and before Six

o'Clock, calling them Six, Seven, and Eight, as in the Figure, and continue them thro' the Center for the Hours of Four and Five, it is an erect direct North Dial; in which the Style must be fixed on the Twelve o'Clock Line, pointing upwards, as in the Scheme.

Of East and West Dials.

The Planes of all direct Eaft and Weft Dials are in the Meridians, which paffing thro' the Poles of the World, Eaft and Weft Dials have no Latitude, and therefore no Center; and the Hour-Lines are all parallel to one another. The Style in these Dials is either an upright Pin, or a Plate fixed on the Hour-Line of Six o'Clock, the Height being equal to the Distance of the Hour-Lines of Six and Nine in East Dials, or Three and Six in Weft Dials.

To calculate the Distances of the Hour-Lines from the Six o'Clock Line for direct Eaft or Weft Dials.

To do this, the Height of the Style must be given, which fuppofe ten Inches; then, for two Hours either before or after Six, the Proportion is,

As the Co-fine of 30°, or two Hours,
Is to 10 Inches, the Height of the Style,
So is the Sine of 30°,

To 5.77 Inches,

Co. Ar. 0.062469

1.000000

9.698970

c.761439

In the fame Manner may any other Hour, Half, or Quarter be found; as for four Hours and an Half, which is

By the fame Proportion may all the others be found, as in the annexed Table; where it is to be obferved, that the Hour-Distances are here reckoned from Six, the Subftyle of thefe Dials, as they are from Twelve in Horizontal and South Dials.

A Table of the Hour-Distances for an East Dial.

To draw an Eaft Dial for the Latitude of 51°. 32.

Let ABCD be the Dial-Plane; take 60° from the Line of Chords, fet one Foot of the Compaffes in B, and draw the Arch ba; take 38°. 28', the Complement of the Latitude, and fet it from b to a, and draw Ba thro' the whole Plane to D; and obferve, that the Diagonal B D must be above fix times the Length of the Style's Height; at about Once and an Half of the Style's Height from D, as at e, draw 6e 6 for the Six o'clock Line; from e, by the general Rule, Page 216,

lay

C

B

In making an Eaft Dial we have a West Dial, with only this Difference, that the Diagonal is drawn from the left-hand

Corner to the right-hand, and, inftead of the Morning Hours from Four to Eleven, here we have the Evening Hours from Eight to One, the fame Diftances as in the Table; fo that the Table will ferve for the Distances

of any direct

at

Eaft or Weft Dial, in any Latitude; as alfo for Polar Dials, as fhall be fhewn hereafter.

The Smallness of the Schemes not admitting the Divifions into Quarters, I have done it only betwixt Ten and Eleven in the Eaft, and One and Two in the Weft Dial.

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Ia

In making an Eaft or Weft Dial, the Height of the intended Style being given, the Hour-Diftances may be found by the Rule of Three from this Table: As fuppofe your Style were fix Inches, to find the Diftance of the firft Hour from Six, fay,

As 10 Inches is to 6 Inches, fo is 2.68 Inches.

-6

10) 16.08 (1.61 very near.

Thefe five Dials may be all fixed on a Poft, the Horizontal Dial on the Top, and the other four on the four Sides; Care being taken that the Sides are set so as to face the four Cardinal Points of Eaft, West, North, and South directly.

Of Declining Dials.
of

Dials being ufually fixed against the Walls of Houfes, which do not always ftand directly facing the Cardinal Points, but more commonly declining, the most common Dials are what are ufually called Declining Dials, that is, South or North Dials, declining towards the Eaft or Weft: In this Cafe, the Declination of the Plane from the North or South Points, towards the East or Weft, must be first known, before the Dial can be, made.

To find the Declination of any Plane.

There are a Variety of Methods to find the Declination of Planes, of which the following, as it may be performed without Mathematical Inftruments, will be of more universal Use: Take an even, well-planed Board, of fix, eight, or ten Inches fquare, and draw a Line, a b c, thro' the Middle, perpendicular to the Sides A B and CD; on the Center b draw several eccentric Circles at fmall Distances, at Pleasure, it not being neceffary to make them at equal Diftances one from another ; and stick a Pin in the Center, which muft ftand directly upright Place the Edge A B against the Wall whofe Declination is required, between the Hours of Eight and Ten in the Forenoon; obferve when the Shadow of the Top of the Pin just touches one of the Circles, and make a Mark at that Place in the Circle; then, in the Afternoon, watch 'till the Shadow comes to touch the fame Circle again, and make another Mark,

Mark, as at A sandt: Open your Compaffes to above Half the Di

ftance of those two Marks, fet one Foot in one of the Marks, ass, and draw a fmall Arch, u; then fet the Compaffes in the other, and draw an Arch croffing the former in u; draw a Line from the Cen

ter b thro' the

C

Interfection of those Arches, which will be a true MeridianLine; and the Angle u bc, being measured on a Line of Chords, gives 18°.25, the Declination of the Plane East, as the Line be is to the right Hand of the Meridian-Line u b.

Thus having the Declination 18.25 Eaft, and the Latitude 51°.32 North, there are three Things required to be found before we come to calculate the Hours, viz. the Height of the Style, or Elevation of the Pole above the Plane, the Angle the Subftyle makes with the Meridian on the Dial, and the Plane's Difference of Longitude.

i

To find the Height of the Style, or Elevation of the Pole above the Plane:

As the Radius"

Is to the Co-fine of the Latitude, 51°. 32
So is the Co-fine of the Declination, 18.25,

To the Sine of 36°. 10', the Height of the Style,

10.

9.793832 9.977167

9.770999

Which is also the Height of the Pole above the Plane, for the Styles of all Dials must point directly to the Poles of the World.

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T.