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Meridians are not equidiftant from each other, therefore the Parts of the Earth cannot be laid down in their true and juft Proportions.

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2. The Projection of the Sphere on the Plane of the Horizon of London, Latitude 51° 30°.

1. Draw the Primitive Circle WNES, reprefenting the Horizon of London; and cross it with two Diameters WE, NS the first of which is the Projection of the Prime Vertical of East and West; the other NS is the Projection of the General Meridian for Solftitial Colure which divides the Globe into the aftern and Western Hemifpheres as thefe two Circles interfect each other at Right Angles in the Vertex or Zenith of London, therefore the faid Zenith will be projected into the Center of the Primitive at Z.

2. The Equinoctial is the next Circle to be projected, which, because it is diftant from the Zenith Z, by the of Latitude 51° 30', therefore the Half-Tangent of 51° 30' fet from the Center Z to E, gives its Interfection in the Diameter NS; and the Tangent of its Complement 38° 30' fet from Z the other way to f, gives the Center f, on which the Equinoctial WEE is to be defcribed.

3 The Ecliptic is projected into two Semicircles, or Halfs, the Northern Half into WE; and the Southern Half into WVS E. They are thus projected by Prob. 7, and Theor. 8. and Theor. 8. Set the Half-Tangent of its Distance from the Zenith fouthward, viz. 28° to

then fet the Tangent of its Complement 62° from z to k, on SN continued; on k, as a Center, and with the Radius, defcribe the North Part of the Ecliptic W E, in the fame manner, by having the Distance 75° of the other South Part from the Zenith Z, may it be defcribed alfo. The

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4. The Ecliptic Semicircles are d Cafe 3. into their proper Signs, and you please; thus; let the Primiti duly graduated, then find the Pole VOL. II,

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Part, and laying a Ruler on g, and to each 30° in*-
the Primitive, you will find it cut the Ecliptic in the
Signs,, and a,, ; after the fame manner, by
finding the Pole i, of the Southern Semicircle Ws E,
it is divided into, ; and, m; and thus you
may very accurately divide each Sign into its proper
Degrees.

5. The Hour Circles, (which all pass thro' the Poles of the World, and interfect the Equinoctial at Right Angles) are next to be drawn. In order to this, the Pole muft be projected, which is done by fetting the Half-Tangent of the Complement of the Latitude, viz. 38° 30', from Z to P the Pole required, Then becaufe the Hour Circle of Six a-Clock, not only paffeth thro' the Poles, but alfo interfects the Horizon in the Points of Eaft and Weft; therefore an Oblique Circle paffing thro' the Points W, P, E, fhall be the Hour Circle of 6. Therefore fet the Tangent of the Latitude (which is the Complement of the Pole's Distance Z P38° 30' from the Zenith) viz. 51° 30', from Z to G, in the Diameter NS continued. Then on G, with the Radius G P, defcribe the Circle D WP EF, and this fhall be the Hour Circle of 6, as required. Let this Circle be now looked upon as a Primitive Circle, and draw the Diameter DG F, which in this Cafe will be the New Projection of the Equinoctial, and confequently by fetting the Tangents of 15o, 30°, 45°, &c. each way from the Center G, towards D and F, the Hour Circles may be all defcribed here as they were in the foregoing Projection; as is evident by viewing the Scheme only; thofe Parts which belong to the Projection now under Confideration, being therein drawn in Black Lines, and continued, in their proper Projection, in dotted Lines.

6. The

3

D

6. The Tropics, and other Parallels of Declination, are all drawn by Prob. 7. Cafe 3. However, because; it may happen that fome may have occafion to defcribe the Parallels of every Degree of the Sun's Declination, and it being tedious fo to do without the Help of Tables, but eafy thereby; I have here adjoined the following Tables for that purpose.

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The Conftruction of the Tables of Intersections and Centers is evident from the following Scheme.

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Let the Interfection and Center of the Tropic of Capricorn be to be found, for Example.

Describe the Primitive Circle AZ HN for the Solftitial Colure; crofs it with two Diameters AH, the Horizon, and Z N the Prime Vertical; then draw the Equinoctial ÆL; and from the Chords fet 23° 30' from A to W, and draw vs n, which will be the Diameter of the faid Tropic. Then (fuppofing the Eye in the lower Pole N, or Nadir, of the Horizon) this Diameter will be projected into the Line f F, by Theorem 2. Alfo the Point Z is projected into C; the Point wy into f; and the Point n into F; but fC is the Half-Tangent of Z = 51° 30′ + 23° 30' 75°; therefore the Half-Tangent of 75° (that is, the Tangent of 37° 30') fet from C to f, gives the Point of Interfection f. Now the other Part C F, is the Half-Tangent of the Arch Z HN = 90° + 62° 152°; But

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The Half-Tangent of 152° = CF 401078
And the Half-Tangent of 75°C f 76732

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These added, make the Diameter f F = 477810
The Half of which is the Semidia. Ef 238905

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