354 Proceedings of the Royal Physical Society. 



so, describe intersecting arcs with any convenient radius, and 

 draw a line radial to o outwards, marking it D. From the point 

 where this line cuts the primitive, draw a line towards the 

 point of sight, which will cut ox in the position of d (101). 



QS. To project the corresponding point on the negative 

 side, d (101), set off a rectangle in viii. from the inclined 

 axis OA, as before, to cut the point where the circle a crosses 

 ox (on the right hand side in the present position), and 

 join the point where the circle c cuts ob, as before, producing 

 the line on either side to cut the primitive, erect a perpen- 

 dicular from 0, and, as before, project from the point of 

 sight on to oa, whereby d (101) is found. To determine 

 positions between either d, and c, or a, lines through a, on 

 either side parallel to c, have to be produced until they 

 meet d on each side, and another, parallel to oa, has to 

 be drawn also to meet d on each side. Mark a cross where 

 oc crosses this line, so as to indicate where measurements 

 on the negative or the positive side of c are to commence. 

 Now project c on to the primitive by a line radial to o, and from 

 the primitive by a line radial to the point of sight into a-a. 

 The uses of all these lines having been already explained, it 

 only remains to add that arcs of circles have to be drawn 

 for the zones in all cases, except that representing the trace 

 of the plane of symmetry, which passes through aca. To 

 project the points determined from ch zone, arcs of circles 

 must be drawn through each of these points and a, front 

 and back. Then arcs of circles must be drawn through each 

 h and the several points on the line aoa, commencing with 

 the projection of c. Next, arcs of circles must be drawn 

 through m (110) and c (001), and so on, as already described, 

 in the simpler cases taken earlier in the present paper. 



69. It is often required to find the centre from which to 

 describe an arc of a great circle which shall pass through 

 two points, m and n, within the primitive. This is done as 

 follows : — Let be the centre ; join mO, nO, and produce 

 these lines indefinitely beyond the primitive. From erect 

 perpendiculars to mO, nO, signing the points where these 

 lines cut the primitive respectively M, N. From M and N 

 erect perpendiculars to Mm, Nn, and produce these lines 



