Simpler Methods in Crystallography. 409 



ingly, a right angle to ox is drawn from the point marking 

 the full length of a, and the length 1*017 on ox, so determined, 

 is the fore-shortened representative of a required. 



In like manner, as I is inclined 13° 18' 7" below, and h^ as 

 much above the plane of the primitive, these are also fore- 

 shortened by the same method of construction, so that their 

 length on each side of the centre is less than unity by "03 

 of the radius. 



Connect these points representing respectively the fore- 

 shortened a with h and &^, and prolong the lines to the 

 primitive. Eaise perpendiculars to these lines, passing 

 through the centre to fully the length of the radius outside 

 the primitive in each direction. The points where these 

 lines cut the primitive are the true projections of (110), 

 (110), and the lines joining these with c are the zones con- 

 taining the unit hemipyramids. Draw lines outside of the 

 primitive respectively parallel to aa^, bh^ to meet the pro- 

 longation of the lines through (110), (110). Proportional 

 lengths measured upon these give the macroprisms (between 

 a and mM) and the brachyprisms (between mM and bb^) 

 whose positions are required, as in the case of the other pro- 

 jection described in the former paper above referred to. In 

 Ehodonite these are/ (130), g (150), t (310), d (210), e (130). 



3. Projection of the Poles of the Macrodomes. — To draw the 

 Macrodomes and Brachydomes, it is well to use a separate 

 working map, as already mentioned, and to transfer the posi- 

 tions, when found on these, to the final copy. Firstly, we 

 have to suppose that the sphere of projection is viewed from 

 the side looking from b to h^. Measure off -62127 of the unit 

 length on what here serves as the vertical axis of reference 

 OY, OY^, and draw an inclined /? (the angle with the vertical 

 axis of reference 108° 44' 8" already mentioned). This, of 

 course, can be simply transferred to the present map from 

 the one lately used. Draw lines connecting these points, 

 and prolong them to cut the primitive. Erect perpendiculars 

 upon them, passing through the centre, and prolonging them 

 to a distance equal to the radius beyond the primitive. The 

 projections of the points where these cut the primitive upon 

 the front-and-back axis of reference ox, ox^, give the posi- 

 VOL. XIV. 2e 



