off from the pallet, until the force of the pendulum-spring, (which is not represented in the figure,) being continually increased by being wound up, overcomes the momentum of the balance, which for an instant of time is then stationary, but immediately returns by the action of the pendulumspring, which exerts a considerable force upon it in unwinding itself. As the balance returns, the point i, of the lifting-pallet in, passes by the ends of two springs, EF and YO, and, in passing by, pushes the projecting end o of the slender spring in towards the balance-wheel, until it has passed it; after this, the projecting end o again returns, and applies itself close to the hooked end of the spring E F as before. The spring yo is made so slender, that it gives but little resistance to the balance, during the time the point i of the lifting-pallet is passing it, and of course causes but little, if any, decrease in its momentum. During the time the point i of the lifting-pallet is pressing in the small spring yo, the long spring E F remains steadily bearing against the head of the adjusting screw m, as the hooked end at o just lets the end of the lifting-pallet pass by without touching it. As the spring has now been continually acting upon the balance, from the extremity of its vibration in the direction MS K, it has given it the greatest velocity when the point i of the lifting-pallet is passing the end o of the slender spring; for at this instant the spring which was wound up by the contrary direction of the balance, is now unwound again, or in the same state as it was in its quiescent position at first, and of course has no effect at all upon the balance in either direction; but the balance, having now all the velocity it would acquire from the unwinding the spring, goes on in the direction S M K until the force of this spring again stops it, and brings it back again, moving in the same direction as at first, with a considerable velocity. By this return of the balance, the point i of the lifting-pallet comes up again to the projecting end o of the slender spring, pushes back the long spring EF, and unlocks the wheel; and another tooth falling upon the face of the pallet hl, gives fresh energy to the balance; and thus the action is carried on as before.

ESCAPEMENT, OR 'SCAPEMENT.

THE motions of a clock or watch are regulated by a pendulum or balance, which serves as a check, without which, the wheels impelled by the weight in the clock, or spring in the watch, would run round with a rapidly accelerating motion, 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 manner that only one tooth of a wheel can pass, the revolutions of the wheel will depend on the vibration of the pendulum or balance.

We know that the motion of a pendulum or balance 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 escaping of the tooth has given rise to the term escapement

The ordinary 'scapement is extremely simple, and may be thus illustrated. Let ry, fig. 523, represent a horizontal axis, to which the pendulum is attached by a slender rod. This axis has two leaves, e and d, one near each end, and not in the same plane, but so that when the pendulum hangs perpendicularly at rest, e spreads a few degrees to the right, and d as much to the left. These are called the pallets. Let a fb represent a wheel, turning on a perpendicular axis, e o, in the order a ƒ 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. It in general 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 arc pg, the tooth b still presses on the pallet d, and thus accelerates the pendulum, both in its descent along ph, and its ascent up hg, and that when d, by turning round the axis ry, 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 gp is accelerated. Again, while the pendulum hangs perpendicularly in the line ah, 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 the more remarkable if the rod of the pendulum be continued through xy, 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, and soon stops its motion in that direction, and, continuing to press on c, urges the balance in the opposite direction. In this, it is evident that the motion of the wheel is hobbling and unequal, by which this escapement has received the appellation of the recoiling 'scapement.

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

As the defect of the recoiling 'scapement was long apparent, several ingenious artists attempted to substitute in its place a 'scapement that should produce a more regular and uniform motion. Of these, the 'scapement contrived by Mr. Cumming appears to be one of the most ingenious in its construction, and most perfect in its operation. The follow

ing construction is similar to that of Mr. Cumming, but rendered rather less complex for the purpose of shortening the description.

Let A BC, fig. 524, represent a portion of the swing-wheel, of which O is the centre, and A one of the teeth, and Z the centre of the crutch, the pallets, and pendulum. The crutch is represented of the form of the letter A, having in the circular cross-piece a slit i k, which is 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, movable round the same centre with the detents, but independent of them. The arm, de, to which the pallet D is attached, lies wholly behind the arm Z F of the detent, being fixed to a round piece of brass, efg, having pivots turning concentric with the axis of the pendulum. To the same piece of brass is fixed the horizontal arm c H, carrying at 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 represented. Z Pp represents the fork, or pendulum-rod, behind both detent and pallet. A pin p projects forward, coming through the slit ik, 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 nq from the rod e q 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 8, 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 represented in the figure 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 8, 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 semi-vibration, is represented as having attained the vertical position. Proceeding still to the left, the pin p reaches the extremity i of the slit ik; and, at the same instant, the arm n touches the rod e H in q. The pendulum proceeding a hair's-breadth further, withdraws the detent F from the tooth, which now 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 inclined 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 mn, and before the pin p again reaches the 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 'scapement, both pallets and detents are detached from the pendulum, except in the moment of unlocking the wheel, so that, excepting during this short interval, the pen

