in the art of war, a number of men posted at any passage, or a company of the guards who go on the patrol.

in the navy, the space of time wherein one division of a ship's crew remains upon deck, to perform the necessary services, whilst the rest are relieved from duty, either when the vessel is under sail or at anchor.

The length of the sea-watch is not equal in the shipping of different nations. It is always kept four hours by our British seamen, if we except the dog-watch, between four and eight in the evening, that contains two reliefs, each of which are only two hours on deck. The intent of this is to change the period of the night-watch every 24 hours; so that the party watching from eight till 12 in one night, shall watch from midnight till four in the morning on the succeeding one. In France the duration of the watch is extremely different, being in some places six hours, and in others seven or eight; and in Turkey and Barbary it is usually five or six hours.

A ship's company is usually classed into two parties; one of which is called the starboard and the other the larboard watch. It is, however, occasionally separated into three divisions, as in a road or in particular voyages.

In a ship of war the watch is generally commanded by a lieutenant, and in merchant ships by one of the mates; so that if there are four mates in the latter, there are two in each watch; the first and third being in the larboard, and the second and fourth in the starboard watch; but in the navy, the officers who command the watch usually divide themselves into three parties, in order to lighten their duty.

is also used for a small portable movement, or machine, for the measuring of time; having its motion regulated by a spiral spring.

Watches, strictly taken, are all such movements as show the parts of time; as clocks are such as publish it, by striking on a bell, &c. But commonly the name watch is appropriated to such as are carried in the pocket; and clock to the large movements, whether they strike the hour or not. See CLOCK.

The invention of spring or pocket watches belongs to the present age. It is true, we find mention made of a watch presented to Charles V. in the history of that prince: but this, in all probability, was no more than a kind of clock to be set on a table, some resemblance whereof we have still remaining in the ancient pieces made before the year 1670. There was also a story of a watch having been discovered in Scotland belonging to King Robert Bruce; but this we believe has turned out altogether apocryphal. The glory of this very useful invention lies between Dr Hooke and M. Huygens; but to which of them it properly belongs, has been greatly disputed; the English ascribing it to the former, and the French, Dutch, &c. to the latter. Mr Derham in his Artificial Clockmaker, says roundly, that Dr Hooke was the inventor; and adds, that he contrived various ways of regulation. One way was with a loadstone: Another with a tender-straight spring, one end whereof played backwards and forwards with the balance; so that the balance was to the spring as the bob to a pendulum, and the spring as the rod thereof: A third method was with two balances, of which there were divers sorts; some having a spiral spring to the balance for a regulator, and others without. But the way that prevailed, and which continues in mode, was with one balance, and one spring running round the upper part of the verge thereof: Though this has a disadvantage, ...such those with two springs, &c. were free from; in that a sudden jerk, or confused shake, will alter its vibrations, and put it in an unusual hurry.

The time of these inventions was about the year 1658; as appears among other evidences, from an inscription on one of the double balance watches presented to King Charles II. viz. Rob. Hooke inven. 1658; T. Tompion fecit, 1675. The invention presently got into reputation, both at home and abroad; and two of them were sent for by the dauphin of France. Soon after this M. Huygens's watch with a spiral spring got abroad, and made a great noise in England, as if the longitude could be found by it. It is certain, however, that his invention was later than the year 1673, when his book de Horol. Oscillat. was published; wherein he has not one word of this, though he has of several other contrivances in the same way.

One of these the lord Brouncker sent for out of France, where M. Huygens had got a patent for them. This watch agreed with Dr Hooke's in the application of the spring to the balance; only M. Huygens's had a longer spiral spring, and the pulses and beats were much slower. The balance, instead of turning quite round, as Dr Hooke's, turns several rounds every vibration.

Mr Derham suggests, that he has reason to doubt M. Huygens's fancy first was set to work by some intelligence he might have of Dr Hooke's invention from Mr Oldenburgh, or some other of his correspondents in England; and this, notwithstanding Mr Oldenburgh's attempt to vindicate himself in the Philosophical Transactions, appears to be the truth. Huygens invented divers other kinds of watches, some of them without any string or chain at all; which he called, particularly, pendulum watches.

