68 S. L. Penfield — Crystal Drawing. 



understood. The complicated figure of anorthite was drawn 

 by Mr. J. C. Blake of the writer's laboratory. 



Conclusion. — It is not the object of the present communica- 

 tion to make the subject of crystal drawing easy. The draw- 

 ing of a complex combination requires patience, skill, and 

 above all a knowledge of the principles of crystallography and 

 mechanical drawing. For some persons the subject is a very 

 easy one, while others acquire it only with difficulty, differences 

 depending upon personal peculiarities. That correct ideas of 

 the shapes of crystals should be obtained from figures is evi- 

 dent, and those who are familiar with crystallography, especially 

 if they are not called upon to teach it, have difficulty perhaps 

 in appreciating how hard it is for some persons to see the rela- 

 tions between a figure and the crystal which it represents. The 

 clinographic projection is undoubtedly as good a one as can be 

 found for representing the shapes of crystals, but, as has been 

 pointed out, in many cases a figure thus drawn should be sup- 

 plemented by one in orthographic projection. Orthographic 

 projections are so simple that they may be made easily, even 

 sketched free hand with some approximation to accuracy, and 

 it is especially desired to emphasize their value as a help both 

 in drawing and in the understanding of crystal figures. In 

 the majority of cases two figures, one in orthographic and the 

 other in clinographic projection, may be made in less time than 

 a single figure in clinographic projection. The engraved axes, 

 axial protractor and special triangles, having been in use for more 

 than four years in the writer's laboratory, have proved their 

 efficiency : by means of them increased accuracy in drawing is 

 attained, time is saved, and, what is of no little importance, 

 strain on the eyes is materially lessened. 



Drawing from the Stereographic Projection. — A stereo- 

 graphic projection of the faces of a crystal, or, for that matter, 

 of any geometrical figure with plane surfaces, furnishes all the 

 data needed for constructing figures in both orthographic and 

 clinographic projections. In the methods to be described use 

 will be made of three lines or axes ; one a vertical, correspond- 

 ing to the north and south axis of a sphere, the others at right 

 angles to one another in the plane of the equator. In the 

 upper part of figure 55 the two diameters of the graduated 

 circle, A, —A and D, —JB, represent the front-to-back and 

 right-to-left axes in the plane of the equator, the vertical axis, 

 C, — C, being foreshortened to a dot at the center. The axes 

 have been turned as it were through an angle of 18° 26' in 

 order to make A, —A and D, — B correspond with the direc- 

 tions of the axes for orthographic projection of figure 1. It is 

 supposed that in figure 55 p is the pole of some crystal face : 

 From the graduated circle it is seen that p is on the meridian 



