ABC

ABC (fig. 9.) represents 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 or detents is represented of a form resembling the letter A, having in the circular cross-piece a slit $ik$, also circular, Z being the centre. This form is very different from Mr Cumming's, and inferior to his, but was adopted here in order to avoid a long description. 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 Zd moveable

round the same centre with the detents, but moveable independently of them. The arm $de$, to which the pallet D is attached, lies altogether behind the arm ZF of the detent, being fixed to a round piece of brass $efg$, which has pivots turning concentric with the verge or axis of the pendulum. To the same round piece of brass is fixed the horizontal arm $eH$, carrying at its extremity the ball H, of such size, that the action of the tooth A on the pallet D is just able (but without any risk of failing) to raise it up to the position here drawn. ZP represents the fork, or the pendulum rod, behind both detent and pallet. A pin $p$ projects forward, coming through the slit $ik$, without touching the upper or under margin of it. There is also attached to the fork the arm $mn$ (and a similar one on the other side), of such length that, when the pendulum rod is perpendicular, as is represented here, the angular distance of $nq$ from the rod $egH$ is precisely equal to the angular distance of the left side of the pin $p$ from the left end $i$ of the slit $ik$.

The mode of action on this apparatus is abundantly simple. 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 fore side of the arm at Z, comes into the same plane with the detent F and the swing-wheel. It is drawn, however, in the figure in another position. The tooth C of the wheel is supposed to have escaped from the second pallet, on which the tooth A immediately engages with 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. F is brought into this situation in a way that will appear presently. 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 $ik$; and, at the same instant, the arm $n$ touches the rod $egH$ in $q$. The pendulum proceeding a hair's breadth further, withdraws the detent F from the tooth, which now even pushes off the detent, by acting on the slant 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 slant face of F. It was a similar action of C on its detent, in the moment of escape, which brought F into a fit position for locking the wheel by the tooth A. The pendulum still going on, the arm $mn$ carries the weight of the ball H, and the pallet connected with it, and it comes to rest before the pin $p$ again reaches the end of the slit, which had been suddenly withdrawn from it by the action of A on the slant face of F. The pendulum now returns towards the right, loaded on the left with the ball H, which restores the motion which it had lost during the last vibration. When, by its motion to the right, the pin $p$ reaches the end $k$ of the slit $ik$, it unlocks the wheel on the right side. At the same instant the weight H ceases to act on the pendulum, being now raised up from it by the action of a tooth like B on the pallet D.

Let us now consider the mechanism of these motions. The prominent feature of the contrivance is the almost complete disengagement of the regulator from the wheels.

The wheels, indeed, act on the pallets; but the pallets are then detached from the pendulum. The sole use of the wheel is to raise the little weights while the pendulum is on the other side, in order to have them in readiness at the arrival of the pendulum. They are then laid on the pendulum, and supply an accelerating force, which restores to the pendulum the momentum lost during the preceding vibration. Therefore no inequalities in the action of the wheel on the pallets, whether arising from friction or oil, has any effect on the maintaining power. It remains always the same, namely, the rotative momentum of the two weights. The only circumstance, in which the irregularity of the action of the wheels can affect the pendulum is at the moment of unlocking. Here indeed the regulator may be affected; but this moment is so short, in comparison with other escapements, that it must be considered as a real improvement.

It is very uncandid to refuse the author a claim to the character of an ingenious artist on account of this contrivance, as has been done by a very ingenious university Professor, who taxes Mr. Cumming with ignorance of the first elements of mechanics, and says that the best thing in his book is his advice to suspend the pendulum from a great block of marble, firmly fixed in the wall*. This is certainly a good advice, and we doubt not but that the Professor's clock would have performed still better if he had condescended to follow it. It is still less candid to question the originality of the invention. We know for certain that it was invented at a time and place where the author could not know what had been done by others. It would have been more like the urbanity of a well-educated man to have acknowledged the genius, which, without similar advantages, had done so much.

