in the Study of Crystallography 323 



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 

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

 the node which occurs first in azimuth, when travelling from 

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

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

 nodes (i, 3) and (i', 3'); the former of these is situated in 

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

 principal hemisphere of construction. Node (o, i) being dis- 

 tinguished from the others by being made zero of azimuths, 

 is called node (o), the node opposite it is called node (o, i'). 

 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 (o, i), (i, 2), and the like, the greater or 

 smaller of the two supplemental angles being chosen according 

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

 of the great circle, another element is required besides its 

 inclination to the great circle of reference or equator ; this 

 is given by the azimuth of its node on great circle No. o. 

 This also fixes the position of their common diameter and the 

 direction of the corresponding edge. Hence the specification 

 of a great circle representing a face includes the specification 

 of the edge which it makes with the fundamental face of 

 reference No. o, and also that of its equatorial node. The 

 plane angle made on any one face by the meeting of two 

 other faces in it is equal to the angle between the diameters 

 formed by the meeting of the planes of the representative 

 great circles. Thus, the plane angle formed in face No. o by 

 faces No. i and 2 meeting in it is equal to the angle between 

 the diameters formed by the intersections of the planes of 

 Nos. i and 2 with No. o, and it is represented by the arc 

 of great circle No. o contained between nodes (o, i) and 

 (O, 2). Such angles will be designated by the numbers of 

 the three faces which are concerned in their production ; the 



