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.

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.

Table of contents

Title page

The Preface.

THE CONTENTS.

CHAP. I. Of the Terms of Art, or Names by which the parts of an Automaton are called.

CHAP. II. The Art of Calculation.

SECT. I. General preliminary Rules and Directions for Calculation.

SECT. II. The way to Calculate, or contrive the Numbers of a piece of Watch work.

SECT. III. To Calculate the Striking part of a Clock.

SECT. 4. Of Quarters and Chimes.

SECT. 5. To Calculate any of the Celestial Motions.

CHAP. III. To alter Clock-work, or convert one Movement into another.

CHAP. IV. To size the Wheels and Pinions, or proportion them to each other, both Arithmetically and Mechanically.

CHAP. V. Of Pendulums.

CHAP. VI. The Antiquity, and general History of Watch, or Clock-work.

CHAP. VII. Of the Invention of Pendulum Watches.

CHAP. VIII. Of the Invention of those Pocket-Watches, commonly called Pendulum Watches.

CHAP. IX. The Invention of Repeating Clocks.

CHAP. X.

Numbers for several sorts of Movements.

Automata shewing the Motion of the Celestial Bodies.

Numbers for Pocket▪Watches.

CHAP. XI

Tables of Time relating to Watch-work.

Explanation of the Table.

Remarks upon the Table.

Addenda.

[Page]The Artificial CLOCK-MAKER.

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[Page]

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. M. A.

LONDON, Printed for James Knapton, at the Crown in St. Pauls Church-yard, 1696.

The Preface.

[Page]

[Page]

THe following Book was at first drawn up in a rude manner, only to please my self, and divert the vacant hours of a Solitary Country Life. But it is now published, purely in hopes of its doing some good in the World, among such, whose Genius and Leisure lead them to Mechanical Studies, or those whose business and livelihood it is.

Many there are, whose fault, or calamity it is, to have time lying upon their hands; and for want of innocent, do betake themselves to hurtful pleasures. This is the too common misfortune of Persons of Quality. Among some of the courser sort of these, if this Book shall find some acceptance, it may be a means to compose their loose Spirits; and by an innocent guile, initiate them in other Studies, of greater use to themselves, their family, and country. However it may hinder their commission of many sins, which are the effects of idleness.

If there be any one person, in whom these good effects are produced, I shall think my idle hours well bestowed, and bless God for it. However upon the account of the innocence of my end in publishing this Book, and that it was written only as the ha [...]less (I [Page] may add also the vertuous) sport of leisure hours; I think my self excusable to God and the World, for the expence of so much time, in a subject different from my Profession.

But besides, I think my self under some little obligations of Justice and Charity, to publish the ensuing papers for the sake of those, whose business the Mechanick part is. I take it to be a Charity to the Trade; because there are many (altho excellent in the working part) who are utterly unskilled in the artificial part of it. And then, it is a debt I pay: because I owe somewhat of health, as well as diversion to the Study, and practice of these sort of Mechanicks. And the best requital I can make for my trespass, is to publish what I have had better opportunities perhaps of Learning, than many Workmen have.

And further yet, there is another rea&;son, which much prevailed with me to publish this Book, viz. Because no body, that I know of, hath prevented me, by treating so plainly and intelligibly of this subject, as to be understood by a vulgar Workman. I have often wondered at it, that so useful and delightful a part of Mechanical Mathematicks should lie in any obscurity, in an age wherein such vast improvements have been made therein, and when many Books are daily published upon every subject. I speak here of this Art remaining in obscurity; not as if nothing was ever written of it, and I the [Page] in venter of Automatical Computation.

But altho I cannot assume the glory of being the first Writer upon this subject, yet very few have as yet done it; of which I shall next give some account.

Cardan, Kircher, and Scottus promised it; but I do not find they ever published any thing to the purpose of it. Our great Mr. Oughtred I take to be the first that ever wrote to any purpose about the Calculation of Automata: And I believe he was the first that brought that Art under Rules, in his little treatise called Automtaa. This Book was first surreptitiously published in English in a little Book, called Horolog. Dialogues, in the year 1675; and afterwards far more compleatly in Latin, at the Theatre in Oxon, among Mr. Oughtred s Opusc. Mathem. in the year 1677. This last edition it was my misfortune not to meet with, until it was too late, and therefore I have been forced to quote the first, and worst in my Book.

What Mr. Oughtred had wrapt up in [...]his Algebraick obscure Characters, was afterwards put into plainer Language▪ by that excellent Mathematician Sir Jon. Moor, with some additions of his own; which you have in his Math. Compend. and since him, by Mr. Leyborne, in his Pleasure with Profit.

I hope I shall not be judged to have transgressed the Rules of Modesty, in coming af [...]r three such famous men; neither should I [Page] venture that censure, but for two reasons. One is, I find by experience, that what they have written, is understood by very few Workmen. And therefore I have endeavoured, with all industry, to make the matter as plain as I could for such. For which reason, I hope the more learned Reader will excuse my using many words, when fewer would have served his turn; and that I have condescended to low things, (and to him needless) as teaching the Golden-rule, &c. The other reason is, that what those three have written, relates only, or chiefly to the Watch-part. To which I have added several other things of my own: particularly the Calculation of the Clock-part, &c. I have been forced to reduce to Rules my self, and to name no more, the Historical part hath not been so much as attempted before, that I know of.

These Reasons will, I hope, excuse me with the most censorious Reader, not only for presuming to write after so accurate a▪piece, as Mr. Oughtred s is, but also the Novelty of the subject, will I hope procure for me a candid interpretation of the faults and blunders, that I may have unwittingly committed.

To the preceeding account of what others have written (which shews what help I have had from printed Books) I shall subjoyn my acknowledgments, and thanks to the principal of my friends, who have given me thei [...] assistance in compiling this Book. But thei [...] [Page] names I shall not make more publick than mine own, being unwilling to be discovered my self. In the Chap. of the Terms of Art, I owe much to the assistance of L. Br.... a judicious Workman in White-chappel, who drew me up a Scheme of the Clock-maker▪s Language. In the History of the Modern Inventions, I have had (among some others) the assistance chiefly of the ingenious Dr. H.... and Mr. T....▪ The former being the Author of some, and well acquainted with others, of the Mechanical Inventions of that fertile Reign of King Charles the II. and the latter actually concerned in all, or most of the late inventions in Clock-work, by means of his famed skill in that, and other Mechanick operations.

There are some other contrivances of this last age (besides those I have mentioned) which I have passed over in silence; because either they are only branches, or improvements of the inventions I have taken notice of, (such as several ways of repeating work, &c.) or else, they only collaterally relate to Watch-work (as the inventions of Cutting-Engines, Fusy-Engines, &c.) To treat of all these, would swell my Book far beyond its intended bounds; which I have already somewhat exceeded. I shall therefore commit this task to some better Pen, hoping that no person will take it amiss, that I have not mentioned what I have been beholding to him for the relation of.

[Page] For the resons last mentioned, I have also left out of my Book, a Chapter of the Art of making, and using many sorts of Sodders, the way of colouring Metals, &c. useful in the practice of Clock-work. This I had prepared for the sake of Mercurial Gentlemen, but omitted printing it, and some other things, out of Charity to poor Apprentices and other Workmen, whose purses I am unwilling my volume should too much exceed.

If I have at any time invaded the Workman's province, it was not because I pretend to teach him his Trade; but either for Gentlemen's sakes, or when the matter led me necessarily to it.

I have nothing more to add, but that I would have this little Treatise looked upon only as an Essay, which I hope will prompt some abler pen to perform the task better, especially in the Historical part. For since Watch-work oweth so much to our Age, and Country, tis pity that it should not be remembred: especially when we cannot but lament the great defect of History, about the beginning and improvements of this ingenious and useful Art.

THE CONTENTS.

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CHap. I. Of the Terms of Art.

The more general Terms. p. 2.

Names belonging properly to the Watch-part. p. 8.

Names of the Clock-part. p. 5.

Chap. II. The Art of Calculation.

Sect. 1. Preliminary Rules.

To find the turns of a Wheel or Pinion, 8.

The way of writing down the Numbers, 9.

To find the turns of any, or all the Wheels in the Movement, 10.

To find the Beats of the Ballance in all the Watches going, or in one turn of any Wheel, 11.

Two strokes to every tooth of the Crown▪wheel, 14.

Sect. 2. Calculation of the Watch-part.

Several ways of performing one and the same motion, 15.

A Rule to vary Numbers, 16.

The way of working the Golden Rule, 17.

A very useful Rule to vary inconvenient Numbers, 18.

Rules of perpetual use in proportioning the parts of a Watch, 19.

Examples of contriving a piece of ordinary Watch-work, 22.

Examples thereof for Minutes, and Seconds, 29.

Sect. 3. Calculation of the Striking-part.

[Page] General Observations and Rules relating to the Wheel-work of a Clock, p. 33.

Rules of perpetual use in proportioning the parts of a Clock, 35.

Examples of Calculating the Numbers of a small Clock, 38.

Examples of Clocks of longer continuance, 39.

An useful Rule to find the number of Strokes in one turn of the Fusy, 33.

Examples of fixing the Pinion of Report, 34.

Sect. 4. Of Quarters and Chimes.

Notes concerning the Quarters, 45.

Of making the Chime-barrel, 46.

Of dividing it, and setting on the Chime-pins, 47.

Chimes of Psal. 100, and of a Song-tune, 50.

Another way of setting Chimes on the Barrel, 52.

Sect. 5. To calculate Numbers to represent the Celestial Motions.

Contrivance of Movements only to shew these Motions, 53.

To add it to a Watch that shews the hour of the day, 55.

A motion to shew the day of the month, 56.

To shew the Age of the Moon, 57.

To shew the day of the Year, and Sun's place in the Ecliptick, his Rising or Setting, &c. 58.

To shew the Tydes, ib. To represent the motion of the Planets, fixed Stars, &c. 60.

Chap. III. To alter Clock-work, p. 62.

Example of converting a 12 hour Ballance-clock into a Pendulum, 63.

To make it go 30 hours, 65.

To change the Clock-part, 67.

Chap. IV. To size Wheels and Pinions.

To do it Arithmetically, 69.

Mechanically, 70.

Chap. V. Of Pendulums.

Irregularities of Pendular motions remedied, 71.

Cause of the difference of the motion of the same [Page] Pendulum, 72.

True length of a Pendulum that vibrateth Seconds, 73.

To find the Center of Oscillation, 74.

To calculate the Lengths, or Vibrations of Pendulums, 75.

A Table of Lengths and Swings, 78.

To correct the motion of a Pendulum, 79.

Chap. VI. The Antiquity, and general History of Watch-work.

The ancientest Time-engine, 82.

The Grecian and Roman ways of measuring Time, 83.

Some horological Instruments mentioned by ancient Authors, 84.

Watch, or Clock-work, no new German Invention, 86.

The Sphere of Archimedes, 87.

Of Po [...]idonius, 89.

The beginning of our present Clock-work, 91.

Clocks that perform strange feats, 92.

Chap. VII. The Invention of Pendulum Watches.

Mr. Hugens the Inventer, p. 93.

Others claiming it, 94.

Their beginning in England, 95.

The contriver of their carrying a heavy Ball, &c. 96.

Their use, ibid.

The Circular Pendulum, 97.

Chap. VIII. Of the Invention of Pocket Pendulum Watches.

Inventer, p. 99.

Several ways of them, ib.

The time when invented, 103.

Mr. Hugens's Watch, 104.

Chap. IX. The Invention of Repeating Clocks.

The Inventer, p. 106.

When and by whom first used in Pocket Clocks, 107.

Chap. XI. Numbers for various Movements.

The way of Watch-makers writing down their [Page] Numbers, 109.

Numbers of an 8 day Piece, 110.

A Month Piece, 112.

A Two Month Piece, 113.

A Quarter of Year piece, 114.

An Half Year Piece, ib.

A Year Piece, 115.

A lesser 30 hours Piece, ib.

A small Week Piece, ib.

A small Month Piece, 116.

A small Year Piece, ib.

An 8 day Piece Pend. 3 inches, 117.

Numbers representing the Motion of the Planet Saturn, 118.

Of Jupiter, ib.

Monsieur Romer's Instrument for Jupiter's Satellites, 119.

Numbers for Mars, Venus, and Mercury, 120.

For the Dragons Head and Tail, 121.

Numbers for Pocket Watches of 8 days, ib.

Of 30 hours, 122, 123.

The way to amend the Numbers, 123.

Chap. XI. Tables of Time.

A Table for ready casting up the parts of Time, 124.

A Table to set a Watch by the Fixed Stars, 125.

A Table of the Variations of the Hour by the Sun's Refraction, 117.

Observations concerning Refractions, and the Variations of the Hour, 128▪

CHAP. I. Of the Terms of Art, or Names by which the parts of an Automaton are called.

IT is necessary that I should shew the meaning of those Terms which Clock-makers use, that Gentlemen and others, unskilful in the Art, may know how to express themselves properly, in speaking; and also understand what I shall say in the following Book.

I shall not trouble the Reader with a recital of every name that doth occur, but only such as I shall have occasion to [Page] use in the following discourse, and some few others that offer themselves, upon a transient view of a piece of work.

I begin with the more general Terms: as, the Frame; which is that which contains the Wheels, and the rest of the work. The Pillars, and Plates, are what it chiefly consists of.

Next for the Spring, and its appurtenances. That which the Spring lies in, is the Spring-box; that which the Spring laps about, in the middle of the Spring-box, is the Spring-Arbor; to which the Spring is hooked at one end. At the top of the Spring-Arbor, is the Endless-Screw, and its Wheel.

That which the Spring draweth, and about which the Chain or String is wrapped, and which is commonly taper, is the Fusy. In larger work, going with weights, where it is cylindrical, it is called the Barrel. The small Teeth at the bottom of the Fusy, or Barrel, that stop it in winding up, is the Ratchet. That which stops it when wound up, and is for that end driven up by the String, is the Garde-caut, or Guard-Cock, as others; and Garde-du-Cord, and Gard-du-Gut, as others call it.

[Page] The parts of a Wheel are, the Hoop, or Rim: the Teeth: the Cross: and the Collet, or piece of Brass, soddered on the Arbor, or Spindle, on which the Wheel is rivetted.

A Pinion is that little Wheel, which plays in the teeth of the Wheel. Its teeth (which are commonly 4, 5, 6, 8, &c.) are called Leves, not Teeth.

The ends of the Spindle, are called Pevetts: the holes in which they run, Pevet-holes.

The guttered Wheel, with Iron spikes at the bottom, in which the line of ordinary House-Clocks doth run, is called the Pully.

I need not speak of the Dial-plate, the Hand, Screws, Wedges, Stops, &c.

Thus much for general Names, which are common to all parts of a Movement.

The parts of a Movement, which I shall consider, are the Watch, and Clock.

The Watch-part of a Movement is that which serveth to the measuring the hours. In which the first thing I shall consider is the Ballance: whose parts are, the Rim, which is the circular part of it: the Verge, is its Spindle: to which belong the two [Page] Pallets, or Nuts, which play in the fangs of the Crown▪Wheel: in Pocket-Watches, that strong Stud in which the lower Pevet of the Verge plays, and in the middle of which one Pevet of the Crown-Wheel runs, is called the Pottans: the wrought piece which covers the Ballance, and in which the upper Pevet of the Ballance plays, is the Cock. The small Spring in the new Pocket-Watches is the Regulator.

The parts of a Pendulum are, the Verge▪ Pallets and Cocks, as before. The Ball in long Pendulums, the Bob in short ones, is the Weight at the bottom. The Rod, or Wire is plain. The terms peculiar to the Royal Swing, are the Pads, which are the Pallets in others, and are fixed on the Spindle. The Fork is also fixed on the Spindle, and about 6 inches below, catcheth hold on the Rod, at a flat piece of Brass, called the Flatt, in which the lower end of the Spring is fastened.

The names of the Wheels next follow. The Crown-Wheel in Small pieces, and Swing-Wheel in Royal Pendulums, is that Wheel which drives the▪ Ballance, or Pendulum.

[Page] The Contrate-Wheel, is that Wheel in Pocket-Watches, which is next to the Crown-Wheel, whose Teeth and Hoop lye contrary to those of other Wheels.