But, while we thus pay the tribute of justice to Mr. Cumming, we do not adopt all his opinions. The clock has the same defects of the former in respect of the laws of the force which accelerates the pendulum. The sudden addition of the small weight, and this almost at the extremity of the vibration, would derange it very much, if the addition were susceptible of any sensible variation. The irregularity of the action of the wheels may sensibly affect the motion during the unlocking, when the clock is foul; and the pendulum just able to unlock; for any disturbance at the extremity of the vibration greatly affects the time. We acknowledge that the parts which we here suppose to be foul may not be so in the course of twenty years, these parts being only the pivots of the escapement. The great defect of the escapement is its liability to unlock by any jolt. It is more subject to this than the others already mentioned. This risk is much increased by the slender make of the parts, in Mr. Cumming's drawings, and in the only clock of the kind we have seen; but this is not necessary; and it should be avoided for another reason; the interposing so many slender and crooked parts between the moving power and the pendulum weakens the communication of power, and requires a much more powerful wheelwork.

All these, however, are slight defects, and only the

last can be called a fault. The clocks made on this principle have gone remarkably well, as may be seen by the registers of his majesty's private observatory. But the greatest objection is, that they do not perform better than a well-made dead escapement; and they are vastly more troublesome to make and to manage. This is strictly true, and is a serious objection. The fact is, that the dominion of a heavy pendulum is so great, that if any one of the escapements now described be well executed with pallets of agate, and a wheel of hard steel, and if the pendulum be suspended agreeably to Mr. Cumming's advice, there is hardly any difference to be observed in their performance. We shall content ourselves with a single proof of this from fact. The clock invented by the celebrated Harrison is at least equal in its performance to any other. Friction is almost annihilated, and no oil is required. It went fourteen years without being touched, and during that time did not vary one complete second from one day to another, nor ever deviated half a minute by accumulation from equable motion: Yet the escapement, in so far as it renews the law of the accelerating force, deviates more from the proportion of the spaces than the most recoiling escapement that ever was put to a good clock. It is so different from all hitherto described, both in form and principle, that we must not omit some account of it, and with it we shall conclude our escapements for clocks.

Let GIDG represent the swing-wheel, of which M is the centre. A is the verge or axis of the pendulum. It has two very short arms AB, AE. A slender rod BC turns on fine pivots in the joint B, and has at its extremity C a hook or claw, which takes hold of a tooth D of the swing-wheel when the pendulum moves from the right side to the left. This claw, when at liberty, stands at right angles, or, at least, in a certain determinate angle, with regard to the arm AB; and when drawn a little from that position, it is brought back to it again by a very slender spring. The arm AE is furnished with a detent EF, which also, when at liberty, maintains its position on the arm by means of a very slender spring.

Let us now suppose that the tooth D is pressing on the claw C, while the pendulum is moving to the right. The joint B yields, by its motion round A, to the pressure of the tooth on the claw. By this yielding, the angle ABC opens a little. In the mean time, the same motion round A causes the point F of the detent on the other side to approach the circumference of the wheel in the arch of a circle, and the tooth G at the same time advances. They meet, and the point of G is lodged in the notch under the projecting heel f. When this takes place, it is evident that any farther motion of the point E round A must push the tooth G a little backward, by means of the detent EF. It cannot come any nearer to the wheel, because the point of the tooth stops the heel f. The instant that F pushes G back, the tooth D is withdrawn from the claw C, and C flies out, by the action of its spring, and resumes its position at right angles to BA; and the wheel is now free from the claw, but is pushing at the detent F (c). The pendulum, having

ving finished its excursion to the right (in which it causes the wheel to recoil by means of the detent F), returns toward the left. The wheel now advances again, and, by pressing on F, aids the pendulum through the whole angle of scapement. By this motion the claw C describes an arch of a circle round A, and approaches the wheel, till it take hold of another tooth, namely, the one following D, and pulls it back a little. This immediately frees the detent F from the pressure of the tooth G, and it flies out a little from the wheel, resuming its natural position by means of its spring. Soon after, the motion of the pendulum to the left ceases, and the pendulum returns; D pulling forward the hook C to aid the pendulum, and the former operation is repeated, &c. &c.

Such is the operation of the pallets of Harrison and Hindley. Friction is almost totally avoided, and oil entirely (d). The motion is given to the pendulum by a fair pull or push, and the teeth of the wheel only apply themselves to the detents without rubbing. There is no drop, and the scapement makes no noise, and is what the artists call a silent scapement. The mechanic will readily perceive, that by properly disposing the arms AB, AE, and disposing the pallets on the circumference of the wheel, the law, by which the action of the wheel on the pendulum is regulated, may be greatly varied, so as to harmonize, as far as the nature of scapement, alternately pushing and pulling, will admit, with the action of gravity.

