52 



TJ. S. COAST AND GEODETIC SURVEY. 



If then the angle Bp^F=-^ — \, we shall have 



^i^=a sec a cot X. 



The arc GH must be taken as the complement of the 

 longitude, for which we wish to construct the meridian. 

 6^/f is 30°; therefore C is the center of the meridian for 

 X = 60°. The meridians all pass through p and p', so 

 that they may be constructed as soon as we have located 

 the centers. F is, of course, the center for the meridian 

 ofX = 90°. 



Fig. 14. — Elements of a small circle on stereographic projection. 



SOLUTION OF PROBLEMS IN STEREOGRAPHIC PROJECTIONS. 



We shall now give the demonstration of the solutions 

 of a few problems connected with stereographic projections. 

 The plane of the projection is called the primitive plane, 

 and the circle formed by the intersection of the primitive 

 plane with the sphere is called the primitive circle. The 

 polar distance of a point on the sphere is the angular 

 distance on the sphere from one of the poles of the primi- 



