S. L. Penfield — Stereographio Projection. 1 5 



To draw the projected arc of a great circle through two 

 points, one of which, p, figure 8, is on the divided circle and 

 the other, a, within the circle, is a simple matter. The circular 

 arc must intersect the divided circle' at p', antipodal to p, and 

 its center must be on a line x y intersecting the divided circle 

 at 90° from p and p ! . The center c may be found by a few 

 trials with a pair of dividers, or it may be determined analyti- 

 cally as follows : With dividers opened up to some convenient 

 distance construct two circular arcs u u and v v, figure 8, hav- 

 ing the same radius r, and draw a line through their intersec- 

 tions. The line thus drawn will be at right angles to the cen- 



ter point of a line joining a and p\ and will intersect the line 

 x y at c, which will be the center of the circular arc p a p' . 



To draw the projected arc of a great circle through two 

 points a and b, both of which are within the divided circle, the 

 following principles may be used : That the great circle pass- 

 ing through a and b must also pass through points a' and b\ 

 antipodal, respectively, to a and b ; also that the great circle 

 must intersect the divided circle at antipodal points p and p' . 

 If, therefore, there are two points, a and b, figure 9, anywhere 

 within the circle, draw a diameter through one of them, a for 

 example, and continue it beyond the circle. Apply the base 

 line of protractor No. I to the diameter, determine the dis- 

 tance, in stereographically projected degrees, of a from the 

 divided circle, and, making use of scale 'No. 3, figure 3, locate 



