344 Proceedings of the Royal Physical Society. 



compasses when the centre happens to be far off. An 

 approximation to the position of the centre for the descrip- 

 tion of such arcs may be arrived at by a little contrivance 

 I have used for some time. A rather large set-square 

 is taken, and about a millimetre is cut up the obtuse, 

 or right-angled corner. On the face of the square over 

 this point, a small cork of firm texture is fastened at its 

 base with seccotine, or other cement, and a fine needle is 

 passed through it in such a manner that its point coincides 

 with the intersection of the two rectangular sides of the 

 square. The object is to enable one to rotate the set-square 

 in its own plane, about its rectangular corner as a centre. 

 Its use is to enable us to find the centre from which certain 

 arcs of circles have to be described. Suppose we take the 

 simple case just referred to, and wish to find the position of 

 (111) on the map. This lies at the intersection of an arc 

 through h (010) and cl (101) with a line from m (110) to c 

 (001). To find the centre from which to describe the arc, 

 we may in many cases make use of the set-square. The 

 needle is placed at a, and the square moved around that 

 point with its left edge cuts d, which is on the left side of 

 the circumference of the circle required. In this position 

 the right edge of the square on the prolongation of ch marks 

 the right side of the circumference of the same circle. A 

 point midway between this and d is the centre required. 

 Another and a simpler method of finding the centres from 

 which great circles inclined to the primitive may be described, 

 is as follows : — Let be the centre of the primitive, a the 

 front-and-back diameter, and h another diameter cutting it 

 at right angles, and let it be required to describe, on the left 

 side, the projections of two great circles /and g, respectively 

 inclined 20° and 70° to the primitive. In the lower right- 

 hand quadrant set off '347 of the radius from h, and sign the 

 point F ; produce Oh indefinitely to the right ; from F erect 

 a perpendicular to fO, cutting the extension of Oh at F. 

 Likewise set off in the same quadrant 1*147 of the radius 

 from h, and sign it G ; erect a perpendicular to gO, cutting 

 06 in G. Then, with the radius Fa describe the projection 

 /, and with that of Get describe the required projection g. 



