172 Use of tlie Globe in the Study of Crystallography. 



Set a pair of compasses to a span of 68°, which is the supple- 

 ment of 112°, and with this radius describe small circles from 

 adjacent extremities of the diameters (0, 1) and (0, 2). These 

 circles cut each other in one point in the hemisphere. The 

 position of this point is found by measurement to be azimuth 

 238°, and altitude 48^°. Through this point and the zero of 

 azimuths (0°, 0°) draw a great circle which marks the position 

 of the circle representing face No. 1. Also through the 

 points (238°, 48i°) and (112°, 0°) draw a great circle which 

 is parallel to face No. 2. The arcs intercepted on each great 

 circle by the other two are 112°, and they represent the plane 

 angles of the three faces meeting in the corner ; with the 

 quadrant clamped at 90°, place the meridian on the points of 

 intersection of No. 1 with Nos. and 2, and the altitude of 

 No. 1 is found to be 54°. By similar measurement the alti- 

 tude of No. 2 is 54°. Therefore the faces 1 and 2 make 

 angles with face No. of 54° or 126°, according as the inside 

 or the outside of the solid is considered. When the metro- 

 sphere is placed so as to measure the inclination of Nos. 1 

 and 2, it is found to be 53^°. The azimuth and altitude of 

 the point of intersection of Nos. 1 and 2, which have been 

 found by measurement to be 238° and 48J°, give the position 

 and direction of the edge made by Nos. 1 and 2. The alti- 

 tude 48J° is also the inclination of the edge made by two of 

 the faces to the third face. 



Let the plane angle on No. be 120°, and the p^ne angles 

 on Nos. 1 and 2 be 108° and 90° respectively. By exactly 

 the same construction we find, on measurement, that the faces 

 which fulfil these conditions are inclined to 1 at 73J°, to 2 at 

 58°, and 1 to 2 also 58°. The edge formed by Nos. 1 and 2 

 meets the sphere in 210° azimuth and 58° altitude. The 

 plane angles here assumed are those of the square and the 

 regular hexagon and pentagon. 



If the edge made by Nos. 1 and 2 lies in azimuth 220° and 

 altitude 50°, the base angle being 120°, to find the inclination 

 of the faces and the plane angles of 1 and 2. Great circles 

 are drawn through the points (0°, 0°) and (220°, 50°) giving 

 circle No. 1, and through (120°, 0°) giving No. 2. The 

 angles which they make w r ith each other are then measured and 

 found to be :— to 1, 61° ; to 2, 50° ; and 1 to 2, 53i°. 

 The plane angles are: — on No. 1, 118° ? and on No. 2, 97°, 

 the angle on No. being given 120°. 



The resources of the globe are inexhaustible ; but the above 

 examples may suffice for the purpose with which this paper 

 was written ; namely, to inform some, and to remind others, 

 of the usefulness of the globe as an instrument of research. 



