The artificial clock-maker a treatise of watch, and clock-work, wherein the art of calculating numbers for most sorts of movements is explained to the capacity of the unlearned : also, the history of clock-work, both ancient and modern, with other useful matters, never before published / by W.D.

CHAP. X. (Book 10)

Numbers for several sorts of Move∣ments.

I Think it may be very convenient to set down some Numbers, fit for seve∣ral Movements; partly, to be as Exam∣ples to exercise the young Reader, in the foregoing Art of Calculation: and part∣ly, to serve such, who want leisure or understanding to attain to this Art.

§ 1. But first it may be requisite, to shew the usual way of Watch-makers wri∣ting down their Numbers, which is some∣what different from that in the preceding Book.

Their way representeth the Wheel and Pinion, on the same Spindle; not as they play in one another. Thus the numbers of an old House-Watch, of 12 hours, is written thus;

My way:	The Watch-makers way.
4) 48	▪48
7) 56	56—4
6) 54	54—7
19	19—6

According to my way, the Pin. of Re∣port [4] drives the Dial-wheel [48:] the Pinion [7] plays in the Great-wheel [56] &c. But according to the other way, the Dial-wheel stands alone; the Great-wheel hath the Pinion of Report on the same arbor: the Wheel [54] hath the Pin: [7] and the Crown-wheel [19] the Pin: [6] on the same Spindles.

This latter way (tho very inconveni∣ent in Calculation) representeth a piece of work handsomely enough, and some∣what naturally.

§ 2. Numbers of an 8 day Piece, with 16 turns the Barrel, the Pend. vibrates Se∣conds, the shews Minutes, Seconds, &c.

The Watch-part.	The Clock part.
8) 96	8) 78
8) 60—48) 48—6) 72	6) 48 8 pins.
7) 56	6) 48
30	6) 48

In the Watch-part, the Wheel 60 is the Minute-wheel, which is set in the middle of the Clock, that its Spindle may go thro the middle of the Dial-plate to carry the Minute-hand.

Also on this Spindle is a Wheel 48, which driveth another Wheel of 48, which last hath a Pinion 6, which driveth round the Wheel 72 in 12 hours. Note here two things: 1. That the two Wheels 48, are of no other use, but to set the Pi∣nion 6 at a convenient distance from the Minute-wheel, to drive the Wheel 72, which is concentrical with the Minute-wheel. For a Pinion 6 driving a Wheel 72, would be sufficient, if the Minute-hand and Hour-hand had two different centers. ▪2. These numbers, 60▪ 48) 48-6) 72, set thus, ought (according to the last §) be thus read, viz. The Wheel 60, hath another Wheel 48 on the same Spindle; which Wheel 48 divideth, playeth in, or turns round another Wheel 48; which hath a Pinion 6 concentrical with it: which Pinion driveth, or divideth a Wheel of 72. For a Line parting two numbers (as 60-48) denoteth those two numbers to be concentrical, or to be placed upon

the same Spindle. And when two num∣bers have a hook between them (as 48) 48) it signifies one to run in the other, as hath before been hinted.

In the Striking-part, there are 8 Pins on the Second wheel 48. The Count∣wheel may be fixed unto the Great-wheel, which goeth round once in 12 hours.

§ 3. A Piece of 32 days, with 16, or 12 turns both parts: the Watch sheweth Hours, Minutes, and Seconds; and the Pend. vibrateth Seconds▪

The Watch-part,

With 16 turns.	With 12 turns.
16) 96	12) 96
9) 72	9) 72
8) 60—48) 48—6) 72	8) 60—48) 48—6) 72
7) 56	7) 56
30	30

The Striking part.

With 16 turns.	With 12 turns.
10) 130	8) 128
8) 96	24 pins	8) 104	26 pins
12) 39	8) 24
6) 72 Double hoop.	8) 96 Double hoop.
6) 60	8) 80

The Pinion of Report is fixed on the ••nd of the arbor of the Pin▪wheel. This Pinion in the first is 12, the Count-wheel 39; thus, 12) 39. Or it may be 8) 26. ••n the latter (with 12 turns) it may be 6) 18, or 8) 24.

§ 4. A two month Piece, of 64 days; with 16 turns; Pend. vibrateth Seconds, and sheweth Minutes, Seconds, &c.

