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Above That End of the Hori.

zontal Line, that looks

the same way with the Less than a Polar

Coast of the Plain's the Meridian inust

Declination--And this be drawn.

Meridian thus drawn,, in North Recliners, re

presents 12 at Mido

Below. right. 15 lipi! 10; North Re-Equal to a Polir, the Meridian" must be drawn cliners below the Horizontal Line, at that end which

is contrary to the Coast of Declination: And: South In

the Six-a Clock Hour-line, is (always) the Subcliners filar.

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Below And from that Eudof

the Horizontali Line,

which liés contrary to More than a Polar

the Coast of the Plain's. the Meridian muftis Declination And,

- , be drawn.

in South Incliners, is: only ferviceable to

help to draw the rest. Above of the Dial..

V. How the Dial (being made according to the Neto Latitude .wand Ned Declination is to be transferred from the Paper 11 Draught, upon the Rectining or Incliniing Plain. ruus

Having drawn an Horizontal Line upon your Dial Plain, in the most convenient part thereof, and made choice of a Point therein for the Centre of your Dial ; apply the Centre of your Paper Draught to this Centre, moving the Paper Draught about till the Meridian Line thereof do make an Angle with the Horizontal Line drawn upon the Plain, equal to what you found it to be by the Third Section of this CHA P. And to its Proper Coast, as you found it by the Fourth Section: Then (if you have not erred in any of your former workings) will the Stile of vour Paper Draught (or rather :a pattern.of it cut in Paft-board) being placed upon the Sub-stile of the Paper Dranght, have direct respect to the Elévated Poleti And.thus dare respect being had to what is here

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delivered, you may easily transfer the Stile and the rest of the Hour-lines to the Plain ; putting thereon so many as the Plain is capable to receive at any time of the Year ; and leaving out such as are superfinous.

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CH A P. XIII.

Of the Inscription of other Great and Small Circles of the Sphere upon all sorts of Dial Plains,

I

N the foregoing Chapters is Thewed how the Meridians (or of Plain Superficies howsoever fituate : And as those Hour-Circles were described, so may all other Circles of the Sphere be also delineated : And the inanner how, I have largely treated of in my particular Treaties of Dialling already extant : So that in this place I shall be but brief therein, and yet fufficiently Plain. And whereas the How of the Day on all Sun-Dials is Thewed by the whole Axis of the Stile ; fo. all other Circles fo described, are Ihewed by one fingle point taken in some convenient place of the faid Axis, from which Pointa Perpendicular let fall to the Plain upon the Sub-ftilar Line shall be called the perpendicular Stile : And the point upon the Plain, The Foot of the Perpendicular Stile ; and the Point in the Axis (before assumed) the Gnodus or Apex of the Stile. Now, for the performances of the Work following (besides the Trigonometrical Calculation ) the Practitioner must be provided with a Scale for a Se&tor rather), which must have upon it Scales of Sines, Tangents, Secarts, Chords, and equal parts: or if he have by him, Tables of Natural Sines, Tangents, and Secants, then a Line of equal parts only drawn from the Centre, will perform the work rather better than by the other Scales. Being thus provided ;. The firft business must be

How to proportion the Perpendicular Stile to the Plaiu. If your Dial Plain be small, consider whether it be Direct, or Declining if Dire& the Sub-file may be placed in the Middle :

the coast of Declixation. The Sub-stile well made choice at, and the Perpendicular

Stik

If Declining, more to the fide contri

1

Stile thereon Erected : Make the perpendicular Stile the Radius (or Equal to the Tangent of 45 degrees) and make that part of the Sub-stile which lies beyond the foot of the Stile and towards. the Centre, equal to the Tangent Complement of the heighth of the Pole (or Stile) above the Plair and the other part of the Substile, below the Foot of the Stile, Equal to the Tangent Complement of the Meridian Altitude of the Su, when he is in that Tropick which is to be most reinote from the Centre of the Diah

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CH:A P. XIV.

Of the Inscription of the Signs or: Parallels: of the Sun's

Course

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Sigur is the Twelfth part of the the Ecliptick, and therefore

contains 30 degrees. A Parallel, is the Sun's Diurnal Motion Day by Day; and because there are 47 deg between the two Tropicks, there may be so many Parallels

, that is, Circles, which the Sun describeth every 24 Hours : and although there be 47 of these yet in the Latitude of şi deg. 30 ihin. we'.account but nmé, viz: those, which are the Day from Sm to Sun, when it is 8, 9, 10, 11, 12, 13, 14, 15, or 16 juft hours long. The Description of these Parallels and Signs is made the same way ; only due respect must be had to the quantity of the Sun's Declination: For. (in all Dire& Horizontals) the Perpendicular Stile being made Radius, the Tangent Complement of the Sun's height, in any Sign or Parallel; at any hour of the Day, set off from the Foot of the Stile, and extended to that Hour-line, gives a Mark upon the Hour-line, by which the Parallel of that Day shall pass : So that this Work, repeated fo often as the mimber of Parallels to be infcribed, and the Hour-lines require ; shall give respective Points enough, in each Hour, to draw

; each Parallel by.. Exampk. In the Latitude of 51 de. 32 m. the Sun being in the

beginning (or entring) of Pisces; The Sini's height above the Horizon at every Hour may be found (by CASE IX of O. A.S. T.) to be as followeth, viz..

