in the Study of Crystallography 335 



meet in a corner, the plane angles then are: on face No. I, 

 107; No. 3, 76 ; and No. 5, 74. This is a group of similar 

 faces to the last. If faces I, 3, and 4, a different group, be 

 prolonged they meet in a corner with plane angles on No. I, 

 59 ; on 3, 77 ; and on 4, 103. 



The interdependence between the plane angles of the faces 

 of a crystal and the inclinations of the faces and the edges 

 can be very conveniently studied on the globe. 



Consider a face No. o, as represented by its parallel great 

 circle on the sphere, which shall be the equator of reference. 

 It is cut by any other face, No. I, along a diameter one 

 extremity of which is taken as zero of azimuths. Let the 

 plane angle to be formed on No. o by faces Nos. i and 2 be 

 112. Lay off on the great circle No. o an arc of 112 

 azimuth ; the face No. 2 cuts No. o, on the diameter of which 

 this point is an extremity. 



Let the plane angles of I and 2 be equal and 112; we 

 have to find their inclinations to No. o and to each other, 

 and the direction of the edge which they make with each other. 



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

 supplement of 1 12, and with this radius describe small circles 

 from adjacent extremities of the diameters (o, i) and (o, 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 (o, o) draw a great circle which marks the 

 position of the circle representing face No. i. Also through 

 the points (238, 48^) and (112, o) draw a great circle which 

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

 circle by the other two are 1 12, 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. i with Nos. o and 2, and the altitude of 

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

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

 angles with face No. o of 54 or 1 26, 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. i 



