PROBLEM II. To project the sphere orthographically on the plane of the equator. 1. Project the equator, divide it, and draw the merid jans, as in Problem I. 2. Lay a rule over 100, 110, &c. on the quadrant WN, and the respective correspondent points 80, 70, &c. on EN, and mark PN in 80, 70, &c. Through these points describe concentric circles for parallels of latitude, as in Problem, I. The polar circle and tropic are found by setting 23 °28', and 66° 32', from W and E toward N, and then proceeding as for parallels of latitude passing through those points, where a rule laid across, as before, cuts PN. Orthographic PROBLEM III. To project the sphere stereographically on the plane of the meridian. 1. Draw the circle NESW, of a convenient size. Draw the diameter WE, which, in this case, is the equator; and cross it at right angles with the meridian NS, which is the equinoctial colure. 2. Divide the quadrants, each into 9 equal parts, at 10, 20, &c. which reduce to the meridian NS at a, b, &c. And through 10a, 20b, &c. draw the parallels of latitude, the centres of which may be easily found by a square. For, if any radius be drawn, as Px, the perpendicular xy will intersect the extended diameter NS at the centre. Hence also is derived an easy method of projecting the parallels of latitude, viz. by continuing the diameter NS, without any reduction of the points 10, 20, &c. and applying one side of a square to P10, P20, &c. and the other will shew the centres y, y, &c. from which, with the radius y10, y20, &c. draw the parallels of latitude required. 3. The tropics and polar circles may be projected by setting 23° 28′, and 66° 32′, on each side of the equator on the primitive, and then drawing parallels of latitude at those distances. The projection of the ecliptic is also obvious. 4. For the meridians, lay a rule from N to 10, 20, &c. reckoned both from W and E toward S, and reduce them to c, d, &c. on WE; and through SaN, SbN, &c. draw the meridians required; the centres of which will always be in the diameter WE continued, and distant from P on the opposite side twice as many degrees as the respective meridians are from the primitive. Thus, e is the centre of NcS; f, of NdS, &c. Stereographic |