The Great-Wheel, or First-Wheel, is that which the Fusy, &c. immediately driveth. Next it, are the Second-Wheel, Third-Wheel, &c.

Next followeth the Work between the Frame and Dial-Plate. And first, is the Pinion of Report; which is that Pinion which is commonly fixed on the Arbor of the Great-Wheel, and in old Watches used to have commonly but four Leaves; which driveth the Dial-Wheel, and this carrieth about the Hand.

The last Part which I shall speak of, is the Clock, which is that part which serveth to strike the Hours: In which I shall

First speak of the Great▪ or First-Wheel; which is that which the Weight or Spring first drives. In 16 or 30 hour Clocks, this is commonly the Pin-Wheel; in 8 Day pieces▪ the Second-Wheel is commonly the▪ [...] This Wheel with Pins is sometimes called the Striking-Wheel, or Pin-Wheel.

[Page] Next to this Striking-Wheel, followeth the Detent-Wheel, or Hoop-Wheel, having a Hoop almost round it, in whic [...] is a vacancy, at which the Cloc [...] locks.

The next is the Third, or Fourth▪Wheel (according as it is distant fro [...] the First-Wheel) called also the Warning▪Wheel.

And lastly is the Flying-Pinion, with a Fly or Fan to gather Air, and so bridle the rapidity of the Clock's motion.

Besides these, there are the Pinion o [...] Report, of which before; which driveth round the Locking-Wheel, called also the Count-Wheel, with 11 Notches in it commonly, unequally distant from one another, to make the Clock strike the hour [...] of 1, 2, 3, &c.

Thus much for the Wheels of the Clock part.

Besides which there are the Rash, or Ratch; which is that sort of Wheel, of twelve large Fangs, that runneth concentrical to the Dial-Wheel, and serveth to lift up the Detents every hour, and make the Clock strike.

The Detents are those Stops, which [Page] by being lifted up, or let [...]all down, do lock and unlock the Clock in striking.

The Hammers s [...]rike the Bell: The Hammer-tails are what the Strikingpins draw back the Hammers by.

Latches are what li [...]t up, and unlock the Work.

Catches are what hold by hooking, or catching hold of.

The Lifting-pieces do lift up, and unlock the Detents, in the Clock part.

CHAP. II. The Art of Calculation.

SECT. I. General preliminary Rules and Directions for Calculation.

§ 1. FOR the more clear understanding this Chapter it must be observed, that those Automata (whose Calculation I chiefly intend) do by little Interstices, or Strokes, measure out longer [Page] portions of Time. Thus the strokes o [...] the Balance of a Watch, do measure ou [...] Minutes, Hours, Days, &c.

Now to scatter those strokes among Wheels and Pinions, and to proportionat [...] them, [...]so as to measure Time regularly is the design of Calculation. For th [...] clearer discovery of which, it will be necessary to proceed leisurely, and gradually.

Oughtred of Autom. sect. 4. § 2. And in the first place, you are to know, that any Wheel being divided by its Pinion, shews how many turns that Pinion hath to one turn of that Wheel. Thus a Wheel of 60 teeth driving a Pinion of 6, will turn round the Pinion 10 times in going round once.

From the Fusy to the Ballance the Wheels drive the Pinions; and consequently the Pinions run faster, or go more turns, than the Wheels they run in. But it is contrary from the Great-Wheel to the Dial Wheel. Thus in the last Example, The Wheel drives round the Pinion 10 times: but if the Pinion drove the Wheel, it must turn 10 times to drive the Wheel round once.

§ 3. Before I proceed further, I must [Page] shew how to write down the Wheels and Pinions. Which may be done, either as Vulgar Fractions, or in the way of Division in Vulgar Arithmetick. E. C. A Wheel of 60 moving a Pinion of 5, may be set down thus, 60/3: or rather thus, 5) 60: where the first figure is the Pinion, the next without the hook, is the Wheel.

The number of Turns, which the Pinion hath in one turn of the Wheel, is set without a hook on the right hand: as 5) 60 (12, i. e. a Pinion 5 playing in a Wheel of 60, moveth round 12 times, in one turn of the Wheel.

4)36(95)55(115)45(95)40(8  17A whole Movement ma [...] be noted thus, 4/ [...] 55/5 45/5 40/5 17 Notches in the Crown▪Wheel. Or rather as you see here in the Margin: where the uppermost number, above the line, is the Pinion of Report 4, the Dial-wheel 36, and 9 turns of the Pin. of Report. The second number (under the line) is 5 the Pinion, 55 is the Great-wheel, and 11 turns of the Pinion it driveth. The third numbers, are the Second-wheel, &c. [Page] The fourth the Contrate-wheel, &c. An [...] the single number 17 under all, is th [...] Crown-wheel.

§ 4 By the § 2. before, knowing th [...] number of turns, which any Pinion hath in one turn of the Wheel it worketh in▪ you may also find out how many turns a [...] Wheel or Pinion hath, at a greater distance; as the Contrate-wheel, Crown▪wheel, or &c. For it is but multiplying By the Quotients I commonly mean the [...]umber of Turns; which number is set on the right hand, without a hook, as is shewn in the last Paragraph. Which I no [...]e [...]ere now once for all.together the Quotients, and the number produced, is the number of Turns. An Example will make what I say plain: 5)5 [...](115)45(95)40(8let us chuse these 3 numbers here set down; the first of which hath 11 turns, the next 9▪ and the last 8. If you multiply 11 and 9 it produceth 99, for 9 times 11 is 99, that is, in one turn of the Whee [...] 55, there are 99 turns of the second Pinion 5, or of the Wheel 40. If you multiply 99 by the last Quotient 8 (that is, 8 times 99 is 792) it shews the number of turns, which the third and last Pinion 5 hath. So that this third, and last Pinion turns 792 times in [Page] one turn of the first Wheel 55. 8)80(106)54(95)40(8  15Another Example will make it still more plain The Example is in the Margin. The turns are 10, 9 and 8. These multiplied as before run thus, viz. 10 times 9 is 90, that is, the Pinion 6 (which is the Pin. of the third Wheel 40) turns 90 times in one turn of the First▪wheel 80. This last product 90 being multiplied by 8, produces 720▪ that is, the Pinion 5 (which is the Pin. of the Crown-wheel 15) turns 720 times in one turn of the First-wheel, of 80 teeth.

§ 5. We may now proceed to that, which is the very groundwork of all; which is, not only to find out the turns, but the Beats also of the Ballance in those turns of the Wheels. By the last Paragraph, having found out the number of turns, which the Crown-wheel hath in one turn of the Wheel you seek for, you must then multiply those turns of the Crown-wheel by its number of Notches, and this will give you half the number of Beats, in that one turn of the Wheel. Half the number, I say, for the reasons in the following [Page] 6 §. For the Explication of what hath been said, we will take the example in the last §: the Crown-wheel there, has 720 turns in one turn of the first Wheel [...] This number multiplied by 15, the Notches in the Crown-wheel, produceth 10800, which are half the number o [...] strokes of the Ballance, in one turn of the first wheel 80. The like may be done for any of the other Wheels; as the Wheel 54, or 40: but I shall not insist upon these, having said enough.

I shall give but one Example more which will fully, and very plainly illustrate the whole matter. 4)32(85)55(115)45(95)40(8  17The example is in the margin, and 'tis of a 16 hour Watch, wherein the Pinion of Report is 4, the Dial-wheel 32, the Great-wheel i [...] 55, the Pinion of the secon [...]-Wheel is 5, &c. the numbe [...] of Notches in the Crown▪wheel are 17: the quotients or number of turns in each, are 8, 11 9, 8. All which being multiplied as be▪fore, make 6336: this number multiplied by 17, produceth 107712; which la [...] summ is half the number of Beats in on [...] [Page] turn of the Dial-wheel. The half number of Beats in one turn of the Great-wheel, you will find to be 13464: For 8 times 17 is 136, which is the half number of Beats in one turn of the Contrate-wheel 40: and 9 times 136, is 1224, the half beats in one turn of the Second-wheel: and 11 times 1224, is 13464, the half beats in one turn of the Great-wheel 55. And 8 times this last, is 107712 before named. If you multiply this by the two Pallets, that is, double it, it is 215424, which is the number of Beats in one turn of the Dial-wheel, or 12 hours. If you would know how many beats this Watch hath in an hour, 'tis but dividing the beats in 12 hours, into 12 parts, and it gives 17952, the Train of the Sir J. Moor▪ Mat. Com. p. 109.Watch, or beats in an hour. If you divide this into 60 parts, it gives 299 and a little more, for the beats in a minute. And so you may go on to seconds and thirds, if you please.

Thus I have delivered my thoughts as plainly as I can, that I may be well understood; this being the very foundation of all the artificial part of Clock-work. And therefore let the young practiser exercise [Page] himself thorowly in it, in more than one example.

If I have offended the more learned, quick-sighted Reader, by using m [...]y words; my desire to instruct the most ignorant Artist▪ must plead my excuse.

Ibid. p. 116. § 6. The Ballance or Swing hath two strokes to every tooth of the Crown-wheel. For each of the two Pallets hath its blow against each tooth of the Crown-wheel▪ Wherefore a Pendulum that swings Seconds, hath its Crown-wheel but 30.

SECT. II. The way to Calculate, or contrive the Numbers of a piece of Watch work.

HAving in the last Section led on the Reader to a general knowledge of Calculation; I may now venture him further into the more obscure, and useful parts of that Art: Which I shall explain with all possible plainness, tho less brevity, than I could wish.

Oughtred Autom. Sect. 14. § 1. The same motion may be performed either with one Wheel and one [Page] or by many Wheels and many Pinions: provided that the number of turns of all those Wheels bear the same proportion to all those Pinions, which that one Wheel bears to its Pinion. Or (which is the same thing) that the number produced by multiplying all the Wheels together, be to the number produced [...]y multiplying all the Pinions together; as that one Wheel is to that one Pinion. 28)1440Thus suppose you had use for a Wheel of 1440 teeth, with a Pin. of 28 leaves, you may make it into 3 Wheels and Pinions, viz. 4 [...] 36, 7) 8, and 1) 5. For if you multiply the three Wheels together, viz. 36, 8 and 5; and the three Pinions together by themselves, viz 4, 7 and 1, you will find 1440 to arise for the Wheels, and 28 for the Pinions. Or if you try the example by the number of turns, it will be the same. For 28) 1440 (51 3/7. And the quotients and turns of the 3 Wheels and Pinions multiplied together, are 51 3/7 also, as in the last example.

It matters not in what order the Wheels and Pinions are set, or which Pinion runs [Page] in which Wheel: Only for convenien [...] sake, they commonly set the biggest numbers to drive the rest.

§ 2. Two Wheels and Pinions of diff [...] rent Ought. ib.numbers may perform the same m [...] tion. As, a Wheel of 36 drives a Pinio [...] of 4, all one as a Wheel of 45 drives Pin. of 5; or as a Wheel of 90 drives Pin. of 10. The turns of each are 9.

§ 3. If in breaking your Train int [...] parcels (of which by and by) any of you [...] Quotients should not please you; or Id. ib.you would alter any other two number which are to be multiplied together, yo [...] may vary them by this Rule: Divid [...] your two numbers by any two oth [...] numbers which will measure them; th [...] multiply the Quotients by the alternat [...] divisors, the product of these two la [...] numbers found, shall be equal to the product of the two numbers first give [...] Thus if you would vary 36 times 8, d [...] vide these by any two numbers that wi [...] evenly measure them, as 36 by 4, and by 1. The fourth part of 36 is 9, and divided by 1 gives 8. Multiply 9 by [...] the product is 9; and 8 multiplied by [...] produceth 32. So that for 36 times 8 [...] [Page] you shall have found 32 times 9. 9 836X84 132X9The operation is in the Margin, that you may see, and apprehend it the better. These numbers are equal, viz. 36 times 8 is equal to 32 times 9; both producing 288. If you divide 36 by 6, and 8 by 2, and multiply as before is said, you will have for 36 times 8, 24 times 12, equal to 288 also.

If this Rule seem to the unskilful Reader hard to be understood, let him not be discouraged, because he may do without it, altho it may be of good use to him that would be a more compleat Artist.

§ 4. Because in the following Paragraphs, I shall have frequent occasion to use the Rule of Three, or Rule of Proportion, it will be necessary to shew the unskilful Reader, how to work this noble Rule.

If you find 3 or 4 numbers thus set, with four spots after the second of them, 'tis the Rule of Proportion; as in this example, 2. 4:: 3. 6. i. e. As 2 is to 4:: So is 3 to 6.

The way to work this Rule, viz. by the 3 first number to find a fourth, is, [Page] To multiply the second number and the third together, and divide their product by the first. Thus 4 times 3 is 12, which 12 divided by 2, gives 6; which is the number sought for, and stands in the fourth place.

You will find the great use of this Rule hereafter; only take care to bear it in mind all along.

§ 5. To proceed. If in seeking for your Pinion of Report, or by any other means, you happen to have a Wheel and Pinion fall out with cross numbers, too big to be cut in Wheels, and yet not to be altered by the former Rules, you may find out two numbers of the same, or a near proportion, by this following Rule, viz. As either of the two numbers given, is to Id. ib.the other:: So is 360 to a fourth: Divide that fourth number, as also 360 by 4. 5. 6. 8. 9. 10. 12. 15. (each of which numbers doth exactly measure 360) o [...] by any one of those numbers that bringeth a quotient nearest to an integer (or whole number.) Thus if you had these two numbers, 147 the Wheel, and 170 the Pinion, which are too great to be cut in small Wheels, and yet can't be reduced [Page] into le [...]s, because they have no other common measure, but unity: say therefore according to the last paragraph, As 170 is to 147; or as 147 is to 170:: So is 360 to a fourth number sought. In numbers thus, 170 147:: 360. 311. or 147. 170:: 360. 416. Divide the fourth number and 360 by one of the foregoing numbers; as 311 and 360 by 6, it gives 52 and 60. In numbers 'tis thus,

6) | 311 | (52
360 | (60

Divide by 8 'tis thus,

8) | 311 | (39
360 | (45

If you divide 360 and 416 by 8, it will fall out exactly to be 45 and 52

8) | 360 | (45
416 | (52

Wherefore for the two numbers 147 and 170, you may take 52 and 60; or 39 and 45; or 45 and 52, o [...] &c.

§ 6. I shall add but one Rule more, before I come to the practice of what hath been laid down; which Rule will be of perpetual use, and consists of these five particulars.

Oughtred Sect. 12. Sir J. Moor Ibid. p. 109. 1. To find what number of turns the Fusy will have, thus, As the Beats of the Ballance in one turn of the Great-Wheel or Fusy (suppose 26928) To the Beats of the Ballance in one hour (suppose 20196) [Page] :: So is the continuance of the Watches going in hours (suppose 16) To the number of the turns of the Fusy 12. In numbers 'twill stand thus, 26928. 20196:▪ 16. 12. By § 4. you may remember tha [...] you are to multiply 20196 by 16, the product is 323136. Divide this by 26928, and there will arise 12 in the Quotient, which must be placed in the fourth place▪ and is the number of turns which the Fusy hath.

2. By the Beats and turns of the Fusy▪ to find how many hours the Watch will go, thus,

As the Beats of the Ballance in one hour, are to the Beats in one turn of the Fusy:: So is the number of the turns o [...] the Fusy, to the continuance of the Watches going. In num [...]ers thus,

2196. 26928:: 12▪ 16.

3. To find the strokes of the Ballance in one turn of the Fusy, say, As the number of turns of the Fusy, to the continuance of the Watch's going in hours:: S [...] are the Beats in one hour, to the Beats o [...] one turn of the Fusy. In numbers it [...] thus,

12. 16:: 20196▪ 26928.

[Page] 4. To find the Beats of the Ballance in an hour, say thus, As the hours of the Watch's going, To the number of turns of the Fusy:: So are the Beats in one turn of the Fusy, To the Beats in an hour. In numbers thus,

16. 12:: 26928. 20196.

5. To find what Quotient is to be laid upon the Pinion of Report, say thus, As the beats in one turn of the Great-wheel, To the beats in an hour:: So are the hours of the Face of the Clock (viz. 12 or 24) To the Quotient of the Hour-Wheel divided by the Pinion of Report, i. e. the number of turns, which the Pinion of Report hath in one turn of the Dial-Wheel. In numbers thus,

26928. 20196:: 12. 9.

