3. Upon all direct Eaft and Weft Planes reclining (how far foever) is the North Pole elevated; but on their oppofite Incliners, the South Pole.

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

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

PROBLEM XI.

To defcribe 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 fet perpendicular in the Center of a Circle divided into twenty-four equal Parts, will conftitute a Polar Dial, as required. The Foundation, and alfo a Figure thereof, you have in the Stereographic Projection of the Sphere on the Plane of the Equinoctial, in the former Part of this Book.

PROBLEM XII.

To draw Hour-Lines on a Plane paffing through the Poles directly beholding the South; or to make an Equinoctial Dial.

VOL. II.

Practice.

Practice.

'Tis evident, that as thofe Planes which pass through the Poles can have no Elevation of the Pole above them, fo 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 ;

Suppofe 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 defcribe the Semicircle AD B, one Quadrant of which D B divide into fix equal Parts in the Points a, b, c, d, e; thro' each of thofe Divifions, 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, 1X, &c. on the other Side are to be drawn; and thus will

the

the Dial be compleated as you fee it in the Figure Here the Reader muft obferve the following Things. 1. That the Foot of the Stile muft always be placed in the Hour-Line' of XII.

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

3. Hence if you firft chufe the Height of your Stile, fuppofe 9 Inches, you may determine the Distance of any Hour-Line thus; As Radius: Stile's Height 9 Inches Tangent of D b = 60°: 15 Inches, the Distance of the Hour-Line of IV, Tangent of Da = 75° : 33 Inches, the Distance of the HourLine of V. And thus you may determine the Length of your Plane with eafe.

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

PROBLEM XIII.

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

VOL. II.

X X 2

Practice.

The Method of making this Dial is the fame with the foregoing, and the Dial it felf is in fubftance the fame with that; only as in that the Stile ftood on the Hour-Line of XII, here it muft ftand on the HourLine of VI; and as the Height of the Stile there was equal 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.

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

Weft

The Weft direct Dial is made in the fame manner alfo; 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 FE G.

PROBLEM XIV.

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

Practice.