in the Study of Crystallography. 171 



made by pairs of its contiguous faces. Here also we have 

 actually occurring and possible angles. 



Nos. of contiguous faces . . . 



1,2 



1,3 



1,4 



1,5 



2,3 



Plane angle observed 



103° 



30° 



27° 



100° 



107° 



,, calculated 



102^° 



30° 



29° 



102|° 



106.| c 





io 

 2 







— 2° 



2^° 



IO 

 2 



Nos. of contiguous faces . . . 



2,4 



2,5 



3,4 





4,5 



Plane angle observed 



50° 



22° 



123° 



50° 



108° 



„ calculated . . . 



50° 



25i° 



121*° 



50° 



106^° 



Excess 







-3±° 



n° 







H° 





If we suppose faces Nos. 1, 2, and 4 to be produced, they 

 meet in three edges forming a corner. The three plane 

 angles forming this corner are readily found on the globe. 

 They are the angles contained between the edges (1,2), (2, 4), 

 and (4, 1) on the faces 4, 1, and 2 respectively. Hence we have 

 only to measure the arcs on great circles 4, 1, and 2 included 

 between their intersections with circles 1 and 2, 2 and 4, and 

 4 and 1 respectively ; and by measurement they were found to 

 be :• — plane angle on face 1, 108° ; on face 2, 72°; and on 

 face 4, 75J°. Similarly, if we produce faces 1, 3, and 5 to 

 meet in a corner, the plane angles then are : — on face No. 1, 

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

 similar faces to the last. If faces 1, 3, and 4, a different 

 group, be prolonged they meet in a corner with plane angles 

 on No. 1, 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. 0, 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. 1, along a diameter one 

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

 plane angle to be formed on No. by faces Nos. 1 and 2 be 

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

 azimuth ; the face No. 2 cuts No. 0, on the diameter of which 

 this point is an extremity. 



Let the plane angles of 1 and 2 be equal and 112°, we have 

 to find their inclinations to No. and to each other, and the 

 direction of the edge which they make with each other. 



N2 