Striking Watches are such as, besides the proper watch-part for measuring of time, have a clock part for striking the hours, &c.

Repeating Watches, are such as by pulling a string, &c. repeat the hour, quarter, or minute, at any time of the day or night.—This repetition was the invention of Mr Barlow, and first put in practice by him in larger movements or clocks about the year 1676. The contrivance immediately set the other artists to work, who soon contrived divers ways of effecting the same. But its application to pocket-watches was not known before King James II.'s reign; when the ingenious inventor above mentioned, having directed Mr Thompson to make a repeating watch, was soliciting a patent for the same. The talk of a patent engaged Mr Quare to resume the thoughts of a like contrivance, which he had had in view some years before: he now effected it; and being pressed to endeavour to prevent Mr Barlow's patent, a watch of each kind was produced before the king and council; upon trial of which, the preference was given to Mr Quare's. The difference between them was, that Barlow's was made to repeat by pushing in two pieces on each side the watch-box; one of which repeated the hour, and the other the quarter; whereas Quare's was made to repeat by a pin that struck out near the pendant, which being thrust in (as now it is done by thrusting in the pendant itself), repeated both the hour and quarter with the same thrust.

Of the Mechanism of a Watch, properly so called. Watches, as well as clocks, are composed of wheels and pinions, and a regulator to direct the quickness or slowness of the wheels, and of a spring which communicates motion to the whole machine. But the regulator and spring of a watch are vastly inferior to the weight and pendulum of a clock, neither of which can be employed in watches. In place of a pendulum, therefore, we are obliged to use a balance (fig. 1.) to regulate the motion of a watch; and a spring (fig. 2.) which serves in place of a weight, to give motion to the wheels and balance.

The wheels of a watch, like those of a clock, are placed in a frame formed of two plates and four pillars. Fig. 3. represents the inside of a watch, after the plate (fig. 4.) is taken off. A is the barrel which contains the spring (fig. 2.), the chain is rolled about the barrel, with one end of it fixed to the barrel A (fig. 5.), and the other to the fusee B.

When a watch is wound up, the chain which was upon the barrel winds about the fusee, and by this means the spring is stretched; for the interior end of the spring is fixed by a hook to the immovable axis, about which the barrel revolves; the exterior end of the spring is fixed to the inside of the barrel, which turns upon an axis. It is therefore easy to perceive how the spring extends itself, and how its elasticity forces the barrel to turn round, and consequently obliges the chain which is upon the fusee to unfold and turn the fusee; the motion of the fusee is communicated to the wheel C (fig. 5.); then, by means of the teeth, to the pinion c, which carries the wheel D; then to the piston d, which carries the wheel E; then to the pinion e, which carries the wheel F; then to the point f, upon which is the balance-wheel G, whose pivot runs in the pieces A called the potance, and B called the follower, which are fixed on the plate fig. 4. This plate, of which only a part is represented, is applied to that of fig. 3., in such a manner that the pivots of the wheels enter into holes made in the plate fig. 3. Thus the impressed force of the spring is communicated to the wheels; and the pinion f being then connected to the wheel F, obliges it to turn (fig. 5.). This wheel acts upon the palettes of the verge, 1, 2, (fig. 1.), the axis of which carries the balance HHI, (fig. 1.). The pivot I, in the end of the verge, enters into the hole c in the potance A (fig. 4.). In this figure the palettes are represented; but the balance is on the other side of the plates, as may be seen in fig. 6. The pivot 3 of the balance enters into a hole of the cock BC (fig. 7.), a perspective view of which is represented in fig. 8. Thus the balance turns between the cock and the potance c (fig. 4.), as in a kind of cage. The action of the balance-wheel upon the palettes 1, 2, (fig. 1.), is the same with what we have described with regard to the same wheel in the clock; i.e. in a watch, the balance-wheel obliges the balance to vibrate backwards and forwards like a pendulum. At each vibration of the balance a palette allows a tooth of the balance-wheel to escape; so that the quickness of the motion of the wheels is entirely determined by the quickness of the vibrations of the balance; and these vibrations of the balance and motion of the wheels are produced by the action of the spring.

