a machine constructed in such a manner, and regulated so by the uniform motion of a pendulum (a), as to measure time, and all its subdivisions, with great exactness.

The invention of clocks with wheels is referred to Pacificus, archdeacon of Verona, who lived in the time of Lotharius son of Louis the Debonnaire, on the credit of an epitaph quoted by Ughelli, and borrowed by him from Panvinius. They were at first called nocturnal dials, to distinguish them from sun-dials, which showed the hour by the sun's shadow. Others ascribe the invention to Boethius, about the year of 510. Mr Derham makes clock-work of a much older standing; and ranks Archimedes's sphere mentioned by Claudian, and that of Posidonius mentioned by Cicero, among the machines of this kind: not that either their form or use were the same with those of ours, but that they had their motion from some hidden weights or springs, with wheels, or pulleys, or some such clockwork principle. But be this as it will, it is certain the art of making clocks, such as are now in use, was either first invented, or at least retrieved, in Germany, about 200 years ago. The water-clocks, or clepsydrae, and sun-dials, have both a much better claim to antiquity. The French annals mention one of the former kind sent by Aaron, king of Persia, to Charlemagne, about the year 807, which seemed to bear some resemblance to the modern clocks: it was of brass, and showed the hours by twelve little balls of the same metal, which fell at the end of each hour, and in falling struck a bell and made it sound. There were also figures of 12 cavaliers, which at the end of each hour came forth at certain apertures or windows in the side of the clock, and shut them again, &c.

The invention of pendulum clocks is owing to the happy industry of the last age: the honour of it is disputed by Huygens and Galileo. The former, who has written a volume on the subject, declares it was first put in practice in the year 1657, and the description thereof printed in 1658. Becher, de Nova Temporis dimetendi Theoria, anno 1650, contends for Galileo; and relates, though at second-hand, the whole history of the invention; adding, that one Treller, clock-maker to the then father of the Grand Duke of Tuscany, made the first pendulum-clock at Florence, by direction of Galileo Galilei; a pattern of which was brought into Holland. The Academy de' Cimento say expressly, that the application of the pendulum to the movement of a clock was first proposed by Galileo, and first put in practice by his son Vincenzo Galilei, in 1649. Be the inventor who he will, it is certain the invention never flourished till it came into Huygens's hands, who insists on it, that if ever Galileo thought of such a thing, he never brought it to any degree of perfection. The first pendulum-clock made in England was in the year 1662, by Mr Fromantil a Dutchman.

Amongst the modern clocks, those of Strasbourg and Lyons are very eminent for the richness of their furniture, and the variety of their motions and figures. In the first, a cock claps his wings, and proclaims the hour; the angel opens a door, and salutes the virgin; and the Holy Spirit descends on her, &c. In the second, two horsemen encounter, and beat the hour on each other: a door opens, and there appears on the theatre the Virgin, with Jesus Christ in her arms; the Magi, with their retinue, marching in order, and presenting their gifts; two trumpeters sounding all the while to proclaim the procession. These, however, are excelled by two lately made by English artists, and intended as a present from the East India company to the emperor of China. The clocks we speak of are in the form of chariots, in which are placed, in a fine attitude,

(a) A balance not unlike the fly of a kitchen-jack was formerly used in place of the pendulum. attitude, a lady, leaning her right hand upon a part of the chariot, under which is a clock of curious workmanship, little larger than a shilling, that strikes and repeats, and goes eight days. Upon her finger sits a bird finely modelled, and fet with diamonds and rubies, with its wings expanded in a flying posture, and actually flutters for a considerable time on touching a diamond button below it; the body of the bird (which contains part of the wheels that in a manner give life to it) is not the bigness of the 16th part of an inch. The lady holds in her left hand a gold tube not much thicker than a large pin, on the top of which is a small round box, to which a circular ornament fet with diamonds not larger than a sixpence is fixed, which goes round near three hours in a constant regular motion. Over the lady's head, supported by a small fluted pillar no bigger than a quill, is a double umbrella, under the largest of which a bell is fixed at a considerable distance from the clock, and seems to have no connection with it; but from which a communication is secretly conveyed to a hammer, that regularly strikes the hour, and repeats the same at pleasure, by touching a diamond button fixed to the clock below. At the feet of the lady is a gold dog; before which from the point of the chariot are two birds fixed on spiral springs; the wings and feathers of which are fet with filons of various colours, and appear as if flying away with the chariot, which, from another secret motion, is contrived to run in a straight, circular, or any other direction; a boy that lays hold of the chariot, behind, seems also to push it forward. Above the umbrella are flowers and ornaments of precious stones; and it terminates with a flying dragon fet in the same manner. The whole is of gold, most curiously executed, and embellished with rubies and pearls.

Of the general Mechanism of Clocks, and how they measure Time. The first figure of Plate CXLVI. is a profile of a clock: P is a weight that is suspended by a rope that winds about the cylinder or barrel C, which is fixed upon the axis a o; the pivots b b go into holes made in the plates TS, TS, in which they turn freely. These plates are made of brass or iron, and are connected by means of four pillars ZZ; and the whole together is called the frame.

The weight P, if not restrained, would necessarily turn the barrel C with an uniformly accelerated motion, in the same manner as if the weight was falling freely from a height. But the barrel is furnished with a ratchet wheel KK, the right side of whose teeth strikes against the click, which is fixed with a screw to the wheel DD, as represented in fig. 2, so that the action of the weight is communicated to the wheel DD, the teeth of which act upon the teeth of the small wheel d which turns upon the pivots c c. The communication or action of one wheel with another is called the pitching; a small wheel like d is called a pinion, and its teeth are leaves of the pinion. Several things are requisite to form a good pitching, the advantages of which are obvious in all machinery where teeth and pinions are employed. The teeth and pinion leaves should be of a proper shape, and perfectly equal among themselves; the size also of the pinion should be of a just proportion to the wheel acting into it; and its place must be at a certain distance from the wheel, beyond or within which it will make a bad pitching.

