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Spherical Trigonometry applied to Dial

ling; shewing the Grounds and Reason, as well as the Practical Method, of drawing Hour - Lines on all Sorts of Planes, in all Places.

T

HIS most ingenious and surprising of all the
Mathematical Arts can never be well under-

stood by any Person, who hath not very well studied the Doctrine of the Projection of the Sphere, and the Nature of Spherical Triangles, in the Manner as delivered in the former Part of this Book. For on these two Hinges turns all the Mystery of the Art of Shadows.

The Planes on which Dials are described, receive their Denominations according to their Situations and Positions, with regard to the Horizon, and the Cardinal Points thereof. For all Planes are either

1. Horizontal, or parallel to the Horizon.
2. Erect, or perpendicular to the Horizon.
3. Reclining, or Oblique to the Horizon.

4. Inclining Planes.
1. Of Horizontal Planes there is but one Kind.
2. Of Erect Planes there are two principal Kinds ;
1. Direct, or those which directly behold the East,

Weft, North, and South Points of the Horizon. 2. Declining, or those which, declining from those

four Cardinal Points, do behold some intermedi-
ate Point between them.
VOL. II.

Tt 2

Of

Of Erect Direct Planes there are these subdivisions. 1. East Erect Direct)

| East. 2. Weft Erect Direct Planes directly

Weft. 3. North Erect Direct beholding the North, 4. South Erect Direct

| South. Of Declining Planes there are the following Sorts 1. South Declining East Planes whose! S and E, 2. South Declining West

S and W.

N and E.

twween the 4. North Declining Welt i

N and W.

3. North Declining East Poles lie be

3. Of Reclining Planes, or those which are posited

oblique to the Horizon, like the Roofs of Houses, &c. there are these kinds. 1. Eaft Direct Reclining Planes which

( East. 2. West Diree? Reclin.

West. 3. North Direct Reclin.

directly do

North.

behold the 4. South Direct Reclin.

| South. If the Planes behold none of these Points direct, but some other between them, they are thus denominated.

1. South Recl. Decl. East) Planes whose 'S and E. 2. South Recl. Dec). West

S W. 3. North Recl. Decl. Eaft? Poles lie be4. North Rec!. Decl. West)

(Nand W. 4. Of Inclining Planes there are the fame Divisions and Denominations as are just enumerated of Recliners ; 'for an Inclining and Reclining Plane are the same, only the Reclining beholds the Zenith, the Inclining the Horizon of the Place ; and one Dial serves for both.

These

Poles lie be- Nand.E.

tween

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These are all the Varieties of Planes on which Dials may be described, and it behoves every one who pretends to this Art to have a perfect Notion thereof.

I shall now shew the Geometrical Construction of Dials on all the foregoing Planes, from the Principles of Spherical Trigonometry, in the ensuing Problems.

PROBLEM I.

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To find the Sun's Altitude by a Quadrant.

PraEtice. When you are to make a Dial, you must first find the Sun's' Altitude by a Quadrant, thus ; hold your Quadrant against the Sun in such manner as that the Ray of the Sun Beams which pasfeth through the Hole of the upper Light may fall precisely on the Hole of the lower Light ; then will the Thread cut the Limb of the Quadrant in the Degree and Minute of the Sun's Altitude.

PROBLEM II.

To find the Horizontal Distance of the Sun from the Pole of the Plane.

Practice. Drawan Horizontal Line on the Plane or Wall, and apply the Edge of the Quadrant thereto at Right Angles, taking Care that the Limb of the Quadrant, be towards the Sun. Having thus applied the Quadrant, and in a Position as level as possible, hold up a Thread and Plummet against the Limb of the Quadrant, at full liberty, moving this way and that 'till the Shadow of the Thread falls just on the Center of the Quadrant ; and then observe what Number of De

grees

grees are contained between the Shadow of the Thread and that Side of the Quadrant standing perpendicular to the Plane, for they are the Horizontal Distance required.

PROBLEM III.

To find the Plane's Declination.

1

Practice. The Declination of the Plane is the Distance or Quantity of the Arch of the Horizon contained between the Pole of the Plane, or a Line drawn perpendicular thereto, and the true Point of North and South.

Having found the Altitude of the Sun, and Horizontal Distance of the Plane, proceed for the Declination by these Rules.

1. First, find the Sun's Azimuth by Prob. 17 Of Astronomy. Or if it be Collin's, or Sutton's Quadrant, you may find the Azimuth near enough the truth by it.

2. When you make your Observation of the Horizontal Distance, mind whether the Thread's Shadow doth fall between the South and that Side of the Quadrant which was perpendicular to the Plane.

3. If the Shadow fell between them, then the Sun's Azimuth from the South, and the Horizontal Distance added together do give the Declination of the Plane. And in this Case the Declination is towards the same Coast on which the Sun's Azimuth is.

4. If the Shadow fall not between them, then the Difference of the Sun's Azimuth and Horizontal Diftance, is the Declination of the Plane ; and in this Cafe, if the Azimuth be the greater of the two, the Plane declines towards the Coast on which the Sun is ; but if

the

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