S. L. Penfield — Crystal Drawing, 71 



Still another way in which the direction Ci may be found is 

 as follows : Among the stereographic protractors described 

 by the writer there was one consisting only of great circles 

 printed on celluloid (Protractor No. IV). Having p and q 

 located, the protractor is centered over the projection and 

 turned until jp and q fall on the same great circle, and then the 

 points where the great circle intersects the divided circle (15° 

 40' from B in figure 55), are noted, although it is not necessary 

 to draw the great circle as in the figure. It follows from this 

 that^> and q are in a zone with a vertical plane, the pole of 

 which is located at 15° 40' from B : The intersection of such 

 a vertical plane with the plane of the equator would be parallel 

 to the line tt, tangent at 15° 40', or, simpler, it would be par- 

 allel to a line from the center C to a point on the graduated 

 circle 15° 40' from A, which is identical with the direction Ci 

 found by means of the linear projections of p and q. The 

 method of the great circle protractor has one decided advan- 

 tage ; it is not necessary to make any construction lines ; the 

 position of the protractor alone determines the desired direc- 

 tion. The line Ci in orthographic projection may be regarded 

 as representing two things : (1) a radius drawn on the plane 

 of the equator, and (2) the projection of the edge between p 

 and q, passing through unity on the C axis and intersecting 

 the plane of the equator at i : the point i is an important 

 one to determine, and may be found by noticing the angle 

 which the great circle through p and q makes with the diam- 

 eter, 37° 10' in figure 55, and locating i by means of the 

 cotangent scale. 



In order to find the intersection between two planes in clino- 

 graphic projection, p and q, figure 55, proceed as follows : 

 Through C and a point 18° 26' to the right of A on the grad- 

 uated circle, draw a line, and continue it for some distance 

 below the circle, to represent the vertical axis. As shown in 

 figure 23, page 53, the vertical axis is next made parallel with 

 the edge of the special triangle Ila resting on a T-square, then, 

 at some convenient distance 0, the lines B, — B and A, —A 

 are drawn with the aid of a T-square and the special triangle 

 IK to represent the right-to-left and front-to-back axes. Unit 

 lengths on the axes are determined by projecting down from 

 A, —A and B, —B of the orthographic axes above, and a 

 distance equal to the radius of the graduated circle is laid off 

 above and below O, at (7, and — C, to represent unity on the 

 vertical axis. If the special triangle referred to is not at hand, 

 the clinographic A, —A and B, —B axes may be constructed 

 readily from the details given on pages 40 and 41, in connection 

 with figures 1 to 4. If on the orthographic axes above the linear 

 projection of p, that is the line II, has been drawn, its intersec- 



