322 F. F. Wright — Measurement of the Optic Axial Angle 



The actual modus operandi of this and the stereographic pro- 

 jection will appear more clearly later when actual data of 

 observation are plotted. 



In the stereographic projection,* the eye of the observer is 

 considered at the lower extremity of the vertical radius, the 

 lines of sight being directed toward the points of intersection 

 of given radii with the surface of the sphere. The intersection 

 of the line of sight for a given radius or direction of light wave 

 propagation with the central horizontal plane determines then 

 the stereographic projection point of that radius. (Plate I 

 and figs. 2 and 4.) 



In this figure the point P of the sphere, corresponding to the direc- 

 tion CP within the crystal and located in this instance by the great circle 

 ATP and the small circle DPK, becomes E in the stereographic projection 

 plat and is there located at the intersection of the great circle arc AHE, 

 the stereographic projection of ATP, and by the small circle arc DEL, the 

 stereographic projection of DPK. E is also the point of intersection of the 

 line OP with the horizontal diametral plane CGB. 



The stereographic projection is unique in that all circles, 

 whether great or small, appear in the projection as circles 

 instead of ellipses, as might be supposed at first thought. The 

 angle, moreover, which two great circles make with each other, 

 is preserved unaltered in the projection. The projection is 

 thus angle-true. In Plate I, the portions of great circles of 

 the upper half of the sphere are represented by the circular 

 arcs of which the horizontal radius is the limiting case, and 

 the small circles by the arcs of which the vertical radius is the 

 limiting case. 



JBiofs or FresneVs rule. — In several of the optic methods to 

 be described, frequent use is made of a rule first formulated 



*S. L. Penfield, this Journal (4), xi, 1,115 ; E. Fedorow, Zeitschr. Kryst., 

 vols, xxvi, xxvii, xxix, and G. Wulff, Zeitschr. Kryst., xxi, 249, 1893 ; xxxvi, 

 14-15, 1902, have given complete descriptions of the stereographic projection. 