Or rather (to avoid trouble) say thus, As the hours of the Watch's going, Are to the numbers of the turns of the Fusy:: So are the hours of the Face, To the Quotient of the Pinion of Report▪ In numbers thus, 16. 12:: 12. 9. If the hours of the Face be 24, the Quotient will be 18; thus, 16. 12:: 24. 18.

§ 7. Having given a full account of all things necessary to the understanding the [Page] Art of Calculation, I shall now reduc [...] what hath been said into practice, by shewing how to proceed, in Calculating a piece of Watch-work.

The first thing you are to do, is to pitch upon your Train, or beats of the Ballance in an hour: as, whither a swi [...] Train, about 20000 beats (which is the usual Train of a common 30 hour Pocket▪Watch) or a slower Train of about 16000 (the Train of the new Pendulum Pocket▪Watches;) or any other Train.

Having thus pitched upon your Train, you must next resolve upon the number of turns you intend your Fusy shall have; and also upon the number of Hours, you would have your Piece to go: As suppose 12 turns; and to go 30 hours, or 192 hours (which is 8 days) or &c.

These things being all soon determined; you next proceed to find out the beats of the Ballance, or Pendulum, in one turn of the Fusy, by the last § 6. part 3. viz. As the turns of the Fusy, To the hours of the Watch's going:: So is the Train, To the number of beats in one turn of the Fusy. In numbers thus, 12. 16:: 20000. 26666. Which last [Page] number are the beats in one turn of the Fusy, or Great-Wheel; and (by Sect. I. § 5. of this Chap.) are equal to the Quotients of all the Wheels unto the ballance, multiplied together. This number therefore is to be broken into a convenient parcel of Quotients: which you are to do after this manner. First, half your number of beats, viz. 26666, for the reasons in Sect. I. § 6. of this Chap. the half whereof is 13333. Next you are to pitch upon the number of your Crown-wheel, as suppose 17. Divide 13333 by 17, the Quotient will be 784 (or to speak in the language of one that understands not Arithmetick, divide 13333 into 17 parts, and 784 will be one of them.) This 784 is the number left for the Quotients (or turns) of the rest of the Wheels and Pinions: which being too big for one or two Quotients, may be best broken into three. Chuse therefore 3 numbers, which when multiplied all together continually will come nearest 784. As suppose you take 10, 9, and 9. Now 10 times 9 is 90; and 9 times 90 is 810, which is somewhat too much. You may therefore try again other numbers▪ as suppose 11, 9, and 8. [Page] These multiplied as the last, produce 792▪ which is as near as can be, and convenient Quotients.

Thus you have contrived your Piece▪ from the Great-Wheel to the Ballance▪ But the numbers not falling out exactly according as you at first proposed; you must correct your work thus. First to find out the true number of beats, in one turn of the Fusy, you must multiply 792▪ aforesaid, which is the true product of al [...] the Quotients, by 17, the notches of the Crown-wheel; the product of this i [...] 13464, which is half the number of true beats in one turn of the Fusy, by Sect. [...] § 5. of this Chap. Then to find the tru [...] number of beats in an hour, say by § 6▪ part 4. of this Section, as the hours o [...] the Watch's going, viz. 16, to the 1 [...] turns of the Fusy:: So is 13464 the ha [...] beats in one turn of the Fusy, to 1009 [...] the half beats in an hour: the numbe [...] will stand thus 16. 12:: 13464. 1009 [...]

Then to know what Quotient is to b [...] laid upon the Pinion of Report, say by [...] 6. part 5. of this Sect: As the hours [...] the Watch's going, viz. 16, to the tur [...] of the Fusy, viz. 12:: So are the hou [...] [Page] of the Dial-plate, viz. 12, To the Quotient of the Pinion of Report. In numbers thus, 16. 12:: 12. 9.

4)36(95)55(115)45(95)40(8  17 Having thus found out all your Quotients, 'tis easie to determine what numbers your Wheels shall have: for chuse what numbers your Pinions shall have, and multiply the Pinions by their Quotients, and that produceth the numbers for your Wheels, as you see in the Margin. Thus 4 is the number of your Pinion of Report, and 9 its quotient; therefore 4 times 9, which makes 36, is the number for the Dial-wheel. So the next Pinion being 5, and its quotient 11, this multiplied produces 55 for the Great-wheel. And the like of the rest of the following numbers.

Thus, as plain as words can express it, I have shewed how to Calculate the numbers of a 16 hour Watch.

Oughtred Sect. 21. § 8. This Watch may be made to go a longer time, by lessening the Train, and altering the Pinion of Report. Suppose you could conveniently slacken the Train to 16000, the half of which is 8000. [Page] § 8. Then say (by § 6 part 2. of this Sect.) As the halfed Train, or Beats in an hour, viz. 8000, To the halfed beats in one turn of the Fusy, viz. 13464:: So are the turns of the Fusy, viz. 12, To the hours of the Watch's going: in numbers thus, 8000. 13464:: 12. 20 So that this Watch will go 20 hours.

Then for the Pinion of Report, say, by the same § part 5, As 20 the Continuance; To 12 the turns of the Fusy:: So are 12 the hours of the Face, To 7 the quotient of the Pinion of Report. In numbers thus, 20. 12:: 12. 7.

4)28(75)55(115)45(95)40(8  17 The work is the same as before, as to the numbers; only the Dial-wheel is but 28, because its quotient is altered to 7; as appears in the Margin, by the Scheme of the work.

§ 9. I shall give the Reader one example more, for the sake of shewing him the use of some of the foregoing Rules, not yet taken notice of in the former operations. Suppose you Id. ib. § 22.would give numbers to a Watch of about 10000 beats in an hour, to have 12 turns [Page] of the Fusy, to go 170 hours, and 17 notches in the Crown-wheel.

This work is the same as in the last Example § 7. In short therefore thus, As the turns 12: are To the Continuance 170:: So is the Train 10000, To 141666, which are the beats in one turn of the Fusy. The numbers will stand thus, 12. 170:: 10000 14 [...]666. Half this last is 70 [...]33. Divide this half into 17 parts, and 4167 will be for the quotients. And because this number is too big for 3 quotients, therefore chuse 4: as suppose 10, 8, 8, and 6 ⅗ (i. e. 6 and 3 fifths) These multiplied together as before, and with 17, maketh 71808, which are half the true beats in one turn of the Fusy. By this you are to find out your true Train first▪ saying as in the former example, As 170 to 12:: So 71808, to 5069; which last is the half of the true Train of your Watch. Then for the Pinion of Report, say, as 170, to 12:: So 12, to 1/ [...]4/74/ [...]. Which Fraction ari [...]eth thus: If you multiply 12 by 12 it makes 144; and divide 144 by 170, you cannot; but setting the 144 (the dividend) over 170 (the Divisor) and there ari [...]eth this fraction [...]/24/ [...]4/ [...], [Page] which is a Wheel and Pinion; the lower is the Pinion of Report, and the upper is the Dial-wheel, according to Sect. I. § 3. of this Chapter. Or (which perhaps will be more plain to the unlearned Reader) you may leave those two numbers, in their Divisional posture thus, 170) 144, which does express the Pinion and Wheel, in the way I have hitherto made use of. But to proceed. These numbers being too big to be cut in small 24)2020/246)60(106)48(85)40(85)33(6⅗  17 Wheels, may be varied, as you see a like Example is § 5. of this Section: viz. Say, as 144▪ is To 170:: So is 360, To 425. Or, as 170, to 144:: So is 360, To 305. In number thus, 144. 170:: 360. 425. Or 170. 144:: 360. 305. Divide 360, and either of these two fourth and last numbers by 4, 5, 6, 8, &c. (as is directed in the Rule last cited.) If you divide by 8, you will have for your numbers 1/14/74/ [...] 4/ [...]5/ [...] or 3/48/5. If you divide by 15 (which will not bring it so near an integer) you will have 2/24/8 or 2/ [...]0/4: which last are the numbers set down in the Margin▪ [Page] where the numbers of the whole Movement are set down.

§ 10. Having said enough, I think, concerning the Calculation of ordinary Watches, to shew the hour of the day: I shall next proceed to such as shew minutes and seconds. The process whereof is thus: First, having resolved upon your beats in an hour, you are next to find how many beats there will be in a minute, by dividing your designed Train into 60 parts. And accordingly you are to find out such proper numbers for your Crown-wheel, and quotients, as that the Minute-wheel shall go round once in an hour, and the Second-wheel once in a minute.

An Example will make all plain. Let us chuse a Pendulum of 6 inches to go 8 days, with 16 turns of the Fusy. By Horol. Disq.Mr Smith's Tables, a Pendulum of 6 inches vibrates 9368 in an hour. This divided by 60 gives 156 beats for a minute. Half these summs are 4684 and Sect. 1. § 6.78. Now the first work is to break this 78 into good proportions; which will fall into one quotient, and the Crown-wheel. First, for the Crown-wheel; let [Page] it have 15 notches. Divide 78 afore [...] by this 15, the quotient will be 5. A [...] so this first work is done: for a Crow [...] wheel of 15, and a Wheel a [...] Pinion, whose quotient is 5 ( [...] in the Margin)8)40(5  15 will go rou [...] in a minute, to carry a Ha [...] to shew Seconds.

Next for a Hand to go round in [...] hour, to shew Minutes. Now becau [...] there are 60 minutes in an hour, 'tis b [...] breaking 60 into two goo [...] 8)64(88)60(7½8)40(5  15 quotients (which may be [...] and 6, or 8 and 7½, or &c. and the work is done.

Thus your number 4684, broken, as near as can be, int [...] proper numbers.

But because it does not fall out exact into the above-mentioned numbers, yo [...] must Correct (as you were directed before) and find out the true number [...] beats in an hour, by multiplying 15 by 5, which makes 75; and this by 6 [...] makes 4500, which is the half of the tru [...] Train. Then to find out the beats in on § 6. Par. 3. and § 7.turn of thy Fusy, operate as before, vi [...] As the number of turns, 16, To the co [...] tinuan [...] [Page] 192:: So is 4500 to 54000, which are half the beats in one turn of [...]he Fusy. In numbers thus, 16. 192:: 4500. 54000. This 54000 must be di [...]ided by 4500, which are the true [...]umbers already pi [...]ched upon, or beats▪ [...]n an hour. The quotient of this division [...]s 12, which being not too big for one single quotient, needs not be divided into more. The work will stand, as you see in the Margin. [...])108(12 [...])64(8 [...])60(7½ [...])40(5  15

As to the Hour-hand, the Great-Wheel, which performs only one revolution in 12 turns of the Minute-wheel, will shew the hour. Or rather you may order it to be done by the Minute-wheel, [...]s shall be shew'd hereafter.

§ 11. I shall add but one Example more, and so conclude this Section; and [...]hat is, To calculate the numbers of a [...]iece whose Pendulum swings▪ Seconds, [...]o shew the hour, minutes, and seconds, [...]nd to go 8 days; which is the usual per [...]ormance of those Movements called Sir J. Moo [...] Ibid. p. 116. [...]oyal Pendulums at this day. First, cast [...]p the number of seconds in 12 hours [Page] (which are the beats in one turn of [...] Great-wheel) These are 12 times [...] minutes, and 60 times that, gives 432 [...] which are the seconds in 12 hours. H [...] V. Sect. 1. §▪ 6.this number (for the reasons before) 21600. The Swing-wheel must ne [...] be 30, to swing 60 seconds in one of [...] revolutions. Divide 21600 by it, a [...] 720 is the quotient, or number left to [...] broken into quotients. Of these quo [...] ents, the first must needs be 12 for [...] Great-wheel, which moves round on [...] in 12 hours. Divide 720 by 12, [...] quotient is 60; which may be conve [...] ▪ently broken into two quotients, as [...] and 6, or 5 and 12, or 8 and 7 ½, whi [...] last is most convenient. A [...] if you take all the Pinions the work will stand as in [...] Margin.8)96(128)64(88)60(7½  30

According to this compu [...] ▪tion, the Great-wheel will [...] about once in 12 hours, shew the hour, if you please: the Seco [...] wheel once in an hour, to shew the [...] nutes; and the Swing-wheel once in a [...] nute, to shew the seconds.

[Page] Thus I have endeavour'd with all possible plainness, to unravel this most mysterious, as well as useful part of Watchwork. In which, if I have offended the more learned Reader, by unartificial terms, or multitude of words, I desire the fault may be laid upon my earnest intent to condescend to the meanest capacity.

SECT. III. To Calculate the Striking part of a Clock.

§ 1. ALtho this part consists of many Wheels and Pinions, yet respect needs to be had only to the Count-wheel, Striking-wheel, and Detent-wheel: which move round in this proportion; The Count-wheel moveth round commonly [...]nce in 12, or 24 hours. The Detent-wheel moves round every stroke the Clock striketh, sometimes but once in two strokes. From whence it follows,

1. That as many Pins as are in the Pin-wheel, so many turns hath the Detent-wheel, in one turn of the Pin-wheel. Or (which is the same) the Pins of th [...] [Page] Pin-wheel are the Quotient of that Wheel, divided by the Pinion of the Deten [...]-wheel. But if the Detent-wheel moveth but once round in two strokes o [...] the Clock, then the said Quotient is bu [...] half the number of Pins.

2. As many turns of the Pin-wheel a [...] are required to perform the strokes of 1 [...] hours (which are 78) So many tur [...] must the Pinion of Report have, to turn round the Count-wheel once. Or thus▪ Divide 78 by the number of Striking pins, and the Quotient thereof shall b [...] the Quotient of the Pinion of Report. Al [...] this is, in case the Pinion of Report b [...] fixed to the arbor of the Pin-wheel, as i [...] very commonly done.

All this I take to be very plain: or [...] it be not, the example in the Margin wil [...] clear all difficulties.8)48(66)78(13 pins6)60(106)48(8 Her [...] the Locking-wheel is 48 [...] the Pinion of Report is 8 [...] the Pin-wheel is 78, th [...] Striking-pins are 13. An [...] so of the rest. I need onl [...] to remark hero, that 7 [...] being divided by the 13 pins, gives 6 [...] which is the Quotient of [...] ▪ the Pinion [...] [Page] of Report: as was before hinted.

As for the Warning-wheel, and Flying-Pinion, it matters little what numbers they have, their use being only to bridle the rapidity of the motion of the other Wheels.

Besides the last observation, there are other ways to find out the Pinion of Report, which will fall under the next §.

§ 2. These following Rules will be of great use in this part of Calculation, viz.

Rule 1. As the number of turns of the Great-wheel, or Fusy;

.To the days of the Clock's continuauc [...]:

::So is the number of strokes in 24 hours, viz. 156▪

.To the strokes in one turn of the Fusy, or Great-wheel.

Rule 2. As the number of strokes in 24 hours, which are 156,

.To the strokes in one turn of the Fusy, or Great-wheel,

::So are the turns of the Fusy, or Great-wheel,

.To the days of the Clock's continuance, or going.

Rule 3. As the strokes in one turn of the Fu [...]y,

[Page] .To the strokes of 24 hours, viz. 156.

::So is the Clock's continuance,

.To the number of turns of the Fusy, or Great-wheel.

These two last Rules are of no great use (as the first is) but may serve to correct your work, if need be, when in breaking your Strokes into Quotients (of which presently) you cannot come near the true number, but a good many strokes are left remaining. In this case, by Rule 2. you may find whether the continuance of your Clock be to your mind▪ And by Rule 3, you may enlarge or diminish the number of turns for this purpose. The praxis hereof will follow by and by.

The 2 following Rules are to find fit numbers for the Pinion of Report, and the Locking-wheel, besides what is said before § 1. Inference 2.

Rule 4. As the number of Strokes in the Clock's continuance, or in all it [...] turns of the Fusy,

.To the turns of the Fusy,

::So are the Strokes in 12 hours, which are 78,

.To the Quotient of the Pinion of Report, fixed upon the arbor of the Great-wheel.

[Page] But if you would fix it to any other Wheel, you may do it thus, as is before § 1. Infer 2 [...]hinted, viz.

