258 Penjield — Solution of Problems in Crystallography 



face «, 100 (the axes being properly orientated within a sphere, 

 and the latter standing sufficiently far away to give the effect 

 of orthographic projection), the relations shown in figure 9 

 would be seen. The outer circle represents the bounding sur- 

 face of the imaginary sphere. The h and c axes are seen 

 within the sphere with their ti-ue inclination and lengths ; 

 a = 103° 18', and ^ : c = 1.00 : 0'621. Normals to all cr^jstal 

 faces parallel to the e axis (compare figure 5) are located in a 

 plane at right angles to the c axis, which plane would be fore- 

 shortened in orthographic projection to the line CC. Like- 

 wise normals to all faces parallel to the h axis lie in the plane 

 represented by the line BB' . Since the planes represented in 

 figure 9 by CC and BB' are at right angles, respectively, to 



the G and h axes, they must make with one another an angle 

 equal to that of the axes, that is a. All forms intersecting the 

 1) and c axes at their unit lengths, therefore, having the -direc- 

 tion of their intersections represented by the line hc^ figure 9, 

 would have their normals in a plane at right angles to the 

 direction 5 c. This plane seen in orthographic projection is 

 represented by the line PP\ and, therefore, owing to the con- 

 struction, the planes BB' and PP' make with one another an 

 angle equal to ti. In like manner the planes CC and PP' 

 make with one another an angle equal to p. Hence it is that 

 the angles made by the planes in which the normals are located, 

 represented by CC\ BB' and PP' in figure 9, are to be found 

 in the stereographic projection, figure 8, at «, a line from a 

 to the center of the spliere being the common intersection edge 

 of the three planes. In like manner it may be demonstrated 