dulum 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 'scapement for watches requires peculiar delicacy, owing to the small size of the machine, from which the error of 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 only be done 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 'scapements 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 'scapement 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 water 'scapement, and is represented by fig. 525, as it appears when looking straigh down on the end of the balance arbor. C marks the centre of the balance and verge; C A 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 CˇA, and the tooth E as having just come in contact with C B. In practice, the 'scapement should not be quite so close, as, by a small inequality of the teeth, D might be kept from escaping at all. In the best proportioned watches, the distance between the front of the teeth, that is, of G F È D, and the axis C of the balance, is of F A, the distance between the points of the teeth. The length C A, CB, of the pallets is of the same degrees, and the front D H, or F K of the teeth makes an angle of 25o 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 a, 120° from C L, the line of the crown-wheel axis. To this if we add BC A=95o, we shall have L Ca=120o. Again, B will throw out as far on the other side. Now, if from 240o, the sum of the extent of vibration of both pallets, we take 95o, the angle of the pallets, the remainder 145o 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 120° is reckoned a sufficient vibration in the best ordinary 'scapement. Encyclopædia Britannica.

In 1812, Mr. Prior, jun. was rewarded by the Society of Arts for the construction of a remontoire escape which possesses considerable merit.

The advantage of this escapement is such as will give an exact and equal impulse to the pendulum without any friction, and which cannot be at all affected by any irregularities or variations arising by the clogging of oil and increasing of friction from the train, except during the very small part of the vibration that the pendulum is removing the spring detents from off the points of the teeth of the escape-wheel, the effect of which can never be discovered in the rate by any variation the oil on the pivots and the increase of friction can ever produce, as long as the wheels will be able to wind up the renovating spring, which will be nearly as long as they can move at all, as the renovating spring has not either to be wound up quick, or to be pushed beyond any catch or spring to keep it in its proper situation, nor can there ever be any increase of friction in winding up the renovating spring, as it is formed in nearly as right a line as possible; consequently must go almost endlessly without cleaning, and will never require any oil.

The swing-wheel A, figs. 526 and 527, has thirty teeth cut in its periphery, and is constantly urged forward by the maintaining power, which is supplied by a small weight X, figs. 527 and 527*; CD are two spring detents catching the teeth of the wheel alternately, these are, at the proper intervals, unlocked by the parts marked 2 and 3, fig. 526, upon the pendulum rod H, intercepting small pins ab, fig. 527, projecting from the detents, as it vibrates towards the one or the other; E is the renovating or remontoire spring, fixed to the same stud F, as the detents; it is wound up by the highest tooth of the wheel, as seen in fig. 526, (its position when unwound being shown by the dotted line.) This being a case, suppose a tooth of the wheel is caught by the detent D, which prevents the wheel from moving any further, and keeps the renovating spring from escaping off the point of the tooth; in this position, the pendulum is quite detached from the wheel; now, if the pendulum be caused to vibrate towards G, the part of it marked 2 comes against the pin b, fig. 527, projecting from the renovating spring E, and pushes this spring from the point of the wheel's tooth; on vibrating a little further, it removes the detent D, which detained the wheel, by the part 3 striking the pin a, fig. 2, which projects from the detent; the maintaining power of the clock causes the wheel, thus unlocked, to advance, until detained by a tooth resting upon the end of the detent C, on the opposite side; by this means the renovating spring will be clear of the tooth of the wheel as it returns with the pendulum, and gives it an impulse, by its pin b pressing against the part 2 of the pendulum, until the spring comes to the position shown by the dotted line, in which position it is unwound, and rests against a pin fixed in the cross bar of the plate; the pendulum continues vibrating towards I, nearly to the extent of its vibration, when the part 1 meets the pin in the detent C, and removes it from the wheel, and unlocks it; the maintaining power now carries it forward, pushing the renovating spring E before it, until another tooth is caught by