Simpler Methods in Grystallographij. 353 



to the indices in tlie cb zone, and are projected in the 

 manner already sufficiently described, from the point of 

 sight represented by the front a. The method just referred 

 to, of determining the projections of poles whose angular (or 

 whose proportional) distance from a given point on the pro- 

 jection of a great circle inclined to the primitive is known, 

 is as follows : — Let be the centre, aa} the front-and-back 

 diameter, IH^ the diameter right-and-left, and d the projec- 

 tion of the inclined great circle, cutting the primitive at hh^ ; 

 and that it is required to lay down the position of a pole e 

 on f^ at a given angular (or a given proportional) distance 

 from h. From h^ draw a right line through the point where 

 d cuts Oa^ and produce it from the primitive, and from the 

 point so determined set off upon the primitive towards a the 

 chord of a quadrant. Then^ from this point draw a right 

 line to V-. The point where it intersects Oa is the projection 

 of the POLE, p, of the inclined great circle d. Then, from h 

 set off the given angular (or the given proportional) distance 

 of e from h, signing it E. Join E^?, and the point where this 

 line cuts the great circle e is the projection required. This 

 method is much used in constructing maps of mono- 

 symmetric and of anorthic species. 



67. Finally, there remains the zone ac, with its positive 

 and negative poles. For these the quadrants v. and viii. 

 are reserved, and we are supposed in this case to be viewing 

 the sphere of projection from &, and that the line aoa 

 represents the trace of the plane of projection upon which 

 these poles are to be drawn, and that h on the right is the 

 position of the point of sight. The earlier stages, at least, 

 of the work are most clearly comprehended by turning 

 the map round and placing h, the point of sight, at the 

 bottom, and thus reading ox as oz, o and Y will therefore 

 coincide in this position. A will change places with A, 

 and A with c, in this reading in the new position. From 

 the point where the circle a cuts ox, draw a line which is 

 at right angles to OA (quadrant vi.), and from this point 

 draw a line through the point where the circle c cuts OY 

 (or oz in the new position), and produce the line on either 

 side to cut the primitive; from each point where it does 



