THEORY OF POLYCONIC PROJECTIONS. 



57 



Fig.. 19.— Locus of centers of great circles througli a given point on stereographic projection. 



In figure 19 let P' be the projection of the given point 

 through which the great circles are to pass; draw the diam- 

 eter iVP'/S and the perpendicular diameter WE. The pro- 

 jections of all great circles through P' must also pass 

 through a point at the distance of tt from P'; accordingly 

 draw the diameter PQ and draw WQ, cutting NS the lino 

 of measures inQ'; then Q' is the projection of the antipode 

 of P. Since all the required circles pass through P' and 

 Q' , their centers must lie on the straight line perpendicular 

 to P'Q' at its middle point c; this line is called the line of 

 centers. 



Since a great circle may always be drawn through the 

 points W.P', and E, the point c may be found b^;^ drawing 

 a perpendicular bisector to WP' intersecting NS in c. 