Vol. VI. Part I.

The wheel E E is fixed upon the axis of the pinion d; and the motion communicated to the wheel DD by the weight is transmitted to the pinion d, consequently to the wheel E E, as likewise to the pinion e and wheel F F, which moves the pinion f, upon the axis of which the crown or balance wheel G H is fixed. The pivots of the pinion f play in holes of the plates L M, which are fixed horizontally to the plates T S. In a word, the motion begun by the weight is transmitted from the wheel G H to the palettes I K, and by means of the fork U X riveted on the palettes, communicates motion to the pendulum A B, which is suspended upon the hook A. The pendulum A B describes, round the point A, an arc of a circle alternately going and returning. If then the pendulum be once put in motion by a push of the hand, the weight of the pendulum at B will make it return upon itself; and it will continue to go alternately backward and forward till the resistance of the air upon the pendulum, and the friction at the point of suspension at A, destroys the originally impelled force. But as, at every vibration of the pendulum, the teeth of the balance-wheel G H, act upon the palettes I K (the pivots upon the axis of these palettes play in two holes of the potence s t), that after one tooth H has communicated motion to the palette K, that tooth escapes; then the opposite tooth G acts upon the palette I, and escapes in the same manner; and thus each tooth of the wheel escapes the palettes I K, after having communicated their motion to the palettes in such a manner that the pendulum, instead of being stopped, continues to move.

The wheel E E revolves in an hour; the pivot e of the wheel passes through the plate, and is continued to r; upon the pivot is a wheel NN, with a long socket fastened in the centre; upon the extremity of this socket r the minute-hand is fixed. The wheel NN acts upon the wheel O; the pinion of which p acts upon the wheel g g, fixed upon a socket which turns along with the wheel N. This wheel g g makes its revolution in 12 hours, upon the socket of which the hour-hand is fixed.

From the above description it is easy to see, 1. That the weight p turns all the wheels, and at the same time continues the motion of the pendulum. 2. That the quickness of the motion of the wheels is determined by that of the pendulum. 3. That the wheels point out the parts of time divided by the uniform motion of the pendulum.

When the cord from which the weight is suspended is entirely run down from off the barrel, it is wound up again by means of a key, which goes on the square end of the arbor at Q, by turning it in a contrary direction from that in which the weight descends. For this purpose, the inclined side of the teeth of the wheel R (fig. 2.) removes the click C, so that the ratchet-wheel R turns while the wheel D is at rest; but as soon as the cord is wound up, the click falls in between the teeth of the wheel D, and the right side of the teeth again act upon the end of the click, which obliges the wheel D to turn along with the barrel; and the spring A keeps the click between the teeth of the ratchet-wheel R.

We shall now explain how time is measured by the motion of the pendulum; and how the wheel E, upon the axis of which the minute-hand is fixed, makes but one precise revolution in an hour. The vibrations of a pendulum are performed in a shorter or longer time in proportion to the length of the pendulum itself. A pendulum of 3 feet 8 French lines in length, makes 3600 vibrations in an hour, i.e., each vibration is performed in a second of time, and for that reason it is called a second pendulum. But a pendulum of 9 inches 2 French lines makes 7200 vibrations in an hour, or two vibrations in a second of time, and is called a half second pendulum. Hence, in constructing a wheel whose revolution must be performed in a given time, the time of the vibrations of the pendulum which regulates its motion must be considered. Supposing, then, that the pendulum AB makes 7200 vibrations in an hour, let us consider how the wheel E shall take up an hour in making one revolution. This entirely depends on the number of teeth in the wheels and pinions. If the balance-wheel consists of 30 teeth, it will turn once in the time that the pendulum makes 60 vibrations; for at every turn of the wheel, the same tooth acts once on the pallets I, and once on the pallets K, which occasions two separate vibrations in the pendulum; and the wheel having 30 teeth, it occasions twice 30, or 60 vibrations. Consequently, this wheel must perform 120 revolutions in an hour; because 60 vibrations, which it occasions at every revolution, are contained 120 times in 7200, the number of vibrations performed by the pendulum in an hour. Now, in order to determine the number of teeth for the wheels E, F, and the pinions e, f, it must be remarked, that one revolution of the wheel E must turn the pinion e as many times as the number of teeth in the pinions is contained in the number of teeth in the wheel. Thus, if the wheel E contains 72 teeth, and the pinion e 6, the pinion will make 12 revolutions in the time that the wheel makes 1; for each tooth of the wheel drives forward a tooth of the pinion, and when the 6 teeth of the pinion are moved, a complete revolution is performed; but the wheel E has by that time only advanced 6 teeth, and has still 66 to advance before its revolution be completed, which will occasion 11 more revolutions of the pinion. For the same reason, the wheel F having 60 teeth, and the pinion f 6, the pinion will make 10 revolutions while the wheel performs one. Now, the wheel F being turned by the pinion e, makes 12 revolutions for one of the wheel E; and the pinion f makes 10 revolutions for one of the wheel F; consequently, the pinion f performs 10 times 12 or 120 revolutions in the time the wheel E performs one. But the wheel G, which is turned by the pinion f, occasions 60 vibrations in the pendulum each time it turns round; consequently the wheel G occasions 60 times 120 or 7200 vibrations of the pendulum while the wheel E performs one revolution; but 7200 is the number of vibrations made by the pendulum in an hour, and consequently the wheel E performs but one revolution in an hour; and so of the rest.

From this reasoning, it is easy to discover how a clock may be made to go for any length of time without being wound up: 1. By increasing the number of teeth in the wheels; 2. By diminishing the number of teeth in the pinions; 3. By increasing the length of the cord that suspends the weight; 4. By increasing the length of the pendulum; and, 5. By adding to the number of wheels and pinions. But, in proportion as the time is augmented, if the weight continues the same, the force which it communicates to the last wheel GH will be diminished.

