46 



MINERALOGY 



FIG. 71. 



Example. Let it be required to project a barite crystal with 

 the following forms: (100) (010) (001) (110) (102) (Oil) (111) 

 (112) : 110J10 = 78 22' : 001J02 = 38 51' : OOL011 = 52 

 43' : 001 J12 = 45. 



Draw, Fig. 71, the primitive circle within or upon which all 

 poles will fall. As the c axis is projected at the center of the primi- 

 tive, and is normal to the base, 

 ooi, c at the center will be the pole 

 of oo i. Draw two diameters aa', 

 bb' at 90 ; these will represent the 

 a and b axes. The poles of all the 

 faces belonging to the zone of which 

 c is the axis will fall on the primi- 

 tive circle, as their normals will lie 

 in the plane of the paper, the last 

 term of their indices will be o. 

 100 will be projected at the ex- 

 tremities of the axis a, oio at the 

 extremities of b; the remaining member of this zone (no) will lie 

 symmetrically on either side of the axis b. Draw the two diame- 

 ters at 78 22', and the poles of (no) will lie at their extremities. 

 The form (on) is a member of the zone of which the axis a is 

 the zonal axis ; its poles will lie on the diameter of the primitive, 

 perpendicular to a, 52^3' from the pole c. From a' lay off a'e = 

 52 ^3', draw ea and where it crosses be is the pole on ; oli will 

 be an equal distance on the other side of c. The poles of (102) will 

 lie on the diameter aa' and are located by the same method as (01 1). 

 The two pyramids (in), (112) are members of the zones no ooi 

 and Tio ooi, their poles will lie on these two diameters. The form 

 (111) is also a member of the zone on 100 and 011 100, 

 its poles will be situated at the intersection of the two zonal circles. 

 Draw the zonal circle 100, on, Too; where this intersects the zone 

 no, ooi, no as at in will be the pole of the unit pyramid. Poles 

 of (112) are located by the angle ooi A ii2 = 45 ; when the angle 

 between the base and any face is given, the zone being known, its 

 poles are quickly found by the tangent rule, or by construction, 

 problem V. 



The advantages of the stereographical projection are, that it 

 shows at once the symmetry of the crystal, connects all faces be- 

 longing to the same zone, and by simple construction the angle 

 between any two faces may be measured. 



