332 Proceedings of the Royal Physical Society. 



circle from on a centre, and radius OA in connection with 

 quadrant i. Now, we have to conceive that we are looking 

 down upon the sphere from above ; but as all points on its 

 surface are equidistant from its centre, the point of view is 

 quite immaterial. We require to find a line which will 

 touch OA in the quadrant I., and be parallel to a line touch- 

 ing the front axis oa on the one side and the right axis oh 

 on the other, h being understood to be unity (or the radius 

 of the circle of projection), we have only to join a point at 

 •8452 of the one axis in ii. with the unit length on the other. 

 As before, produce these lines to cut the circle of projection, 

 draw intersecting arcs from the points where they do so, and 

 rule a line through them to the o in one direction, and to any 

 arbitrarily chosen distance in the other. At right angles to 

 this draw a line touching the outer arc of the circle in L, 

 and produce it both ways until it cuts ox, OY. The line so 

 obtained gives the length of the base of the gnomonogram of 

 this species to the radius and the point of contact chosen. 

 Where it cuts the perpendicular in i. is the important 

 crystallographic pole m (110) ; where it cuts OY is the posi- 

 tion of h (010), and where it cuts ox is the position of a (100). 

 Measure on ox, in iv., the distance oa, and draw ac, and 

 erect a perpendicular to that line so that it passes through o. 

 Sign the point where this line cuts ac with a d (101). Next, 

 from with a radius oh describe an arc of a circle cutting ox 

 on the right in III. Join this point with c, and erect a per- 

 pendicular upon it, passing outward from o, as in the other 

 quadrants, signing the point where it cuts he with e (Oil). 



25. With these data on the working map, we are prepared 

 to set out the chief lines and poles on the required gnomono- 

 gram. On a separate sheet of paper, not less than imperial 

 size, draw a line about five centimetres from the base, and on 

 the right half of this line, at about three decimetres from the 

 end, mark a fine dot and sign it m (110). From this point 

 measure to the right mh, taken from the working map, and 

 to the left ma, signing a (100) and h (010). From a as a 

 centre with radius ac, and from h with a radius he, describe 

 intersecting arcs, and mark the point thus determined c (001). 

 From c draw a line to m: if the work has been properly done, 



