in the Study of Crystallography. 



169 



Face No 



1 



0° 

 53° 



2 



102° 



66i° 



(0,1) 

 0° 

 0° 



(0,2) 

 0° 



(1,2; 

 288° 

 52° 



Edge No 



Azimuth 



Altitude 





These constructions were made with no greater care than is 

 absolutely essential in carrying out any quantitative graphical 

 work, and the plane angles agree within 1 J° of the theoretical 

 values. With the very greatest care, errors of half a degree 

 cannot be insured against with a globe of 22 centimetres and 

 a metrosphere divided into whole degrees. With a larger 

 globe and divided circles, especially adapted to this kind of 

 work, greater accuracy could be obtained ; but when the 

 errors do not exceed one degree, the angles obtained are 

 sufficiently exact to be used in the construction of models, 

 which always forms the crucial test of the student's work on 

 the globe or in crystallographic composition. 



By an exactly similar construction we lay down circle 

 No. 3 representing face No. 3, and on measurement we find 

 for the positions of circle No. 3 — (151^°, 65J°), and edge 

 No. (2, 3; (25°, 61°). When we now come to face No. 4, it 

 is inclined to No. at 66^° and to No. 3 at 53°; we have 

 therefore to find a great circle which cuts No. at 66^° and 

 No. 3 at 53°. 



The operation presents no more difficulty than when the 

 angles were equal. The quadrant of the metrosphere is set 

 to 66^° and applied to circle No. : then it is set to 53° and 

 applied to No. 3 ; experimental poles being marked in each 

 case giving the radius of the small circles to be drawn from 

 the poles of Nos. and 3 respectively. The intersection of 

 these circles marks the pole of the great circle sought, No. 4. 

 The quadrant is now set either to 53° or 66^; if to 53°, then 

 it is applied to circle No. 3 and slid along it until the pole of 

 the meridian is in the intersection of the two small circles. 

 The meridian of the metrosphere then coincides with circle 

 No. 4, which is accordingly drawn. When the quadrant, set 

 to 66^°, is applied to circle No. and slid along it till the 

 pole of the meridian is again in the intersection of the two 

 small circles, the meridian ought to coincide with the circle 

 No. 4, already drawn. This construction was carried out and 

 the resulting great circles fell less than half a degree apart. 

 The coordinates of the plane are (209°, M°). Circle No. 5 

 is inclined at an angle of 6tii° to both its neighbouring faces 

 and is laid down exactly as No. 2. 



Phil. Mag. S. 5. Vol. 40. Nq. 243. Aug. 1895. N 



