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But if such Erect Plains do not behold the Direct East, w'eff North or South Points of the Horizon, they then will behold either

South-East
The

South-Wef And then they are called "?
North-East

North-West
North 2

SEaft >Ere&t Plains ; Declining or South

West.

A

or

III. Of Plains that lie Obliquely to the Horizon : (such as the Roofs of Houses, the Cooping of Walls, &c.) are called Reclining Plains. And if such Plins do behold the direct

East. West North

Points of the Horizon: They are then South called Direct Edft, West, North or South Plains : Reclining from the Zenith of the place in which such Plain stands.

But if such Reclining Plain doth not respect the true Eaft, West, North, or South Points, then they will lie open either to the

South-Ealt
South-West
North-East
And then they are called

1 North-West

Seaft Reclining Plains : Declining or North

Weft. And these are all the Varieties of Plains, upon which Haur-Lines, may be described. Only note,] That all Reclining Plains whatsoever ; whether Direct

or Declining, have Two Faces; the Upper-Face, which beholds the Zenith of the Place, is called the Reclining Plain : And the Under-Face, which beholds the Horizon of the Place, is called the-Incliner : And one and the fame Dial serves for both Places.

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South 2

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CH A P. III.

How to find the Situation of any Plain, in respect of De

clination and Reclination, in any Latitude.

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I. To find the Reclination. Fig. LI. Difrition. T the Arch of that Vertical or Azimuth Circle which

HE Quantity of the Reclination of a Plain, is: is perpendicular to the Reclining Plain, comprehended between the Zenith of the Place and the Plain.

To find which, let A B C D represent such a Reclining Plain : Draw, first, thereon, by, help of a Ruler and Quadrant, a Right

a Line G H, parallel to the Horizon of the place ; which thall be the Horizontal Line of the Plain. . Crofs this Line G H, with another Right Line K S at Right-Angles to it ; which Line K S shall be the Vertical Line of the Plain. - To this Line K S, apply a streight Ruler K L : And to that end of it which lyeth clear of the Plain, as at L; apply a Quadrant O E P, having a Thrid and Plummet hanging from the Centre. Then see what number of Degrees of the Quadrant are contained between 0 and E; for so much doth that Plain Res cline from the Zenith of the Place; and is the Reclination of the Plain.

Defnition: T

II. To find the Declination. *HE Declination of a Plain, Is an Arch of the Hoa

rizon comprehended between the Pole of the Plain, and the Meridian of the Place. - Or, It is the distance of the Plain it felf, from the Prime Vertical Circle, or Azimuth of East or West.

To find out the Declination of any Plain, there are required two Observations to be made by the Sun, both at the same Time, as near as may be. The First, Of the Horizontal Distance of the Sun, from the Pole of the Plain.----And the Second, Of the Sam's. Altitude.

I: 'To find the Horizontal Distance:.
Apply one Edge of the Quadrant to the Horizontal Line of the
Plain, so that the other may be Perpendiculur to it; and let the
Zimb of rhe Quadrant, be towards the Sun. The Quadrant thus

applied

applied to the Plain, and held Level (as near as you can conje- Fig. LI: cture) hold up a Thrid and Plummet at full Liberty, near the Limb of the Quadrant ; so that the Shadow of the Thrid may pass. through the Centre and Limb of the Quadrant : And then observe the Degrees cut by the Shadow of the Thrid in the Limb of the Quadrant; and number them from that side of

; the Quadrant, that_standeth Squire or Perpendicular to the Plair : For those Degrees are the Horizontal Distance fought for.

II. To find the Sun's Altitude. Hold up a Quadrant with both your Hands; turning the Leftfide of your Body to the Sun ; then raise up, or depress the Quadrant, fo held, till the Sun shining through the Hole in that Sigbt which is nearest the Centre, do caft its Beam of Light upon the Hole in the other Sight farthest from the Centre : And at such time mark exactly what Degrees of the Quadrant are cut by the Thrid , for those Degrees are the Sun's Altitude at that time. The Horizontal Distance, and the Sun's Altitude thus Obferved,

at the same instant (as near may be) will help you to the

Plain's Declination ; by the Rules following: For,
I. By having the Sun's Altitude; you may find the Sun's Azimuth,

as in PROBL. IX. of the Use of the Coleftial Globe in Afro

nomy :- And by CASE XI. of O. A. S. T. Then,
II. When you make your Observation of the Horizontal Distance ;

Mark whither the Shadow of the Thrid did fall between the
South, and that Side of the Quadrant which was Perpendicu--
lar to the Plain.

First. If the Shadow fall between them: Then the Sun's Azimuth from the South, and the Horizontal Distance added together, do give the Declination of the Plain : And (in this Case) the Declination is unto the same Coast with the Sun's Azien · mutb; that is, Eastrard, if the Observation were made in the Forenoon ; or Westward; if in the Afternoon.

