And it matters not in what Order the Wheels and Pinions are fet, or which Pinion stands under every Wheel.

3. These Factors 36 in 8, i. e. 288, may thus be varied, viz. Divide them by fuch Numbers as will Measure them, and Multiply the Quotients by the Alternate Divifors: The 38 Product of these two laft Numbers fhall be two to the Product of the Factors given. For 36 in 8 is 288: Equal to 9 in 32, equal alfo to 288.

4

9

8

32 9

4. If fit Numbers cannot be had by any of the Three former ways, you must feck fome Ratio, as near as poffible, in this manner.

As one of the two Numbers

Is to the other;

So is 360,

To a Fourth Number:

Divide this Fourth Number, and alfo 360, by 4, 5, 6, 7, 8, 9, 10, 12, 15, or which of them bringeth the Quotient nearest to an IntigerAs if the two Numbers be 247 end 170, (which are too great to be cut into Wheels) and yet cannot be reduced into lefs, because they have no greater Common Measure than Unity: Say therefore,

170: 147 :: 360: 3114

147: 170 :: 360: 4164

(6

311(39

(8

360645

360(45

416(52

Wherefore, For the two Numbers 147, and 170, you may and 60-39 and 45-45 aud 52.

RULE V.

take 52

TH

He Diameter, or Circumference of any Wheel being given, in Inches and hundred parts of an Inch;and the Number of Teeth it is divided into; to give the Diameter, or Circumference of a Leffer Wheel or Pinion, with a number of Teeth given, fhall exactly agree with the Teeth of the Greater Wheel.

Example. The Great Wheel hath One Inch Diameter, and 50 Teeth: The Lefler Wheel or Pinion 10 Teeth, fay,

For the Circumference of the Pinion, whofe Diameter will be .2 Tenths of an Inch.

RULE

RULE VI.

To give Numbers to a Watch that shall have a swift Train, about 20000 Beats in an Hour,that may haveTurns about the Fufie,and go 16 Hours; and the Number of the Crown Wheel 17.

Say (by RULE II.)

As 12 is to 16 :: So is 20000 to 26666, the Beats for one turn of the Fufie: And becaufe (by RULE L.) 26666 is equal to all the Quotients Multiplyed together into 17, and into 2, that Number be ing halv'd is 13333, and that again divided by 17, gives for the Quotient 784, which being broken into Three Numbers, which Multiplyed together, will be 784, or near to it; let them be 11, 9 and 8, which Multiplyed into each other, are 792 Then 792 in 17 in 2, are equal to 26928, And then lay,

As 16 12 26928: 20196, the Beats in one Hour. Also,
As 16: 12 :: 12 : 9.

EXAMPLE, Of a Clock or Watch proposed to go a Week (or Eight Days) with this Order: That the Ballance Wheel, or that which moves the Pendulum, may go about in a Minute, with an Index to shew Seconds: That the Great Wheel may go about in 12 Hours: And that the Wheel next it may go about in One Hour to fhew Minutes.

8) 96 (12

First, Find how many Seconds there are in 12 Hours, by Multiplying 12 in 60, equal to 43200, and the fe are the Beats that fhall be in one turn of the Great Wheel. These are double, because there are two Swings to one Tooth of the Ballance Wheel; The half of 43200 is 216005 Now the Ballance Wheel must needs be 30; Divide 21600 by 30, the Quotient will be 720, which is to be broke into Three Quotients, whereof the first must needs be 12 for the Teeth of the Great Wheel; Divide 720 by it, the Quotient is 60 for the two Quotients remaining, which may be either 10 and 6, or 5 and 12, or 8 and 71, which laft let ftand, and then the Work will ftand as in the Margine, thus: And the Pinions to be taken as you please, to be all 8, the Wheels must be 96, 64, and 60; fo then the great Wheel will go about in 12 hours; the fecond Wheel in an Hour, and the Ballance Wheel in a Minute, as was defired.

I 2

8) 64 (8
8) 60 (7/2

30

10.140

8.128

8.120

72.

RULE.

RULE VII.

Of giving particular Motion to any Movement.