But the quickness or slowness of the vibrations of the balance depend not solely upon the action of the great spring, but chiefly upon the action of the spring a, b, c, called the spiral spring (fig. 9.), situated under the bar Fig. 9. lance H, and represented in perspective (fig. 6.). The exterior end of the spiral is fixed to the pin a, (fig. 9.). This pin is applied near the plate in a, (fig. 6.) ; the interior end of the spiral is fixed by a peg to the centre of the balance. Hence if the balance is turned upon itself, the plates remaining immovable, the spring will extend itself, and make the balance perform one revolution. Now, after the spiral is thus extended, if the balance be left to itself, the elasticity of the spiral will bring back the balance, and in this manner the alternate vibrations of the balance are produced.

In fig. 5. all the wheels above described are represented in such a manner, that you may easily perceive at first sight how the motion is communicated from the barrel to the balance.

In fig. 10. are represented the wheels under the dial-plate by which the hands are moved. The pinion a is adjusted to the force of the prolonged pivot of the wheel D (fig. 5.), and is called a cannon pinion. This wheel revolves in an hour. The end of the axis of the pinion a, upon which the minute-hand is fixed, is square; the pinion (fig. 10.) is indented into the wheel b, which is carried by the pinion a. Fig. 11. is a wheel fixed upon a barrel, into the cavity of which the pinion a enters, and upon which it turns freely. This wheel revolves in 12 hours, and carries along with it the hour-hand. For a full account of the principles upon which watches and all time-keepers are constructed, we must refer our readers to a short treatise, entitled Thoughts on the Means of improving Watches, by Thomas Mudge.

Watch-Glasses, in a ship, are glasses employed to measure the period of the watch, or to divide it into any number of equal parts, as hours, half-hours, &c. so that the several stations therein may be regularly kept and relieved, as at the helm, pump, look-out, &c.

Watch-Work. There is one part of the movements of clocks and watches of which we have yet given no particular account. This is the method of applying the maintaining power of the wheels to the regulator of the motions, so as not to injure its power of regulation. This part of the construction is called Scapement, and falls to be described under the present article, to which we have referred from Scapement.

The motions of a clock or watch are regulated by Objects a pendulum or balance, without which check the wheels of scape-impelled by the weight in the clock, or spring in the watch, would run round with a rapidly accelerating mo- tion, till this should be rendered uniform by friction, and the resistance of the air. If, however, a pendulum or balance be put in the way of this motion, in such a manner that only one tooth of a wheel can pass, the re-volution of the wheels will depend on the vibration of the pendulum or balance.

We cannot here enter on an historical account of the improvements that have been made on the regulating powers of clocks and watches, nor can we detail the principles on which their action depends. It will be sufficient here to notice the most simple construction of scapements, and then to describe two or three of the most improved constructions that have been applied to time-keepers.

We know that the motion of a pendulum or balance Watch. is alternate, while the pressure of the wheels is constantly exerted in the same direction. Hence it is evident that some means must be employed to accommodate these different motions to each other. Now, when a tooth of the wheel has given the pendulum or balance a motion in one direction, it must quit it, that the pendulum or balance may receive an impulsion in the opposite direction. This escape of the tooth has given rise to the term escapement.

