Stereographic and Gnomonic Projections. 



209 



small circle, shown in the figure, but since this circle passes 

 through C , which in figure 1 is the pole of the stereographic 

 projection (antipodal to G\ it follows that it will be projected 

 in figure 1 as a straight line, drawn through P and a?.* (3) 

 In figure 6, B is located midway between E and A', BS B' 

 is a great circle, and W, 40° from C, is its pole : It is now 

 evident from the symmetry of the figure that a great circle 

 through W and x so intersects the great circle AS' A', that the 



distances S'x and S'x' are equal. Transferring the foregoing 

 relations to figure 1, W, 40° from 0, is the pole of the great 

 circle SBS', and a great circle drawn through W and x falls 

 at x' . However, it is not necessary to draw the great circle 

 through W and x to locate the point x' on the graduated 

 circle : By centering the great circle protractor, described by 

 the writer, f at G, and turning it so that W and x fall on the 

 same great circle, the point x may be transposed to x', and 

 other points, w', y' and s', would be found in like manner. 



The three foregoing methods of transposing x to x\ z to s', 

 etc., are about equally simple, and it may be pointed out that, 

 supplied with transparent stereographic protractors, and hav- 

 ing the poles of a crystal plotted in stereographic projection, 

 it is only necessary to draw the great circle SES' and to locate 

 one point, either IF or P, in order to find the directions 

 needed for a parallel-perspective drawing, corresponding to 

 figure 3. Thus, with only a great circle protractor, the great 

 circle through the poles of any zone may be traced, and its 

 intersection with SES' noted and spaced off with dividers 



*This Journal (4), xiii, pp. 247-249 and 269-271, 1902. 

 flbid. (4), xi, pp. 21-22, 1901. 



