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



As a general rule, it is neither convenient nor feasible to 

 work with actual models in the study of optical phenomena. 

 Several different types of projection have been devised to 

 overcome this difficulty by representing the spacial relations 

 on a plane. In all cases the relation of the object to its pro- 

 jection plot is one of definite construction, and is dependent 

 on the method of projection adopted. 



In optical work, any one of three different methods of pro- 

 jection, the gnomonic, the orthographic, and the stereographic, 

 may be used, each of which possesses certain favorable and 

 certain unfavorable features. In each projection, the points 

 on the sphere are pictured in a fixed plane. 



In the gnomonic projection,* the plane of projection is the 

 horizontal tangent plane passing through the crest of the unit 

 sphere. (Fig. 2.) The point of intersection . of the radius 



In this figure, the point D is the gnomonic projection point of the 

 point P on the sphere, or of the direction CP in the crystal. The distance 

 MD is evidently r. tan p, r being the radius of the sphere arid p the angle 

 MCD. Similarly, the distance CE in the stereographic projection is r tan 



— and CF in the orthographic projection, r sin p. 



drawn through any given point on the sphere with. the tangent 

 plane is the projection rDoint for that direction. In this pro- 

 jection, the great circles of the sphere become straight lines in 

 the plat, and are small circles, hyperbolae. In the following 

 pages, however, the gnomonic projection will not be used to 

 any extent and. will not therefore be described here in greater 

 detail. It is particularly well suited to crystallographic work, 



* For a comparative study of projections, see V. Goldschmidt, Ueber 

 Projektion und graphische Krystallberechnung, Berlin, 1887. 



