STEREOGRAPH 1C, ORTHOGRAPHIC, GNOMONIC, AND ANGLE PROJECTIONS. 65 
upper half of the sphere are represented by the circular arcs, of which the 
horizontal radius is the limiting case, and the small circles are represented 
by the arcs of which the vertical radius is the limiting case (radius of pro- 
jection sphere = 10 cm.) 
In the orthographic (also called orthogonal or parallel or ocular) pro- 
jection the eye of the observer is supposed to be at an infinite distance above 
the plane of projection and to look directly down upon the sphere (c= oo and 
3; = sin p). The lines of sight are then parallel and the points on the sphere 
are vertically above their projection points on the central diametral plane 
(Fig. 42 and Plate 4). In this projection great circles appear as ellipses and 
vertical small circles appear as straight lines. This projection is especially 
important, since all interference phenomena observed in convergent polar- 
ized light under the microscope appear to the eye of the observer as they 
Fig. 42. In this figure the point P of the sphere, located in this case by the intersection 
of the great circle A TP and the small circle DPK, becomes in the orthographic projection 
F and is there located by the ellipse AHF, the orthographic projection of A TP, and the 
straight line DFL, the projection of DPK. F is also the point of intersection of the 
diametral plane CGB with the line PF, normal through P to that plane. 
would were the actual interference phenomena plotted in this projection. 
The serious drawback to its general application in optical work lies in the 
rapid decrease of its sensitiveness to differences in angular distances near 
its outer margin. In Plate 4 (meridian orthographic projection) the ellipses 
represent great circles with a common diameter of intersection and drawn 
at intervals of 2, while the straight lines are the projections of vertical 
small circles, also 2 apart, and correspond to small circles of latitude. As 
on the sphere itself, the angular distance between any two points in pro- 
jection can be found by passing through the two points, the common great 
circle (ellipse in projection) and counting directly the distance in degrees by 
means of the small circles. The actual modus operandi of this and the stere- 
ographic projection will appear more clearly later when actual data of 
observation are plotted. 
These three methods of projection are commonly used in crystallograhpic 
and optical work. Each type possesses certain favorable and certain un- 
favorable features. The gnomonic projection shows excessive distortion 
for large polar angles and can not be used to advantage for polar angles 
much above 75. The stereographic projection shows less distortion, but 
