44 



MINERALOGY 



zones or great circles inclined to the plane of projection are pro- 

 jected in arcs of circles cutting the primitive circle at the ends 

 of a diameter. Before illustrating by an example the method of 

 drawing the spherical projection of a crystal, it is necessary to have 

 well in mind several problems constantly in use during the con- 

 struction. 



If from the pole of a zone circle, lines be drawn through the poles 

 of any two faces lying upon the zonal circle, and extended until they 

 intersect the primitive circle, the arc of the primitive circle inter- 

 sected will measure the angle between the normals of the faces. 



Problem I. Given the projection 

 of any great or zone circle, to find 

 the projection of its pole. Let dsc, 

 Fig. 67, be the zone circle ; draw the 

 diameter dc, and the diameter so 

 perpendicular to dc, so will be the 

 projection of a great circle, with 

 its pole at c and at 90 to dsc; 

 therefore the pole of dsc must lie on 

 so 90 from s ; draw cs and extend 

 to intersect the primitive circle at s, 

 lay off sa = 90, connect ac, and 



where it crosses os at p will be a point on a great circle at right 

 angles to the given zone dsc and 90 from it ; it is therefore the 

 pole of dsc. 



Problem II. Given the projection of the pole of any zonal 

 circle, to draw the projection of the circle, is simply the reverse of 

 problem I, Fig. 67. 



Problem III. Through 

 any two given poles to draw 

 the projection of the great 

 or zonal circle to which they 

 belong. 



In Fig. 68 let P, S be the 

 two given poles ; then draw 

 the diameter po, and oa at 

 90 to it, then a is the pole 

 of the great circle of which 

 Po is the projection and the 

 given pole P will lie upon it ; draw aP, extend it to P', lay off 

 P'b = 1 80 ; draw ab to meet Po extended at B ; B will be the 



FIG. 67. 



FIG. 68. 



