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PROBLEM VII.

To project the sphere stereographically on the plane of the tropic

of capricorn.

1. Project the equator A:B qr 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 28 do at x, and draw the ecliptic gr 8 , &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.

Stereographic

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PROBLEM VIII.

To project the sphere stereographically on the plane of a circle

oblique to the horizon.

EXAMPLE.

Required a stereographic projection of the sphere on the plane of a great circle, declining 24° 30' westward from the south at Cambridge, in lat. 42° 23' 28" N. and reclining 36° 30' from the zenith northward.

1. Project the great oblique circle HDOL, and quarter it by the diameters HO, DL.

2. Set the reclination northward from Oto A, considering the upper as the northern part ; reduce A to Z ; then Z is the zenith of Cambridge, and Q is that of the place, where the oblique circle is a horizontal plane. Also reduce a, 90° distant from A, to ż; and through H, 2, O, project HWzSo, the horizon of Cambridge, and continue it through O to E.

3. Set the western declination from H to y, from D to c, and from 0 to d. From the pole Z reduce y, c, d, to W, S, E, on the horizon, which will be the west, south, and east, points of the horizon of Cambridge.

4. From Qto F set the tangent of 53° 30', the complement of the reclination 36° 30' ; from F raise the perpendicular FG, and continue the diameter EW till it intersect FG. Then with centre G, and radius GS, describe PZSK, the meridian of Cambridge.

5. A rule on W, Z, cuts the primitive at C. Set the complement of the latitude from C to B ; and a rule over W, B, cuts the meridian at P, which is the north pole. Set a quadrant from B to I, and also from I to M. Then a rule on W, I, cuts the meridian at Æ, the point where the equinoctial intersects it ; and on W, M, it cuts the meridian produced in K, the south pole.

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6. Draw the equinoctial RWÆTE through the three points W, Æ, E; and VOK, the axis, and meridian of

; the place

7. Through the three points R, P, T, describe the circle PRKT, and draw the diameter UX perpendicular to PQK. Then describe the meridians, and parallels of latitude, asi in the stereographic projection on the plane of the horizon ; finding the intersections of the parallels with the axis by reducing from the point R.

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