322 On the Use of the Globe 



to one another ; so that parallel faces and edges are repre- 

 sented by one independent face or edge. When we have 

 placed the poles of all the faces of a crystal on the globe, we 

 can represent all the faces by drawing suitable small circles 

 round the poles, and we represent all the independent faces by 

 drawing great circles round the poles. If we adopt the latter 

 process one crystal is represented by a group of great circles, 

 the plane of each great circle being parallel to the face or 

 faces which it represents, and the points of intersection of any 

 pair of great circles or their nodes mark the extremities of 

 the diameter which is parallel to and represents the edge 

 made by the pair of faces, and all other edges parallel to it. 

 The diagram produced on the globe by following the latter 

 process will be called the central representation ; that obtained 

 by the former, the radial projection of the crystal or poly- 

 hedron. The radial projection of a crystal when constructed 

 with due regard to the length of the normal radii of the faces, 

 and, consequently, to the exact position as well as to the 

 direction of the edges, has the great advantage of affording 

 to the eye a bodily presentation of the crystal, with all its 

 irregularities of development. In the central representation 

 the variability of the normal radii and, consequently, of the 

 size of the faces, which distinguishes the crystal from the 

 polyhedron, is effaced, and only the geometrical properties 

 remain. The one process or the other will be adopted according 

 to the purpose in view. 



We shall designate the great circles representing the 

 independent faces by numerals, o, i, 2, 3, etc., and the inde- 

 pendent edges by the numbers of the two great circles which 

 produce, by the meeting of their planes, the parallel diameter. 

 Thus, the edge made by the meeting of faces Nos. o and i 

 corresponds to the diameter made by the meeting of the 

 planes of great circles o and i, and it is designated edge 

 (o, i); similarly we have edges (o, 3), (i, 5), (2, 4), and the 

 like. The position and inclination of a diameter is fixed 

 when the point where it meets the surface of the sphere is 

 known ; for it necessarily passes through the centre. It 

 meets the surface in the node of the two great circles to 



