PROBLEM V.

To project the sphere stereographically on the plane of the

horizon.

1. Describe a circle, with any convenient radius, as XCWPED; ́divide it into four quarters, and subdivide each of them into nine equal parts. Set the given latitude, suppose 42° 23′ 28′′, from D to E, and from C to W. Draw WE, which will be the east and west line; also continue SP to N, and SN will be the first meridian. Lastly, at the intersection of SN and WE, as a centre, describe the circle SWNE, which is the horizon of the place, and plane of projection.

2. For the meridians, project the circles aP, bP, &c. on the plane SCWPED, in the same manner as in the stereographic projection on the plane of the meridian; and continue them beyond P, through the plane of the horizon, to c, d, &c. with the same radius and centre.

3. For the parallels of latitude, and consequently the polar circles, tropics, and equator, lay a rule over W and the several divisions on the quadrant PD; also over the divisions on the quadrant Dx, and reduce them to the meridian PS; and through these points the parallels will pass on that side of P, or toward S. Then lay a rule from W to the several divisions on PC, which will give as many points on PN extended, through which the parallels will pass on the other side of P. The distances of corresponding points on opposite sides of P being considered as diameters, the parallels, &c. are to be described on them.

NOTE. To know how large the meridian projection must be to form a horizontal one of any given diameter, say, as cosine of the latitude radius: the given semidiameter : the semidiameter of the meridian projection.

PROBLEM VI.

To project the sphere stereographically on the plane of the ecliptic.

1. On C, as centre, with radius C, which is taken at discretion, draw the ecliptic, which divide into twelve equal parts, viz. v 8, 8, &c. To the points Y, 8, П, &c. right lines, drawn from the centre C, are circles of longitude; the most remarkable of which are ~, and, one the equinoctial, and the other the solstitial, colure.

2. From toward 8 set 23° 28', and reduce the bounding point to P; then P will be the pole of the world; whence the meridians and parallels of latitude may be projected, as in the last Problem; but they are here projected by

ANOTHER METHOD.

1. At P, with radius PD = the semidiameter of the circle P, project the quadrant Dyy, &c. E, which divide into nine equal parts at y, y, &c. Then draw the tangent Dxx, &c. From P reduce the points y, y, &c, to x, x, &c. which will be the centres of as many of the meridians. And these divisions being transferred from D to u, u, &c. will give as many other centres for other meridians.

vat b, b.

2. For the parallels of latitude, tropics, equator and polar circles, reduce the pole P to O; from O, on each side, set 10° to a, a, which reduce to the diameter And from b on one side of P to b on the other, diameter of the parallel of 10° from the pole. are found in a similar manner.

will be the The others

PROBLEM VII.

To project the sphere stereographically on the plane of the tropic of capricorn.

1. Project the equator A B on the centre P, and then draw the parallels of latitude, polar circle, and tropic in the northern part, with the meridians, as in the projection on the plane of the equator.

2. Bisect the distance at x, and draw the ecliptic 8 II, &c. Divide it into the 12 signs by the proper rule in Stereographic Projection.

3. The circles of longitude and the parallels to the ecliptic are found in the same manner, as the meridians and parallels of latitude respectively in the last projection.