Page images
PDF
EPUB

PROBLEM IV.

To project the sphere orthographically on the plane of the meridian.

1. Divide the primitive as in the last projection. The parallels of latitude, tropics, and polar circles are right lines, drawn through the corresponding points 10 and 10, 20 and 20, &c.

2. The meridians are ellipses, which are easily drawn with elliptical compasses. But if this instrument cannot be obtained, use may be made of the following

Method.

Set the radius of the primitive from 90 to 90 on the line of sines on the sector. Then set the parallel sines of 10, 20, &c. from C toward E and W. By adapting the sector to the radius of each parallel of latitude, and marking it in a similar manner, the points of the equator and parallels, through which the meridians are to pass, will be obtained, and the meridians are then drawn, each through the corresponding points, with a steady hand.

Or,

:

Since CE CB: ce ch universally, WE being divided as before, the corresponding points of the parallels of latitude may be obtained, by finding geometrically a sufficient number of fourth proportionals to three given right lines, and marking them on the parallels. To make the ellipses more accurate, cther parallels may be drawn, and corresponding points found on them in a similar

manner.

NOTE. This projection is commonly called the Analemma.

Orthographic

W

Orthographic Projection on the Meridian.

1&

PROBLEM

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.

Stereographic

[merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][graphic][subsumed][subsumed][merged small][ocr errors][subsumed][subsumed][subsumed][merged small][subsumed][ocr errors][subsumed][subsumed][subsumed][merged small]

PROBLEM VI.

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

1. On C, as centre, with radius Coo, which is taken at discretion, draw the ecliptic, which divide into twelve equal parts, viz. r 8, 8, &c. To the points, &,

, &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 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.

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

at

b, b. And from b on one side of P to b on the other, will be the diameter of the parallel of 10° from the pole, The others are found in a similar manner.

Stereographic

« PreviousContinue »