But this is evidently a recoiling scapement, and one of the worst kind; for the recoil is made at the very confines of the vibration, where every disturbance of the regular cycloidal vibration occasions the greatest disturbance to the motion. Yet this clock kept time with most unexampled precision, far excelling all that had been made before, and equal to any that have been made since. This is entirely owing to the immense superiority of the momentum of the pendulum over the maintaining power.

THE execution of a proper scapement for watches is a far more delicate and difficult problem than the foregoing, on account of the small size, which requires much more accurate workmanship, because the error of the hundredth part of an inch has as great a proportion to the dimensions of the regulator as an inch in a common house clock. It is much more difficult on another account. We have no such means of accumulating such a dominion (to use Mr Harrison's expressive term) over the wheel-work in the regulator of a watch as in that of a clock. The heaviest balance that we can employ, without the certainty of snapping its pivots by every

flight jolt, is a mere trifle, in comparison with the pendulum of the most ordinary clock. A dozen or twenty grains is the utmost weight of the balance, even of a very large pocket watch. The only way that we can accumulate any notable quantity of regulating power in such a small pittance of matter is by giving it a very great velocity. This we do by accumulating all its weight in the rim, by giving it very wide vibrations, and by making them extremely frequent. The balance-rim of a middling good watch should pass through at least ten inches in every second. Now, when we reflect on the small momentum of this regulator, the inevitable inequalities of the maintaining power, and the great arch of vibration on which these inequalities will operate, and the comparative magnitude even of an almost insensible friction or clamminess, it appears almost chimerical to expect any thing near to equality in the vibrations, and incredible that a watch can be made which will not vary more than one beat in 86400. Yet such have been made. They must be considered as the most matterly exertions of human art. The performance of a reflecting telescope is a great wonder; the worst that can find a market must have its mirrors executed without an error of the ten thousandth part of an inch; but we now know that this accuracy is attained almost in spite of us, and that we scarcely can make them of a worse figure. But the case is far otherwise in watch-work. Here all those wonderful approaches to perfection are the results of rational discussion, by means of sound principles of science; and, unless the artist who puts these principles into practice be more than a mere copyist, unless the principles themselves are perceived by him, and actually direct his hand, the watch may still be good for nothing. Surely, then, this is a liberal art, and far above a manual knack. The study of the means by which such wonders are steadily effected, is therefore the study of a gentleman.

In the account given above of the scapements for pendulums, we assumed as one leading principle that the natural vibrations of a pendulum are performed in equal times, whether wide or narrow. This is so nearly true, when the arches on each side of the perpendicular do not exceed four degrees, that the retardation of the wider arches within that limit will not become sensible, though accumulated for a long time. The common scapement with a plane face of the pallet, helps to correct even this small inequality much better than the nicest form of the cycloidal cheeks proposed by Huyghens.

In watch-work we assume a similar principle, namely, that the oscillations of a balance, urged by its spring, and undisturbed

tion of the arm EA. This communication of pressure is precisely the same that we made use of in explaining the common scapement. MG, FE, and EA, in this fig. 10, are performing the offices which we then gave to the lines MB, BH, and HA, in fig. 3. Harrison's pallet realises the abstract theory.

(d) Mr Harrison was at first by profession a carpenter in a country place. Being extremely ingenious and inventive, he had made a variety of curious wooden clocks. He made one, in particular, for a turret in a gentleman's house. Its exposure made it waste oil very fast, and the maker was often obliged to walk two or three miles to renew it, and got nothing for his trouble. In trudging home, not in very good humour, he pondered with himself how to make a clock go without oil. He changed all his pinion leaves into rollers; which answered very well. But the pallets required it more than any other part. After various other projects, he contrived those now represented, where there was no friction, and no oil is wanted. The turret clock continued to go without being touched till Mr Harrison left the country.