The ordinary escapement is extremely simple, and may be thus illustrated. Let \(xy\), fig. 12. Plate DLXXI., represent a horizontal axis, to which the pendulum \(p\) is attached by a slender rod. This axis has two leaves \(c\) and \(d\), one near each end, and not in the same plane, but so that when the pendulum hangs perpendicularly at rest, \(c\) spreads a few degrees to the right, and \(d\) as much to the left. These are called the pallets. Let \(a\) \(b\) represent a wheel, turning on a perpendicular axis \(e\) \(o\) in the order \(a\) \(f\) \(e\) \(b\). The teeth of this wheel are in the form of those of a saw, leaning forward in the direction of the rim's motion. This wheel is usually called the crown-wheel, or in watches the balance-wheel. See CLOCK and WATCH. It generally contains an odd number of teeth. In the figure the pendulum is represented at the extremity of its excursion towards the right, the tooth \(a\) having just escaped from the pallet \(c\), and \(b\) having just dropped on \(d\). Now it is evident that while the pendulum is moving to the left, in the arch \(p\) \(g\), the tooth \(b\) still presses on the pallet \(d\), and thus accelerates the pendulum, both in its descent along \(p\) \(h\), and its ascent up \(h\) \(g\), and that when \(d\), by turning round the axis \(x\) \(y\), raises its point above the plane of the wheel, the tooth \(b\) escapes from it, and \(i\) drops on \(c\), now nearly perpendicular. Thus \(c\) is pressed to the right, and the motion of the pendulum along \(g\) \(p\) is accelerated. Again, while the pendulum hangs perpendicularly in the line \(x\) \(h\), the tooth \(b\), by pressing on \(d\), will force the pendulum to the left, in proportion to its lightness, and if it be not too heavy, will force it so far from the perpendicular, that \(b\) will escape, and \(i\) will catch on \(c\), and force the pendulum back to \(p\), when the same motion will be repeated. This effect will be more remarkable, if the rod of the pendulum be continued through \(x\) \(y\), and have a ball \(q\) on the other end, to balance \(p\). When \(b\) escapes from \(d\), the balls are moving with a certain velocity and momentum, and in this condition the balance is checked when \(i\) catches on \(c\). It is not, however, instantly stopped, but continues to move a little to the left, and \(i\) is forced a little backward by the pallet \(c\). It cannot make its escape over the top of the tooth \(i\), as all the momentum of the balance was generated by the force of \(b\), and \(i\) is of equal power. Besides, when \(i\) catches on \(c\), and the motion of \(c\) to the left continues, the lower point of \(c\) is applied to the face of \(i\), which now acts on the balance by a long lever, soon stops its motion in that direction, and continuing to press on \(c\), urges the balance in the opposite direction. It is easy to see that the motion of the wheel here must be bobbling and unequal, which has given to this escapement the name of the recoiling escapement.

In considering the utility of the following improved escapement for clocks, we must keep in mind the following proposition, which, after the above illustration, scarcely requires any direct proof. It is, that the natural vibrations of a pendulum are isochronous, or are performed in equal times. The great object of the escapement is to preserve this isochronous motion of the pendulum.

As the defect of the recoiling escapement was long apparent, several ingenious artists attempted to substitute in its place a escapement that should produce a more regular and uniform motion. Of these, the escapement contrived by Mr Cumming appears to be one of the most ingenious in its construction, and most perfect in its operation. The following construction is similar to that of Mr Cumming, but rendered rather less complex for the purpose of shortening the description.

Let \(ABC\), fig. 13, represent a portion of the swing wheel, of which \(O\) is the centre, and \(A\) one of the teeth; \(Z\) is the centre of the crutch, pallets, and pendulum. The crutch is represented of the form of the letter \(A\), having in the circular cross piece a slit \(i\) \(k\), also circular, \(Z\) being the centre. The arm \(ZF\) forms the first detent, and the tooth \(A\) is represented as locked on it at \(F\). \(D\) is the first pallet on the end of the arm \(Z\) \(d\) moveable round the same centre with the detents, but independent of them. The arm \(d\) \(e\) to which the pallet \(D\) is attached, lies wholly behind the arm \(ZF\) of the detent, being fixed to a round piece of brass \(e\) \(f\) \(g\), having pivots turning concentric with the axis of the pendulum. To the same piece of brass is fixed the horizontal arm \(e\) \(H\), carrying to its extremity the ball \(H\), of such size, that the action of the tooth \(A\) on the pallet \(D\) is just able to raise it up to the position here drawn. \(ZP\) \(p\) represents the fork, or pendulum rod, behind both detent and pallet. A pin \(p\) projects forward, coming through the slit \(i\) \(k\), without touching either margin of it. Attached to the fork is the arm \(m\) \(n\), of such length that, when the pendulum rod is perpendicular, the angular distance of \(n\) \(q\) from the rod \(e\) \(g\) \(H\) is just equal to the angular distance of the left side of the pin \(p\) from the left end \(i\) of the slit \(i\) \(k\).

