290 Wright — Optical Character of Birefracting Minerals. 



The mathematical formula above is only an approximate one, 

 while a graphic method can be applied which is theoretically 

 correct and b} r which more accurate results can be obtained. 

 The method has been used by Michel Levy, Viola,* von Fedorow 

 and others in their feldspar studies and is well adapted for 

 general use in the study of optical phenomena. 



The lines along which any face will extinguish can be found 

 by passing planes through the normal to the face and the optic 

 axes respectively, and bisecting the traces of these planes on the 

 face. In order to do this readily, a stereographic projection of 

 the optic axes in any desired position should first be made. By a 

 revolution about each of two horizontal axes in the principal 

 planes in the nicols, any face normal can be brought to coincide 

 with the pole of the projection and the face with that of the 

 paper. The bisectors of the angles between the straight lines 

 drawn through the pole of the projection and the optic axes in 

 their new positions are then the desired directions. The achro- 

 matic black hyperbolas of the interference figure correspond to 

 those face-normals whose extinction lines are parallel to the axes 

 of revolution of the projection. In the projection the achro- 

 matic lines, however, do not appear as they do when observed 

 under the microscope, for its interference figure can be considered 

 with slight error as an orthographic projection of the rays on a 

 sphere, as shown by Mallard's formula above. The curves of 

 the stereographic projection must therefore be replotted by 



E 

 making the polar distance sine E instead of tan — as it is in the 



stereographic projection. The general aspect of the curves is 

 not changed by this transformation. The graphic method has 

 been applied to the methods below with satisfactory results. 

 (Figs. 4 and 6.) 



The interference figure from the section perpendicular to 

 the obtuse bisectrix differs from the above only in the wider 

 optic axial angle, which can be measured by the same methods. 



Plate perpendicular to an optic axis. 



The interference figure obtained from this plate consists 

 ordinarily of a black achromatic bar which revolves in a 

 direction opposite to that of the stage. In general the bar is 

 a straight line only when it is parallel to the planes of polari- 

 zation of the nicols ; in the intermediate positions it is more or 

 less convex, depending on the angle between the optic axes. 

 If 2E, however is equal to 90°, the curve is a straight line in 

 all positions for the usual microscopic field of vision. 



* Michel Levy, Sur la determination des feldspaths, 1894, pp. 15-20. C. 

 Viola, Zeitschr. fur Kryst., xxx, 232, xxxi, 484, xxxii, 805. E. von Fedorow, 

 Zeitschr. fur Kryst., xxxi, 579, xxxii, 246. 



