24 



IT. S. COAST AND GEODETIC SURVEY. 



STEREOGRAPmC MERIDIAN PROJECTION. 



In the discussion of the stereographic meridian and 

 horizon projection, it is probably best to consider first the 

 sphere and later to indicate the manner in which the 

 ellipsoidal shape can be taken into account. To employ 

 the differential formulas given before, we need only to 

 set € equal to zero. 



Any stereographic projection is a perspective projection 

 of the sphere, either upon a tangent plane or upon a dia- 

 metral plane, with the center of the projection lying upon 

 the surface of the sphere in such a way that the diameter 

 through the point of projection is perpendicular to the 



Fig. 5.— Radius from center on stereographic projection, 



plane upon which the projection is made. We shall make 

 use of the diametral plane since there is only a difference 

 of scale between that and the tangent plane. 



In figure 5 let the circle QMRP be a plane section 

 of the sphere determined by the diameter PQ and the 

 projecting line PM, P is the point of projection, OR is 

 the trace of the diametral plane upon which the map is to 

 be constructed, and the point Q projected into O forms 

 the center of the map. Let the angle QOM be denoted 

 by p; then the arc QM \s the measure of f. AU points 

 of the sphere at the arc distance v from Q will lie upon a 

 circle the plane of which is parallel to the plane OR, The 