It only remains to take notice of the number of teeth in the wheels which turn the hour and minute hands.

The wheel E performs one revolution in an hour; the wheel NN, which is turned by the axis of the wheel E, must likewise make only one revolution in the same time; and the minute-hand is fixed to the socket of this wheel. The wheel N has 30 teeth, and acts upon the wheel O, which has likewise 30 teeth, and the same diameter; consequently the wheel O takes one hour to a revolution: now the wheel O carries the pinion p, which has 6 teeth, and which acts upon the wheel q of 72 teeth; consequently the pinion p makes 12 revolutions while the wheel q makes one, and of course the wheel q takes 12 hours to one revolution; and upon the socket of this wheel the hour-hand is fixed. All that has been said here concerning the revolutions of the wheels, &c. is equally applicable to watches as to clocks.

The ingenious Dr Franklin contrived a clock to show the hours, minutes, and seconds, with only three wheels and two pinions in the whole movement. The dial-plate (fig. 3.) has the hours engraved upon it in spiral spaces along two diameters of a circle containing four times 60 minutes. The index A goes round in four hours, and counts the minutes from any hour by which it has passed to the next following hour. The time, therefore, in the position of the index shown in the figure is either 32½ minutes past XII. III. or VIII.; and so in every other quarter of the circle it points to the number of minutes after the hours which the index last left in its motion. The small hand B, in the arch at top, goes round once in a minute, and shows the seconds. The wheel-work of this clock may be seen in fig. 4. A is the first or great wheel, containing 160 teeth, and going round in four hours with the index A in fig. 3. let down by a hole on its axis. This wheel turns a pinion B of 10 leaves, which therefore goes round in a quarter of an hour. On the axis of this pinion is the wheel C of 120 teeth; which goes round in the same time, and turns a pinion D of eight leaves round in a minute, with the second hand B of fig. 3. fixed on its axis, and also the common wheel E of 30 teeth for moving a pendulum (by pallets) that vibrates seconds, as in a common clock. This clock is wound up by a line going over a pulley on the axis of the great wheel, like a common thirty-hour clock. Many of these admirably simple machines have been constructed, which measure time exceedingly well. It is subject, however, to the inconvenience of requiring frequent winding by drawing up the weights, and likewise to some uncertainty as to the particular hour shown by the index A. Mr Ferguson has proposed to remedy these inconveniences by the following construction. In the dial-plate of his clock (fig. 5.) there is an opening, a b c d, below the centre, through which appears part of a flat plate, on which the 12 hours, with their divisions into quarters, are engraved. This plate turns round in 12 hours; and the index A points out the true hour, &c. B is the minute-hand, which goes round the large circle of 60 minutes whilst the plate \(a b c d\) shifts its place one hour under the fixed index \(A\). There is another opening, \(e f g\), through which the seconds are seen on a flat moveable ring at the extremity of a fleur-de-lis engraved on the dial-plate. In fig. 6, is the great wheel of this clock, containing 120 teeth, and turning round in 12 hours. The axis of this wheel bears the plate of hours, which may be moved by a pin passing through small holes drilled in the plate, without affecting the wheel-work. The great wheel \(A\) turns a pinion \(B\) of ten leaves round in an hour, and carries the minute hand \(B\) on its axis round the dial-plate in the same time. On this axis is a wheel \(C\) of 120 teeth, turning round a pinion \(D\) of six leaves in three minutes; on the axis of which there is a wheel \(E\) of 90 teeth, that keeps a pendulum in motion, vibrating seconds by palettes, as in a common clock, when the pendulum-wheel has only 30 teeth, and goes round in a minute. In order to show the seconds by this clock, a thin plate must be divided into three times sixty, or 180 equal parts, and numbered 10, 20, 30, 40, 50, 60, three times successively; and fixed on the same axis with the wheel of 90 teeth, so as to turn round near the back of the dial-plate; and these divisions will show the seconds through the opening \(e f g\), fig. 5. This clock will go a week without winding, and always show the precise hour; but this clock, as Mr Ferguson candidly acknowledges, has two disadvantages of which Dr Franklin's clock is free. When the minute-hand \(B\) is adjusted, the hour-plate must also be set right by means of a pin; and the fineness of the teeth in the pendulum-wheel will cause the pendulum ball to describe but small arcs in its vibrations; and therefore the momentum of the ball will be less, and the times of the vibrations will be more affected by any unequal impulse of the pendulum-wheel on the palettes. Besides, the weight of the flat ring on which the seconds are engraved will load the pivots of the axis of the pendulum-wheel with a great deal of friction, which ought by all possible means to be avoided. To remedy this inconvenience, the second plate might be omitted.

A clock similar to Dr Franklin's was made in Lincolnshire about the end of last century or beginning of this; and is now in London in the possession of a grandson of the person who made it.