Rule 5. First, find out the number of Strokes, in one turn of the Wheel you intend to fix your Pinion of Report upon (which I shall shew you how to do in the following §.) Divide 78 by this number, and the number arising in the Quotient, is the Quotient of the Pinion of Report.

Or thus. Take the number of Strokes in [...] [...]e turn of the Wheel, for the number of the Pinion of Report, and 78 for the Count (or Locking) wheel, and vary them to lesser numbers, by Sect. 2. § 5. of this Chapter.

Rule 6. The foregoing Rules are of greatest use, in Clocks of a larger continuance; altho, where they can be applied, they will indifferently serve all. But this Rule (which will serve larger Clocks too) I add chiefly for the use of lesser Pieces, whose continuance is accounted by hours.

The Rule is to find the Strokes in the Clock's continuance, viz. As 12, is to 78:: So are the hours of the Clocks continuance, [Page] To the number of Strokes in that time.

This Rule (I said) may be made use of for the largest Clock; but then you must be at the trouble of reducing the Days into Hours Whereas the shortest way is to Multiply the strokes in one turn of the Great-wheel, by the number of Turns. Thus in an 8 day piece the Strokes in one turn are 78. These multiplied by 16, the turns, produce 1248; which are the Strokes in the Clock's continuance. If you work by the foregoing Ruled the hours of 8 days are 192. Then say, 12▪ 78:: 192. 1248.

§ 3. In this Paragraph, I shall shew the use of the preceding Rules, and by examples make all plain that might seem obscure in them.

I begin with small Pieces: of which but briefly. And first, having pitched upon the number of turns, and the continuance, you must find, by the last Rule, how many Strokes are in its continuance. Then divide these Strokes by the number of turns, and you have the number of Striking-pins. Or divide by the number of Pins, and you have the number of Turns.

[Page] Thus a Clock of 30 hours, with 15 turns of the Great-wheel, hath 195 strokes. For by the last Rule, 12. 78:: 30. 195. Divide 195 by 15, it gives 13 for the Striking-pins. Or if you chuse 13 for your number of Pins, and divide 195 by it, it gives 15, for the number of [...]urns, as you see in the Margin.15)195(1313)195(15

As for the Pinion of Report, and the rest of the Wheels, enough is said in the § 1.

But suppose you would calculate the numbers of a Clock of much longer continuance, which will necessitate you to make your Pin-wheel further distant from the Great-wheel, you are to proceed thus: Having re [...]olved upon your turns, you must find out the number of strokes in one turn of the Great-wheel, or Fusy, by § 2▪ Rule 1. Thus in an 8 day piece, of 16 turns, 16. 8:: 156. 78. So in a piece of 32 days, and 16 turns, 16▪ 32:: 156. 312. These strokes so found out, are the number which is to be broken into a convenient parcel of Quotients, thus;

First resolve upon your number of Striking-pins: [Page] divide the last named number by it: The quotient arising hence, is to be one, or more quotients, for the Wheels and Pinions. As in the last examples▪ Divide 78 by 8 (the usual pins in an 8 day piece) and the quotient is 9 [...]; which is a quotient little enough. So in the Month-piece: if you take your Pins 8▪ divide 312 by it, the quotient is 39. Which being too big for one, must b [...] broken into two quotients, 10)65(6 [...]8)48(66)48(8 pins for Wheels and Pinions, or as near [...] can be: which may b [...] 7 and 5, or 6 and 6½. Th [...] latter is exactly 39, and may there [...]o [...] stand: as you see is done in the Margin.

The quotients being thus determined and accordingly the Wheels and Pinio [...] as you see; the next work is to find [...] quotient for the Pinion of Report, to [...] ry round the Count (or Locking) wh [...] once in 12 hours, or as you please. [...] you fix your Pinion of Report on th [...] Great-wheel arbor, you must operate [...] the Rule 4. of the last paragraph. As [...] the last example in the Month-piece: [...] Rule 6. before, the strokes in the conti [...] ance [Page] are 4992. Then by Rule 4 say, 4992. 16:: 78. 499 [...]/124 [...] or thus, 4992) 1248. The first of which two numbers is the Pinion, the next is the Wheel. Which being too large, may be varied to [...]/9 or V. Sect. 1▪ §. 3.36) 9; or to [...]4/6 or 24) 6, by Sect. 2 § 5. before.

These numbers being not the usual numbers of a Month-piece, but only made use of by me, as better illustrating the foregoing Rules▪ I shall therefore, for the fuller explication of what has been said, briefly touch upon the calculation of the more usual numbers. They commonly encrease the number of Striking-pins, and so make the Second-wheel the Striking-wheel▪ Suppose you take 24 Pins; Divide 312 by it, and the Quotient is 13. Which is little enough 8)104(136)72(12. 24 pins for one Quotient; and may therefore stand as you see is done in the Margin: where the Quotient of the first Wheel is 13. In the second Wheel of 72 teeth, are the 24 pins, altho its quotient is but 12, because the Hoop-wheel is double, and goes round but once in two strokes of the Pin-wheel.

[Page] The Pinion of Report here, is the same with the last, if fixed upon the arbor of the Great▪wheel. But if you fix it on the arbor of the Second, or Pin-wheel, its quotient then is found by § 1. Infer. 2. or by § 2. Rule 5. viz. Divide 78 by 24, and the number arising in the quotient, is the quotient of the Pinion of 12)39(3¼ Report, which is 3 ¼. The Pinion of Report then being 12, the Count-wheel will be 39, as in the Margin.

To perfect the Reader in this part of Calculation, I will finish this Section with the calculation of a Year-piece of Clockwork. The Process whereof is the same with the last, and therefore I may be more brief with this, except where I have not touched upon the foregoing Rules.

We will chuse a piece to go 395 days with 16 turns, and 26 Striking-pins. By § 2. Rule 1. there are 3851 strokes in one turn of the Great-wheel. For 16. 395:: 156. 3851. This last number divided by the 26 Pins, leaves 148 in the quotient, to be broken into two or more quotients, for Wheels and Pinions. These quotients may be 12 and 12; which multiplied, [Page] makes 144, which is 10)120(128)96(12 78(26 pins as near as can well be, to 148. The work thus far contrived, will stand as you see in the Margin.

Before you go any further, you may correct your work, and see how near your numbers come to what you proposed at first, because they did not fall out exact. And first, for the true continuance of your Clock▪ If you multiply 12, 12, and 26 (i. e. the Quotients un▪o the Stri [...]ing-pins, and those Pins) you have the true number of Strokes, in one turn of the Great-wheel: Which, in this example, make 3744. For 12 times 12, is 144; and 26 times that, is 3744. (This Direction I would have noted, and remembered, as a Rule useful at any time to discover the nature of any piece of Clock-work.) Having thus the true number of Strokes desired, by § 2. Rule 2. you may find the true Continuance to be only 384 days. For 156. 3744:: 16. 384. If this Continuance doth not please you, you may come nearer to your first proposed number, of 395 days, by a small encrease of [Page] the number o [...] Turns; according to § 2. Rule 3. viz. by making your turns almost 16½. For 3744. 156:: 395. 16½ almost.

Lastiy, For the Pinion of Report, if you fix it upon the Great-wheel, it will require an excessive number: if you fix it upon the Pin-wheel (which is usual) then by § 2. Rule 5, the quotient 13)39(3 is 3; and the Pinion of Report being 13, the Count-wheel will be 39; as you see in the Margin.

But for the better exercising the Reader, let us fix it upon the Spindle of the Second-wheel 96. Its quotient is 12; which multiplied by 26 (the pins) produceth 312; which are the Strokes in one turn of that Second-wheel. Then by § 2▪ Rule 5, Divide 78 by 312, i. e. Set them as a Wheel and Pinion thus, 312) 78, and vary them to lesser numbers (by Sect. [...] § 5.) viz. 36▪ 9, or to 24) 6, or th [...] like.

I think it needless to say any thing o [...] Pocket-clocks, whose calculation is the very same, with what goes before.

[Page] That the unlearned Reader may not think any thing going before difficult, I need only to advise him, to look over the working of the Rule of Proportion, in Sect. 2. § 4. For I think all will be plain, if that be well understood.

SECT. 4. Of Quarters and Chimes.

THe Reader will expect that I should say somewhat concerning Quarters and Chimes: but because there is little, but what is purely mechanical in it, I shall say the less, and leave the Reader to his own invention.

§ 1. The Quarters are generally a distinct part from the Clock-part, which striketh the Hour.

The Striking-wheel may be the First, Second, or &c. Wheel, according to your Clock's continuance. Unto which Wheel you may fix the Pinion of Report.

The Locking-wheel must be divided (as other Locking-wheels) into 4, 8, or more unequal parts, [...]o as to strike the Quarter, and lock at the first Notch; the half-hour, and [Page] lock at the second Notch, &c. And in doing this, you may make it to chime the Quarters, or strike them upon two Bells, or more.

'Tis usual for the Pin-wheel▪ or the Locking-wheel, to unlock the Hour-part in these Clocks; which is easily done by some jogg or Latch, at the end of the last Quarter, to lift up the Detents of the Hour-part.

If you would have your Clock strike the Hour, at the Half-hour, as well as whole Hour, you must make the Locking-wheel of the Hour-part double: i. e. it must have two Notches of a sort, to strike 1, 2, 3, 4, &c. twice apiece.

§ 2. As for Chimes, I need say nothing of the Lifting-pieces and Detents, to lock and unlock; nor of the Wheels to bridle the motion of the Barrel. Only you are to observe, that the Barrel must be as long in turning round, as you are in Singing the Tune it is to play. As for the Chime-Barrel, it may be made up of certain Barrs, that run athwart it, with a convenient number of holes punched in them, to put in the Pins, that are to draw each Hammer. By this means, you may change [Page] the Tune, without changing the Barrel. This is the way of the Royal Exchange Clock in London, and of others. In this case, the Pins or Nuts, which draw the Hammers, must hang down from the Barr, some more, some less, and some stand upright in the Barr: the reason whereof is, to play the Time of the Tune rightly. For the distance of each of these Barrs, may be a Semi-brief, or &c. of which hereafter.

But the most usual way is, to have the Pins that draw the Hammers, fixed on the Barrel. For the placing of which Pins, you may make use of the Musical Notes, or proceed by the way of Changes on Bells, viz. 1, 2, 3, 4, &c. The first being far the better way, I shall speak of that chiefly, especially because the latter will fall in to be explained with it.

And first, you are to observe what is the Compass of your Tune, or how many Notes or Bells there are from the highest to the lowest: and accordingly you must divide your Barrel from end to end. Thus in the examples following, each of those Tunes are 8 notes in compass; and accordingly the Barrel is divided into 8 [Page] parts. These Divisions are struck round the Barrel, opposite to which are the Hammer-tails.

I speak here, as if there was only one Hammer to each Bell, that the Reader may more clearly apprehend what I am explaining. But when two Notes of the same sound come together in a Tune, there must be two Hammers to that Bell, to strike it. So that if in all the Tunes you intend to Chime, of 8 notes compass, there should happen to be such double Notes on every Bell, instead of 8, you must have 16 Hammers: and accordingly you must divide your Barrel, and strike 16 strokes round it opposite to each Hammer-tail. Thus much for dividing your Barrel from end to end.

In the next place, you are to divide i [...] (round about) into as many divisions, as there are Musical Barrs, Semibriefs, Minums, &c. in your Tune. Thus the 100th Psalm-tune hath 20 Semibriefs; the Song-tune following, hath 24 Barrs of triple time: and accordingly their Barrels are divided. Each division therefore of the 100th Psalm Barrel is a Semibrief, [...]nd of the Song-tune 'tis three crotchets▪ [Page] And therefore the intermediate Spaces serve for the shorter notes: as, one third of a division, is a Crotchet, in the Song-tune. One half a division, is a Minum; and one quarter a Crotchet, in the Psalm-tune. Thus the first note in the 100th Psalm, is a Semibrief, and accordingly on the Barrel, 'tis a whole division from 5 to 5. The second is a Minum, and therefore 6 is but half a division from 5; and so of the rest. And so also for the Song-tune, which is shorter time: The two first notes being Quavers, are distant from one another, and from the third pin, but half a third part of one of the divisions. But the two next pins (of the bell 3, 3) being Crotchets, are distant so many third parts of a division. And the next pin (of the bell 1) being a Minum, is distant from the following pin (4) two thirds of a division.

From what hath been said, you may conceive the surface of a Chime-barrel, to be represented in the Tables following, as stretched out at length: or (to speak plainer) that if you wrap either of these Tables round a Barrel, the Dotts in the Table, will shew the places of the

[Page]

A Table of Chimes to the 100 Psalm.

[...]

The Musical Notes of Psalm 100.

[...]

[Page][Page]

The Musical Notes of, Such Command o're my Fate, &c A Song

[...]

The Chimes of the Song, Such Command o're my Fate, &c.

[...]

To be inserted between page [...] and [...]

[Page] Pins, to be set on the Barrel.

You may observe in the Tables, that from the end of each Table to the beginning, is the distance of two, or near two divisions: which is for a Pause, between the end of the Tune, and its beginning to Chime again.

I need not say, that the Dotts running about the Tables, are the places of the Pins that play the Tune.

If you would have your Chimes compleat indeed, you ought to have a set of Bells, to the Gamut notes; so as that each Bell having the true sound of Sol, La, Mi, Fa, you may play any Tune, with its Flats and Sharps. Nay, you may by these means, play both the Bass and Treble, with one Barrel.

If any thing going before appears gibberish, I can't help it, unless I should here teach the skill of Musick too.

As to setting a Tune upon the Chimebarrel from the number of Bells, viz. 1, 2, 3, 4, I shall here give you a specimen thereof.

Such Command o're my Fate, in numbers.

[Page]775, 3, 3, 1. 4, 5, 6, 4. 4, 2.
4, 3, 2, 3, 4, 6, 3, 5, 7, 7, 7. ‖
5, 6, 8, 8, 4. 4, 4; 3, 5, 4.
6, 5, 7, 5, 3; 41, 3, 5, 5, 5.
3, 3, 1, 3, 5. 554, 2, 4, 6.
4, 3; 23, 3; 53, 5, 7, 7, 7.

Note, In these numbers, a Comma [,] signifies the note before it, to be a Crotchet. A prick'd Comma, or Semi-colon [;] denoteth a prick'd Crotchet. And a Period [.] is a Minum. Where no punctation is, those Notes are Quavers.

I shall only add further, that by setting the Names of your Bells at the head of any Tune (as is done in the Tables before) you may easily transfer that Tune, to your Chime-barrel, without any great skill in Musick. But observe, that each line in the Musick, is three notes distant; i. e. there is a Note between each line, as well as upon it: as is manifest by inspecting the Tables.

[Page]

SECT. 5. To Calculate any of the Celestial Motions.

The Motions I here chiefly intend, are the Day of the Month, the Moons age, the Day of the Year, the Tides, and (if you please) the slow motion of the Suns Apogaeum, of the Fixed Stars, the motion of the Planets, &c.

§ 1. For the effecting these Motions, you may make them to depend upon the Work already in the Movement; or else measure them by the beats of a Ballance, or Pendulum.

If the latter way, you must however contrive a Piece (as before in Watch-work) to go a certain time, with a certain number of turns.

But then to Specificate, or determine the Motion intended, you must proceed one of these two ways: either,

1. Find how many beats are in the Revolution. Divide these beats by the beats in one turn of the Wheel, or Pinion, which you intend shall drive the intended Revolution; and the Quotient shall be [Page] the number to perform the same. Which, if too big for one, may be broken into more Quotients. Thus, if you would represent the Synodical Revolution of the Moon, which is 29 days, 12 ¾ hours) with a Pendulum that swings Seconds, the Movement to go 8 days, with 16 turns of the Fusy, and the Great-wheel to drive the Revolution. Divide 2551500 (the Beats in 29 days 12 ¾ hours) by 43200 (the Beats in one turn of the Great-wheel) and you will have 59 in the Quotient: which being too big for one, may be put into two Quotients. Or

2. You may proceed as is directed before, Ch. 2. Sect. 2. § 7.in the Section of Calculating Watchwork, viz. Chuse your Train, turns of the Fusy, Continuance, &c. And then instead of finding a Quotient for the Pinion of Report, find a number (which is all one as a Pin. of Report) to Specificate your Revolution, by this following Rule.

