in the Study of Crystallography. 161 



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 accord- 

 ing to the purpose in view. 



We shall designate the great circles representing the 

 independent faces by numerals, 0, 1, 2, 3, &c, 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 1 

 corresponds to the diameter made by the meeting of the 

 planes of great circles and 1, and it is designated edge 

 (0, 1) ; similarly we have edges (0, 3), (1, 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 

 which it is common. Hence the inclination or direction of 

 the edge is given by the position of the corresponding node. 



The nodes of intersection of the great circles will be desig- 

 nated by the numbers of the circles which meet in them, the 

 opposite nodes being distinguished by a dash ('). Thus circles 

 and 2 meet in the nodes (0, 2) and (0, 2'), No. (0,2) being 

 the node which occurs first in azimuth, when travelling from 

 node (0) along the equator in the direction which it has been 

 agreed to call positive. Circles Nos. 1 and 3 meet in the 

 nodes (1, 3) and (1/ 3 ; ) ; the former of these is situated in 

 the hemisphere above circle No. 0, which is taken as the 

 principal hemisphere of construction. Node (0, 1) being dis- 

 tinguished from the others by being made zero of azimuths, is 

 called node (0), the node opposite it is called node (0, 1/). 

 When the faces are represented by great circles, the inclination 

 of any two is equal to the angle made by the plane of the 

 one great circle with that of the other. They will be 

 designated as angle (0, 1), (1, 2), and the like, the greater or 

 smaller of the two supplemental angles being chosen accord- 

 ing to the circumstances of the case. In order to fix the 