27. OI

I 2

62. 59 64.123 68,11

49

4

Deg. M.
12

JI 25. 37
10 21.

The
At
or

Complement
3 9
15. 57

74. 03
8 8. 32

81. 28 Now, the Perpendicular Stile being Radius, the Tangents of the Complements of the respective Altitudes, as 62 deg. 59 m. the Complement of 27 de. oi-m. set from the foot of the Per. Stile, on the Hour-line of 12 (or Suh-file) shall give a point thereon, by which the Parallel of Pisces must pafs : And so, the Tangent of 64 de. 23 m. set from the foot of the Per. Stile, upon the Hour-lines of 11 and 1 a Clock, shall give you two other points by which the said Parallel shall pass : And so for all the rest of the Hour. lines, through which points found upon all the Hour-lines, a Line drawn by an even hard, fhall be the Parallel

required; for along that Line will the Shadow of the Top of the Per, Stile (as it creepeth along) pass, when the Sun is in the beginning of Pisces, viz." about the oth of February: And therefore, generally in Verticals, as also in all

Recliners; that is to say, upon all Plains whatsoever : Draw an Horizontal Dial proper to the Plain, and infcribe the Signs or Parallels upon it, by setting off from the foot of the per. Stile

, the Tangents Complements of the Sun's height at every hour in the beginning of every Sign above that Plain (taken as an Horizontal, the Foot of the per. Stile being ever Radius) and at the end of these Tangents, so set off upon every respective Hour-line, will be a Point By which Points, Lines drawn with an even Hand, shall trace out upon the Dial Plain, the Parallels required. Example. Suppose a Plain Decline 30 deg. and Recline 55

deg. the height of the Pole above the Plain 19 deg. 25 min.
And the Sun's height at the beginning of Taurus to be at the
several Hours, as in this Table.
De. M.

De. M
38. 05

(07. 55 73. 30

29. 57
At

Complements
9
46. 01

43. 59
8

4 31. 53 7 5 1 17. 47;

672. 13

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12
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16. , 30,

2

63. 03

or

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3

58. 07

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Then, The Tangents of the Complements of these Hour-diftail- ces (as 7 deg. 55 m. for 12 : 16 deg. 30 in. for the Hours of u and 1) set off from the Foot of the per. Stile (the faid Stil being the Rádius to those Tangents) to the obfcure Horizontal Hours of 12, 11, 10: and 1, 2, 3, c. give the true distances between the Foot of the Stile, and those auxiliaz y Hours, for the Parallel of * Taurus ; and so points for the describing of other Pur allels of Declination : Having firft (by Trigonomet; ical Calculation) found the Horizontal Distunces, and the Su's Altitude at his entrance into thofe Parallels of Signs or Declination, in such Latitude as you have need of. All which are taught how to do in the foregoing parts of this Book. :

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CHA P. XV.
Of the Inscription of the Vertical Circles (commonly called
Azimuths) upon all Dial Plains.

T

HESE are great Circles of the Sphere, whose Poles lie in

the Horizon, and interfect one another in the Zenith and Nadir Points of the Place wherein the Dial is to stand.

The whole Horizon being divided into 32 equal parts; these Circles passing through those Divisions, are called Points of the Compass, and denominated accordingly, as South, S by E, SSE, &c. But the better way of accounting them is by 10, 20, 30, Esc. Degrees from the Meridian on either side thereof.

First, in all Horizontal Dials ; the Perpendicular Stile being chosen, making the Foot thereof the Centre ; at any convenient

. distance, describe a Circle ; and account from the Meridian both ways, Arches equalto 10, 20, 30, ETC. Degrees : From which Divisions, right Lines drawn to the Foot of the Stile aforesaid, shall " represent those Azimuths upon that Dial.

Secondly, Upon a Prime Vertical (or South ) Dial : Through the Foot of the Per-stili, draw a Right-Lire Parallel

to the Hori201; and making the said.Stile Radius ; upon the Parallel Line, set off, both ways from the Meridian Targents of 10, 20, 30, &c. Degrees ; through which Divisions, Right-lines drawn, all at Right Angles with the Parallel Line, shall be the Azimuths.

Thirdly,

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