A clock, showing the apparent diurnal motions of the sun and moon, the age and phases of the moon, with the time of her coming to the meridian, and the times of high and low water, by having only two wheels and a pinion added to the common movement, was contrived by Mr Ferguson, and described in his Select Exercises. The dial-plate of this clock (fig. 7.) contains all the twenty-four hours, of the day and night. \(S\) is the sun, which serves as an hour index by going round the dial-plate in twenty-four hours; and \(M\) is the moon, which goes round in twenty-four hours fifty minutes and a half, the time of her going round in the heavens from one meridian to the same meridian again. The sun is fixed to a circular plate (see fig. 8.) and carried round by the motion of that plate on which the twenty-four hours are engraved; and within them is a circle divided into twenty-nine and a half equal parts for the days of the moon's age, reckoning from new moon to new moon; and each day stands directly under the time, in the twenty-four hour circle of the moon's coming to the meridian; the XII under the sun standing for noon, and the opposite XII for midnight. The moon \(M\) is fixed to another circular plate (fig. 6.) of the same diameter with that which carries the sun, part of which may be seen through the opening, over which the small wires \(r\) and \(b\) pass in the moon-plate. The wire \(a\) shows the moon's age and time of her coming to the meridian, and \(b\) shows the time of high-water for that day in the sun-plate. The distance of these wires answers to the difference of time between the moon's coming to the meridian and high-water at the place for which the clock is made. At London their difference is two hours and a half. Above the moon-plate there is a fixed plate \(N\), supported by a wire \(A\), joined to it at one end, and fixed at right angles into the dial-plate at the midnight XII. This plate may represent the earth, and the dot \(I\), London, or the place to which the clock is adapted. Around this plate there is an elliptic shade on the moon-plate, the highest points of which are marked high-water, and the lowest low-water. As this plate turns round below the plate \(N\), these points come successively even with \(L\), and stand over it at the times when it is high or low water at the given place; which times are pointed by the sun \(S\) on the dial-plate; and the plate \(H\) above XII at noon rises or falls with the tide. As the sun \(S\) goes round the dial-plate in twenty-four hours, and the moon \(M\) in twenty-four hours fifty minutes and a half, it is plain that the moon makes only twenty-eight revolutions and a half, whilst the sun makes twenty-nine and a half; so that it will be twenty-nine days and a half from conjunction to conjunction. And thus the wire \(a\) shifts over one day of the moon's age on the sun-plate in twenty-four hours. The phases of the moon for every day of her age may be seen through a round hole \(m\) in the moon-plate; thus, at conjunction or new-moon, the whole space seen through \(m\) is black; at opposition or full moon this space is white; at either quadrature half black and half white; and at every position the white part resembles the visible part of the moon for every day of her age. The black shaded space \(NfF\) (fig. 8.) on the sun-plate serves for these appearances. \(N\) represents the new moon, \(F\) the full moon, and \(f\) her first quarter, and \(l\) her last quarter, &c. The wheel-work and tide-work of this clock are represented in fig. 9. \(A\) and \(B\) are two wheels of equal diameters: \(A\) has fifty-seven teeth, with a hollow axis that passes through the dial of the clock, and carries the sun-plate with the sun \(S\). \(B\) has fifty-nine teeth, with a solid spindle for its axis, which turns within the hollow axis of \(A\), and carries the moon-plate with the moon \(M\); both wheels are turned round by a pinion \(C\) of nineteen leaves, and this pinion is turned round by the common clock-work in eight hours; and as nineteen is the third part of fifty-seven, the wheel \(A\) will go round in twenty-four hours; and the wheel \(B\) in twenty-four hours fifty minutes and a half; fifty-seven being to twenty-four as fifty-nine to twenty-four hours fifty minutes and a half very nearly. On the back of the wheel \(B\) is fixed an elliptical ring \(D\), which, in its revolution, raises and lets down a lever \(EF\), whose centre of motion is on a pin at \(F\); and this, by the up- Clock right bar G, raises and lets down the tide-plate H twice in the time of the moon's revolving from the meridian to the meridian again: this plate moves between four rollers R, R, R, R. A clock of this kind was adapted by Mr Ferguion to the movement of an old watch: the great wheel of a watch goes round in four hours; on the axis of this he fixed a wheel of twenty teeth, to turn a wheel of forty teeth on the axis of the pinion C; by which means that pinion was turned round in eight hours, the wheel A in twenty-four, and the wheel B in twenty-four hours fifty minutes and a half.

To this article we shall subjoin a brief account of two curious contrivances. The first, for giving motion to the parts of a clock by making it descend along an inclined plane, is the invention of Mr Maurice Wheeler; the clock itself was formerly seen in Don Saltero's coffee-house at Chelsea. DE, fig. 10, is the inclined plane on which the clock ABC descends; this consists externally of a hoop about an inch broad, and two sides or plates standing out beyond the hoop about one-eighth of an inch all round, with indented edges, that the clock may not slide, but turn round whilst it moves down. One of these plates is inscribed with the twenty-four hours, which pass successively under the index LP, fig. 11, which is always in a position perpendicular to the horizon, and shows the hour on the top of the machine: for this reason the lower part of the index, or HL, is heaviest, that it may preponderate the other HP, and always keep it pendulous, with its point to the vertical hour, as the movement goes on. Instead of this index, an image may be fixed for ornament on the axis g, which with an erected finger performs the office of an index. In order to describe the internal part or mechanism of this clock, let LETQ be the external circumference of the hoop, and f the same plate, on which is placed the train of wheel-work 1, 2, 3, 4, which is much the same as in other clocks, and is governed by a balance and regulator as in them. But there is no need of a spring and fusee in this clock; their effects being otherwise answered, as we shall see. In this machine the great wheel of 1 is placed in the centre, or upon the axis of the movement, and the other wheels and parts towards one side, which would therefore prove a bias to the body of the clock, and cause it to move, even on a horizontal plane, for some short distance: this makes it necessary to fix a thin plate of lead at C, on the opposite part of the hoop, to restore the equilibrium of the movement. This being done, the machine will abide at rest in any position on the horizontal plane HH; but if that plane be changed into the inclined plane DE, it will touch it in the point D; but it cannot rest there, because the centre of gravity at M acting in the direction MI, and the point T having nothing to support it, must continually descend, and carry the body down the plane. But now if any weight P be fixed on the other side of the machine, such as shall remove the centre of gravity from M to the point V in the line LD which passes through the point D, it will then rest upon the inclined plane, as in the case of the rolling cylinder. If this weight P be supposed not fixed, but suspended at the end of an arm, or vectis, which arm or lever is at the same time fastened to a centrical wheel r, moving on the axis M of the machine, which wheel by its teeth shall communicate with the train of wheels, &c., on the other side, and the power of the weight be just equal to the friction or resistance of the train, it will remain motionless as it did before when it was fixed; and consequently the clock also will be at rest on the inclined plane. But supposing the power of the weight P to be superior to the resistance of the train, it will then put it into motion, and of course the clock likewise; which will then commence a motion down the plane; while the weight P, its vectis PM, and the wheel r, all constantly retain the same position which they have at first when the clock begins to move. Hence it is easy to understand, that the weight P may have such an intrinsic gravity as shall cause it to act upon the train with any required force, so as to produce a motion in the machine of any required velocity; such, for instance, as shall carry it once round in twenty-four hours: then, if the diameters of the plates ABC be four inches, it will describe the length of their circumference, viz. 12.56 inches, in one natural day; and therefore, if the plane be of a sufficient breadth, such a clock may go several days, and would furnish a perpetual motion, if the plane were infinitely extended. Let SD be drawn through M perpendicular to the inclined plane in the point D; also let LD be perpendicular to the horizontal line HH, passing through D; then is the angle HDE = LDS = DMT; whence it follows that the greater the angle of the plane's elevation is, the greater will be the arch DT; and consequently the further will the common centre of gravity be removed from M; therefore the power of P will be augmented, and of course the motion of the whole machine accelerated. Thus it appears, that by duly adjusting the intrinsic weight of P, at first to produce a motion showing the mean time as near as possible, the time may be afterwards corrected, or the clock made to go faster or slower by raising or depressing the plane, by means of the screw at S. The angle to which the plane is first raised is about ten degrees. The marquis of Worcester is also said to have contrived a watch that moved on a declivity. See farther Phil. Trans. Abr. vol. i. p. 468, &c. or N° 161.

