Simpler Methods in Crystallography. 407 



The angle between a and h^as measured along the primitive, 

 is given by Dana as 94° 26', which is to be set off towards 

 the right from x«, and towards the right from a^ at the back. 

 Sign the points so determined 5, h^. This is a simpler pro- 

 cedure than that of computing the angle by graphic or other 

 methods from the spherical triangle formed by the angles 

 a/3y from c; and with the solid sphere of projection repre- 

 sented by the ball kept constantly in view, there is no risk 

 of any confusion arising by adopting this method. 



Next deal with the angle ft which is that between the 

 vertical axis of reference c (in the present case coincident 

 with z) and a plane passing through the origin o, and in- 

 clined so as to be parallel to the face c, the basal pinacoid 

 (001). As we have assumed that a is already laid down 

 upon the primitive, we need not at present consider j8 in 

 relation to that; but as the inclination of the face c (001) is 

 parallel to a radius on a plane passing through inclined 

 towards a from c at the angle in question, it follows that the 

 position of e (001) in relation to c may be in part determined 

 accordingly; one mode would be that of setting off the 

 projection of an arc of a small circle from c as a centre, and 

 with a radius equal to the excess of /? over a right angle, i.e,y 

 18° 44', and then finding the intersection of this by another 

 arc of a small circle bearing the same relation to a. The other 

 and simpler plan for laying down the position of c (001) 

 upon the stereogram is as follows : — Conceive, first, that the 

 sphere of projection is viewed from &, which in this case 

 takes the place of z or o. y^ then stands for the upper half 

 of the vertical axis of reference, xx^ remaining as before. 

 From Y^ set off the chord of the angle p past x towards y. 

 This angle is 108° 44', of which the chord is '3255 in excess 

 of that of a right angle. For the present purpose it will 

 suffice to measure off this latter on the primitive from Y^ 

 toward x. The angle from Y^, so determined, is the inclina- 

 tion of a plane parallel to the cystallographic face c (001) 

 measured from o towards a (100). Project this point upon 

 the axis of reference xx^ from Y, and transfer it to the 

 final copy. Next, in this latter, draw an arc of a great 

 circle passing through this point and &, V-. The zone so 



