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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° 301 distant from P, the Pole of the Equinoctial; and because all Circles of Longitude pass 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 last Projection ;
having their Declinations in Right Ascensions, which
yea they will be the very fame things here, as the Meridians were there. But ( to avoid confusion ) I have drawn only one W LE; which is to be reckoned as a Primitive to the rest.
6. The Ecliptic here is divided by laying a Ruler from it: Pole I to every other Hour, X, VIII, &c. in the Primitive ( the Distance being 30°) and it will intersect the Ecliptic in the Points v, 8, II, , r,
7. To Project the Horizon of London, Latitude 51° 30, it must be considered, 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 East and West, as E, W ; therefore it shall be a Great Oblique Circle, whose Center will be in the Line of Measures NS; and is described by Prob. 8, Theor. 7 ; and is here represented by the Circle WO E, 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, so shall Z be the Pole of the Horizon WO E, or Zenith of London ; through which all the Azimuths must pass, and they may be drawn by Prob. 8. Cafe 4. Of these I have drawn only one, viz. the Prime Vertical WZE.
g. As in this Projection, all the Parallels of Declination are compleat Circles concentric with the Primi. tive; fo on the reverse, the Parallels of Altitude, or Almacanthars, are deficient, many of them ; and ail Oblique, as being Parallels to the Great Oblique Circle WOE, the Horizon; and might be drawn by Problem 7. Case 3.
10. The fixt Stars might be represented in this, by
may be found in Books of Astronomy. For where VOL. II.
any Meridian of the Star's Right Ascension, suppose IV P= 30° intersects the Parallel of its Declination, as A - B = 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 Æ 2m; and having fitted the sector to the Radius thereof P Æ, take the Half-Tangent of 90 + 23° 30' = 113° 30' (or Tangent 56° 45') and settting one foot of the Compases in the Center or Pole P, with the other defcribe the Circle WNES, which shall be the Representation of the Tropic of Capricorn, in the Plane of the Projection.
2. Cross the Equinoctial with two Diameters Æ Q, r , and describe the Ecliptic, the Horizon, and other Circles here, just as in the last Projection, respecting the Equinoctial here ( as it was there ) as the Primitive ; and continue them all till they arrive to the Tropic, or outmoff Circle of the Projection.
3. The Difference between this and the last Projection, does consist in these three Things. First, The same 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 thar Scheme only the Prime Vertical was drawn, in this all the Azimuths are drawn, instead of the Meri dians, 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 observe, That Regard iş hạd to the Sphere, as rectified to the Latitude and Longitude of London. I speak this, be
The Projection of the Sphere on the Plane of the Tropic of Capricorn
cause the Reader may observe a Difference in the Position of the Horizon in these two last Projections of mine, and the fame in other Authors ; as Harris, Hawney, &c. Their's being projected on the same side with the Ecliptic ; for the Latitude indeed of 51°
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 proje&t the Sphere on the Plane of a
Great Circle Oblique to the Horizon. All these Great Circles that are oblique to the Horizon, are such ( as in Dialling ) we call Reclining Planes ; and as all Great Circles of the Sphere are Horizons in some parts of the World or other, fo all those Planes, on which Dials are made, are Horizontal Dials in some particular Part of the World.
Suppofe therefore that in the Latitude of London 519 32', the Side of an House should decline from the South Westward 24° 20', and the Roof thereof (which is in the Plane of a Great Circle oblique to the Horizon) should 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. Describe the Primitive Circle HLOD, to represent this Oblique or Reclining Plane.
2: Draw the two Diameters HO, L D, crossing each other at Right Angles in 2.
3. Set the Half-Tangent of 36° 00', the Plane's Reclination, from 2 to Z ; so shall Z be the Zenith of London, as Q is of the Place enquired.
4. Set the Half-Tangent of 54° 00', ( the Co-reclination) from 2 to R ; fo shall R be one Point thro' which the Horizon of London must pass.
5. Then thro' the Points H, R, O, draw the Horizon of London on the Center C, by Prob. 8.