The other contrivance is that of M. de Gennes for making a clock ascend on an inclined plane. To this end let ABC (fig. 12.) be the machine on the inclined plane EDE, and let it be kept at rest upon it, or in equilibrium by the weight P at the end of the lever PM. The circular area CF is one end of a spring barrel in the middle of the movement, in which is included a spring as in a common watch. To this end of the barrel the arm or lever PM is fixed upon the centre M; and thus, when the clock is wound up, the spring moves the barrel, and therefore the lever and weight P in the situation PM. In doing this, the centre of gravity is constantly removed farther from the centre of the machine, and therefore it must determine the clock to move upwards, which it will continue to do as long as the spring is unbinding itself; and thus the weight and its lever PM will preserve the situation they first have, and to do the office of a chain and fusee. Phil. Trans. N° 140. or Abridg. vol. i. p. 467.

By flat. 9 and 10 W. III. cap. 28. § 2. no person shall export, or endeavour to export out of this kingdom, dom, any outward or inward box-case or dial-plate, of gold, silver, brass, or other metal, for clock or watch, without the movement in or with every such box, &c., made up fit for use, with the maker's name engraven thereon; nor shall any person make up any clock or watch without putting his name and place of abode or freedom, and no other name or place, on every clock or watch; on penalty of forfeiting every such box, case, and dial-plate, clock and watch, not made up and engraven as aforesaid; and 20l. one moiety to the king, the other to those that shall sue for the same.

portable, or pocket, commonly denominated Watches. See the article WATCH.

Clock-Work, properly so called, is that part of the movement which strikes the hours, &c. on a bell; in contradistinction to that part of the movement of a clock or watch which is designed to measure and exhibit the time on a dial-plate, and which is termed Watch-work.

1. Of the Clock-part. The wheels composing this part are: The great or first wheel H, which is moved by the weight or spring at the barrel G; in fifteen or thirty-hour clocks, this has usually pins, and is called the pin-wheel; in eight-day pieces, the second wheel I is commonly the pin-wheel, or striking-wheel, which is moved by the former. Next the striking-wheel is the detent-wheel, or hoop-wheel K, having a hoop almost round it, wherein is a vacancy at which the clock locks. The next is the third or fourth wheel, according to its distance from the first, called the warning-wheel L. The last is the flying pinion Q, with a fly or fan, to gather air, and to bridle the rapidity of the clock's motion. To these must be added the pinion of report, which drives round the locking-wheel, called also the count-wheel; ordinarily with eleven notches in it, unequally distant, to make the clock strike the hours.

Besides the wheels, to the clock part belongs the ratchet or ratch; a kind of wheel with twelve large fangs, running concentrical to the dial-wheel, and serving to lift up the detents every hour, and make the clock strike: the detents or stops, which being lifted up and let fall, lock and unlock the clock in striking; the hammer, as S, which strikes the bell R; the hammer-tails, as T, by which the striking pins draw back the hammers; latches, whereby the work is lifted up and unlocked; and lifting-pieces, as P, which lift up and unlock the detents.

The method of calculating the numbers of a piece of clock-work having something in it very entertaining, and at the same time very easy and useful, we shall give our readers the rules relating thereto: 1. Regard here needs only be had to the counting-wheel, striking-wheel, and detent-wheel, which move round in this proportion: the court-wheel commonly goes round once in 12 or 24 hours; the detent wheel moves round every stroke the clock strikes, or sometimes but once in two strokes: wherefore it follows, that, 2. 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 the pin-wheel are the quotients of that wheel divided by the pinion of the detent-wheel. But if the detent-wheel moves but once round in two strokes of the clock, then the said quotient is but half the number of pins. 3. As many turns of the pin-wheel as are required to perform the strokes of 12 hours (which are 78), so many turns must the pinion of report have to turn round the count-wheel once; or thus the quotient of 78, divided by the number of striking-pins, shall be the quotient for the pinion of report and the count-wheel; and this is in case the pinion of report be fixed to the arbor of the pin-wheel, which is commonly done.

An example will make all plain: The locking-wheel being 48, the pinion of report 8, the pin-wheel 78, the striking pins are 13, and so of the rest. Note also, that 78 divided by 13 gives 6, the quotient of the pinion of report. As for the warning-wheel and fly-wheel, it matters little what numbers they have; their use being only to bridle the rapidity of the motion of the other wheels.

