 75°, and 90° is given. Their 

 course in the vicinity of the pole of the projection only is repre- 

 sented since it corresponds to that portion which is seen under 

 the microscope. 



Plate parallel to the plane of the optic axes* 



In the uniaxial minerals this plate corresponds to any section 

 in the prism zone. 



Tbe interference figure from the section can be recognized 

 by the fact that in the position of darkness tiie entire field is 

 practically dark and that a small revolution of the stage (5°) 

 will cause the faint hyperbola to recede entirely from the field 

 of vision. In the diagonal position the colored interference, 

 curves have the form of hyperbolas. 



Since ordinary approximate methods of calculation do not 

 apply to this section, the graphic method with the stereographic 

 projection plat as base was adopted. The result, as depicted 

 by the curves of fig. 6, shows that the recession of the dark 

 achromatic lines for the optic axial angles 2Y — 0°, 10°, 80°, 

 and 90° after a revolution of 1° of the stage is very marked, 

 and that, except in the limiting case of 2Y = 90°, the dark 

 hyperbolas pass out of the field most slowly in the direction of 

 the acute bisectrix. For 2Y = 90° the hyperbolas in all quad 

 rants recede from the center with equal rapidity. In fig. 6 

 * Compare F. E. Wright, this Journal, xvii, 387-391. 



