. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Vol. II. 394 MATHEMATICS, PROBLEM II. To project the sphere orthographically on the plane of the equator. 1. Project the equator, divide it, and draw the meridians,as in Problem I. 2. Lay a rule over 100, 110, &c. on the quadrant WN,and the respective correspondent points 80, 70, Sec. on EN,and mark PN in 80, 70, &c. Through these points de-scribe concentric circles for parallels of latitude, as in Prob-lem I. The polar c
. Mathematics, compiled from the best authors and intended to be the text-book of the course of private lectures on these sciences in the University at Cambridge [microform]. Vol. II. 394 MATHEMATICS, PROBLEM II. To project the sphere orthographically on the plane of the equator. 1. Project the equator, divide it, and draw the meridians,as in Problem I. 2. Lay a rule over 100, 110, &c. on the quadrant WN,and the respective correspondent points 80, 70, Sec. on EN,and mark PN in 80, 70, &c. Through these points de-scribe concentric circles for parallels of latitude, as in Prob-lem I. The polar circle and tropic are found by setting23° 28, and 66° 32, from W and E toward N, and thenproceeding as for parallels of latitude, passing through thosepoints, where a rule laid across, as before, cuts PN. SPHERIC GEOMETRY. 395 Orthographic pojection on the 396 MATHEMATICS. PROBLEM III. To project the sphere stereographically on the plane of the- meridian. 1. Draw the circle NESW, of a convenient size. Drawthe diameter WE, which, in this case, is the equator ; andcross it at right with the meridian NS, which is theequinoctial colure. 2. Divide the quadrants, each into 9 equal parts, at 10,20, &c. which reduce to the meridian NS ?t a b, &c. Andthrough 10a, 20b, he. draw the parallels of latitude, the cen-tres of which may be easily found by a square. For, if anyradius be drawn, as Px, the perpendicular xy will intersectthe extended diameter NS at the centre. Hence also is de-rived an easy method of projecting the parallels of latitude, viz. by continuing the diameter NS, without any reductionof the points 10, 20, &c. and applying one side of a squareto PlO, P20, &c. and the other will show the centres y, y,&c from which, with the radius ylO, y20, &c. draw theparallels of latitude required. 3. The tropics and
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