50 



S, L. Penfield — Crystal Drawing. 



surface of an imaginary sphere on the meridian through p, and 

 OT is the twinning axis. The point t, where the twinning 

 axis pierces the twinning plane, is determined by the intersec- 

 tion of the twinning axis OT with, a line drawn from — J-c to 

 P. The points^?, P and t of the orthographic projection are 

 in vertical alignment with corresponding points on the lower 

 axes, and need no further explanation. Having found t on 

 both the clinographic and orthographic axes, the ends of the 

 axes, — f a, b and — fc, are shifted respectively to — f A, B and 

 — f C, equidistant from t, as would result from a revolution of 



IT 



180° about the twinning axis. Lines from the centers of the 

 two projections through — J- J., B and — \G are the axes in 

 twin position. In figure 17 the axes are shown without con- 

 struction lines, a and b being one-third as long as in figure 16, 

 and in figure 18 two projections of interpenetrating prisms, m y . 

 terminated by basal planes, c, are shown. 



A problem encountered by W. E. Ford and the writer 

 in the study of twin crystals of calcite from Union Springs, 

 !N. Y.,* may be cited as a second example for illustra- 

 ting the uses of the axial protractor in plotting the axes of 

 twin crystals. It was desired to represent a scalenohedron, 

 twinned about the rhombohedron f (0221), so drawn that the 



* This Journal (4), x, p. 237, 1900. 



