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1 68 Mr. J. Y. Buchanan on the Use of the Globe 



the meridian describes. The two small circles cut each other 

 in one point in the hemisphere of construction. Now, with 

 the quadrant coincident with No. 0, bring the pole of the 

 meridian (90° of azimuth) to coincide with the intersection 

 of the two small circles ; the meridian coincides with circle 

 No. 2. Similarly let the quadrant coincide with circle No. 1, 

 and the pole of the meridian with the intersection of the small 

 circles ; then the meridian will be found to coincide with the 

 circle No. 2 already drawn. In actual construction the coin- 

 cidence was within half a degree. The method just described 

 for finding the pole of No. 2 is inconvenient in practice. 

 When the quadrant has been clamped at Q6^° it is slipped 

 along No. to what appears to be a likely position, and the 

 position of the pole of the meridian corresponding to it is 

 marked on the globe. It is now applied to No. 1 at a likely 

 place, and the position of the pole of the meridian corresponding 

 to it is marked. If the first experimental position of the pole 

 of the meridian be called a and the second b ; then, from the 

 pole of circle No. with radius equal to the distance of a 

 draw a small circle, it is necessarily parallel to No. ; and 

 from the pole of No. 1 with radius equal to the distance of b 

 draw another small circle, which is necessarily parallel to 

 circle No. 1. These are the same small circles as those above 

 described, and the great circle described from their intersec- 

 tion as pole is necessarily identical with No. 2 already drawn. 

 In making the construction on the globe the pole of No. 2 

 was found in this way. Small circles can be drawn with the 

 metrosphere, but they are much more easily and accurately 

 drawn with a pair of compasses. The position of the circle 

 as drawn was proved by measuring the inclination of its plane 

 to those of Nos. and 1. The angle (2, 1) was found to be 

 exactly 66^°, and the angle (2, 0) was 67°. The arc or circle 

 No. contained between the nodes made by its meeting with 

 Nos. 1 and 2 is equal to the plane angle on face No. made 

 by faces Nos. 1 and 2 meeting in it. By measurement on 

 the globe it was found to be 101° instead of 102 J°. Similarly 

 the arc between the nodes (1, 2) and (0, 2) is equal to the 

 plane angle on face No. 2 formed by the meeting of faces 

 and 1 in it. It was found, on measurement, to be 122° instead 

 of 121 J°. In the same way the arc between nodes (1, 2) and 

 (0, 1), representing the plane angle in No. 1, was found to 

 be 103° instead of 102£°. 



Great circle No. being our equator of reference, and 

 node (0), one of its intersections with circle No. 1, being our 

 zero of azimuth, we have the positions of the faces and edges 

 entered on the globe as follows : — 