The following rules will be of great service in this calculation.

1. To find how many strokes a clock strikes in one turn of the fusee or barrel: As the turns of the great wheel or fusee are to the days of the clock's continuance; so is the number of strokes in 24 hours, viz. 156, to the strokes of one turn of the fusee.

2. To find how many days a clock will go: As the strokes in 24 hours are to those in one turn of the fusee; so are the turns of the fusee to the days of the clock's going.

3. To find the number of turns of the fusee or barrel: As the strokes in one turn of the fusee are to those of 24 hours; so is the clock's continuance to the turns of the fusee or great wheel.

4. To find the number of leaves in the pinion of report on the axis of the great wheel: As the number of strokes in the clock's continuance is to the turns of the fusee; so are the strokes in 12 hours, viz. 78, to the quotient of the pinion of report fixed on the arbor of the great wheel.

5. To find the strokes in the clock's continuance: As 12 is to 78; so are the hours of the clock's continuance to the number of strokes in that time.

By means of the following table, clocks and watches may be so regulated as to measure true equal time.

The stars make 366 revolutions from any point of the compass to the same point again in 365 days and one minute; and therefore they gain a 365th of a revolution every 24 hours of mean solar time, near enough for regulating any clock or watch.

This acceleration is at the rate of 5 min. 55 sec. 53 thirds, 59 fourths in 24 hours; or in the nearest round numbers, 5 minutes, 56 seconds; by which quantity of time every star comes round sooner than it did on the day before.

Therefore if you mark the precise moment shown by a clock or watch when any star vanishes behind a chimney, or any other object, as seen through a small hole in a thin plate of metal, fixed in a window-shutter; and do this for several nights successively (as suppose twenty); if, at the end of that time, the star vanishes as much sooner than it did the first night, by the clock, as answers to the time denoted in the table for so many days, the clock goes true; otherwise not.

If the difference between the clock and star be less than the table shows, the clock goes too fast; if greater, it goes too slow; and must be regulated accordingly, by letting down or raising up the ball of the pendulum, by little and little, by turning the screw-nut under the ball, till you find it keeps true equal time.

Thus supposing the star should disappear behind a chimney, any night when it is XII. by the clock; and that, on the 20th night afterward, the same star should disappear when the time is 41 minutes 22 seconds past X. by the clock; which being subtracted from 12 hours o min. o sec. leaves remaining 1 hour 18 minutes 40 seconds for the time the star is then faster than the clock: look in the table, and against 20, in the left-hand column, you will find the acceleration of the star to be 1 hour 18 min. 40 sec., agreeing exactly with what the difference ought to be between the clock and star; which shows that the clock measures true equal time, and agrees with the mean solar time, as it ought to do.

II. Of the Watch-part of a clock or watch. This is that part of the movement which is designed to measure and exhibit the time on a dial-plate; in contradiction to that part which contributes to the striking of the hour, &c.

The several members of the watch-part are, 1. The balance, consisting of the rim, which is its circular part; and the verge, which is its spindle; to which belong two pallets or leaves, that play in the teeth of the crown-wheel. 2. The potence, or pontace, which is the strong fluid in pocket-watches, wheron the lower pivot of the verge plays, and in the middle of which one pivot of the balance-wheel plays; the bottom of the pontace is called the foot, the middle part the nose, and the upper part the shoulder. 3. The cock, which is the piece covering the balance. 4. The regulator, or pendulum spring, which is the small spring, in the new pocket-watches, underneath the balance. 5. The pendulum (fig. 13); whose parts are, the verge x, pallets s, s, cocks y, y, the rod, the fork z, the flat t, the bob or great ball 3, and the corrector or regulator, 4, being a contrivance of Dr Derham for bringing the pendulum to its nice vibrations. 6. The wheels, which are the crown-wheel F in pocket-pieces, and swing-wheel in pendulums; serving to drive the balance or pendulum. 7. The contrate-wheel E, which is that next the crown-wheel, &c.; and whose teeth and hoop lie contrary to those of other wheels; whence the name. 8. The great, or first wheel C; which is that the fusee B, &c. immediately drives, by means of the chain or string of the spring-box or barrel A; after which are the second wheel D, third wheel, &c. Lastly, between the frame and dial-plate, is the pinion of report, which is that fixed on the arbor of the great wheel; and serves to drive the dial wheel, as that serves to carry the hand.

For the illustration of this part of the work which lies concealed, let A.B.C (fig. 14.) represent the uppermost side of the frame-plate, as it appears when detached from the dial-plate: the middle of this plate is perforated with a hole, receiving that end of the arbor of the centre wheel, which carries the minute hand; near the plate is fixed the pinion of report a b of 10 teeth; this drives a wheel c d of 40 teeth; this wheel carries a pinion e f of 12 teeth; and this again drives a wheel g h with 36 teeth.

As in the body of the watch the wheels every where divide the pinions; here, on the contrary, the pinions divide the wheels, and by that means diminish the motion, which is here necessary; for the hour hand, which is carried on a socket fixed on the wheel g h, is required to move but once round, while the pinion a b moves twelve times round. For this purpose the motion of the wheel c d is \( \frac{1}{4} \) of the pinion a b. Again, while the wheel c d, or the pinion e f, goes once round, it turns the wheel g h but \( \frac{1}{4} \) part round; consequently the motion of g h is but \( \frac{1}{4} \) of \( \frac{1}{4} \) of the motion of a b; but \( \frac{1}{4} \) of \( \frac{1}{4} \) is \( \frac{1}{16} \); i.e. the hour-wheel g h moves once round in the time that the pinion of report, on the arbor of the centre of the minute wheel, makes 12 revolutions, as required. Hence the structure of that part of a clock or watch which shows the time may be easily understood.

The cylinder A (fig. 13.) put into motion by a weight or inclosed spring moves the fusee B, and the great wheel C, to which it is fixed by the line or cord that goes round each, and answers to the chain of a watch.

