THEORY OF POLYGON IC PROJECTIONS. 69 



passing through the pole of a given great circle has its 

 plane necessarily perpendicular to that of the given great 

 circle; therefore the great circle which passes through the 

 poises of the two great circles has its plane perpendicular 

 to the plane of each of the given circles. K." must then 

 be the projection of the pole of this great circle of which 

 IKK'V is the projected arc. GG' is therefore the great 

 circle arc of which KK^ is the projection; or the angle 

 GOG' is the angle that measures the inclination of the 

 planes of the given great circles. The angle GOG' should, 

 therefore, fequal the angle CK"C'\ the impossibility of 

 making a perfect construction may cause some deviation 

 from equality in the constructed ngure. 



Problem 13. — The projection of a point being given, to 

 construct the meridian and parallel passing through the 

 point: 



If the problem is to be determinate, we must have the 

 primitive circle given and the projection of one of the 

 poles. 



In figure 28 let NES W be the primitive circle and let 

 P be the projection of the pole; locate the south pole by 

 drawing WP and then WP' perpendicular to WP; RR' is 

 the perpendicular bisector of rP'j and is therefore the line 

 of centers for the meridians. Let Q be the projection of 

 the given point; pass a circle through P, Q, and P', and 

 this is the projection of the meridian through the given 

 point. Construct a tangent to PQP' at §, meeting NS 

 m T; then Tis the center of the projection of the parallel 

 and TQ is the radius; this fully determines the projection 

 of the parallel which is the arc QQ', 



