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In making this one Dial, you have in effect made four, viz.

1. A Direct S Declining W 30° 00'.
2. A Direct S Declining E 30° 00'.
3. A Direct N Declining E 30° oo'.
4. A Direct N Declining W
30o 00%

The Distance of the Hour Lines being the fame in each, only in different Pofitions, and differently figured; the Hour Lines alfo of the South being drawn through the Center do make thofe of the North Dials.

All which is plain and evident from the Schemes themselves; and may eafily be understood by any one who knoweth any thing of this excellent Art, without any farther Explanation.

PROBLEM XVIII.

To draw Hour-Lines on any Direct South Reclining Planes.

Practice.

The beft Way to make Dials on thofe Planes is by reducing them to the new Latitude, wherein they will become Horizontal Planes, as taught in Prob. 5, of this Chapter.

Example. Suppofe in the Latitude 51° 32' a Plane reclines from the Zenith 20 Degrees.

Then the Difference of the Co-Latitude 38o 28', and the Reclination 20° 00', viz. 18° 28' is the new Latitude; for which let an Horizontal Dial be made by Prob. 14, and this fhall be the Dial adapted to that Reclining Plane, as required. See the Figure thereof following.

VOL. II.

Z z

Note,

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Note, The Stile of the Dial muft point to the South Pole by Prob. 10, of this.

A South Direct Plane Reclining equal to the Pole is an Equinoctial Dial; the making of which is taught Prob. 12.

Again, fuppofe a Plane recline from the Zenith 70o oo' in the Latitude 51° 32'.

This Dial may be made as the laft preceeding, by reducing it to its new Latitude 31° 32'; but for the fake of Variety for the young Learner, I have fhewn how it is made by a Projection on the Horizon of London.

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For let the Reclination be fet from Z to H, then W HE is the reclined Plane, which the Hour-Lines interfect in the Points 5, 4, 3, 2, 1, H, 11, 10, 9, 8, 7; the Point 2 is the Pole of this Plane, from which if a Ruler be laid to the aforefaid Points of Intersection, it will cut the Horizon in the Points X X X XXX, &c. from which, by a Ruler laid on the Center Z, the Hour-Lines are all to be drawn as in the Figure. Zz2

VOL. II.

From

From this Projection 'tis evident alfo how this Dial may be made by Calculation only, that is, by finding the Quantity of the feveral Arches of the Planes H 1, H2, H3, &c. For in the Spherical Triangle 11 HP, Right-angled at H, there's given P H = 31° 32!, and the Angle HP 11 = 15° 00'; to find H 11, by the fame Analogy as in Prob. 16, 17. These Arches thus found being taken from the Chords and fet each way from the North Point of the Meridian N, give the Marks X X X X X, &c. as before.

PROBLEM XIX.

To defcribe Hour-Lines on Direct North Reclining Planes.

Practice.

1. Suppose a North Plane in the Latitude 51° 32? recline from the Zenith 30° 00'.

The new Latitude found for this Plane is 68° 28' (by Prob. 6,) therefore an Horizontal Dial in that Latitude fhall be proper to this Plane, and fuch is that following.

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