Rule. As the Beats in one turn of the Great-wheel. To the Train:: So are the Hours of the Revolution, To the Quotient of the Revolution.

Thus to perform the Revolution of Saturn (which is 29 years, 183 days) with a [Page] 16 hour Watch, of 26928 Beats in one turn of the Fusy, and 20196, the Train: the quotient of the Revolution, will be 193824. For, As 26928, To 20196:: So 258432 (the Hours in 29 y. and 183 d.) To 193824. Note here, That the Great-wheel Pinion is to drive the Revolution work.

But if you would have the Revolution to be driven by the Dial-wheel, and the Work already in the Movement (which in great Revolutions, is for the most part, as nice as the last way, and in which I intend to treat of the particular Motions) in this case, I say, you must first know the Days of the Revolution. And because the Dial-wheel goeth round twice in a day, therefore double the number of the days in the Revolution, and you have the number of turns of the Dial-wheel in that time. This number of turns is what you are to break into a convenient number of quotients, for the Wheels and Pinions▪ as shall be shewed in the following examples.

§ 2. A Motion to shew the Day of the Month.

[Page] Oughtred. § 26. The days in the largest Month are 31. These doubled are 62, which are the turns of the Dial-wheel, which may be broken into these two quotients 15 ½ and 4; which multiplied together make 62. Therefore chusing your Wheels and Pinions, as hath been directed in the former Sections, your work is done. The Wheels 4)62(15½5)20(4 and Pinions may be, as you see done in▪ the Margin. Or if a larger Pinion than one of 5 be necessary, by reason it is concentrick to a Wheel, you 4)62(15½10(40(4 may take 10 for the Pinion, and 40 for the Wheel, as in the Margin.

The work will lye thus in the Movement, viz. Fix your Pinion 10, concentrical to the Dial-wheel (or to turn round with it upon the same Spindle.) This Pinion 10 drives the Wheel 40: which Wheel has the Pinion 4 in its center, which carrieth about a Ring of 62 teeth, divided on the upper side into 31 days.

Or, you may, without the trouble of many Wheels, effect this motion; vi [...]. By a Ring divided into 30 or 31 days, and as many Fangs or Teeth, like a Crown▪ [Page] wheel teeth, which are caught and pushed forward once in 24 hours, by a pin in a Wheel, that goeth round in that time. This is the usual way in the Royal Pendulums, and many other Clocks; and therefore being common, I shall say no more of it.

§ 3. A Motion to shew the age of the Id. ib.Moon.

The Moon finisheth her course▪ so as to overtake the Sun, in 29 days, and a little above an half. This 29 ½ days (not regarding the small excess) makes 59 twelve hours, or turns of the Dial-wheel, which is to be broken into convenient quotients: which 10)5, 9( [...]94)40(10 4)59(14¾10)40(4 may be 5, 9 and 10 as in the first example; or 14¾ and 4, as in the second example in the Margin. So that if you fix a Pinion of 10 concentrical with your Dial-wheel, to drive a Wheel of 40 (according to the last example) which Wheel 40 drives a Pinion 4, which carries about a Ring, or Wheel of 59 teeth, divided on the upper side into 29 ½ 'twill shew the Moons age.

[Page] Id. ib. § 4. A Motion to shew the day of the Year, the Sun's place in the Ecliptick, Sun's Rising or Setting, or any other annual motion of 365 days.

The double of 365 is 730, the turns of the Dial-wheel in an year: which may be broken into 4)73(18¼4)40(105)20(4 4)73(18¼4)32(84)20(5 these quotients, viz. 18 ¼, and 10, and 4, according to the first example; or 18 ¼, 8, and 5, according to the second. So that a Pinion of 5 is to lead a Wheel of 20; which again by a Pinion of 4, leadeth a Wheel of 40; which thirdly, by a Pinion of 4, carrieth about a Wheel, or Ring of 73, divided into the 12 months, and their days; or into the 12 signs, and their degrees; or into the Sun's Rising and Setting, &c. For the setting on of which last, you have a Table in Mr. Oughtred's Opuscula.

Autom. § 35. Id. ib. § 5. To shew the Tides at any Port.

This is done without any other trouble, than the Moon's Ring (before mentioned § 3.) to move round a fixed circle, divided into twice 12 hours, and numbered the contrary way to the age of the Moon.

[Page] To set this to go right, you must find out at what Point of the Compass the Moon makes full Sea, at the place you would have your Watch serve to. Convert that point into hours, allowing for every point North or S. lost 45′ of an hour. Thus at London-bridge 'tis vulgarly thought to be high Tide, the Moon at N. E. and S. W, which are 4 Points from the N. and S. Or you may do thus: by Tide-tables learn how many hours from the Moon's Southing, 'tis Highwater. Or thus; find at what hour it is Highwater, at the Full or Change of the M [...]on: as at London-bridge, the full Tide is commonly reckoned to be 3 hours from the Moon's Southing; or at 3 of clock at the Full and Change. The day of Conjunction, or New-Moon, with a little stud to point, being set to the hour so found, will afterwards point to the hour of full Tide.

This is the usual way; but it being always in motion, as the Tides are not, a better way may be found out, viz. By causing a Wheel, or Ring to be moved forward, only twice a day, and to keep time (as near as can be) with Mr. Flamsteed's most correct Tables. But this I [Page] shall commit to the Readers contrivance, it being easie, and more of curiosity than use.

§ 6. To Calculate Numbers, to shew the Motion of the Planets, the Slow Motion of the Fixed Stars, and of the Sun's Apogeum, &c.

Having said enough before that may be applied here, and they being only curiosities, seldom put in practice, I shall not therefore trouble the Reader, or swell my Book with so many words, as would be required to treat of these Motions distinctly, and compleatly.

Only thus much in general. Knowing the years of any of these Revolutions, you may break this number into quotients; if you will make the Revolution to depend upon the year's Motion; which is already in the Movement, and described § 4. before. Or if you would have it depend upon the Dial-wheel, or upon the Beats of a Pendulu [...], enough is said before to direct in mis matter.

In all these Slow motions, you may somewhat [...]ten your labour, by endless Screws to serve for Pinions, which are but as a Pinion of one tooth.

[Page] Mat. Com. p. 117. Sir Jonas Moor's account of his large [...]phere going by Clock-work, will suffi [...]ently illustrate this paragraph. In this [...]phere, is a Motion of 17100 years, for [...]he Sun's Apogeum, performed by six [...]heels, thus, as Sir Jonas relates it; For the Great-wheel fixed is 96, a Spindle-wheel of 12 bars turns round it 8 times in 24 hours, that is, in 3 hours; after these, there are four Wheels, 20, 73, 24, and 75, wrought by endless Screws that are in value but one: therefore 3, 20, 73, 24, and 75 multiplied together continually, produceth 7884000 V. Sect. 1 § 4, 5.hours, which divided, by 24 gives 3285000 days, equal to 900 years. Now on the last wheel 75 is a pinion of 6, turning a great Wheel, that carrieth the Apogeum number 114: and 114 divided by 6, gives 19 the quotient: and 900 times 19 is 17100 years.

Thus I have, with all the perspicuity I [...]ould, led my Reader through the whole [...]rt of Calculation, so much of it at least, [...]at I hope he will be master of it all; not [...]ly of those motions, which I have par [...]cularly treated about, but of any other [...]t mentioned: Such as the Revolution [Page] of the Dragons Head and Tail, whereby the Eclipses of the Sun and Moon are found, the Revolution of the several Orbs, according to the Ptolemaick System, or of the celestial bodies themselves, according to better Systems, with many other such curious performances, which have made the Sphere of Archimedes of old famous: and since him, that of William of Zeland, De Subtil. l. 17.and another of Janellus Turrianus of Cremona, mentioned by Cardan: and of late, that elaborate piece of Mr. Watson, late of Coventry, now of London, in her late Majesties Closet.

CHAP. III. To alter Clock-work, or convert one Movement into another.

THis Chapter I design for the use of such, as would convert old Ballance Clocks into Pendulums, or would make any old work serve for the tryal of new motions, or would apply it to any other such like use.

[Page] § 1. To do this, you may draw a Scheme of your old work: and so you will see what Quotients you have, and what you will want. To do all which, there are sufficient instructions in the preceding Chapter. A few instances will make all plain.

§ 2. Let us chuse for instance an old Ballance clock to be turned into a Pendulum of 6 inches. The old work is, The Great-wheel 56, the Pinion 7; the next Wheel 54, the Pinion 6; the Crown-wheel 19, &c. The Scheme 4)48(127)56(86)54(9  19 of this work is in the Margin. The Quotients and Crown-wheel and 2 Pallets multiplied together continually, produce 2736, which are the Strokes of the Ballance, in one turn of the Great-wheel, by Sect. l. § 4, 5. of the last Chapter. And by the Quotient of the Dial-wheel (which is 12) it appears, that the Great-wheel goeth round once in an hour. Or you may find the Beats in an hour, by § 5. last cited. Having thus found the Beats in an hour, of the old work, you must next find the Beats in an hour, of a 6 inches Pendulum; which you may do by [Page] Horol. Dis. p. 54. Chap. 5. § 4. following; or by Mr. Smith's Tables, according to whom the number is▪ 9368. Divide this by 2736, and you have the Quotient, which 2736)9368(3½ is to be added to the Scheme of the old work. This Quotient is 3 and near ½▪ as you see in the Margin.

The work thus altered, will 4)48(127)56(86)54(96(2 [...](3½  19stand as you see in the Margin, viz. a Pinion 6, and a Contrate-wheel 21, must be added.

According to this way, the old work will stand as before, only the Crown-wheel must be inverted.

§ 3. But because the Crown-wheel is too big for the Contrate-wheel (which is unseemly) therefore it will be best, ▪to make both the Contrate, and Crown-wheels new; and encrease the number of the Contrate-wheel, but diminish that of the Crown-wheel. To do which, pitch upon some convenient number for the Crown-wheel. Multiply all the Quotients, and this new Crown-wheel number, as before; and divide 9368 by it. As, [Page] Suppose you pitch upon 11 for the Crown-wheel: if you multiply 8, 9 and 11▪ the Product is 792; which multiplied by the 2 Pallets, makes 1584, which are the Beats in one turn of the Great-wheel, or V. Sect. 1▪ § 6.in an hour. Divide 9368 by it, and you have near 6 for the Quotient 4)48(127)56(86)54(96)36(6  11 of your Contrate-wheel. The work thus ordered, will stand as in the Margin.

If you would correct your work, to find the true number of Beats in an hour, &c. you must proceed, as is shewn Sect. 2. § 6, and latter end of § 7. of the last Chapter.

§ 4. But suppose you have a mind to change the former old Watch, into a 30 hour piece, and to retain the old Ballance-wheel (which may be often done:) in this case, you must add a Contrate-wheel, and alter the Pinion of report. For the Contrate-wheel, chuse such a Quotient, as will best suit with the rest of your work; and then multiply all your Quotients, Crown-wheel and [...] Pallets together, and so find the number of turns in the Great-wheel, as before. Then say by [Page] Sect. 2. § 6. part 5. before, As the Beats in one turn of the Great-wheel, To the Beats in an hour:: So are the hours of the Dial, To the quotient of the Pinion of Report.

Thus in the old work before; to the old quotients 8 and 9, you may add another of 8, for the Contrate-wheel. Those multiplied, as was now directed, make 21888, for the Beats in one turn of the Great-wheel. And then for the quotient of the Pinion of Report, say in numbers thus, 21888. 9368:: 12. 5. 6)30(57)56(86)54(96)48(8  19 The quotient for the Pinion of Report is somewhat more than 5, which overplus may be neglected, as you see by the Scheme of the whole work in the Margin.

If you desire to know what number of turns, the Fusy must have in this work; Say by the last quoted §▪ part 1, in numbers thus, 21888. 9368:: 30. 13 almost. So that near 13 turns will do.

If you would correct your work, to know the exact Beats, &c. you are referred to directions in the end of the last paragraph.

[Page] § 5. I shall add but one thing more, to what hath been said in this Chapter, and that is, to change the Striking part of this old Movement, into a 30 hour piece.

A Scheme of the old 4)39 [...]¾7)56(8 pins6)54(96)48(8 work is in the Margin.

And to alter it, the best way is, to double the number of Striking pins, making the 8, sixteen pins: and the Hoop of the Detent-wheel double, that the Pin-wheel may strike two strokes, in its going round once.

The greatest inconvenience here, will be to bridle the rapidity of the Strokes; because a quotient of (2 only, added to the old work, will be sufficient for this purpose: which being an inconvenient number, 'twill be necessary to be content with the old numbers, or make more Wheels and Pinions new, than may be thought worth the while.

If you would find what number of turns, the Fusy will require; you must find how many Strokes are in 30 hours, by Sect. 3. § 2. R. 6. before. These are 195; which divided by the 16 Pins, [Page] gives somewhat more than 12 turns of the Fusy.

Lastly, for the Pinion of Report, you must pursue the directions in the last quoted place, R. 5.

The work thus altered, 5)24(7/18/67)568. 16 pins6)54(96)48(8 will stand as in the Margin.

CHAP. IV. To size the Wheels and Pinions, or proportion them to each other, both Arithmetically and Mechanically.

§ 1. FOr the exact and easie moving of the Wheels and Pinions together, it is necessary that they should fit each other, by having their teeth and leaves of the same wideness, or near of the same wideness. For many do make [Page] the Leaves of the Pinion narrower than the Teeth of its Wheel, by reason of their running deep in each other; which is as if the Diameters of the Wheel and Pinion were less. But this I leave to those, whose practice and observations are greater than mine in these matters.

§ 2. To make the Teeth of a Wheel and Pinion alike, the way Arithmetically is thus, First you must find the Circumference of your Wheel and Pinion; which you may best do by the Rule of Three (so often made use of before) the Rule is thus, as 7 is to 22:: so is the Diameter to the Circumference. Or more exactly thus, as 1, is to 3, 1416:: So Diam. to Circum.

Suppose you have a Wheel of 2 inches diameter, and 60 Teeth, and would fit to it a Pinion of 6 Leaves. First 7 22:: 2. 6, 3. The circumference of the Wheel, is then 6 inches, and 3 tenths of an inch. Then say, as the Teeth of the Wheel, to the circumference Sir J. Moor Mat. Com. R. 5.of it:: So are the Leaves of the Pinion, to the circumference thereof. In numbers thus 60▪ 6, 3:: 6▪, 63. The Pinion then is 63 hundredth parts of an inch round.

[Page] Now to find the Diameter, 'tis but the reverse of the former Rule, viz. As 22. to 7:: So the Circumference to the Diameter. In numbers thus, for the foregoing Pinion, 22. 7::, 63▪ 2, The Diameter then of the Pinion must be two tenths of an inch, to fit the aforesaid Wheel of 2 inches diameter.

sect 3. But because this way may be difficult to persons unacquainted with Decimal Arithmetick, which is very necessary here; therefore I shall set down a way to do it mechanically. Having drawn a Circle, divide it into as many parts, as you intend leaves in the Pinion you would size. From two of these points in the Circle, draw two lines to the Center: to which apply two of the Teeth of your Wheel, guiding them up and down until they touch at the same width on these Radii. Mark where this agreement is, and a small circle drawn there, will represent the circumference of the Pinion sought after.

CHAP. V. Of Pendulums.

[Page]

sect 1. AMong all known Motions, none measureth Time so regularly, as that of a Pendulum. But yet Watches governed hereby are not so persect, but that they are subject to the variations of weather, foulness, &c. And the shorter, and lesser the Pendulum is, so much the more subject such Watches are to these annoyances.

There are two ways to obviate these inconveniences in some measure. One way is, to make the Pendulum long, the Bob heavy, and to vibrate but a little way from its settlement. Which is now the most usual way in England. The other is the contrivance of the ingenious Mr. Hu [...]ens, which is, to make the upper part of the rod, play between two cheek parts of [...] Cycloid. Sir Jonas Moor says, that af [...]er some time, and charge of Experiments, [Page] Id. ib. Rule 3. he believes this latter to be the better way. And Mr Hugens calls it admirable.

