210 8. L. Penfield — Drawing of Crystals from 



from either 8 or 8' ; then the great circle through the inter- 

 section just found and iris determined, and where it falls on 

 the divided circle noted, when the desired direction may be 

 had by means of a \ straight edge and 90° triangle, as already 

 explained. 



The gnomonic projection is preferred by many for repre- 

 senting crystallographic relations, and it seems best, therefore, 

 to indicate how readily the methods just explained may be 

 adapted to this kind of projection. This subject has received 

 careful treatment from Goldschmidt * and G. F. H. Smith, f 

 hence what follows might seem somewhat superfluous ; but 

 although the final results of the crystal drawings are essen- 

 tially the same as those of the authors just mentioned, the 

 presentation and explanations here given are somewhat dif- 

 ferent, and it is hoped that some of the suggestions may be of 

 service to students of crystallography. 



As an illustration, the method of drawing a simple com- 

 bination of barite has been chosen. The forms shown in 

 figures 7, 8 and 9 are c (001), m (110), o (011) and d (102). 

 The location of the poles in the gnomonic projection is shown 

 in figure 7, where, as in figure 1, the frst meridian is taken at 

 20° from the horizontal direction 88'. A simple method for 

 locating the poles o and d on their respective meridians is by 

 means of the stereographic scale No. 3,' described by the 

 writer,;}: by laying off with this scale double the angle c ,\ o 

 and g /\ d\ for both stereographic and gnomonic scales are 

 derived from a table of natural tangents, 2° .of the former 

 being equal to 1° of the latter. The poles of the prism m 

 and the locations of 8 and S' (compare figure 1) fall in the 

 gnomonic projection at infinity. In any plan, such as figure 

 8, the direction of an edge made by the meeting of two faces 

 is at right angles to a line joining the poles of the faces, shown 

 in figures 7 and 8 by the direction at 90° to the line joining 

 m" and c. 



The parallel-perspective view, figure 9, is an orthographic 

 projection (compare figures 1 and 3) drawn on a plane passing 

 through 8 and 8', and intersecting the sphere on which the 

 gnomonic projection is based as a great circle,§ passing through 

 E, figure 7, and drawn parallel to 88', the distance cE being 

 10° : This great circle is called by Goldschmidt the Leitlinie. 

 To find such intersections as between rn!" and c, and m and d, 

 figure 9, note, as in figure 1, where the great circles through 

 the poles of the faces intersect the Leitlinie j thus, the one 



* Zeitschr. Kryst., xix, p. 352, 1891. 



fMin. Mag., xiii, p. 309, 1903. 



{This Journal (4), xi, p. 7, 1901. 



§ All great circles in the gnornonic projection are represented by straight 



lines. 



