THEORY or POLYCONIC PROJECTIONS. 



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67 



Fig. 26,— Projection of great circle with given inclination to the primitive plana 

 on stereographic projection. 



In figure 26 if the given point lies on the primitive circle, 

 as iV, draw iV^S and 'WE, the line of measures. Construct 

 the angle OlSlC equal to the given angle z; then (7 is the 

 center and 0"N the radius of the required projection. If 

 the projection of the given point is not on the primitive 

 circle, but is at some other point, as P, construct the are 

 CD with as a center with OC' as a radius. Construct 

 another arc with P as a center and with CIS! as a radius 

 intersecting the first arc in i>; then with Z? as a center 

 and with DP as a radius construct the required projection. 

 (Remark. — ^If the given point does not lie on the primi- 

 tive circle, the construction is not always possible; in 

 fact, the angle z can not be less than the angle "WOA.) 



Problem 12. — To determine the inclination of two great 

 circles with respect to each other: 



This problem is solved by determining the projections 

 of the poles of the given circles, and then by measuring 

 the great-circle-arc distance between them. Apply the 

 method of problem 6 and then that of problem 8. With 

 great circles the inclination of the planes is equal to the 

 angle between the radii of the two circles drawn to the^ 