If any desire to know how to make those Cycloidal Cheeks, fit to all Pendulums, I refer him to the aforesaid Mr. Zulichem's De Horol. Oscil. p. 10, 11, 12.Book, because I can't shew how to do it, without the trouble of Figures; and this way is much ceased, since the Crown-wheel method (to which it is chiefly proper) is swallowed up by the Royal Pendulums.

sect 2. Another thing to be remark'd in Pendulums is, That the longer the Vibration is, the [...]lower it is. For if two isochrone Pendulums do move, one the quadrant of a circle, the other not above 3 or 4 degrees, this latter shall move some-what quicker than the former. Which is the true reason, why small Crown-wheel Pendulums go faster in cold weather, or when soul, than at other times. Yea, in the best Royal Pendulum, if you put a divided plate behind the Ball, and observe its swings, you may perceive the Vibrations to be sometimes shorter; and that then the Watch doth gain too much▪ Somewhat also may perhaps be attributed to the rarity or density of the air; which [Page] I have not yet had an opportunity of observing, by comparing with a good Baroscope, the various vibrations of a good Royal Pendulum. But Mr. Boyl says, that a Pendulum moveth as long, and as Machina Pneumat. Exp. 26.fast in a thick medium, as a thin one; contrary to the opinion of some Naturalists, who think the contrary. His opinion is grounded upon the experiment of a Pendulum vibrating in his air-pump, the air sucked out, and in the open air; wherein was no alteration.

sect 3. For the calculation of all Pendulums, 'tis necessary to fix upon some one, to be as a Standard to the rest. I pitch upon a Pend▪ to vibrate Seconds each stroke.

Mr. Hugens lays down the length of a Pend. to swing Seconds to be 3 feet, 3 inches, and 2 tenths of an inch (according to Sir J. Moor's reduction of it to English measure. Ibid.)

‘Ibid. The Honourable Lord Bru [...]cker (saith Sir Jonas) and Mr. Rook, found the length to be 39, 25 inches, which a little exceeds the other: and may be, was justened by Mr. Hugens's Rule for the Center of Oscillation. For Mounton's Pendulum, that▪ [Page] vibrate 132 times in a minute, it will be found likewise 8, 1 inches, agreeing to 39, 2 inches English. Therefore for certain 39, 2 inches may be called the Ʋniversal measure, and relied on, to be the near length of a Pend. that shall swing Seconds each vibration.’

But forasmuch as the different size of the Ball, will make some difference in the length of this Standard Pend., therefore to make this Pend. an Ʋniversal measure, to fit all Places and Ages, you must measure from the Point of Suspension, to the Center of Oscillation. Which Center is found by this Rule, As the length of the Fiugenius [...]i supra, p. 141. Sir J. Moor ibid.String from the point of▪ Suspension to the center of a round Ball: is to the Semidiameter of a round Ball: is to the Semidiameter, to a fourth number. Add two fifths of that fourth number, to the former length, and you have the center of Oscillation; and thereby the true length of this Standard Pendulum.

If it be desired to fit a Ball of a triangular, quadrangular, or any other form to this Pend, the center of Oscillation in any of these bodies, may be found in the last cited book of Mr Zulichem.

[Page] If it be asked, What is the meaning of the Center of Oscillation? The most intelligible answer (altho not perfectly true) is, That it is that point of the Ball, at which if you imagine it divided into two parts, by a circle, whose center is in the point of Suspension, the lower part of the Ball shall be of the same weight (or near so) with the upper.

§ 4. Having thus fixed a Standard, I shall next shew how from thence to find the Vibrations, or Lengths of all other Pendulums. Which is done by this Rule, Hugen▪ Moor, ib [...] ▪ The squares of the Vibrations, bear the same Proportion to each other, as their Length [...] do. And so contrary wise. Wherefore to find the length of a Pend▪ say▪ As the Square of the Vibrations given: To the Square of 60 (the Standard):: So is the length of the Standard (viz. 39, 2) To the length of the Pend. sought.

If by the length, you would find the Vibrations, 'tis the reverse of the last Rule, viz. As the length proposed: To the Standard (39, 2):: So is the Square of 60 (the vibrations of the Standard): To the Vibrations sought.

[Page] Suppose for example, you would know what length a Pend. is, that vibrates 153 strokes in a minute. The Square of 153 (i. e. 153 times 153) is 23409. Say, 23409. 3600:: 39, 2. 6. A Pend. then that vibrates 153 in a minute, is about 6 inches long.

On the other hand, if you would know how many strokes a Pend. of 6 inches hath in a minute; Say, 6. 39, 2:: 3600. 23520. The square root whereof is 153, and somewhat more.

Note, Because 141120 is always the Product of the two middle terms multiplied together, therefore you need only to divide this number by the Square of the Vibrations, it gives the length sought: by the length, it gives the square of the Vibrations.

If you operate by the Logarithms, you will much contract your labour. For if you seek the length, 'tis but Substracting the Logarithm of the Square of the Vibrations, out of the Logarithm of 141120, which is 5. 149588, and the Remainder is the Logarithm of the length sought.

If you seek the Vibrations, it is but Substracting out of the aforesaid Logarithm [Page] 5. 149588, the Logarithm of the length given, and half the Residue is the Logarithm of the Vibrations required. The following examples will illustrate each particular.

To find the Length.

| Logarithms.
141120 | 5. 149588
153 Squared is 23409 | 4. 369382
Length is more than 6. | 0. 780206

To find the Vibrations.

| Logarithms.
141120 | 5. 149588
6 inches long | 0. 778151
Square of the Vibr. | 4. 371437
Square-toor, or numb. of Vibr. is 153, and somewhat more. | 2. 185718

According to the foregoing Directions▪ I have calculated the following Table▪ to Pendulums of various lengths: and have therein shewed the Vibrations in a minute, [Page] and an hour, from 1 to 100 inches. If any desire a more minute account, I refer Horolog. Disquis.him to Mr Smith's Tables in his late Book. The reason why his calculation and mine differ, is because he measureth the length of the Pend. from the point of Suspension, to the lower part of the Bob; and I only to the center of the Bob. His Standards are 6½ inches, and 41 inches; and mine is 39, 2, for the reasons aforegoing.

A Table of Swings in a Minute, and in an hour, to Pendulums of several lengths.

Pend. length in inches | Vibrat. in a Minute. | Vibrat. in an Hour.
1 | 375,7 | 22542
2 | 265,6 | 15936
3 | 216,9 | 13014
4 | 187,8 | 11268
5 | 168,0 | 10080
6 | 153,3 | 9204
7 | 142,0 | 8520
8 | 132,8 | 7968
9 | 125,2 | 7512
10 | 118,8 | 7128
20 | 84,0 | 5040
30 | 68,6 | 4116
39,2 | 60.0 | 3600
40 | 59,4 | 3264
50 | 53,1 | 3186
60 | 48,5 | 2910
70 | 44,9 | 2694
80 | 42,0 | 2520
90 | 39,6 | 2376
100 | 37,5 | 2250

[Page] The use of this Table is manifest, and needs no explication. As to the Decimals in the column of Minute-Swings, I have [...]dded them for the sake of calculating the column of Hour-Swings; which would have been judged false without them, and would not have been exactly true without them.

§ 5▪ I have but one thing more to add to this Chap. of Pendulums, and that is, [...]o Correct their Motion.

The usual way is, to screw up, or let down the Ball. In doing of which, a small alteration will make a considerable [...]ariation of Time: as you will find by calculation, according to the last paragraph. To prevent the inconvenience of [...]crewing the Ball too high, or low, Mr Smith hath contriv'd a very pretty Table Ibid. [...]or dividing the Nut of a Pendulum Screw, [...]o as to alter your Clock but a Second in [...]day. But by reason no Screw and Nut can be so made, as to be most exactly strait [...]nd true, therefore it may happen, that instead of altering your Watch to your mind, you may do quite contrary; as [...]nstead of letting the Ball down, you may raise it higher, by the false running [Page] of the Nut upon the Screw.

Considering this irremediable inconvenience, I am of opinion, that Mr Hugens's Ibid. de Centro Oscil. Prop. 23.way would do very well, added to this. His way is, To have a small Weight, or Bob, to slide up and down the Pend. rod, above the Ball (which is immoveable.) But I would rather advise, that the Ball be made to screw up and down, to bring the Pend. pretty neer its gauge: and that this little Bob should serve only for more nice corrections; as the alteration of a Second, or &c. Which it will do, better than the Great Ball. For a whole turn of this little Bob, will not affect the motion of the Pend. near so much as a small alteration of the Great Ball.

The Directions Mr Hugens gives, about this little Corrector, is, That it should be equal to the weight of the Wire, or Rod of the Pend., or about a 50th part of the weight of the Great Ball, which he appoints to be three pounds.

Perhaps this Bob may do its office, if it be made to screw only up and down the lower part of the Rod, below the Ball. If not, you must make it slide above the Ball, or be screwed up and down there.

[Page] Seeing this little Bob is not the only Corrector (as in Mr Zulichem's way) therefore it is not necessary to insert here, that ingenious person's Table, shewing what alterations of Time will be made by sliding the Bob up and down the rod. Only thus much may be observed in that Table of his, viz. That a small alteration of the Corrector towards the lower end of the Pend▪, doth make as great an alteration of Time, as a greater raising or falling of it, doth make higher. Thus the little Bob raised 7 divisions of the Rod, from the Center of Oscillation, will alter the Watch 15 seconds; raised 15, 2 'twill alter it 30″. But whereas, if it be raised to 154▪ 3 parts of the Rod, it will make the Watch go faster 3 minutes, 15 seconds, the Watch shall be but 3′. 30″ faster, if the Bob be raised to 192▪ 6. So that here you have but 15″ variation, by raising the Bob above 38 parts; whereas lower, you had the same variation, when raised not above 7 or 8 parts.

From what hath been said, it appears, that about half a turn of this little justening Bob, will at no time alter the Watch, above a second in 24 hours▪ and that [Page] above a whole turn, will not alter it so much, higher on the Rod; supposing that the Bob at every turn ascended or descended a whole degree of the Rod; which perhaps it will not do in 20 turns: and consequently, it will require many turns, to alter the Watch but one second.

CHAP. VI. The Antiquity, and general History of Watch, or Clock-work.

§ 1. IT is probable, that in all Ages, some Instruments or other have been used, for the Measuring of Time. But the earliest we read of, is the Dial of Ahaz. Concerning which, little of certainty 2 Kings [...]0▪ 11. Isai. 38. 8.can be said. The Hebrew word Ma [...]aloth doth properly signifie Degrees, Steps, or Stairs, by which we ascend to any place. And so this word Ma [...]aloth is rendered Ezek. 40. 26. And accordingly the LXXII translate the Ma [...]aloth of Ahaz, by the words [...], and ' [...], [Page] i. e. Steps or Ascents. The like doth the Syriack, Arabick, and other Versions.

Some pretend to give a description of this Dial of Ahaz: but it being meer guessing, and little to my purpose, I shall not trouble the Reader with the various opinions about it.

Among the Greeks and Romans, there were two ways chiefly used to measure their Hours. One was by Clepsydrae, or Hour▪ glasses. The other by the Solaria, or Sun-dials. The [...], says Suidas and Phavorinus, was [...] Lexic. in verbo [...] [...] i. e. An Astronomical Instrument, by which the Hours were measured. Also, That it was a Vessel, having a little hole in the bottom, which was set in the Courts of Judicature, full of water; by which the Lawyers pleaded. This was, says Phavorinus, to prevent babbling, that such as spake, ought to brief in their Speeches.

As to the Invention of those Waterwatches (which were, no doubt, of more common use, than only in the Law-Courts) De die Natali c. 23.the Invention, I say, of them, is attributed, by Censorinus, to P. Cornelius Nasica, the Censor (Scipio Nasica, Pliny calls him.)

[Page] The other way of measuring the Hours, Ibid.with Sun-dials, seems, from Pliny and Censorinus, to have been an earlier invention Nat. Hist. l. 2. c. 76.than the last. Pliny says, that Anaximenes Milesius, the Scholar of Anaximander, invented Dialling, and was the first that shewed a Sun-dial at Lacedoemon. Vitruvius De Archit. l. 6. c. 48.calls him Milesius Anaximander. This Anaximander or Anaximenes was cotemporary with Pythagoras, says Laertius; and flourished about the time of the Prophet Daniel.

But enough of these ancient Timeengines, which are not very much to my purpose, being not pieces of Watch-work.

§ I shall in the next place take notice of a few Horological Machines, that I have met with; which, whether pieces of Clock-work, or not, I leave to the Readers judgment.

In the Life of Dions The first is that of Dionysius, which Plutarch commends for a very magnificent, and illustrious Piece. But this might be only a well delineated Sun-dial.

Another Piece, is that of Sapor King of Persia. Whether that Sapor, who was Euseb. Vit. Const▪ l. 3.cotemporary with Constantine the Great, I [Page] [...]ow not. [...]ardan saith it was made of De Subtil▪ l. 17.Glass; that the King could sit in the middle of it, and see its Stars rise and set▪ But not finding whether this Sphere was moved by Clock-work, or whether it [...]ad any regular motion, I shall say no [...]ore concerning it.

The last Machine I shall mention in [...]his Paragraph, is one I find des [...]ribed by De Architect. l. 9. c. 9 [...] [...]itruvius. Which to me seems to be a piece of Watch-work, moved by an equal [...]nflux of Water.

If the Reader will consult the French [...]dition of Vitruvius, he will find there a [...]ir Cut of it.

Among divers seats which this Ma [...]hine performed (as sounding Trumpets, [...]hrowing Stones, &c.) one use of it was, [...]o shew the Hours (which were unequal [...]n that age) through every month of the [...]ear. The words of Vitruvius are, Aequa [...]iter influens aqua sublevat Scaphum inversum (quod [...]b artificibus Phellos sive Tympanam [...]icitur) in quo collocata regula▪ versatilia [...]mpana denticuli [...] a▪qualibus s [...]nt perfecta. [...]ui denticuli alius alium impelientes, ver [...]iones modicas faciant, ac motiones. Item [...] Reg [...]loe, aliaque Tympana ad eundem [Page] modum dentata, quoe una motione coacta, versando faciunt effectus, varietatesque motionum: in quibus moventur Sigilla, vertuntur Metoe, calculi aut Tona projiciuntur, Buccinoe canunt, &c. In his etiam, aut in colu [...]na, ant parastatica Horoe describuntur; quas Sigillum egrediens ab imo virguloe, significat, in diem totum: quarum brevitates ant crescentias, cuneorum adjectus aut exemptus, in singulis diebus & mensibus, perficere cogit.

The Inventer of this famous Machine, Vitruvius says, was one Ctesibius, a Barbers Son of Alexandria. Which Ctesibius flourished under Ptolomy Euergetes, says V [...]d. Phi [...]nd. not. in Vitruv. Athenoeus, l. 4. And if so, he lived about 240 years before our Saviours days; and might be cotemporary with Archimedes.

§ 3. Thus having given a small account of the ancient ways of Measuring Time, it is time to come closer to our business, and say something more particularly of Clock-work.

Which is thought to be a much younger invention, than the fore-mentioned Pieces; and to have had its beginning in Germany, within less than these 200 years.

It is very probable, that our Ballance [Page] Clocks, and some other Automata, might have their beginning there; or that Clock-work (which had long been buried in oblivion) might be revived there. But that Clock work was the Invention of that age purely, I utterly deny; having (besides what goes before) two instances to the contrary, of much earlier date.

§ 4. The first example is the Sphere of Archimedes; who lived about 200 years before our Saviours days. There is no mention of this Sphere in Archimedes his extant works: but we have an account of it in others. Cicero speaks of it more than once. In his 2d Book De Nature Deorum, are these words; ‘Archimedem arbitrantur plus valuisse in imitandis Sphoeroe conversionibus, quam Naturam in efficiendis, &c.’ And in his Tusculane Questions, Lib. 1. § 25. Edit. El [...]ivir.the Collocutor, proving the Soul to be of a Divine Nature, argues from this Contrivance of Archimedes, and says, Nam cum Archimedes Lunoe, Solis, quinque Errantium motus in Sphoeram illigavit, effecit, &c. The Sense is, That Archimedes contrived a Sphere, which shewed the motion of the Moon, Sun, and five Planets.

