252 Penfield — Solution of Prohlems in Crystallography 



through B a small circle ABA' is to be drawn, every point of 

 which is 25° from S^ the radius r' is given by the scale. On a 

 sphere, the center for describing such a circle would be at S ; 

 in the stereographic projection, however, the center c' lies be- 

 yond xS, on the diameter JVS. Scale ]^o. 3 is a stereographic 

 scale, giving the distance in degrees from the center C to any 

 desired point ; for example, in figure 1, to the point a?, which 

 is 51° from C. About x a small circle has been drawn, every 

 point of which is 46° from x.- By means of scale Ko. 3 the 

 needed points were located ; a?, 51° ; ^, 5° = 51° — 46° ; and j?', 



97° = 51°-|-46°, all measured from C\ and the radius /''' for 

 describing tiae circle is half the distance from j? to^:>^, the cen- 

 ter c" falling somewhat beyond x. Scale JS'o. 4 gives decimal 

 parts of tlie radius of the divided circle, and is used for meas- 

 uring the lengths of axes, assuming the radius of the circle as 

 unity. 



The stereographic protractors needed are three in number. 

 One of these (referred to as protractor Eo. I and shown in 

 figure 4 of the former article) is printed on cardboard, and 

 has along its base line a graduation which will be referred to 

 in this paper as the stereographic scale. The scale is the same 

 as a portion of that designated as No. 3 on the drawing paper; 

 hence this protractor is not essential, but its convenience will 



