1

II. To find the New Declination.

The Canon for Calculation.

As the Radius, Sine 90 d.

9.769218

To the Co-fine of the Reclination 54 d. So is the Sine of the Old Declination, 24 d. 20 m. 9.614944

To the Sine of 41 de. of min.

9.384162

Which 41 de. I min. is the NEW DECLI
ΝΑΤΙΟ Ν.

And now, if (according to the Precepts delivered in the VIIIth. CHAP. hereof) you do make an Upright South Dial Declining 14 deg. I m. in the Latitude of 72 deg. That Dial shall serve for. A South Plain, in the Latitude of 51 de. 30 m. Declining 24 deg. 20 m, and Reclining 54 deg

And

in such a Dial you will find the Requisites belonging thereunto, to be as the Table in the Margin. And thus much for the Making of the Dial according to its New Latitude, and New Declination.

-chip.

72.00

New Latiude
New Declination 14. 01

Stiles heigth 17 26
Dift. Sub. & Merid. 4. 17
Difference of Long. 13. 59

But to apply this Dial to the Res clining Plain in the Old Latitude, you are not to place the Hour-line of XII 41 VII perpendicular to the Horizon, as in 4 VIII Upright Plains, but it must make an 4 IX Angle with the Horizontal Line of 4x the Reclining Plain: And therefore 41 the quantity of that Angle must be first found. Therefore,

III. To find the angle made be

tween the Meridian and the
Horizon.

4IXI

191

1911
19II

19IV
19V

XII

Eq. Di. Tr.HD.

V89 17 89 47 IV 74 17 46 48 III 59 17 26 46 II 44 17 16 17 129 17 9 32 14 17 4 22

X100 43 Ο 12 X15 43 4 49 IX 30 43 10 06 VIII 45 43 17 05 VII 60 43 28 06 75 43 149 39

19

VI

The Canon for Calculation.

As the Radius, Sine 90 d.

Is to the Sine of the Reclination 54 d.

10.

9.655347

So is the Tangent of the Old Declination 24 d. 20 m. 9.907957

To the Tangent of 20 deg. 6 m.

Whose Complement 69 deg. 54 min. is the Angle that the Me ridian (or Hour-line of XII.) must make with the Horizontal Line of the Reclining Plain. Thus for the Quantity of the Angle. But

IV. To know which way (or to what Coast) the Meridi an Line, Ascending or Descending Above or under the Horizon tal Line of the Plain, is to be drawn...

i

In

cliners

Above That End of the Hori

Less than a Polar
the Meridian must >
be drawn.

1

Below

zontal Line, that looks the fame way with the Coast of the Plain's Declination--And this Meridian thus drawn, in North Recliners, re-presents 12 at Mid-night...

NorthRe- Equal to a Polar, the Meridian must be drawn below the Horizontal Line, at that end which is contrary to the Coast of Declination: And the Six a Clock Hour-line, is (always) the Subftilar.

South In-
cliners

More than a Polar,
the Meridian must
be drawn..

T

:i

Above of the Dial.

V. How the Dial (being made according to the New Latitude Drand New Declination) is to be transferred from the Paper Draught, upon the Reclining or Inclining Plaing 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 CHAP. And to its Proper Coaft, 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-ftile of the Paper Draught, have direct refpect to the Elevated Pole. And thus due refpect being had to what is here deliver'di

2

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 fuch as are superfinous.

7

CHAP. ΧΙΙΙ.

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

:

L

こ

N the foregoing Chapters is shewed how the Meridians (or

1 Hour-Circles) of the Sphere may be described upon all forts

of Plain Superficies howsoever situate: And as those Hour-Circles were defcribed, so may all other Circles of the Sphere be also delineated: And the manner 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 sufficiently Plain. And whereas the Hour of the Day on all Sun-Dials is shewed by the whole Axis of the Stile; so all other Circles so described, are shewed by one fingle point taken in some convenient place of the faid Axis, from which Point a 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 (befides the Trigonometrical Calculation) the Practitioner must be provided with a Scale (or a Sector rather) which muft have upon it Scales of Sines, Tangents, Secants, 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 first business must be

How to proportion the Perpendicular Stile to the Plain. If your Dial Plain be small, consider whether it be Direft, or Declining; if Direct the Sub-file may be placed in the Middle : If Declining, more to the fide contrary to the Coaft of Decli

nation.

رار

The Sub-stile well made choice of, and the Perpendicular

Stile

Stile thereon Erected: Make the Perpendicular Stile the Radius (or Equal to the Tangent of 45 degrees) and make that part of the Sub-ftile 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 Plain and the other part of the Subftile, below the Foot of the Stile, Equal to the Tangent Complement of the Meridian Altitude of the Sun, when he is in that Tropick which is to be most remote from the Centre of the Dial.

:

15

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

Course.

A Sig

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 defcribeth every 24 Hours: and although there be 47 of these, yet in the Latitude of 51 deg. 30 min. we account but nine, viz. those, which are the Day from San to Sun, when it is 8, 9, 10, 11, 12, 13, 14, 15, or 16 juft hours long. The Defcription 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 Direct 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 number of Parallels to be inscribed, and the Hour-lines require; shall give respective Points enough, in each Hour, to draw each Parallel by..

:

:

Example. In the Latitude of 51 de. 32 m. the Sun being in the beginning (or entring) of Pisces; The Sun's height above the Horizon at every Hour may be found (by CASE IX of O. A. S. T.) to be as followeth, viz.

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