[Page] Epigr. in Sphoer. Archimed. Vid. Card. de Subtil. l. 17. But the most accurate description is that of Claudian, in these words.

Jupiter in parvo cum cerneret oethera vitro,

Risit, & ad Superos talia dicta dedit:

Huccine mortalis progressa potentia curoe?

Jam meus in fragili luditur or be labor.

Jura poli, rerumque fidem, leges (que) Deorum,

Ecce Syracusius transtulit arte Senex.

Inclusus variis famulatur Spiritus astris,

Et vivum certis motibus urget opus.

Percurrit proprium mentitus Signifer annum.

Et simulata novo Cynthia mense redit.

Jamque suum volvens audax industria mundum

Gaudet, & humana Sidera mente regit.

Quid falso insontem tonitru Salmonea miror?

Aemula Naturoe parva reperta manus.

In English thus:

When Jove espy'd in Glass his Heavens made,

He smil'd, and to the other Gods thus said:

Strange feats! when human art so far proceeds,

To ape in brittle Orbs my greatest deeds.

The heav'nly motions, Natures constant course,

Lo! here old Archimede to art transfers.

Th' inclosed Spirit here each Star doth drive;

And to the living work sure motions give.

[Page] The Sun in counterfeit his year doth run,

And Cynthia too her monthly circle turn.

Since now bold man has Worlds of's own descry'd

He joys, and th' Stars by human art can guide.

Why should we so admire proud Salmons cheats

When one poor hand Natures chief work repeats.

From this description it appeareth, that in this Sphere, the Sun, Moon, and other heavenly bodies, had their proper motion: and that this motion was effected by some enclosed Spirit. What this enclosed Spirit was, I cannot tell, but suppose it to be Springs, Wheels or Pullies, or some such means of Clock-work: Which be [...]ng hidden from vulgar eyes, might be [...]ken for some Angel, Spirit, or Divine power; unless by Spirit here, you un [...]erstand some aerious, subtiliz'd liquor, [...] vapours. But how this, or indeed any [...]hing, but Clock-work, could give such [...]ue, and regular motions, I am not able [...]o guess.

§ 5. The next instance I have met with [...] ancient Clock-work, is that famous [...]ne in Cicero, which, among other irre [...]agable De Nat. Deor. Lib. 2. § 34.arguments▪ is brought in to [...]ove, ‘That there is some intelligent, [Page] divine, and wise Being, that inhabiteth, ruleth in, and is as an Architect of so great a work, as the World is,’ as the Collocutor expresseth himself▪ His words (so far as they relate to my present purpose) are these: ‘Cum Solarium vel descriptum, aut ex Aqua contemplere, intelligere declarari horas arte,non casu, &c.’ And a little after, Quod si in Scythiam, aut in Britanniam, Sphaeram aliquis tulerit hanc, quam nuper familiaris noster effecit Posidonius, cujus singulae Conversiones idem efficiunt in Sole, & in Luna, & in quinque Stellis errantibus, quod efficitur in coelo singulis diebus, & noctibus; quis in illa barbarie dubitet, quin ea Sphaera sit perfecta ratione? The sum of the Authors meaning is, ‘That there were Sun-dials described, or drawn’ [with Lines, after the manner as our Sun-dials are:] ‘and some made with Water’(which were the Clepsydrae, or Hour-glasses, before-mentioned.) ‘That Posidonius had lately contrived a Sphere, whose Motions were the same in the Sun, Moon, and 5 Planets, as were performed in the heavens each day and night.’

[Page] The age wherein this Sphere was in [...]ented, was Cicero's time, which was a [...]out 80 years before our Saviours birth.

And that it was a piece of Clock-work, [...]s not (I think) to be doubted, if it be [...]onsidered, that it kept time with those [...]elestial bodies, imitating both their an [...]ual, and diurnal motions, as from the [...]escription we may gather it did.

It may be questioned, whether those Machines were common or not: I believe [...]hey were rarities then, as well as Mr Wat [...]n's and others are accounted now. But [...]nethinks it is hard to imagine, that so [...]seful an Invention should not be reduced [...]to common use; it being natural, and [...]sie to apply it to the measuring of [...]ours (tho unequal) especially in two [...]ch Ages, as those of Archimedes and [...]ully were, in which the Liberal Arts so greatly flourished.

§ 6. After the times last mentioned, I [...]nd little worth remark, till the last Age; [...] which Clock-work was revived, or [...]holly invented anew in Germany▪ as is [...]enerally thought, because the ancient [...]ieces are German work. But who was [...]e Inventer, or in what time, I cannot [Page] M [...]lyneaux, Scioth. Telescop. Ep. Dedic. discover. Some think Sever. Boethius invented it about the year 510. Perhaps it was in Regiomontanus his time (if not so early as Boethius) which was above 200 years ago. It is very manifest, it was before Cardan's time, because he speaketh of it, as a thing common then. And he lived about 150 years since.

§ 7. As to those curious contrivances in Clock-work, which perform strange, surprizing feats, I shall say little. Dr. Heylin Cosmog. l. 2.tells us of a famous Clock and Dial in the Cathedral Church of Lunden in Denmark. ‘In the Dial (saith he) are to be seen distinctly the Year, Month, Weekday, and Hour of every day throughout the Year; with the Feasts, both moveable and fixed; together with the Motion of the Sun and Moon, and their passage thro each degree of the Zodiack. Then for the Clock, it is so framed by artifical Engines, that whensoever it is to strike, two Horse-men encounter one another, giving as many blows apiece, as the Bell sounds hours: And on the opening of a door, there appeareth a Theatre, the Virgin Mary on a Throne, with Christ in her arms, and the three [Page] Kings or Magi (with their several trains) marching in order, doing humble reverence, and presenting severally their Gifts; two Trumpeters sounding all the while, to adorn the Pomp of that Procession.’

Magia Univers. P. 1. Proleg: & Magia Thaumaturg. To this I might add many more such curious performances; but I rather chuse to refer the Reader to Schottus, where he may find a great variety, to please him.

CHAP. VII. Of the Invention of Pendulum Watches.

§ 1. THe first that invented the way of applying Pendulums to Watch-work, was Mr Christian Hugens of Zulichem; as he affirmeth of himself, with very cogent reasons.

This excellent invention, he says, he put first in practice in the year 1657▪ and Hor. Oscil. p. 3▪ Edit. Paris.in the following year 1658, he printed a delineation and description of it.

[Page] Others have claimed the honour of this Invention; among which, the great Galileo hath the most to be said on his side. Dr. John Joachim Becher (who printed a Book when he was in England, entituled; De Nova Temporis dimetiendi ratione Theoria, &c. which he dedicated to the English Royal Society, Anno 1680.) he, I say, tells p. 8.us, ‘That the Count Magalotti (the Great Duke of Tuscany's Resident at the Emperors Court) told him the whole History of these Pendulum Clocks, and denied Mr Zulichem to be the Author of them.’ Also, ‘That one Treffler (Clock-maker to the Father of the then G. Duke of Tuscany) related to him the like History: and said moreover, That he had made the first Pend. Clock, at Florence, by the command of the Great Duke, and by the direction of his Mathematician Galilaeus a Galilaeo; a pattern of which was brought into Holland. And further he saith, That one Caspar Doms, a Fleming, and Mathematician to John Philip a Schonborn, the late Elector of Mentz) told him, that he had seen at Prague, in the time of Rudolphus the Emperor, a Pend. Clock, made by the famous Justus Borgen, Mechanick [Page] and Clock-maker to the Emperor: which Clock the great Tycho-Brahe used in his Astronomical observations.’

Exper▪ made in the Acad▪ del Cimento by Mr. Wal [...]er, p. 12. Thus far Becher. To which I may add, what is said by the Academie del Cimento, viz. ‘It was thought good to apply the Pendulum to the Movement of the Clock▪ a thing which Galilaeo first invented, and his Son Vincenzio Galilei put in practice in the year 1649.’

As to these matters thus related by hearsay by Becher, and so expressly affirmed by the Academy, I have little to reply, but that Mr Hugens does expressly say, He was the Inventer, and that if Galilaeo ever Hugen. ib.thought of any such thing, he never brought it to any perfection. It is certain, that this Invention never flourished till Mr Hugens set it abroad.

§ 2. After Mr Hugens had thus invented these Pendulum Watches, and caused several to be made in Holland, Mr Fromantil, a Dutch Clock-maker, came over into England, and made the first that ever were made here: which was about the year 1662. One of the first Pieces that was made in England, is now in Gresham-Colledg, given to that Honorable Society by [Page] the late eminent Seth, Lord Bishop of Salisbury: which is made exactly according to Mr Zulichem's directions.

§ 3. For several years this way of Mr Zulichem was the only method, viz. Crown-wheel Pendulums, to play between two cycloidal cheeks, &c. But afterwards Mr W. Clement, a London Clock-maker, Horolog. Disquis. p. 3.contrived them (as Mr Smith saith) to go with less weight, an heavier Ball (if you please) and to vibrate but a small compass. Which is now the universal method of the Royal Pendulums. But Dr Hook denies Mr Clement to have invented this; and says that it was his Invention, and that he caused a piece of this nature to be made, which he shewed before the R. Society, soon after the Fire of London.

§ 4. The Use of these Pendulum Watches Mr. Hugens setteth forth in several instances. Particnlarly, he giveth two examples of their great use at Sea, in discovering the Difference of Meridians, more exactly than any other way: which he deduceth from the Observations of an English, and French Ship.

On Land, they were found very serviceable, among other uses, particularly [Page] to these two. 1. To measure the time more exactly, and equally than the Sun. [...]. To be (as Sir Christoph. Wren first proposed) a perpetual, and universal Measure, or Standard, to which all Lengths may be reduced, and by which they may be udged, in all ages, and countries. For as our Royal Society, Mr Hugens, and Mountonus have proposed after Sir Christopher Wren) this Horary foot, or Tripedal length, which vib [...]teth Seconds, will fit ill ages and places▪ But then respect must be had to the Center of Oscillation, which you have an account of in Mr Hugens his [...]soresaid book, de Horologio Oscillatorio, [...]s hath before been said.

§ 5. There is one contrivance more of Pendulums, still behind, viz. the Circular Pendulum: which is mentioned by Mr Hugens as his own, but is claimed by the ngenious Dr. Hook as really his. This [...]end▪ doth not vibrate backward and forward, as [...]hose we have been speaking of [...]o; but always round, round; the String being suspended above, at the tripedal length, and the Ball fi [...]ed below, as suppose at the end of the fly of a common [...]ack.

[Page] The motion of this Circular Pend▪ is as regular, and much the same with what goeth before: and was thus far made very useful in Astronomical observations, by the said Dr Hook, viz. To give warning at any moment of its circumgyration, either when it had turned but a quarter, half, or any lesser, or greater part of its circle. So that here you had notice not only of a Second, but of the most minute part of a Second of Time. You may find a description of this Pendulum, and other matters belonging to it, in Dr Hook's Lectiones Cutlerianoe: Animad. in Hevelius Mach▪ Caelest. p. 60.

CHAP. VIII. Of the Invention of those Pocket-Watches, commonly called Pendulum Watches.

§ 1. THe reason they are called Pendulum-Watches, is from the regularity of their Strokes, and Motion. [Page] Which exactness is effected by the government of a small Spiral Spring, running round the upper part of the Verge of the Ballance: which Spring is called the Regulator.

§ 2. The first Inventer hereof, was [...]hat ingenious and learned member of our Royal-Society, Dr Hook: who contrived va [...]ious ways of Regulation. One way was [...]ith a Load-stone: another was with a [...]nder strait Spring▪ one end whereof [...]layed backward, and forward, with the [...]allance: So that the ballance was to this [...]pring as the bob of a Pendulum, and the [...]ttle Spring, as the Rod thereof. And se [...]eral other contrivances he had besides of [...]is nature.

§ 3. But the Invention which best an [...]ered expectation, was at first, with two [...]llances: of which I have seen two sorts, [...]ho there were several others. One [...]ay was without Spiral Springs, the [...]her with. They both agreed in this, [...]hat the outward Rims of both the Bal [...]nces, had alike number of Teeth; which [...]nning in each other, caused each Bal [...]nce to vibrate alike.

[Page] But as to the former of these, which had no Spiral Spring▪ the Verges of its Ballances, had each but one Pallet apiece, about the middle of the Verge. The Crown-wheel lay (contrary to others) reversed, in the middle of the Watch, in the place, and after the manner of the Contrate-wheel. The teeth of this Crown-wheel, were cut after the manner of Contrate-wheel teeth, viz. lying upwards, but very wide apart, so as that the Pallets (which were about one tenth of an inch long, and n [...]rrow) might play in and out between each tooth. The Verges of the two Ballances, were set one on one side, the other on the other side of the Crown-wheel, so that the Pallets might play freely in its teeth. And when the Crown-wheel in moving round, had delivered its self of one Pallet, the other Pallet on the opposite side, was drawn on to make its Beat, by means of the motion which the other Ballance had given its Ballance, (the two Ballances moving one another, as hath been said in the beginning of this Paragraph.) And so the same back again.

[Page] It may be here noted, that for the more clear understanding of the last contrivance, I have described the two Ballances, as having Teeth on the edges of their Rims, running in one another. But the contrivance was really thus▪ There was a small Wheel under each Ballance, proportioned to the width of the Crown-wheel. But the Ballances were much larger. And so the Teeth of these two little foresaid Wheels or Ballances, running in one another, moved the larger Ballances above them, all one, as if these two great Ballances had been toothed and played in each other.

§ 4. The other way, with two Ballances also, moving each other (as was said in the beginning of the last §) had a Spiral Spring to each Ballance, for its Regulator. In this Invention, only one Ballance had the Pallets, as the common Ballances have: and the Crown-wheel operated upon it, according to the usual way. But then when this Ballance vibrateth, it giveth the same motion backward and forward, to the other ballance; as hath been said.

[Page] The first of these two ways, was never prosecuted so far, as perhaps it deserved. And the excellency of the latter is, that no jirk, or the most confused shake, can in the least alter its Vibrations. Which it will do in the best Pendulum Watch with one ballance now commonly used. For if you lay one of these Watches upon a Table, and by the Pendant jirk it backward and forward, you will put it into the greatest hurry; whereas the last mentioned Watch, with two ballances, will be nothing affected with it. But notwithstanding this inconvenience, yet the Watch with one ballance and one Spring (which was also Dr. Hooks Invention) prevailed, and grew common, being now the universal Mode: but of the other very few were ever made. The reason hereof, I judge, was the great trouble and vast niceness required in it, and perhaps a little foulness in the ballance-teeth may retard the motion of the ballances. But the other is easier made, and performeth well enough, and in a pocket is scarce subject to the aforesaid disorder, which is caused rather by a turn, than a shake.

[Page] § 5. The time of these Inventions was about the year 1658, as appears (among other evidence) from this inscription, upon one of the aforesaid double Ballance-Watches, presented to K. Charles II, viz. Robert Hook inven. 1658. T. Tompion fecit 1675.

This Watch was wonderfully approved of by the King; and so the Invention grew into reputation, and was much talked of at home, and abroad. Particularly its same flew into France, from whence the Dauphine sent for two; which that eminent Artist Mr. Tompion made for him.

§ 6. Dr. Hook had long before this, caused several pieces of this nature, to be made, altho they did not take till after 1675. However he had before so far proceeded herein, as to have a Patent (drawn, tho not sealed) for these, and some other Contrivances, about Watches, in the year 1660. But the reason why that Patent did no further proceed, was some disagreement about some Articles in it, with some Noble Persons who were concerned for the procuring it. The same ingenious Dr. had also a Grant for a Patent for this last way of Spring Watches [Page] in the year 1675: but he omitted the taking it out, as thinking it not worth the while.

§ 7. After these Inventions of Dr. Hook, and (no doubt) after the Publication of Mr. Hugens's book de Horolog. Oscil. at Paris 1673 (for there is not a word of this, tho of several other Contrivances) after this, I say, Mr. Hugen's Watch with a Spiral Spring came abroad, and made a great noise in England, as if the Longitude could be now found. One of these the Lord Bruncker sent for out of France, (where Mr Hugen [...] had a Patent for them) which I have seen.

