214 



8. I. Penfield — Drawing of Crystals from 



the stereograpliic and gnomonic projections, for they may be 

 employed to advantage when drawing from axes becomes dif- 

 ficult or impossible. For example, in some twin crystals, 

 when drawing from axes, serious difficulties are at times 

 encountered in finding the intersections of interpenetrating 

 surfaces ; difficulties readily overcome, however, by drawing 

 from the projections, if the poles of the twin crystal have 

 been plotted ; or again, the projections may be employed in 

 drawing some odd shape or some obscure crystal, the planes of 

 which cannot be referred to axes. 



To any one desiring to make much use of the methods of 

 drawing from either of the two projections, it is recommended 

 to employ a T-square and, in connection with it, special tri- 

 angles, figure 13, similar to those previously described by the 

 writer*, as follows : — The drawing paper is fastened to a board 

 so that a T-square gives the direction SS', figures 1 and 7. 

 A 20°, 90° triangle, I, gives the direction of the first meridian 

 of the two projections? and, in any plan, the direction of the 

 front-to-back, or a, — a axis, and, triclinic system excepted, the 

 right-to-left, or b, -o axis. A 90°, 25° 30' triangle, II, is used 



Figuee 13. Special triangles to be used in connection with a T-square 

 when drawing from the stereographic or gnomonic projections. 



for uniting corresponding points of plan and parallel-perspec- 

 tive figures, parallel to the c,— c axis, and it also gives 'the 

 front-to-back or a, — a axis in any parallel-perspective figure, 

 when the axis is 90° to the vertical. A truncated 3° 37' 

 triangle, III, gives the direction of the right-to-left or b, — b 

 axis of parallel-perspective figures, provided the system is not 

 triclinic. An 8° 17', 44° 34' triangle, IV, gives the directions 

 of two of the horizontal axes in the hexagonal system, triangle 

 III giving the third. Lastly, a circular arc, V, is used for 

 * This Journal (4), xix, p. 53, 1905. 