The method of calculation is easily understood by the sequel of this article; for, suppose the great wheel C goes round once in 12 hours, then if it be a royal pendulum clock, vibrating seconds, we have \( 60 \times 60 \times 12 = 43200 \) seconds or beats in one turn of the great wheel. But because there are 60 swings or seconds in one minute, and the seconds are shown by an index on the end of the arbor of the swing-wheel, which in these clocks is in an horizontal position; therefore, it is necessary that the swing-wheel F should have 30 teeth; whence \( \frac{43200}{30} = 1440 \), the number to be broken into quotients for finding the number of teeth for the other wheels and pinions.

In spring-clocks, the disposition of the wheels in the watch part is such as is here represented in the figure, where the crown-wheel F is in an horizontal position; the seconds not being shown there by an index, as is done in the large pendulum clocks. Whence in these clocks the wheels are disposed in a different manner, as represented in fig. 14. where C is the great wheel, and D the centre or minute wheel, as before; but the contrate wheel E is placed on one side, and F the swing-wheel is placed with its centre in the same perpendicular line GH with the minute-wheel, and with its plane perpendicular to the horizon, as are all the others. Thus the minute and hour hands turn on the end of the arbor of the minute-wheel at a, and the second hand on the arbor of the swing-wheel at b.

Theory and calculation of the Watch-part, as laid down by The same motion, it is evident, may be performed either by one wheel and one pinion, or many wheels and many pinions; provided the number of turns of all the wheels bear the proportion to all the pinions which that one wheel bears to its pinion: or, which is the same thing, if the number produced by multiplying all the wheels together be to the number produced by multiplying all the pinions together, as that one wheel to that one pinion. Thus, suppose you had occasion for a wheel of 1440 teeth, with a pinion of 28 leaves; you make it into three wheels of 36, 8, and 5, and three pinions of 4, 7, and 1. For the three wheels, 36, 8, and 5, multiplied together, give 1440 for the wheels, and the three pinions 4, 7, and 1, multiplied together, give 28 for the pinions. Add, that it matters not in what order the wheels and pinions are set, or which pinion runs in which wheel; only, for convenience sake, the biggest numbers are commonly put to drive the rest.

2. Two wheels and pinions of different numbers may perform the same motion. Thus, a wheel of 36 drives a pinion of 4; the same as a wheel of 45 a pinion of 5; or a wheel of 90 a pinion of 10; the turns of each being 9.

3. If, in breaking the train into parcels, any of the quotients should not be liked; or if any other two numbers, to be multiplied together, are desired to be varied; it may be done by this rule. Divide the two numbers by any other two numbers which will measure them; multiply the quotients by the alternate divisors; the product of these two last numbers found will be equal to the product of the two numbers first given. Thus, if you would vary 46 times 8, divide these by any two numbers which will evenly measure them: so, 36 by 4 gives 9; and 8 by 1 gives 8; now, by the rule, 9 times 1 is 9, and 8 times 4 is 32; so that for 36 X 8, you have 32 X 9; each equal to 288. If you divide 36 by 6 and 8 by 2, and multiply as before, you have 24 X 12 = 36 X 8 = 288.

4. If a wheel and pinion fall out with cros numbers, too big to be cut in wheels, and yet not to be altered by these rules; in seeking for the pinion of report, find two numbers of the same, or a near proportion, by this rule: as either of the two given numbers is to 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 exactly measures 360), or by any of those numbers that bring a quotient nearest to an integer. As suppose you had 147 for the wheel, and 170 for the pinion; which are too great to be cut into small wheels, and yet cannot be reduced into less, as having no other common measure but unity; say, as 170 : 147 :: 360 : 311. Or, as 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; divide them by 8, you have 39 and 45; and if you divide 360 and 416 by 8, you have 45 and 52 exactly. Therefore, instead of the two numbers 147 and 170, you may take 52 and 60, or 39 and 45, or 45 and 52, &c.

5. To come to practice in calculating a piece of watch-work: First pitch on the train or beats of the balance in an hour; as, whether a swift one of about 20,000 beats (the usual train of a common 30 hour pocket-watch), or a slower of about 16,000 (the train of the new pendulum pocket-watches), or any other train. Next, resolve on the number of turns the fusee is intended to have, and the number of hours the piece is to go: suppose, e.g., 12 turns, and to go 30 hours, or 192 hours (i.e., 8 days), &c. Proceed now to find the beats of the balance or pendulum in one turn of the fusee; thus in numbers; 12 : 16 :: 20000 : 26666. Therefore, 26666 are the beats in one turn of the fusee or great wheel, and are equal to the quotients of all the wheels unto the balance multiplied together. Now this number is to be broken into a convenient parcel of quotients; which is to be done thus: first, halve the number of beats, viz., 26666, and you have 13333; then pitch on the number of the crown-wheel, suppose 17: divide 13333 by 17, and you have 784 for the quotient (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. Choose therefore three numbers; which, when multiplied all together continually, will come nearest 784: as suppose 10, 9, and 9, multiplied continually, give 810, which is somewhat too much; therefore try again other numbers, 11, 9, 8: these, drawn one into another continually, produce 792; which is as near as can be, and is a convenient quotient. Having thus contrived the piece from the great wheel to the balance, but the numbers not falling out exactly, as you first proposed, correct the work thus: first multiply 792, the product of all the quotients pitched upon, by 17 (the notches of the crown-wheel); the product is 13464, which is half the number of beats in one turn of the fusee: Then find the true number of beats in an hour. Thus, 16 : 12 :: 13464 : 10098, which is half the beats in an hour. Then find what quotient is to be laid upon the pinion of report (by the rule given under that word). Thus, 16 : 12 :: 12 : 9, the quotient of the pinion of report. Having thus found your quotients, it is easy to determine what numbers the wheels shall have, for choosing what numbers the pinions shall have, and multiplying the pinions by their quotients, the product is the number for the wheels. Thus, the number of the 4) 36 (9 pinion of report is 4, and its quotient is 9; therefore the number for the dial-wheel must be 4 X 9, or 36: so the next pinion being 5, its quotient 11, therefore the great wheel must be 5 X 11 = 55; and so of the rest.