Now, the natural position of the pallet \(D\) is at \(i\), represented by the dotted lines, resting on the back of the detent \(F\). It is naturally brought into this position by its own weight, and still more by the weight of the ball \(H\). The pallet \(D\), being set on the foreside of the arm at \(Z\), comes into the same plane with the detent \(F\) and the swing-wheel, though here represented in a different position. The tooth \(C\) of the wheel is supposed to have escaped from the second pallet, on which the tooth \(A\) immediately seizes the pallet \(D\), situated at \(i\), forces it out, and then rests on the detent \(F\), the pallet \(D\) leaning on the tip of the tooth. After the escape of \(C\), the pendulum, moving down the arch of semivibration, is represented as having attained the vertical position. Proceeding still to the left, the pin \(p\) reaches the extremity \(i\) of the slit \(i\) \(k\); and, at the same instant, the arm \(n\) touches the rod \(e\) \(H\) in \(q\). The pendulum proceeding a hairsbreadth further, withdraws the detent \(F\) from the tooth, which now even pushes off the detent, by acting on the inclining face of it. The wheel being now unlocked, the tooth following \(C\) on the other side acts on its pallet, pushes it off, and rests on its detent, which has been rapidly brought into a proper position by the action of \(A\) on the inclining face of \(F\). By a similar action of \(C\) on its detent at the moment of escape, \(F\) was brought into a position proper for the wheels being locked by the tooth \(A\). As the pendulum still goes on, the ball \(H\), and pallet connected with it, are carried by the arm \(m\) \(n\), and before the pin \(p\) again reaches the end. end of the slit, which had been suddenly withdrawn by the action of A on F, the pendulum comes to rest. It now returns towards the right, loaded with the ball H on the left, and thus the motion lost during the last vibration is restored. When the pin p, by its motion to the right, reaches the end k of i k, the wheel on the right side is unlocked, and at the same instant the weight H being raised from the pendulum by the action of a tooth like B on the pallet D, ceases to act.

In this escapement, both pallets and detents are detached from the pendulum, except in the moment of unlocking the wheel, so that, except during this short interval, the pendulum may be said to be free during its whole vibration, and of course its motion must be more equable and undisturbed.

The constructing of a proper escapement for watches requires peculiar delicacy, owing to the small size of the machine, from which the error of \( \frac{1}{2} \) of an inch has as much effect as the error of a whole inch in a common clock. From the necessary lightness of the balance, too, it is extremely difficult to accumulate a sufficient quantity of regulating power. This can be done only by giving the balance a great velocity, which is effected by concentrating as much as possible of its weight in the rim, and making its vibrations very wide. The balance rim of a tolerable watch should pass through at least ten inches in every second.

In considering the most proper escapements for watches, we may assume the following principle, viz., that the oscillations of a balance urged by its spring, and undisturbed by extraneous forces, are isochronous.

In ordinary pocket watches, the common recoiling escapement of clocks is still employed, and answers the common purposes of a watch tolerably well, so that, if properly executed, a good ordinary watch will keep time within a minute in the day. These watches, however, are subject to great variation in their rate of going, from any change in the power of the wheels.

