£. L. Penfield — Crystal Drawing. 47 



the length of the foreshortened a axis. For the clinographic 

 projection locate ft, 108° 44', on the graduation of the ellipse 

 passing through A and G, draw a diameter through the center 

 and fix the length of a by projecting down vertically from a 

 of the orthographic axis above. If one does not wish to make 

 rise of the orthographic axes, draw the diameter of the ellipse 

 at the inclination ft, and find the length 3a by laying off a 

 distance equal to 3a on the vertical axis (3*219 in figure 13), 

 using the scale of decimal parts, and then transpose the length 

 thus found to the inclined a axis by drawing a line parallel to 

 ft, — C, as shown in the figure : One-third of the length thus 

 determined is the desired length of the a axis. 



Two processes are involved in plotting the b axis of a tri- 

 clinic crystal. (1) The vertical plane in which the b and c axes 

 are located is revolved about the c axis so as to conform to the 

 measurement a^b, 100 a 010. Care must be taken to note the 

 direction in which the plane of the b and c axes is turned : 

 (1) As shown in figure 14, since 100A010 (angle between 

 normals) is 94° 26' in rhodonite, the " 



right-hand end of the b axis is first 

 swung forward 4° 26 ; in the plane of 

 the equator. Carrying out the fore- 

 going process in figure 13, a point p 

 is located on the equator, 94° 26 7 , 

 measured from —A, and likewise b 

 of the orthographic projection above 

 is brought forward to a position 94° 

 26' from -a. (2) The horizontal 

 b axis, in its new position, must next 

 be inclined to the vertical axis at the angle a, which in rhodo- 

 nite is 103° 18'. For the orthographic projection above, this 

 inclination of the b axis causes some foreshortening, which is 

 determined by laying off two points o and o' ', figure 13, 

 13° 18' (103°' 18' -90°) on either side of where the b axis 

 intersects the divided circle, and projecting through the points 

 thus formed at right angles to the direction b, — b, as indicated 

 by the arrows. To give the b axis of the clinographic projec- 

 tion its proper inclination, the value of a, 103° 18', is laid off 

 on two, or preferably three, of the vertical ellipses, as at x, y 

 and z, figure 13, measured from C. Next draw three chords, 

 Ap, —Ap and Bp, on the plane of the equator, and parallel 

 to them, respectively, the chords xx r , yy f and zz f . The com- 

 mon intersection of the three chords determine a point 3b, on 

 the surface of an imaginary sphere and on a meridian Me 

 passing through p. The point 3b is 13° 18' below the equator 

 and 103° 18', that is a, from C. A line from 3b through the 

 center is the projection of the b axis, and a perpendicular from 



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