This Watch of Mr. Zulichem's agreed with Dr. Hook's, in the application of the Spring to the ballance: only Mr. Zulichem's had a longer Spiral Spring, and the Pulses and Beats were much slower. That wherein it differs, is 1. The Verge hath a Pinion instead of Pallets; and a Contrate-wheel runs therein, and drives it round, more than one turn. 2. The Pallets are on the Arbor of this Contrate-wheel. 3. Then followeth the Crown wheel, &c. 4. The ballance, instead of turning scarce quite round (as Dr. Hook's) doth turn several rounds every vibration.

[Page] § 8. As to the great abilities of Mr. Hugens, no man can doubt, that is acquainted with his Books, and his share in the Philosophical Transactions, &c. But I have some reason to doubt, whether his fancy was not first set on work, by some Intelligence he might have of Dr Hook's Invention, from Mr Oldenburgh, or others his correspondents here in England.

But whether or no that ingenious person doth owe any thing herein to our ingenious Dr Hook, it is however a very pretty, and ingenious contrivance; but subject to some defects: viz. When it standeth still, it will not vibrate, until it is set on vibrating: which, tho it be no defect in a Pendulum Clock, may be one in a Pocket-Watch, which is exposed to continual jogs. Also, it doth somewhat vary in its Vibrations, making sometimes longer, sometimes shorter turns, and so some slower some quicker vibrations.

I have seen some other contrivances of this sort, which I mention not, because they are of younger standing. But these two (of Dr Hook and Mr Hugens) I have taken notice of, because they were the first that ever appeared in the world.

CHAP. IX. The Invention of Repeating Clocks.

[Page]

§ 1. THe Clocks I now shall speak of, are such as by pulling of a String, &c. do strike the Hour, Quarter, or Minute, at any time of the day and night.

§ 2. These Clocks are a late Invention of one Mr Barlow, of no longer standing than the latter end of K. Charles II. about the year 1676.

This ingenious Contrivance (scarce so much as thought of before) soon took air, and being talked of among the London Artists, set their heads to work; who presently contrived several ways to effect such a performance. And hence arose the divers ways of Repeating work, which so early might be observed to be about the Town, every man almost practising, according to his own Invention.

[Page] § 3. This Invention was practised chief [...], if not only, in larger Movements, [...] K. James II.'s Reign: at which time it as transferred into Pocket-Clocks. But [...]ere being some little contest concern [...]g the Author hereof, I shall relate the [...]e matter of fact, leaving the Reader to [...]own judgment.

About the latter end of K. James II.'s [...]gn, Mr Barlow (the ingenious Inventer [...]ore-mentioned) contrived to put his [...]ention into Pocket▪watches; and en [...]voured (with the Lord Chief Justice [...]bone, and some others) to get a Patent [...]it. And in order to it, he set Mr Tom [...] the famous Artist, to work upon it: [...]o accordingly made a Piece according [...]is directions.

[...]r Quare (a very ingenious Watch▪ [...]er in London) had some years before [...] thinking of the like Invention: but bringing it to perfection, he laid by thoughts of it, until the talk of Mr Bar [...] Patent revived his former thoughts; [...]ch he then brought to effect. This [...]g known among the Watch-makers, [...] all pressed him to endeavour to hin [...] Mr Barlow's Patent. And accordingly [Page] applications were made at Court, and a Watch of each Invention, produced before the King and Council. The King, upon tryal of each of them, was pleased to give the preference to Mr Quare's: of which, notice was given soon after in the Gazette.

The difference between these two Inventions was, Mr Barlow's was made to Repeat by pushing in two pieces on each side the Watch-box: one of which Repeated the Hour, the other the Quarter▪ Mr Quare's was made to Repeat, by a [...] Pin that stuck out near the Pendant which being thrust in (as now 'tis done by thrusting in the Pendant) did Repeat both the Hour, and Quarter, with the sam [...] thrust.

It would (I think) be very frivolous, to [...] speak of the various contrivances, and methods of Repeating work, and the Inventers of them; and therefore I shall sa [...] nothing of them.

CHAP. X.

[Page]

Numbers for several sorts of Movements.

I Think it may be very convenient to set down some Numbers, fit for several Movements; partly, to be as Examples to exercise the young Reader, in the foregoing Art of Calculation: and partly, 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 writing down their Numbers, which is somewhat 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;

[Page]

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 Report [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 inconvenient in Calculation) representeth a piece of work handsomely enough, and somewhat naturally.

§ 2. Numbers of an 8 day Piece, with 16 turns the Barrel, the Pend. vibrates Seconds, 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

[Page] 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 Pinion 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 [Page] the same Spindle. And when two numbers 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 Countwheel 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

[Page] 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

[Page] § 5. A piece of 13 weeks, with Pendulum, 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 |

[Page] § 7. A Year Piece, of 384 days, with Turns, Pendulum, and Motions, as before.

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.

[Page]

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.

[Page]

The Watch part.

10) 90 | Or thus▪ with a Wheel less, and not to shew Minutes and Seconds.
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 Numbers, 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

[Page]

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 depend upon a Wheel going 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 [Page] of Saturn, may be the two first of Jupiter also.

By the permission of my ingenious friend Mr Flamsteed, I here insert a description of Mr Olaus Romer, the French King's Mathematician's Instrument, to represent the Motion of Jupiter's Satellites; 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 asoresaid Wheels. The first is a Wheel, or Pinion of 22 leaves, driven by the Wheel 87, which carrieth round the first Satellite. The second is 32, driven by the Wheel 63, which carrieth round the second 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 pointeth to a circle divided into 168 parts, which are the hours in 7 days.

[Page] 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 fixed, with a little Ball at the top, representing 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 distance from Jupiter's Globule) to represent the 4 Satellites going round that Planet.

§ 4. Numbers for Mars, whose Revolution is 1 year 322 days.

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

§ 5. Numbers for Venus, whose Revolution is in 224 days.

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

§ 6. Numbers for Mercury, whose Revolution is near 88 days.

[Page]

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 Copernican, 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

[Page] § 2. Another of the same, without Minutes 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

[Page] § 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 foregoing Book. The way in short is this: Divide 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 instead of 6) 96 (16 thus, viz. 5) 80 (16: i. e. chusing the Pinion only 5, and multiplying it by 16 (the turns) the Wheel will be 80.

CHAP. XI

[Page]

Tables of Time relating to Watch-work.

A Table of Time.

Seconds. |  |  |  |  |  |
60 | Minutes. |  |  |  |  |
3600 | 60 | Hours. |  |  |  |
86400 | 1440 | 24 | Day. |  |  |
604800 | 10080 | 168 | 7 | Week. |  |
2592000 | 43200 | 720 | 30 | 4 | Month. |
31536000 | 525600 | 8760 | 365 | 52 | 12 | Year.

The foregoing Table will be of good use in Calculation, for the ready finding out the parts of Time: which is thus. Find the parts of time you seek for, the number in the concurrence of Squares, is the answer to your question. Thus, suppose you seek for the number of Seconds [Page] [...]n a Year: in the Square under Seconds, and in the same line with Year (which is the [...]owermost Square on the left hand) is the number sought, viz. 315, &c. So Minutes in a Month, are 43200.

If you would know any number, where there is the addition of an odd number to it, as the Seconds in a Month and one day; add the Seconds in a month (which are 259—) and the Seconds in a Day (which are 86—) and you have the number sought, viz. 2678400.

A Table to set a Watch by the Fixed Stars▪

Night | Hour. | Min. | Sec. | Night | Hour. | Min. | Sec.
1 | 0 | 3 | 57 | 16 | 1 | 3 | 20
2 | 0 | 7 | 54 | 17 | 1 | 7 | 17
3 | 0 | 11 | 51 | 18 | 1 | 11 | 14
4 | 0 | 15 | 47 | 19 | 1 | 15 | 11
5 | 0 | 19 | 44 | 20 | 1 | 19 | 8
6 | 0 | 23 | 41 | 21 | 1 | 23 | 5
7 | 0 | 27 | 38 | 22 | 1 | 27 | 1
8 | 0 | 31 | 35 | 23 | 1 | 30 | 58
9 | 0 | 35 | 32 | 24 | 1 | 34 | 55
10 | 0 | 39 | 29 | 25 | 1 | 38 | 52
11 | 0 | 43 | 26 | 26 | 1 | 42 | 49
12 | 0 | 47 | 23 | 27 | 1 | 46 | 46
13 | 0 | 51 | 29 | 28 | 1 | 50 | 43
14 | 0 | 55 | 26 | 29 | 1 | 54 | 40
15 | 0 | 59 | 23 | 30 | 1 | 58 | 36

[Page]

Explanation of the Table.

This Table shews how much the Sidereal, goeth faster than the Solar day, in any number of nights for a month. So that observing by your Watch, the nice time when any fixed Star cometh to the Meridian, or any other point of the Heavens: if after one Revolution of that same Star to the same point, your Watch goeth 3′. 57″ [...]lower than the Star; or after two nights 7′. 54″; or 16 nights, 1 h. 3′. 20″, &c. then doth your Watch keep time rightly with the Mean motion of the Sun. If it vary from the Table, you must alter the length of your Pend▪ to make it so keep time.

To observe the time nicely, when the Star cometh again to the same point of the heavens, 'tis necessary to make the observation with a Telescope, that hath cross threads in the focus of the object-glass; and so leaving the Telescope fixed in the same posture, till a second Observation. You may do this with the telescopular sights of a Quadrant, or Sextans, and so leaving it standing until anoher night of Observation. Or for want of this more nice way, you may do it by looking along by the edge of two Strings, suspended with Plumbets, [Page] in a room, at some distance from one another. Or by looking at the edge of a Chimney, &c. as Mr Watson hath directed, at the end of Mr Smith's Horo [...]. Disquis. But to make a tolerable observation any of these last ways, 'tis necessary to have a Candle shine upon the edge of the furthermost String, or Chimney; without which you cannot see exactly when the Star cometh thereto.

A Table shewing the Variations made in the true Hour of the Day, by the Refraction of ▪the Sun in the Equator, and both the Solstices.

Sun's altitude. Deg. | Sun's Refraction. | Variation at the N. Solstice. | Variation at the Equator. | Variation at the S. Solstice.
′ | ″ | ′ | ″ | ′ | ″ | ′ | ″
00 | 33 | 00 | 4 | 34 | 3 | 32 | 4 | 38
1 | 23 | 00 | 2 | 34 | 2 | 28 | 3 | 19
2 | 17 | 00 | 2 | 24 | 1 | 49 | 2 | 31
3 | 13 | 30 | 1 | 46 | 1 | 27 | 2 | 3
4 | 11 | 30 | 1 | 29 | 1 | 12 | 1 | 40
5 | 9 | 30 | 1 | 12 | 1 | 1 | 1 | 33
6 | 7 | 30 | 0 | 56 | 0 | 49 | 1 | 17
7 | 7 | 00 | 0 | 52 | 0 | 44 | 1 | 16
8 | 6 | 00 | 0 | 43 | 0 | 39 | 1 | 8
9 | 5 | 00 | 0 | 36 | 0 | 34 | 1 | 2
10 | 4 | 40 | 0 | 25 | 0 | 29 | 1 | 2

[Page]

Remarks upon the Table.

The Column of the Sun's Refractions, I owe to that accurate observer of the celestial motions, Mr▪ Flamsteed. Which Refractions, altho in the Table the same, yet do differ at different seasons of the year, nay perhaps, according to the different temperature of the air sometimes, in the same day. Thus Mr Flamsteed found the Refractions in February, very different from those in April: and it is observed, that the Refractions are commonly greater, when the Mercury is higher in the Barometer.

The Table therefore doth not shew what the Refractions always are, but only about the middle quantity of them, at every degree, of the 10 first of the Sun's altitude. And accordingly I have calculated the Variations thereby made in the hour of the day.

These Variations of the hour are greater or lesser, according as the angle of the Sun's diurnal motion is acuter with the horizon. The reason is plain; because as the Sun appears by refraction higher than [Page] really he is; so this false height doth affect the hours in Winter, more than the Summer half year.

There is no ray indeed of the Sun, but what cometh refracted to a Sun▪dial▪ and consequently, there is no Dial but what goeth more or less false (except at Noon in Dials that cast a Shade, where the refraction makes no variation▪) But the Refraction decreaseth apace, as the Sun gets higher, and causeth a variation of not above half a minute, at 10 degrees of the Sun's altitude; except when the Sun is in, or near the Southern Tropick. Nearer than half a minute, few common Sun-dials shew the time. And therefore, partly for this reason, and partly, because Mr. Flamsteed's observations reach not much farther, I have calculated my Table to only 10 degrees.

The Table needs little explication. For having the Sun's height, you have against it, in the next Column, the Refraction▪ and in the 3 next the alterations of the hour, at 3 times of the year. Taking therefore by a Quadrant the Sun's altitude, and observe at the same time, the hour of the day by a Sun-dial, by the Table, [Page] you see how many minutes, and seconds, the Dial is too fast. As at the Sun-rising a Sun-dial is too fast 4′. 34″, about June 11, and 3′. 32″, about Mar. 10. and Sept. 12, and 4′ 38″ about Dec. 11.

Addenda.

[Page]

TO the Fifth part of the Rule in § 6. p. 21. If you have occasion to lay the Pinion of Report upon any other Wheel, and not the great-Wheel, you may do it by this Rule, As the Beats in one turn of any Wheel; To the Beats in an hour:: So are the hours of the Dial; To the Quotient of the Hour-wheel divided by the Pinion of Report.

To page 66. Suppose in altering an old Watch, you would have it shew minutes, as well as hours; you may do it thus: Divide the Beats in one turn of the Great-wheel, by the Beats in an hour; the Quotient will shew in how many hours the Great-wheel goeth round once. If the Beats in the Great wheel exceed the Train, you must chuse your Minute-wheel first, and multiply it by the Quotient; this will give the Pin. of Report. But if the Train exceeds the Beats of the Great-wheel, you must chuse the Pin. of Rep. and multiply the Quotient by it: the product is the Minute-wheel.

[Page] But it often falls out, that the Train and Beats of the Great-wheel will not exactly measure one another: if so, the best way is to half the two numbers, as far as they will equally admit of halfing; or divide them by some common divisor, and so having brought them to as small numbers as you can, you may suppose them to be a Wheel and Pinion, and reduce them to lesser numbers▪ by Chap. 2. Sect. 2. § 5. Thus suppose you would make the old dull Movement there mentioned, a Minute-watch; you may reduce the numbers of the Great-wheel 2188 [...] ▪ and the Train 9368, to a Pinion and Wheel 28) 12. Which Pin. 28 being set upon the Spingle of the Gr. Wh. will drive a Wheel 12 round once in an hour, to shew Minutes. If you make this▪ Wh. 12 drive another of 48; (concentrical to which, is a Pin. 12 driving a Wheel 36 (which Wheel is concentrical with the Minute-wheel) this will carry a Hand round in 12 hours. But in this case, you must place the Pin. 28 on the Spindle of the Gr. Wh. so as to slide round stiffly, when you turn the Minutehand to rectifie the Watch.

FINIS.

Information about this book

Title statement

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.

Derham, W. (William), 1657-1735.

Edition statement

1696

Publication

Publisher

Text Creation Partnership,

Place of publication

Ann Arbor, MI ; Oxford (UK) :

Date

2008-09 (EEBO-TCP Phase 1).

ID [DLPS]

A35722

ID [STC]

Wing D1099

ID [STC]

ESTC R24292

ID [EEBO-CITATION]

08118750

ID [OCLC]

ocm 08118750

ID [VID]

40878

Availability

This keyboarded and encoded edition of the work described above is co-owned by the institutions providing financial support to the Early English Books Online Text Creation Partnership. This Phase I text is available for reuse, according to the terms of Creative Commons 0 1.0 Universal. The text can be copied, modified, distributed and performed, even for commercial purposes, all without asking permission.

Series

Early English books online.

Notes

(EEBO-TCP ; phase 1, no. A35722)

Transcribed from: (Early English Books Online ; image set 40878)

Images scanned from microfilm: (Early English books, 1641-1700 ; 1227:17)

Source

— 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., Derham, W. (William), 1657-1735..

Extent

[10], 132 p., [1] leaf of plates : ill.

Printed for James Knapton,. London :: 1696.. (Reproduction of original in the Bodleian Library.)

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