The following is considered as the best construction of the common watch escapement, and is represented by fig. 14, as it appears when looking straight down on the end of the balance arbor. C marks the centre of the balance and verge; CA represents the upper pallet, or that next the balance, and CB the lower pallet; F and D are two teeth of the crown wheel, moving from left to right; E, G, are two teeth in the lower part, moving from right to left. The tooth D appears as having just escaped from the point of CA, and the tooth E as having just come in contact with CB. In practice, the escapement should not be quite so close, as by a small inequality of the teeth, D might be kept from escaping at all. The following are thought the best proportions:

The distance between the front of the teeth (that is, of G, F, E, D), and the axis C of the balance, is \( \frac{1}{2} \) of FA, the distance between the points of the teeth. The length CA, CB of the pallets is \( \frac{3}{4} \) of the same degrees, and the front DH or FK of the teeth makes an angle of 25° with the axis of the crown wheel. The sloping side of the tooth must be of an epicycloidal form, suited to the relative motion of the tooth and pallet.

It appears from these proportions, that by the action of the tooth D, the pallet A can throw out till it reach 4, 125° from CL, the line of the crown-wheel axis. To this if we add BCA = 95°, we shall have LC = 120°. Again, B will throw out as far on the other side.

Now, if from 240°, the sum of the extent of vibration of both pallets, we take 95° the angle of the pallets, the remainder 145° will express the greatest vibration which the balance can make, without striking the front of the teeth. From several causes, however, this measure is too great, and 125° is reckoned a sufficient vibration in the best ordinary escapement.

Of the improvements on the escapements of watches, Graham's one of the most important is that by Mr. George Graham, horizontal which we shall proceed to describe. DE, fig. 15, presents part of the rim of the balance wheel; A and C, two of its teeth with their faces b c formed into planes, inclined to the circumference of the wheel in an angle of about 15°, so that the length b e of the face may be nearly quadruple of its height c m. Let a circular arch ABC be described round the centre of the wheel, and through the middle of the faces of the teeth. The axis of the balance will pass through some point B of this arch, and the mean circumference of the teeth may be said to pass through the centre of the verge. On this axis is fixed a portion of a thin hollow cylinder b c d, made of hard tempered steel, or of some hard and tough stone, such as ruby or sapphire. By this construction the portion of the cylinder occupies 210° of the circumference. The edge b, to which the tooth approaches from without, is rounded off on both angles. The other edge d is formed into a plane, inclined to the radius about 30°. Now, suppose the wheel pressed forward in the direction AC, the point b of the tooth, touching the rounded edge, will push it outwards, turning round the balance in the direction b c d. The heel e of the tooth will escape from this edge when it is in the position h, and e is in the position f. The point b of the tooth will now be at d, but the edge of the cylinder will be at i. The tooth therefore rests in the inside of the cylinder, while the balance continues its vibration a little way, in consequence of the impulse it has received from the action of the inclined plane. When this vibration is ended, by the opposition of the balance spring, the balance will return, and the tooth now in the position B, rubbing on the inside of the cylinder, the balance comes back into its natural position b c d, with an accelerated motion by the action of its spring, and would of itself vibrate as far as the other side. It is, however, assisted again by the tooth, which presses on the edge a, pushes it aside till it attain the position k, when the tooth entirely escapes from the cylinder. At this instant the other edge of the cylinder, having attained the position l, is in the way of the next tooth, which is now in the position A, while the balance continues its vibration, the tooth resting and rubbing on the outside of the cylinder. When this vibration is finished, the balance, by the action of the spring, resumes its first motion, and as soon as the balance gets into its natural position, the tooth begins to act on the edge b, pushes it aside, escapes from it, and drops as before in the inside of the cylinder. In this construction the arch of action or escapement is 30° = twice the angle which the face of a tooth makes with the circumference.

It is necessary to explain how the cylinder is connected with the verge, so as to make such a great revolution round the tooth of the wheel. The triangular tooth e b m is placed on the top of a little pillar fixed into the end of the piece of brass m D formed in the rim of the wheel. Thus the plane of the wedge tooth is parallel. parallel to the plane of the wheel, but at a small distance above it. The verge is represented at fig. 16, and consists of a long hollow cylinder of cast steel, having a great portion of the metal cut out. If spread out flat, this cylinder would assume the form of fig. 17; and if we conceive this flat piece rolled up till the edges GH and G'H' unite, we shall have the exact form. The part acted on by the point of the tooth is denoted by the dotted line b'd', and the part D, I, F, E serves to connect the two ends.