Watch-part.	Clock-part.
9) 90	10) 80
8) 76	10) 65
8) 60—48) 48—6) 72	9) 54	12 pins
7) 56	—8) 52
	5) 60-Double Hoop
30	5) 50

Here the third Wheel is the Pin-wheel; which also carrieth the Pinion of Report 8, driving the Count-wheel 52.

Or thus.

Watch-part.	Clock-part.
8) 80	6) 144
8) 76	6) 78	26 pins
8) 60—48) 48—6) 72	—8) 24
7) 56	6) 72-Double Hoop
30	6) 60

§ 5. A piece of 13 weeks, with Pendu∣lum, Turns, and Motions, as before.

The Watch part.

8) 96 Or thus.	6) 72
8) 88	6) 66
8) 60—48) 48—6) 72	6) 48—48) 48—6) 72
7) 56	6) 45
30	30

The Clock part.

8) 72 Or thus.	5) 145
8) 64—37) 30	6) 90	—30 pins
8) 48—12 pins	—24) 62
6) 48 Double Hoop	6) 72
5) 40	6) 60

§ 6. A Seven Month Piece, with Turns, Pendulum, and Motions, as before.

The Watch.	The Clock.
8) 60	8) 96
8) 56	8) 88—27) 12
8) 48	8) 64—16 pins
6) 45—48) 48—6) 72	6) 48 Double Hoop
5) 40	6) 48
30

§ 7. A Year Piece, of 384 days, with Turns, Pendulum, and Motions, as be∣fore.

The Watch.	The Clock.
12) 108	10) 120
9) 72	8) 96—36) 9
8) 64	6) 78 26 pins
8) 60—48) 48▪6) 72	6) 72 Double Hoop
7) 56	6) 60
30

If you had rather have the Pinion of Report, on the Spindle of the Pin-wheel, it must be 13) 39.

§ 8. A Piece of 30 Hours, Pendulum about 6 inches.

The Watch.	The Clock.
12) 48	8) 48
6) 78	6) 78 13 pins
6) 60	6) 60
6) 42	6) 48
15

§ 9. A Piece of 8 days, with 16 turns, Pendulum about 6 inches, to shew Minutes, Seconds, &c.

The Watch.	The Clock may be the same with the 8 day piece before, § 2.
8) 96
8) 64—48) 48—6) 72
8) 60
8) 40 The Seconds Wheel.
15

§ 10. A Month Piece of 32 days, with Pendulum, Turns, and Motions, as the last.

The Watch.	The Clock may have the same numbers, as the Clock § 3.
8) 64
8) 48
6) 48—48) 48—6) 72
6) 45
6) 30 Seconds Wheel.
15

§ 11. A Year Piece of 384 days, with Pendulum, Turns, &c. as the last.

The Watch part.

10) 90	Or thus▪ with a Wheel less, and not to shew Minutes and Se∣conds.
8) 64
7) 56	8) 96
6) 48	6) 72—36) 9
6) 45—48) 48—6) 72	6) 66
6) 30	6) 60
Seconds Wheel.	6) 54
15	19

In the latter of these two Numbers, the Pinion of Report is 36, on the Second Wheel. The Dial Wheel is 9.

The Clock-part may have the same Num∣bers, as the Year-piece before § 7.

§ 12. An 8 Day Piece, to shew the Hour and Minute, Pend. about 3 inches long.

6) 96	The Clock may have the same numbers, as the 8 day piece before, § 2.
8) 64—6) 72
7) 49
6) 36
19

Automata shewing the Motion of the Celestial Bodies.

§ 1. Numbers for the Motion of the Sun and Moon. See before in Chap. 2. Sect. 5. § 3, 4.

§ 2. Numbers to shew the Revolution of the Planet Saturn, which consists of 10759 days.

On the Dial-wheel.	If you would make it de∣pend upon a Wheel go∣ing round in a year, thus.
5) 69
4) 52
4) 48	10) 59 or thus, 4) 118
4) 40	6) 30

Note, The lowermost Pinion in these, and the following numbers, is to be fixed concentrical to the Wheel, which is to drive the Motion, viz. the Dial-wheel, Year-wheel, or &c.

§ 3. Numbers for the Planet Jupiter, whose Revolution is 4332 ½ days. On the Dial-wheel.

4) 48	Or thus, on the Year-wheel.
4) 40	6) 71
4) 36
4) 32

Note here, That the two last numbers

of Saturn, may be the two first of Jupiter also.

