Yet, that the Stars are really innumerable, is evidently proved by the Ufe of the Telescope, which, being directed to any Part of the Heavens, difcovers great Numbers which are invifible to the naked Eye. In the Pleiades, instead of fix or seven seen by the Eye, Dr. Hook, with a Telescope twelve Feet long, told feventy-eight; and, with larger Glaffes, difcovered many more of different Magnitudes. Huygens, looking at the Star in the Middle of Orion's Sword, found it to be a Concourfe of twelve Stars. To this we may add, that the Galaxy, or Milky-Way, is now known to be an Affemblage of innumerable Stars too fmall for the Sight.

If these Stars are all Suns, with Chorufes of Worlds moving about them, as is generally fuppofed, what an exalted Idea muft it give us of the great Author of Nature? Without fome fuch Suppofition, we can fcarce form any Idea of the Ufe fuch a prodigious Number of vaft Bodies can be of, as far the greater Part are, by their immenfe Distance, hid from our Sight, and had not been known to exift 'till fince the Invention of Telescopes in the laft Age.

D

Of DIALLING.

IALLING is the Art of drawing Lines on a Plane, in fuch Manner as that the Shadow of a Style may point out the Hours of the Day.

Of Dials there are various Sorts, according to the Situation of the Planes on which they are defcribed: The most usual are the Horizontal, Vertical, Equinoctial, Polar, &c.

i An Horizontal Dial is defcribed on an Horizontal Plane: This is the moft ufeful of all Dials, as it gives the Hour of the Day at all Times, while the Sun is above the Horizon, both in Summer and Winter.

To calculate an Horizontal Dial for the Latitude of 51°.32. For the Angle the Hour-Lines of Eleven and One make with the Meridian, the Proportion is,

As the Radius

Is to the Sine of the Latitude, 51°.32′,
So is the Tangent of 15°, or one Hour,

10.

9.893745 9.428052

To the Tangent of 11°. 51', the Angle the Hour-
Lines of II and I make with the Meridian,

}9-321797

Το

To find the Angle the Hour-Lines of Ten and Two make

with the Meridian :

As the Radius

Is to the Sine of the Latitude,

So is the Tangent of 30', or two Hours,

To the Tangent of 24°. 19',

In the fame manner may the Angles of the Hour-Lines for Nine and Three be found, by putting the Tangent of 45°, or three Hours, in the third Place of the Proportion: And fo of the reft. Then, for the Halves and Quarters, obferve, that each Half-Hour is 7°. 30', and each Quarter 3.45: Thus, to find the Angle for Half an Hour after Three, or Half an Hour before Nine, the Proportion is,

As the Radius

Is to the Sine of 51°. 32',

10.

9.893745 So is the Tangent of 52° 30', or three Hours 10.117113

and an Haif,

To the Tangent of 45°. 43',

10.010858

By the fame Proportion may all the Hours, Halves, and Quarters be found, as in the following Table:

A Table of the Angles of the Hour-Lines,

draw a Semicircle, EOW, on which, by the Line of Chords, fet off the feveral Hours, Halves, and Quarters in the Table; draw a fmall Circle round A, then lay a Ruler from the Center A to each of the Divifions, and draw Lines from the fmall Circle to the inner Square for each Hour, and fhorter for the Halves and Quarters: The Hours before and after Six are made by drawing the Hours of Four and Five in the Afternoon thro' the Center, for Four and Five in the Morning; and Seven and Eight in the Morning being drawn thro' the Center, you have the Hour-Lines for Seven and Eight at Night.

Then, for the Style, Jay 51°. 32', the Latitude of the Place, from O to G, and draw A G; the Angle OAG will be the Height of the Style. Or, the Dial being made, you may affume any Part of the Line A ON on which to erect the Style; and meafure the Distance from A to that Point, as D, which let be eighteen Inches, to find the perpendicular Height of Dd:

As

As the Sine of the Angle AGD, 38°.28', Co. Ar. 0.206168

Is to A D, 18 Inches,

1.255272

So is the Sine of the Angle O A G, 51°. 32',

9.893745

To Dd, 22.67 Inches,

1.355185

And fo high muft the upper Surface of the Style be from the Plane at D.

To make an erect direct South Dial for the Lat. of 51°. 32.

To calculate the Hour-Lines for this Dial the fame Proportion is used as in the former, only the fecond Number in the Proportion is the Co-fine of the Latitude, which there was the Sine. And it is to be obferved, that the Sun never fhines on this Dial but from Six in the Morning to Six at Night. For the Hours of Eleven and One fay,

As the Radius

Is to the Co-fine of the Latitude, 51°. 32",
So is the Tangent of 15°, or one Hour,

To the Tangent of 9°. 28′,

The other Hours as in the following Table:

A Table of the Angles of the Hour-Lines with the Meridian.

Lines to encompass it, leaving Room for the Figures: With any small Extent of the Compaffes, fet one Foot in N, and draw the fmall Semicircle a xe; and, with the Chord of 60°, draw the Semicircle urst, on which lay the Hours, as in the Table, from the Meridian N S towards E and W; then lay a Ruler from N to each of thofe Divifions, and draw the HourLines from the inner Circle to the inner Square: In the fame Manner may the Half-Hours and Quarters be drawn.

For the Style, take 38°. 28', the Complement of the Latitude, from the Line of Chords, and lay it from s to r, and draw the Line Nr; thus will the Angles N r be the Height of the Style, which is to ftand on the Meridian, or Twelve o'Clock Line. Or, the Distance N s being measured on the Plane, which let be fourteen Inches, to find the perpendicular Height of the Style sy,

As the Sine of the Angle s y N, 51°. 32, Co. Ar. 0.106255 Is to s N, 14 Inches,

So is the Sine of the Angle sr N, 38°.28′,

1.146128 9.793832

To the perpendicular Height of sr, 11.12 Inches, 1.046215

And this is the Height of the upper Surface of the Style at the Point y.

The