162 Mr. J. Y. Buchanan on the Use of the Globe 



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. 0. 

 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. 0, 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. by 

 faces No. 1 and 2 meeting in it is equal to the angle between 

 the diameters formed by the intersections of the planes of 

 Nos. 1 and 2 with No. 0, and it is represented by the arc 

 of great circle No. contained between nodes (0, 1) and 

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

 the three faces which are concerned in their production ; the 

 face containing the angle coming first. Thus angles 

 (0 — 1, 2) (2 — 1, 3) mean the plane angle on face No. made 

 by faces Nos. 1 and 2 and that formed on face No. 2 by faces 

 Nos. 1 and 3. The great circle corresponding to the funda- 

 mental face of reference w T ill always be called No. 0, and the 

 fundamental edge (0, 1) is the diameter made by the inter- 

 section of the planes of great circles Nos. and 1. One of 

 the nodes of these two circles, which will be called node 0, is 

 chosen as the zero of arcs of azimuth, which are measured 

 along great circle No. 0, from 0° to 3(J0°. Points lying out- 

 side of great circle No. 0, which is the equator of our system, 

 are further fixed by their altitude above or below it. The 

 original position of the metrosphere means the one which it 

 had when great circle No.O was drawn and node was marked : 

 then the equator of the metrosphere coincided with the 

 equator of the diagram on the globe, and the zero of azimuths 

 on the metrosphere corresponded with that on the globe. 



In central representation, positions on the sphere are ex- 

 pressed by the azimuth from node (0j in which a great circle 

 passing through the pole of circle No. and the point cuts 

 circle No. 0, and the arc on this circle contained between its 

 intersection with circle No. and the point. This is the 

 altitude of the point and it is + or — according as it is to 

 the right-hand or the left of the equator, when moving in the 

 positive direction of the measurement of azimuths. The 

 coordinates of a point will be expressed shortly in the 

 form (0°, <j)°) y where is the azimuth and <fi the altitude. 

 The azimuth will always come first. In central representation 



