342 Proceedings of the Royal Physical Society. 



distance that m is from ox on the corresponding points of 

 the primitive in the otlier quadrants, and sign the lines 

 m on the primitive and M on the indefinite continuation 

 of the line. Draw parallels to ox and OY in v. and vi. 

 at any convenient distance outside the primitive, figuring 

 them 1 to 4, as before. Along these lines, as in the 

 gnomonogram, the fractional parts for the prism zone a5, 

 ha, are to be measured. 



44. Next lay off the distance '313 beyond the radius ox 

 between vil. and vm., and produce lines from l on vii. 

 through this point. Draw a perpendicular from o through 

 this line, marking the line as a whole e. Draw parallels to 

 ox, OY, as before, to meet E at any convenient distance out- 

 side the primitive, and figure these parallels 5 and 6, as 

 before. Next, in quadrant viii., set off "313 of the radius on 

 ox beyond the primitive, between vii. and viii.; and '815 from 

 between v. and viir.; join these points, and produce them 

 to cut the primitive in V. Erect a perpendicular to pass 

 from outward, mark the line, supposed to be continued 

 indefinitely, D, and draw parallels to ox, OY to meet od as 

 before, marking the lines 7 and 8. It is well to remark 

 again, here, that we are at liberty to turn the sphere of pro- 

 jection about so as to view it in any direction ; and as its 

 boundaries are all represented by a circle, we may represent 

 any octant of the sphere by any quadrant of the circle, and 

 project from the part of the primitive in that quadrant, quite 

 irrespective of the other. Thus the poles on ca are measured 

 on 7 and 8, drawn thence to the primitive by lines directed 

 to 0, and from the primitive again projected on to ox between 

 VII. and VIII. from the right-hand &, from which similarly- 

 placed poles are set off with the compasses on the same line 

 beyond o. In like manner, the poles on he are measured on 

 5 and 6, are projected on to the primitive by lines radial to 

 0, and are thence again projected by lines radial on a 

 between 2 and 3 to he between vi. and viL, from which the 

 corresponding points on the opposite side of o are to be set 

 off in their proper position. A reference to Fig. 2 will make 

 this description clearer. 



45. Before passing on to the description of the various 