By the permission of my ingenious friend Mr Flamsteed, I here insert a de∣scription of Mr Olaus Romer, the French King's Mathematician's Instrument, to represent the Motion of Jupiter's Satel∣lites; a copy of which he sent to Mr Flamsteed in 1679.

Upon an axis (which turns round once in 7 days) are four Wheels fixed: one of 87 teeth; a second of 63; the third 42; and the last of 28 teeth. On another axis run 4 other Wheels (or Pinions you may call them) which are driven by the asore∣said Wheels. The first is a Wheel, or Pi∣nion of 22 leaves, driven by the Wheel 87, which carrieth round the first Satel∣lite. The second is 32, driven by the Wheel 63, which carrieth round the se∣cond Satellite. The third hath 43 leaves, driven by the Wheel 42, which carrieth the third Satellite. And lastly, is the Pinion 67, driven by the Wheel 28, which carrieth round the fourth Satellite.

On the first axis is an Index, that point∣eth to a circle divided into 168 parts, which are the hours in 7 days.

On the other axis all the Pinions run concentrically, by means of their being hollow in the middle. In the midst of them all, the axis of Jupiter himself is fix∣ed, with a little Ball at the top, repre∣senting Jupiter's body. On the ends of 4 small Wires, fixed in the four several Sockets of the aforesaid Pinions, may 4 lesser Globules be placed (at their due di∣stance from Jupiter's Globule) to repre∣sent the 4 Satellites going round that Pla∣net.

§ 4. Numbers for Mars, whose Revo∣lution is 1 year 322 days.

On the Dial-wheel▪
4) 48	The two last Numbers of Sa∣turn may be the two first of Mars also.
4) 40
4) 45

§ 5. Numbers for Venus, whose Revo∣lution is in 224 days.

On the Dial-wheel.
4) 32	Note, The last number of Jupi∣ter may be the first of Venus.
4) 32
4) 28

§ 6. Numbers for Mercury, whose Re∣volution is near 88 days.

On the Dial-wheel.

4) 56

4) 52

§ 7. Numbers to represent the Motion of the Dragon's Head and Tail, (near 19 years) to shew the Eclipses of the Sun and Moon.

On the Dial-wheel.	On the Year-wheel.
4) 48	4) 76
4) 40	Note, The two last numbers of Saturn may be the two first of this on the Dial-wheel.
4) 44
4) 42

As to the placing these several Motions on the Dial-plate, I shall leave it wholly to the Work-mans contrivance. He may perhaps make them to represent the Co∣pernican, or some other Sys••em.

Numbers for Pocket▪Watches.

§ 1. A Watch to go 8 Days, with 1•• turns, to shew Minutes and Seconds, the Train 16000.

6) 96
6) 48—12) 48—12) 36.
6) 45	On the Wheel [42] is the Second's hand placed, and on the Wheel [48] the Minute hand.
6) 42
19

§ 2. Another of the same, without Mi∣nutes and Seconds, to go with only 8 turns.

20) 10

6) 66

6) 60

5) 50

5) 45

19

§ 3. A Pocket-Watch of 32 Hours, with 8 turns, to shew Minutes and Seconds, Train as the last.

12) 48

6) 48—12) 48—12) 36

6) 45

6) 42—Seconds Hand.

19

§ 4. The usual Numbers of 30 hours Pendulum Watches, with 8 turns, to shew the Hour and Minute.

12) 48

6) 54—12) 48—12) 36

6) 48

6) 45

15

§ 5. The usual Numbers of the old 30 hours Pocket-watches.

With 5 Wheels.	With 4 Wheels.
10) 30	6) 32
7) 63	6) 66
6) 42	5) 50
6) 36	5) 45
6) 32	13
15

If any of the Numbers of the preceding Wheels and Pinions should not please the Reader, he may easily correct them to his mind, by the Instructions in the forego∣ing Book. The way in short is this: Di∣vide the Wheel by the Pinion, and so find the number of turns, according to Chap. 2. Sect. 1. § 2. Multiply the Pinion you like better, by this number of turns, and the Product is the Wheel. Thus in the 8 day Pocket-watch § 1, if you think the Great-wheel too large, you make it in∣stead of 6) 96 (16 thus, viz. 5) 80 (16: i. e. chusing the Pinion only 5, and multiply∣ing it by 16 (the turns) the Wheel will be 80.