14 



S. L. Penfield — Stereogrcbphic Projection. 



equator, the line of projection from S to o crosses the plane of 

 the equator at 126° (stereographically projected) from the left- 

 hand end of the diameter XY, or 54° from the right-hand 

 end, while the line of projection from S to a would intersect 

 the plane of the equator far out beyond the divided circle, as 

 indicated by the arrow, at a point which could be determined 

 by scale "No. 3, figure 3, a being 144° from iV. All possible 

 lines of projection from S to the great circle a b are located on 

 the surface of an imaginary oblique cone with its apex at S. 

 Moreover, it could be proved, as was done in the case of the 

 small circle illustrated by figure 5, A (the figures being lettered 

 the same), that the intersection of the cone with the plane of 

 the equator is in this case also a circle. The stereographic pro- 



jection of a great circle is illustrated in figure 7, B. The pro- 

 jection of the point b, 54° from the equator on a north and 

 south meridian, as shown by the upper figure, is quickly found 

 on the diameter x y by means of the graduation on the base line 

 of protractor No. I. A circular arc must then be found passing 

 through b, and intersecting the divided circle at antipodal points 

 at right angles to the diameter x y. To facilitate the construc- 

 tion of such circular arcs, scale ~No. 1 of figure 3 has been con- 

 structed, which gives the radii of possible great circles. As 

 the arcs of projected great circles approach JV (the center of 

 the divided circle) they become flatter ; hence they are best 

 constructed by means of the curved ruler described later on. 

 As seen from scale ~No. 1, figure 3, the shortest radius of any 

 stereographically projected great circle is equal to the radius 

 of the divided circle. 



