THEORY OF POLYCONIC PROJECTIONS. 



25 



lines that project the points of this circle will all lie upon 

 a right circular cone that will* cut the plane OR in a circle 

 the radius of which will be equal to ON, OP is equal to a^ 



and the angle OPN is equal to ^ • 

 Hence 



ON=p = a tan ?• 



If we denote the angle between p and the X axis in the 

 mapping plane by w, we have 



p a sin 7? cos ca 



x = p cos CO = a tan ^ cos w = — :r-r^ 



^ 2 1 + cos 2? 



p . a sin p sin co 



1/ = p sm CO = a tan ^ sm co = ., , ^ • 



^ ^ 2 1 + cos 2> 



Fig. 6,— Transformation triangle for meridian stereographic projection. 



If the point of projection lies on the Equator as it does 

 in the stereographic meridian projection, the values of 

 the functions of p and co must be determined in terms of 

 <P and X. 



In figure 6, let WQV be the Equator and T the pole 

 and let TQ project into the central meridan of the map. 



