S. I. Penfield — Crystal Drawing. 39 



Art. V. — On Crystal Drawing • by S. L. Penfield. 



Introduction. — The methods commonly employed for repre- 

 senting crystals consist in drawing their edges as they appear 

 when projected upon a plane. A peculiarity of the methods 

 used is that the eye, or point of vision, is regarded as being at 

 an infinite distance from the object, so that all edges which 

 are parallel on a crystal appear as parallel lines in the drawing. 

 Thus true perspective, whereby parallel edges would appear in 

 a drawing as lines approaching one another in the distance, 

 is lost sight of. Furthermore, two kinds of projection are 

 employed : orthographic, where the lines of projection fall at 

 right angles, and clinographic, where they fall at an oblique 

 angle on the plane upon which the drawing is made. Most of 

 the figures found in works on mineralogy and crystallography 

 are drawn in clinographic projection. 



The data generally employed in constructing a crystal figure 

 are the inclinations and lengths of the axes and the symbols of 

 the forms, while interfacial angles are not made use of directly, 

 other than as they may have been employed for determiniug 

 the axial relations and the symbols of the several faces. 



To be really successful in drawing, it is essential that one 

 should have a thorough understanding of the form or combi- 

 nation to be represented, and that every step in the process of 

 constructing a figure should be fully comprehended. The 

 reason for offering the present communication is the hope 

 entertained by the writer, that by developing the subject of 

 crystal drawing in a manner somewhat different from that 

 generally adopted, the processes involved may be compre- 

 hended more readily and the work accomplished with greater 

 facility and accuracy. 



Projection of the Axes of the Isometric System. — It is 

 believed that figures 1 to 4 will make clear the principles 

 upon which the projection of the isometric axes are based. 

 Figure 1 is an orthographic projection (a plan, as seen from 

 above) of a cube in two positions, one, abed, in what may be 

 called normal position, the other, A B C D, after a revolution 

 of 18° 26 r about its vertical axis. The broken-dashed lines 

 throughout represent the axes. Figure 2 is likewise an ortho- 

 graphic projection of a cube in the position A B CD of figure 

 1, when viewed from in front, the eye or point of vision being 

 on a level with the crystal. In the position chosen, the appar- 

 ent width of the side face B C B' C is one-third that of the 

 front face A B A' B ', this being dependent upon the angle of 

 revolution 18° 26', the tangent of which is equal to \. To 