The Number of a Motion is the proportion that it bears to one Turn of the Hour Wheel, or the Pinion of Report, from whither foe- ver it be taken, which Proportion being broken into Two or Three Quotients, will fhew the wheels and Pinions, as if you took it for the Beats of the Ballance.

A NOTE Concerning Time. That which is ordinarily called The Hour of the Day: You are to confider this in the length of Days, which are twofold, diftinguished only by the Revolutions of the Earth or Sun. The Firft is the Syderial Day, where any fixt point or points of the Earth in the fame Meridian or Azimuth, returns from any Star to the fame again. The Second is the Solar Day, where the fame Meridian of the Earth returns from the Sun to the fare again: Neither of thefe two are the true Equinoctial day: Indeed, the Syderial is infenfibly the fame, if it be but for fome fmall fpace of Time, the Difference being only fome Fourths and Fifths of a degree flower in a Day; but the Solar is notably Longer than the other, viz. By 3 Minutes, 56 Seconds, 53 Thirds, 19 Fourths of Time in a Day; and from hence the Length of an Hour is generally accounted. Therefore to fit the Pendulum of a Watch or Clock to this Solar Day and Hour :

1. By the Revolution of a Fixed Star to the fome point again, after one or more Revolutions, (which you must curioufly Obferve by fixing your Eye to a Point :) If the Motion for one Revolution want 3 Minutes 56 Seconds of 24 hours; or for Two 7 Minutes 43 Seconds; for Three 40 Miuutes 39 Seconds. &c. Then doth your Watch or Clock go true to the Equall or Middle Motion of the Sun; if otherwife, the Pendulum must be altered to make it go fo.

II. By a Sun Dial, which though it be made never fo exact, and your Motion fo too,yet there will be a confiderable difference after fome Dayes, nay, even in one Day: All which falls out by reafon of the Inequality of Natural Days. And this inequality is now at laft fetled and demonftrated by Mr. William Flamsted: A Table of his for this Equation for every Day in the year, I have here inferted: And although it be not the very fame every year, yet this (being for the year 1693) will fufficiently ferve for any other.

Of the following TABLE of Equation of Time and its Use; How hereby to Regulate a true made Pendulnm Clock or VVatch, showing how much it ought to differ from the fame

Sun Dial.

The following Table fhews the Equation of Time in Minutes and Seconds (as the Letters M and S, at the head of each Column denotes) for every day of the year, having thefe Words in the middle of each Column, Watch too Fast, or Watch too Slow: And is of excellent Ufe, as appears by this which follows out of my loving friend Mr. George Parker in his English Mercury for the Year 1693.

Not

Notwithstanding, all perfons generally conclude, that the Sun by his Motion fhews, the apparent time of the Day, which is true, and that a South Sun always makes Noon, or 12 a Clock; yet this Southing of the Sun, or the space of time from one Noon to the Next, is not equal, but longer or fhorter, according to the Suns pofition in his Elipfis fo that it is impoffible for any Clock, Watch or Movement whatfoever, to keep Time therewith. For this Reafon, many perfons that are furnished with excellent Movements many times blame the Maker of them, when the Errors lie where they are not capable of difcerning: For if a Clock truly Rectified, be fet by the Sun, and kept going a Year, and at the Years end, agree exactly again with the Sun; yet in the interim, it would be fouud, at feveral times, to deviate confiderably; and be fometimes too Fast, and at other times too Slow. The Reafon of this Difference is The Clock measures Time equally, but the Sun unequally, the Quantity of this Difference is, as before expreft: As

thus.

Admit on the first of February I would fet a Clock to fhew the equal time of the Day, I look in the following Table against February the First, and there I find 14 Minutes, 48 Seconds, with the Words, Watch too Fast, which informs me, that I muft fet my Clock fo much faster than the Time given by a Sun-Dial, and then, being kept going, it will by the First of March be but 10 Minutes too Faft; and on April the Third, the Clock and Sun will agree together exactly: Afterwards, the Clock will begin to be Slower than the Sun, as you may fee by the Table.

1

A

!

Thus