408 Proceedings of the Royal Physical Society. 



projected is the projection of Icb^, the zone of the brachy- 

 domes. 



Now conceive that the sphere of projection is viewed from 

 X in the direction of x^ yy^ remain as the right-and-left 

 axes of reference, as before; but the vertical axis of 

 reference stands for zz\ z being uppermost. We have now 

 to project the inclination of the trace of a plane passing 

 through the origin o (or z), and inclined parallel to the 

 crystallographic face c (001), as measured in the direction of 

 XY. The angle in question is measured from the vertical 

 axis of reference, and is denoted by a. In Khodonite a is 

 103° 18' 7", or 13° 18' more than a right angle. As we are 

 not here concerned with a in relation to h (010), but only to 

 c (001), we simply measure off the chord of 13° 18', which is 

 •2316 from z^, the primitive towards Y, project this angle 

 from'z on to yy\ Transfer the point so determined to the 

 final copy, and draw an arc of a great circle through this and 

 aa^. This arc gives the projection of the zones of the macro- 

 domes, or aca^, and therefore the projection of c. 



2. Projection of the Prisms. — The same working map will 

 serve for both the projections already worked out and these. 

 We have first to conceive that we are viewing the sphere of 

 projection from the side, in the direction from l to 6^, and that 

 this latter, in the present case, stands for the upper half of the 

 vertical axis. The ratio of the vertical axis to unity {ob) in 

 Khodonite is "62127, and that of the front-and-back crystallo- 

 graphic axis in the same species is 1-07285 (i.e., greater than 

 unity in this case). It is well to draw a short arc of a circle 

 to this radius near both a and a\ Then as ft the inclina- 

 tion of the crystallographic axis a in Ehodonite, is 108° 

 44' 8", measured from the vertical axis of reference c, which 

 angle is 18° 44' 8" more than a right angle, set off on the 

 primitive from a towards h, the equivalent chord '325, and 

 draw a line from the centre of the primitive through this 

 point to the outer segment just mentioned. The point so 

 determined is a. 



Now, as the projection which is under construction is 

 supposed to be viewed from above, in the directions parallel 

 zoz^, this length of a will have to be fore-shortened. Accord- 