Secondly. If the Shadow fall Not between them ::
Then, The Difference between the Sun's Azimuth and Huri-
zontal Distance is the Declination of the: Plain : And in this
Case) -----If the Azimut! be the Greater of the two, then the
Plain Declines to the famie Coast whereon the Sun is ; But if the
H. Distance be the Greater, then the Plain Declines the contrary

. . Coats

And!

Pig. LI.

And here Note] That the Declination thus found, is always

accounted from the South; and that all Declinations are
counted from either North or South, towards either East
or West : And

must never exceed 90 Degrees.
I. If therefore, The Degrees of Declination do exceed 90 deg.

you must take the residue of that Number to 180 deg. and

that shall be the Plain's Declination from the North.
- II. If the Degrees of Declination exceed 180 ; then the Excefs

above 180, gives the Plain's Declination from the North, to-
wards that Coaft, which is Contrary to the Coast whereon the
Sun was, at the time of Observation.

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CHA P IV.
How Hour-Lines may be described upon an Horizontal
Plain in any Latitude-, viz. of London, 51 d. 30 m.

;

I. By the Globe.
Levate the Globe to the Latitude of the place for which

would make your Dial, (suppose for London, in the Latitude
of si deg. 30 min.). Then bring the Vernal Equinoctial Colure
(which is the first point of Aries alfo) to the Meridian, and (if
you will) the Index of the Hour-Circle to 12. This done,

1. Turn the Globe about Westward, till the Hour-Index points at I a Clock, or rather (till 15 degrees of the Equino&tial come to be just under the Meridian] and there keeping the Globe, look upon the Horizon how many degrees thereof are cut by the Equino&tial Colure ; which you shall find to be 11 deg. 30 min. which

set down in a little Table, as you fee here is d. m. done ; for

this 11 deg. 50 min. is the distance Latitude 51. 3d that the Hour-lines of 11 and 1 a clock are di

d. 2

stant from the Meridian upon the Dial Plain. 12

2. Turn the Globe more Westward, till 30 11.50 degrees of the Equino&tial comes to the Meri

24.20 dian, and then see what degrees of the Hori-
93 . 38. 3

zon are cut by the Equino&tial Colure ; which
4 : 53.35 you will find to be 24 deg. 20 min. which note
7 5
. 71. ( down in a Table as before, for that is the Hour-

90. d distance of 10 and 2 a clock from the Meridian.

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10 2

8

6

a

3. Turn

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3. Turn the Globe still more Westward, till 45 degrees of the
Equinoctial come to the Meridian; and then fhall the Equinoctial
Colure çut 38 deg. 3 min. of the Horizou counted from the dicri-
diat, which is the distance of s9 and 3 a clock.
Do thus with the other hours of 8 and 4, of 7 and s, and fo }

8
shall the Colure cut 95 degrees at 6 a clock, or when 90 degrees
of the Equino&tial comes to the Meridion. And this being done,
your Dial is so far made as the Globe can assist you.
II. The Geometrical Construction of this Dial, in order to the Tiigame-

trical Calculation.

1. With 60 Degrees of a Scale of Chords, defcribe a Circle re- Fig..
presenting your Dial-plain, and Horizon of the Place, (viz. Lon- LII. .
don.) Cross it with 2 Diameters S N; representing the Meridian
of the Globe, and Hour-line of XII; and the Line E W, for the
Hour-lime of VI : then will Z represent the Zexith of the place, and
be the Centre of the Dial.

2. The Latitude of the Place being 51 d. 30 m. Set them froin
S to a, and from W to b: Then a Ruler laid froin Wito a, will
cross the Meridian S N in P, the Pole of the World: And laid
from E to b, it will cross the Meridian N Sin Æ, the interfecti---
on of the Meridian and Equino&tial. And now. you have three
Points, viz. W, Æ, E;_through which you may defcribe the
Æquino&tial Circle W Æ E, whose Centre will be at c, always in
some part of the Line N S, extended, if need be.
3.

Divide the Semicirle W N E, into 12 equal parts, at the
points o o o,&c. And laying a Ruler to Z, and every of those
points o 0-0, it will cross the Æquinotial Circle.W ÆE, in the

***, & c. dividing that Semicircle into 12 unequal parts.

4. A Ruler laid to P, the Pole of the World, and to the feve- ral points

***, Bc. it will cut the Circle of your Plain in the points 1, 2, 3, &c. on the East-side of N, and 11, 10, 9, &c. on: the West-side of N.

Lasily. If you lay a Ruler to the Centre Z, and the respea ētive points 1, 2, 3, 8c. and 11, 10, 9, &c. they shall be the : true Hour-lincs belonging to an Horizontal Dial for the Latitude -of 5ı de. 30 m. And their respective distances from N will be the fame as in the Table they were found to be by the Globe,

III. By

points ***

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