This escapement of Mr Graham is called a horizontal escapement, because the balance is parallel to the other wheels.

Another escapement of a superior construction was contrived by M. Lepaute of Paris, and is of such a singular form as to render it extremely difficult to illustrate it by a figure. The representations at figs. 18 and 19 will, however, give general readers some idea of its mode of action, and a skilful artist will easily see how the several parts may be adapted to each other. ABC fig. 18 represents part of the rim of the balance wheel, having the pins 1, 2, 3, 4, 5, &c., projecting from its faces; the pins 1, 3, 5, being on the side next the eye, and the pins 2 and 4 on the opposite side. D is the centre of the balance and verge, and the small circle round D represents its thickness. But the verge in this place is crooked, that the rim of the wheel may not be intercepted by it. To it is attached a piece of hard tempered steel a'b'c'd', of which the part a'b'c is a concave arch of a circle, having D for its centre. It wants about 30° of a semicircle. The rest c'd' is also an arch of a circle having the same radius with the balance-wheel. In the natural position of the balance, a line drawn from D, through the middle of the face c'd' is a tangent to the circumference of the wheel. But if the balance be turned round till the point d' of the horn come to d', and the point c come to 2 in the circumference in which the pins are placed, the pin pressing on the beginning of the horn or pallet, pushes it aside, slides along it, and escapes at d', having generated a certain velocity in the balance. Let another pallet similar to that now described be placed on the other side of the wheel, but in a contrary position, with the acting face of the pallet turned away from the centre of the wheel. Let it be so placed at E, that the moment the pin 1 on the upper side of the wheel escapes from the pallet c'd', the pin 4 on the lower side of the wheel falls on the end of the circular arch e'f'g' of the other pallet. Now, if the pallets be connected by equal pulleys G and F on the axis of each, and a thread round both so that they shall turn one way; the balance on the axis D having received an impulse from the pin 1, will continue its motion from A towards i, and will carry the other pallet with a similar motion round the centre E from h to k. The pin 4 will therefore rest in the concave arch g'f'e' as the pallet turns round. When the force of the balance is spent, the pallet c'd returns towards its first position. The pallet g'h turns with it, and when the point of the first has arrived at d', the beginning g' of the other arrives at the pin 4; and, proceeding farther, this pin escapes from the concave arch e'f'g', and slides along the pallet g'h, pushing it aside, and of course urging the pallet round the centre E, and the balance on the axis D round at the same time, and in the same direction. The pin 4 escapes from the pallet g'h, when h arrives at 3; but while the pin 4 is sliding along the yielding pallet g'h, the pin 3 is moving in the circumference BDA; and the instant that the pin 4 escapes from h at 3, the pin 3 arrives at 2, where the beginning c of the concave arch c'b is ready to receive it. It therefore rests on this arch, while the balance continues its motion, and this may continue till the point b of the arch comes to 2. The balance now stops, its force being spent, and then returns; and the pin 3 escapes from the circle at c, slides along the yielding pallet c'd', and when it escapes at 1, another pin on the lower side of the wheel arrives at 4, and finds the arch g'f'e ready to receive it. And thus the vibration of the balance will be continued.

From the above description we may deduce the proper dimensions of the parts of the pallet. Thus, the length of the pallet c'd or g'h, must be equal to the interval between two succeeding pins, and the distance of the centres DE, must be double of that interval. The radius Dc or Eg, may be as small as we choose. The concave arches c'b'a and g'f'e, must be continued so far as to allow a pin to rest on them during the whole excursion of the balance. The angle of escapement, in which the balance remains under the influence of the wheels, is obtained by drawing the lines Dc and Dd, and we shall find that this angle c'Dd is here about 3°, though it may be made either greater or less than this.

