74 S. Z. Penfield — Crystal Drawing. 



on tlie plane of the B and C axes, the data are as indicated in 

 figure 55 : The meridians of p and q, 34° 40' and 31° 35 ; , 

 measured from A (their cotangents plotted at it and v\ and the 

 angles which the great circles through A and p and A and a 

 make with the equator, 56° and 67° 30', respectively. The linear 

 projection of p is the line n'n\ drawn through u parallel to the 

 line from B to the point cot. 56° on the vertical axis ; and the 

 linear projection of q is the line m'm\ drawn through v, parallel 

 to the line from — B to the point cot. 67° 30' on the vertical axis. 

 A line drawn from A to the point of intersection of n'n ! and 

 m'm' is the desired direction, and is parallel to the line Ci. 



As an illustration of the application of the methods just 

 described, the details of a drawing of a crystal of axinite may 

 be cited. The forms present are shown in the stereographic 

 projection, figure 56: m (110), a (100), M (110), p (111), 

 r (111) and s (201). It was found that on making the linear 

 projection on the plane of the A and B axes, several of the 

 lines were so nearly parallel that it was difficult to determine 

 some of the intersections. It was decided, therefore, to make 

 the linear projection on the plane of the A and C axes as 

 shown in the figure, the data needed being derived from the 

 stereographic projection, as follows : Meridians of the poles, 

 measured f rom B : m 32° 47' ; p 35° 50': a 48° 21'; * 51°; 

 M 77° 16' and r 85° ; also the angles made by the great circles 

 Bpr and Bs with the equator, 44° 40' and 26° 20', respec- 

 tively. The cotangents of the meridians of the several poles 

 are laid off on the orthographic A axis at m\p\ a\ s\ J/ 7 and r\ 

 and projected down on the clinographic A axis. The linear 

 projections of the faces of the prismatic zone are vertical lines 

 through m', a' and M ; those of p and r are lines through p' 

 and r\ parallel to the direction from A to the point on the 

 vertical axis marked cot. 44° 40' ; and that of s the line through 

 s', parallel to the direction from A to the point on the vertical 

 axis marked cot. 26° 20'. All of the intersections of the figure 

 in clinographic projection are parallel to lines drawn from B 

 to points of intersection on the linear projection, indicated by 

 the lettering. Thus the orthographic and clinographic figures 

 of axinite were made wholly without reference to the lengths 

 and inclinations of the triclinic axes and the symbols of the 

 faces. 



Figure 57 represents a cut stone (brilliant) as seen from 

 above, and figure 58 as seen from below in orthographic pro- 

 jection, while figure 59 is a clinographic projection of the 

 same. These drawings were made from two-circle goniometer 

 measurements plotted in the stereographic projection. The 

 object measured was a glass model of the Regent or Pitt 

 diamond. 



