The Projection of the Sphere on

the Plane of the EQUINOCTIAL

5. The Point L, is the Pole of the Ecliptic; for it is 23° 30 diftant from P, the Pole of the Equinoctial; and because all Circles of Longitude pafs thro' the Poles of the Ecliptic, and interfect it at Right Angles; therefore they will be all Oblique Circles here; and may be drawn in the very fame manner as the Meridians were in the laft Projection;

yea

yea they will be the very fame things here, as the Meridians were there. But (to avoid confusion) I have drawn only one WLE; which is to be reckoned as a Primitive to the reft.

6. The Ecliptic here is divided by laying a Ruler from its Pole to every other Hour, X, VIII, &c. in the Primitive (the Distance being 30°) and it will interfect the Ecliptic in the Points V,, I, S, N, m, m.

7. To Project the Horizon of London, Latitude 51° 30, it must be confidered, that 'tis the Northern Part, or half of it, that is elevated above the Equinoctial on the North; and because the Elevation is 38° 30', and it cuts the Equinoctial in the Points of Eaft and Weft, as E, W; therefore it shall be a Great Oblique Circle, whofe Center will be in the Line of Meafures NS; and is defcribed by Prob. 8, Theor. 7; and is here reprefented by the Circle WOE, falling between the Center P, and the North Point N, of the Equinoctial.

8. Set the Half-Tangent of 38° 30' from P to Z, fo fhall Z be the Pole of the Horizon WO E, or Zenith of London; through which all the Azimuths must pafs, and they may be drawn by Prob. 8. Cafe 4. Of these I have drawn only one, viz. the Prime Vertical WZE.

9. As in this Projection, all the Parallels of Declination are compleat Circles concentric with the Primitive; fo on the reverfe, the Parallels of Altitude, or Almacanthars, are deficient, many of them; and ail Oblique, as being Parallels to the Great Oblique Circle WO E, the Horizon; and might be drawn by Problem 7. Cafe 3.

10. The fixt Stars might be reprefented in this, by having their Declinations and Right Afcenfions, which may be found in Books of Aftronomy. For where VOL. II.

K 2

any

any Meridian of the Star's Right Afcenfion, fuppofe IVP 30° interfects the Parallel of its Declination, as AB 23° 30', there will be the Star's Place.

V. To project the Sphere on the Plane of the Tropic of Capricorn.

1. Draw the Equinoctial Circle Av 2; and having fitted the Sector to the Radius thereof PÆ, take the Half-Tangent of 90+23° 30′ = 113° 30′ (or Tangent 56° 45') and fettting one Foot of the Compaffes in the Center or Pole P, with the other defcribe the Circle W NES, which fhall be the Reprefentation of the Tropic of Capricorn, in the Plane of the Projection.

2. Cross the Equinoctial with two Diameters A 2,

, and defcribe the Ecliptic, the Horizon, and other Circles here, juft as in the laft Projection, refpecting the Equinoctial here (as it was there) as the Primitive; and continue them all till they arrive to the Tropic, or outmoft Circle of the Projection.

3. The Difference between this and the laft Projection, does confift in these three Things. First, The fame Circles which there terminated in the Equinoctial, are here continued beyond to the Tropic of Capricorn. Secondly, There only one Half of the Ecliptic could be drawn, but here the whole Circle of the Ecliptic is exhibited; and divided as before. Thirdly,, In that Scheme only the Prime Vertical was drawn, in this all the Azimuths are drawn, inftead of the Meridians, which are here neglected. So that no more needs be faid concerning this Projection in Particular.

4. In all thefe Projections, the Reader is to obferve, That Regard is had to the Sphere, as rectified to the Latitude and Longitude of London. 1 fpeak this, be

cause

The Projection of the Sphere on the Plane of the Tropic of Capricorn

caufe the Reader may obferve a Difference in the Pofition of the Horizon in thefe two laft Projections of mine, and the fame in other Authors; as Harris, Hawney, &c. Their's being projected on the fame fide with the Ecliptic; for the Latitude indeed of 51° 30', but

30', but not for the Longitude of London; but mine is for both, and therefore is projected on the contrary Part towards the North, agreeable to Truth, and the Reality of the Thing.

VI. To project the Sphere on the Plane of a Great Circle Oblique to the Horizon.

All thefe Great Circles that are oblique to the Horizon, are fuch (as in Dialling) we call Reclining Planes; and as all Great Circles of the Sphere are Horizons in fome Parts of the World or other, fo all thofe Planes, on which Dials are made, are Horizontal Dials in fome particular Part of the World.

Suppofe therefore that in the Latitude of London 51° 32, the Side of an Houfe fhould decline from the South Weftward 24° 20', and the Roof thereof (which is in the Plane of a Great Circle oblique to the Horizon) fhould recline from the Zenith northwards 369 oo'. Now I would know in what Latitude, and how much Differing in Longitude, that Part of the World is, in which this Oblique Plane will be an Horizontal Plane. In order to discover this by Projection, proceed thus;

1. Defcribe the Primitive Circle HLOD, to reprefent this Oblique or Reclining Plane.

2. Draw the two Diameters HO, L D, croffing each other at Right Angles in 2

3. Set the Half-Tangent of 36° 00', the Plane's Reclination, from 2 to Z; fo fhall Z be the Zenith of London, as 2 is of the Place enquired.

Set the Half-Tangent of 54° 00', (the Co-reclination) from 2 to R; fo fhall R be one Point thro' which the Horizon of London muft pafs.

5. Then thro' the Points H, R, Ô, draw the Horizon of London on the Center C, by Prob. 8.