Fig. 19 explains how the two pallets may be combined on one verge. KL is the verge with a pivot at each end. It is bent like a crank MNO, to admit the balance wheel between its branches. BC represents this wheel, seen edgewise, with its pin alternately on different sides. The pallets are also represented by b'c'd' and h'g'f', sized to the inside of the branches of the crank, facing each other. The position of their acting faces may be seen in the preceding figure, on the verge D, where the pallet g'h is represented by the dotted line 2i', situated behind the pallet c'd'. The remote pallet 2i' is so placed, that when the point d of the near pallet is quitted by a pin 1 on the upper side of the wheel, the angle formed by the face and the arch of rest of the other pallet is just ready to receive the next pin 2, which lies on the lower side of the rim. It is plain that the action here will be the same as if the pallets were on separate axes. The pin 1 escapes from d', and the pin 2 is received on the arch of rest, and locks the wheel, while the balance continues in motion. When the balance returns, 2 gets off the arch of rest, pushes aside the pallet 2i', escapes from it when it gets to 1, and then the point c is ready to receive the pin 3, &c. The vibrations may be increased by giving a sufficient impulse through the angle of escapement, but they cannot exceed a certain quantity, otherwise N, the top of the crank, would strike the rim of the wheel. The vibrations may be easily increased to 18°, by placing the pins at the very edge of the wheel; and by placing them at the points of long teeth, so that the crank may get in between them, the vibrations may be carried to a much greater extent.

The construction just described is exceedingly ingenious; and if the machinery be well executed, this escapement will excel the horizontal escapement of Graham, both as it has but two acting faces to form, and as it admits of making the circle of rest extremely small, without lessening the acting face of the pallet. The construction is, however, very delicate and difficult, and must require a very nice workman. An excellent escapement of much more easy construction, is that commonly called Duplaire's escapement, and with this we shall conclude our account of watch-work. Fig. 20 represents the essential parts somewhat magnified. AD a portion of the balance-wheel, having teeth f, h, g, at the circumference. These teeth are for producing the rest of the wheel, while the balance is making excursions beyond the escapement. This is effected by an agate cylinder spg, on the verge. This cylinder has a notch o. When the cylinder turns round in the direction opg, the notch easily passes the tooth B which is resting on the cylinder surface; but when it returns in the direction bpo, the tooth B gets into the notch and follows it, pressing on one side of it till the notch comes into the position o. The tooth being then in the position h, escapes from the notch, and another tooth drops on the convex surface of the cylinder at B. The balance-wheel is also furnished with a set of flat-sided pins, standing upright on its rim represented by a D. There is likewise fixed on the verge a larger cylinder GFC above the smaller one opg, with its lower surface clear of the wheel, and having a pallet C, of sapphire, firmly indented into it, and projecting so far as to keep clear of the pins on the wheel. The position of this cylinder, with respect to the smaller one below it, is such that the tooth b being escaped from the notch, the pallet C has just past the pin a, which was at A while B rested on the small cylinder; but it moved from A to a, while B moved to b. The wheel being now at liberty, the pin a exerts its pressure on the pallet C in the most direct manner, and gives it a strong impulsion, following and accelerating it till another tooth stops on the little cylinder. The angle of escapement depends partly on the projection of the pallet, and partly on the diameter of the small cylinder, and the advance of the tooth B into the notch. Independent of the action on the small cylinder, the angle of escapement would be the whole arch of the large cylinder between C and x. But a stops before it be clear of the pallet, and the arch of impulsion is shortened by all the space described by the pin while a tooth moves from B to b. It stops at d.

For an account of other escapements we must refer our readers to the Memoirs of the Academy of Sciences at Paris for 1748, Cummin's Elements of Clock and Watch-work, a French work entitled Machines approvées par l'Académie des Sciences, and Young's Lectures on Natural Philosophy, vol. i. p. 193, and Plate 16, vol. ii. p. 193.