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Meridians are not equidistant from each other, therefore the:Parts of the Earth cannot be laid; 'down in. their true and just Proportions. 2. The Projection of the Sphere on the Plane of

the Horizon of London, Latitude 51° 30*.

1. Draw the Primitive, Circle WNES, representing the Horizon of London ; and cross it with two Projection of the Prime Vertical of East and West ; the other NS is the Projection of the General Meridian för Solftitial Colure which divides the Globe into the Faitern and Western Hemispheres ; as these two Circlçs interfect each other at Right Angles in the Vertex or Zenith of London therefore the said 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 distant from the Zenith Z, by the of Latitude 51° 30', therefore the Half-Tangent of 51° 30' fet from the Center Z to Æ, gives its Intersection in the Diameter N S ; and the Tangent of its Complement 38° 30' set from Z the other way to f, gives the Center f, on which the Equinoctial E is to be described.

3. The Ecliptic is projected into two Semicircles, or Halfs, the Northern Half into WOE; and the Southern Half into W VS E. They are thus projected by Prob. 7, and Theor. 8. Set the Half-Tangent of its Distance from the Zenith southward, viz. 28° to % ; then set the Tangent of its Complement 620 from z to k, on S N continued ; on k, as a Center, and with the Radius *, describe the North Part of the Ecliptic WG E, in the same manner, by having the Distance 750 of die other South Part from the Zenith 2, may it be described also.

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The Projection of the

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4. The Ecliptic Semicircles' are di Cafe 3. into their proper Signs, ang you please ; thus ; let the Primiti Quly graduated, then find the Pole

VOL. II,

I

Part, and laying a Ruler on g, and to each 30° in** the Primitive, you will find it cut the Ecliptic in the Signs II, 8, and "X ; after the same manner, by finding the Pole i, of the Southern Semicircle W VS Ė, it is divided into my *; and 7, 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 must be projected, which is done by setting the Half-Tangent of the Complement of the Latitude, viz. 38° 30', from 2 to P the Pole required, Then because the Hour Circle of Six a-Clock, not only pasieth thro' the Poles, but also intersects the Horizon in the Points of East and West ; therefore ar Oblique Circle passing thro' the Points W, P, E, fhall be the Hour Circle of 6. Therefore set the Tangent of the Latitude ( which is the Complement of the Pole's Distance Z P = 38° 30' from the Zenith ) viz. 51° 30', from Z to G, in the Diameter NS continued. Then on G, with the Radius GP, describe the Circle D W PEF, and this shall be the 1 Hour Circle of 6, as required. Let this Circle be now looked upon as a Primitive Circle, and draw the Diameter DGF, which in this Cafe will be the New Projection of the Equinoctial, and consequently by fetting the Tangents of 15°, 30°, 45°, &c. each way from the Center G, tovards D and F, thé Hour "Circles may be all described here as they were in the foregoing Projection; as is evident by viewing the Scheme only; those Parts which belong to the Projection now under Consideration, being therein drawn in Black Lines, and continued, in their proper Projection, in dotted Lines.

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6. The Tropics, and other Parallels of Declination, are all drawn by Prob. 7. Case 3. However, becaufe ; it may happen that some may have occasion to describe the Parallels of every Degree of the Sun's Declination, and it being tedious so to do without the Help of Tables, but easy thereby ; I have here adjoined the following Tables for that purpose.

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A Table of the Intersecti. A Table of the Centers of

ons of the Parallels of thu Tropics and Parallels
Declination with the Me. of Declination from the
ridian.

Zenith,
Decl. Inter-Decl. Inter Decl.Centers, Decl. Centrs
Sout. sections Nor.sections Sout. from z.

Nor. (from z.

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oc 23 74 30 23 28 30 22 73 301

22 29 30 21 172 301 21 30 30 20 71 301

20 131 30 19 73 39

19 132 30 18 169 30

18 3 30 17 68 30 17 134

34 37 16 167 30

16 135 30 15 166 30 15 36 37 14 165 30 14 27 30 13 164 30 13 18 30 I2 163 30

12 39 30 **11 162 30 II 110 30 10 161 301

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30 9 160 301 9 +2 30 8 59 30

8 +3

+3 30 7 301 7 14 30 6

517 30 6 175 30 5 56 30 5 116 30 4 155 30 4 +7 30 3 157 30

30 2.53 301

2 19 30 I 52 30 I jo 20 Equi. 51 30

VOL. II.

Vg 158 20

To 127 47) 23 157 41 .23 27 571 22 56 451

22 28 16 21 55 44

21 28 36 20 54. 4?

20 28 G01 19 53 43

19 18 152 41

18

(29.421 17 151 701 16 150 501 15 49 55

15 130 28 14 49

2 14 3151 13 48 al 13 31 17 12 147 17 11 46 28)

II 32 08 10 45 38 10 33 36 9 + 51

2. 33 03 8 +4 03

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I 137 17 13753

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7. The Construction of the Tables of Intersections and Centers is evident from the following Scheme,

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

Describe the Primitive Circle À Z H N for the Sol. ftitial Colure ; cross 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 Æ to V, and draw vs n, which will be the Diameter of the said Tropic. Then (supposing 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. Also the Point Z is projected into C ; the Point ve into f; and the Point n into F; but FC is the Half-Tangent of 2 w = 51° 30' + 230

= 75°; therefore the Half-Tangent of 75° (that is, the Tangent of 37° 30') set from C to f, gives the Point of Intersection f. Now the other Part CF, is the Half-Tangent of the Arch Z HN= 90° + 620 = 152° ; But

The Half-Tangent of 152° = CF= 401078
And the Half-Tangent of 75o = C f = 76732
These added, make the Diameter f F = 477810
The Half of which is the Semidia. Ef = 238905

From

30'

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