206 S. L. Penfield — Drawing of Crystals from 



Art. XIV. — On the Drawing of Crystals from Stereograph ic 

 and Gnomonic Projections ; by S. L. Penfield. 



In a previous communication by the present writer,* some 

 methods for drawing crystal forms from a stereograj)liic pro- 

 jection were described, and, after the publication of the paper, 

 there was observed in a recent volume by Professor C. Viola 

 of K,ome,f a method, based upon different principles, which 

 is so simple and ingenious that it seems wise to give a brief 

 description of it, for the benefit of those readers of this journal 

 who may be interested in the subject : this paper may also 

 serve as a supplement to the writer's earlier article, referred to 

 above. 



In explaining the method, a general example has been 

 choseu ; the construction of a drawing of a crystal of axinite, 

 of the tricilinic system. Figure 1 represents a stereographic 

 projection of the ordinary forms of axinite, m (110), a (100), 

 M (110), p (111), r (111) and s (201). As shown by the figure, 

 the first meridian, locating the position of 010, has been 

 chosen at 20° from the horizontal direction SS': This is wholly 

 arbitrary, but it makes a good starting point for the con- 

 struction of a stereographic projection. 



Figure 2 is a plan, or an orthographic projection of an axi- 

 nite crystal, as it appears when looked at in the direction of 

 the vertical axis. It may be derived from the stereographic 

 projection in a simple manner, as follows : — The direction of 

 the parallel edges made by the intersections of the faces in the 

 zone m, s, r, m\ figure 1, is parallel to a tangent at either m 

 or m', and this direction may be had most easily by laying a 

 straight edge from m to ml and, by means of a 90° triangle, 

 transposing the direction to figure 2, as shown by the construc- 

 tion. 



The construction of figure 3, which is called by Yiola a 

 parallel-perspective view, may next be explained : It is not a 

 clinographic projection like the usual crystal drawings from 

 axes, but an orthographic projection, made on a plane inter- 

 secting the sphere, represented by the stereographic projection, 

 figure 1, along the great circle SHIS' ; the distance EG being 

 10°. The plane on which a drawing is to be made may, of 

 course, have any desired inclination or position, but by making 

 the distance CE equal 10° and taking the first meridian at 20° 

 from S, almost the same effects bf plan and parallel- perspec- 

 tive are produced as in the conventional method of drawing 

 from axes, where the eye is raised 9° 2S' and the crystal turned 



* This Journal (4), xix, p. 39, 1905. 



f Grundzlige der Krystallograpkie, p. 29, W. Engelmafin, Leipzig, 1904. 



