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3. Upon all direct East and West Planes reclining ( how far soever ) is the North Pole elevated ; but on their opposite Incliners, the South Pole.

4. Over all North Reclining Planes, whether Direct or Declining the North Pole is elevated ; and over their opposite Incliners the South Pole.

5. Lastly, Over all South Reclining, Direct or Declining, if the Plane passeth between the Zenith and the Pole, the South Pole is elevated; as is the North Pole on their opposite Incliners ; but if the Plane passeth between the Pole and the Horizon, the North Pole is elevated , but the South over their opposite Incliners.

PROBLEM XI.

To describe Hour-Lines on an Equinoctial Plane ; or to make a Polar Dial.

Practice. As in all Dials the Style is parallel to the Axis of the Earth, and its Height above the Plane equal to the Pole's Elevation above it ; and as the Earth's Axis is perpendicular to the Equinoctial Plane, fo a Pin of Wire set perpendicular in the Center of a Circle divia ded into twenty-four equal Parcs, will constitute a Por lar Dial, as required. The Foundation, and also a Figure thereof, you have in the Stereographic Proječtion of the Sphere on the Plane of the Equino&tial, in the former Part of this Book.

PROBLEM XII.

To draw Hour-Lines on a Plane passing through the Pol s directly beholding the South ; or to make an Equinoctial Dial. VOL. II.

XX

Practice. .

Practice.

'Tis evident, that as those Planes which pass through the Poles can have no Elevation of the Pole above them, so neither for that Reason can they have any Center ; and therefore all the Hour-Lines drawn on them will be parallel to each other.

To make this Dial then, proceed thus ;

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Suppose E F G H the given Plane ; then at a convenient Diftance above it, draw the parallel Line AB; and on the Point C as a Center describe the Sea micircle ADB, one Quadrant of which D B divide into fix equal Parts in the Points a, b, c, d, e; thro' each of those Divisions, draw Lines from the Center to the Side of the Plane, and they will give the Points therein through which the parallel Hour-Lines of XII, I, II, &c. on the one side, and those of XI, X, IX, &c. on the other Side are to be drawn ; and thus will

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the Dial be compleated as you see it in the Figure Here the Reader must observe the following Things.

1. That the Foot of the Stile must always be placed in the Hour-Line' of XII.

2. That the Height of the Stile must always be equal to the Distance between the Hour-Lines of XII and III, -- or XII and IX ; .which is equal also to DL the Tangent of the Arch D C, or 45 Degrees, and therefore equal to the Radius C D.

you first chufe the Height of your Stile, fuppose 9 Inches, you may determine the Distance of any Hour-Line thus ; As Radius : Stile's Height 9. Inches : : Tangent of Db = 60° : 157. Inches, the Distance of the Hour-Line of IV, : : Tangent of Da = 75° : 332 Inches, the Distance of the HourLine of V. And thus you may determine the Length of your Plane with ease.

4. In making this Dial, you have made one for its opposite Plane directly beholding the North ; only the Hour-Lines there stand in a reverse Order to these.

3. Hence if

PROBLEM XIII.

To draw the Hour-Lines on a Plane passing thro' the Poles, and directly beholding the East ; or to make a direct East Dial.

VOL. II.

Xx 2

Practice.

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The Method of making this Dial is the same with the foregoing, and the Dial it self is in substance the fame with that ; only as in that the Stile stood on the Hour-Line of XII, here it must stand on the HourLine of VI ; and as the Height of the Stile there was çqual the Distance between the Hour Lines of XII and III, or IX ; fo here it is equal to the Distance between the Hour-Lines of VI and IX.

Lastly, As there the Hour-Lines were all parallel and determined by Tangent Lines, so they are in this; and equal in their respective Distances, if the Height of each Stile be the fame.

West,

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The Weft direct Dial is made in the same manner also; only here the Hours begin from I, and proceed to VIII ; whereas in the East Dial they begin from IV, and end at XI. The Position is reverse to the other ; but both have the Elevation of the Equinoctial FEG.

PROBLEM XIV.

To make an Horizontal Dial for any Latitude, ( suppose that of London, 51° 32', ) by Projection.

PraEtice.

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