Such is the method of calculating the numbers of a 16 hour watch. Which watch may be made to go longer by lessening the train, and altering the pinion of report. Suppose you could conveniently slacken the train to 16000; then lay, As ½ 16000, or 8000 : 13464 :: 12 : 203 so that this watch will go 20 hours. Then for the pinion of report, say (by the rule given under that word), as 20 : 12 :: 12 : 7. So that 7 is the quotient of the pinion of report. And as to the numbers, the operation is the same as before, only the dial-wheel is but 28; for its quotient is altered to 7. If you would give numbers to a watch of about 10,000 beats in an hour, to have 12 turns of the fusee, to go 170 hours, and 17 notches in the crown-wheel; the work Clock. is the same, in a manner, as in the last example; and consequently thus: as \(12 : 170 : : 10000 : 141666\), which fourth number is the beats in one turn of the fusee; its half, \(70833\), being divided by 17, gives 4167 for the quotient; and because this number is too big for three quotients, therefore choose four, as 10, 8, 8, 6\(\frac{1}{2}\); whose product into 17 makes 71808, nearly equal to half the true beats in one turn of the fusee. Then say, as \(170 : 12 : 71808 : 5069\), which is half the true train of your watch. And again, \(170 : 12 : 12 : \frac{1}{2} : \frac{1}{2}\), the denominator of which expresses the pinion of report, and the numerator is the number of the dial-wheel. But these numbers being too big to be cut in small wheels, they must be varied by the fourth rule above. Thus:

\[ \begin{align*} &\text{As } 144 : 170 : : 360 : 425 : \\ &\text{Or } 170 : 144 : : 360 : 305. \end{align*} \]

24) 20 (\(\frac{2}{3}\)) Then dividing 360, and either of these two fourth proportional (as directed by 6) 60 (10 the rule), suppose by 15; you will have 6) 48 (\(8 \frac{4}{5}\) or \(\frac{3}{4}\)); then the numbers of the whole 5) 40 (8 movement will stand as in the margin. 5) 33 (\(6 \frac{1}{2}\)) Such is the calculation of ordinary watches, to show the hour of the day: 17 in such as show minutes, and seconds, the process is thus:

1. Having resolved on the beats in an hour; by dividing the designed train by 60, find the beats in a minute; and accordingly, find proper numbers for the crown-wheel and quotients, so as that the minute-wheel shall go round once in an hour, and the second wheel once in a minute.

Suppose, you shall choose a pendulum of seven inches, which vibrates 142 strokes in a minute, and 8520 in an hour. Half these sums are 71, and 4260. Now, the first work is to break this 71 into a good proportion, which will fall into one quotient, and the crown-wheel. Let the crown-wheel have 15 notches; then 71, divided by 15, gives nearly 5; so a crown-wheel of 15, and a wheel and pinion whose quotient is 5, will go round in a minute to carry a hand to show seconds. For a hand to go 8) 40 (5 round in an hour to show minutes, there are 60 minutes in an hour, it is but 15 breaking down into good quotients (suppose 10 and 6, or 8 and 7\(\frac{1}{2}\) &c.): and it is 8) 64 (8 done. Thus, 4260 is broken as near as 8) 60 (7\(\frac{1}{2}\) can be into proper numbers. But since it 8) 40 (5 does not fall out exactly into the above-mentioned numbers, you must correct (as 15 before directed), and find the true number of beats in an hour, by multiplying 15 by 5, which makes 75; and 75 by 60 makes 4500, which is half the true train. Then find the beats in one turn of the fusee; thus, \(16 : 192 : : 4500 : 54000\); which last is half the beats in one turn of the fusee. This 54000 being divided by 4500 (the true 9) 108 (12 numbers already pitched on), the quo- 8) 64 (8 tient will be 12; which, not being too big 8) 60 (7\(\frac{1}{2}\) for a single quotient, needs not be divided 8) 40 (5 into more; and the work will stand as in the margin. As to the hour hand, the great wheel, which performs only one revolution in 12 turns of the minute-wheel, will show the hour; or it may be done by the minute-wheel.

It is requisite for those who make nice astronomical observations, to have watches that make some exact number of beats per second, without any fraction; but we seldom find a watch that does. As four beats per second would be a very convenient number, we shall here give the train for such a watch, which would (like most others) go 30 hours, but is to be wound up once in 24 hours.

The fusee and first wheel to go round in four hours. This wheel has 48 teeth, and it turns a pinion of 12 leaves, on whose axis is the second wheel, which goes round in one hour, and carries the minute-hand. This wheel has 60 teeth, and turns a pinion of 10 leaves; on whose axis is the third wheel of 60 teeth, turning a pinion of 6 leaves; on whose axis is the fourth (or contrate) wheel, turning round in a minute, and carrying the small hand that shows the seconds, on a small circle on the dial-plate, divided into 60 parts: this contrate wheel has 48 teeth, and turns a pinion of 6 leaves; on whose axis is the crown or balance-wheel of 15 teeth, which makes 30 beats in each revolution.

The crown-wheel goes 480 times round in an hour, and 30 times 480 make 14400, the number of beats in an hour. But one hour contains 3600 seconds; and 14400 divided by 3600 quotes 4, the required number of beats in a second.

The fusee must have 7\(\frac{1}{2}\) turns, to let the chain go so many times round it. Then, as 1 turn is to 4 hours, so 7\(\frac{1}{2}\) turns to 30 hours, the time the watch would go after it is wound up.

See further the articles Movement, Turn, &c. And for the history and particular construction of Watches properly so called, see the article Watch.