Watch-work undisturbed by all foreign forces, are performed in equal times, whether they be wide or narrow. This principle was assumed by the celebrated mechanician Dr Robert Hooke, on the authority of many experiments which he had made on the bending and unbending of springs. He found that the force necessary for retaining a spring in any constrained position was proportional to its tension, or deflection from its natural form. He expressed this in an anagram, which he published about the year 1660, in order to establish his claim to the discovery, and yet conceal it, till he had made some important application of it. When the anagram was explained some years afterwards, it was, "Ut tensio, sic vis." Dr Hooke thought of applying this discovery to the regulation of watch movements. For, if a slender spring be properly applied to the axis of a watch balance, it will put that balance in a certain determinate position. If the balance be turned aside from this position, it seems to follow that it will be urged back toward it by a force proportional to its distance from it. He immediately made the application to an old watch, which he afterward gave to Dr Wilkins, Bishop of Chester. This was in 1658. Its motion was so amazingly improved, that Hooke was persuaded of the perfection of his principle, and thought that nothing was now wanting for making a watch of this kind a perfect chronometer but the hand of a good workman. For his watch seemed almost perfect, though made in a small country town, in a very coarse manner. Mr Huyghens also claims this discovery. He published his claim about the year 1675, and proposed to make watches for discovering the longitude of a ship at sea. But there is the most unquestionable evidence of Dr Hooke's priority by fifteen years, and of his having made several watches of this kind. One of them was in the possession of his majesty king Charles II. Dr Hooke's first balance spring was straight, and acted on the balance in a very imperfect manner. But he soon saw the imperfections, and made several successive alterations; and, among others, he employed the cylindrical spiral now employed by Mr Arnold; but he gave it up for the flat spiral: and the king's watch had one of this kind before Mr Huyghens published his invention. His project of longitude watches had been carried on along with Lord Brouncker and Sir Robert Moray, and they had quarrelled some years before that publication. See WATCH, Encyc.

But both Dr Hooke and Mr Huyghens were too sanguine in their expectations. We, by no means, have the evidence for the truth of this principle that we have for the accelerating action of gravity on a pendulum. It rests on the nicety and the propriety of the experiments; and long experience has shewn that it is sensibly true only within certain limits. The demonstrations by which Bernoulli supports the unqualified principle of Mr Huyghens, proceed on hypothetical doctrines concerning the nature of elasticity. And even these shew that the law of elasticity which he assumed was selected, not because founded on simpler principles than any other, but because it was consistent with the experiments of Hooke and Huyghens. Besides, although this should be the true law of a spring, it does not follow that this spring, applied in any way to the axis of a balance, will urge that balance agreeably to the same law: and if it did, it still does not follow that the oscilla-

tions of the balance will be isochronous; for the force has to move not only the balance but also the spring. Part of the restoring force of the spring is employed in restoring it rapidly to its quiescent shape, and thus enabling it to follow and still impel the yielding balance. It is therefore only the surplus which is employed in actually moving the balance, and it is uncertain whether this surplus varies according to the same law, being always the same proportion of the whole force of the spring. We find it an extremely difficult problem to determine the law of variation of this surplus, even in the simplest form of the spring; nay, it is by no means an easy problem to determine the law of oscillation of a spring, unloaded with any balance; and we can easily shew that there are such forms of a spring, that although the velocity with which the different parts approach to their quiescent position be exactly as their excursion from it, this is by no means the law of velocity which this spring will produce in a balance. The matter of fact is, that when the spring is a simple straight steel wire, suspending the balance in the direction of its axis, the motions of it, if not immoderate, are precisely agreeable to Huyghens's and Hooke's rule; and that the motion of a balance urged by a spring wound up into a flat, or a cylindrical spiral, as in common watches, and those of Arnold, deviates sensibly from it, unless a certain analogy be preserved between the length and the elasticity of the spring. If the spring be immoderately long, the wide vibrations are slower than the narrow ones; and the contrary is observed when the spring is immoderately short. A certain taper, or gradual diminution of the spring, is also found to have an effect in equalizing the wide and narrow vibrations. There is also a great difference between the force with which a part of the spring unbends itself, and the action of that force in urging the balance round its axis; and the performance of many watches, good in other respects, is often faulty from the manner in which this unbending force is employed.

But, since these corrections are in our power in a considerable degree, we may suppose them applied, and the true motion (which we shall call the cycloidal) attained; and we may then adapt the construction of the escapement to the preserving this motion undisturbed. And here we must see at once that the problem is incomparably more delicate than in the case of pendulums. The vibrations must be very wide, and the angular motion rapid, that it may be little affected by external motions. The smallest inequalities of maintaining power acting through so great a space, must bear a considerable proportion to the very minute momentum of a watch balance. Oil is as clammy on the pallets of a watch as on those of a clock; a viscosity which would never be felt by a pendulum of 20 pounds weight will stop a balance of 20 grains altogether. For the same reason, it is evident that any impropriety in the form of the pallet must be incomparably more pernicious than in the case of a pendulum; the deviation which this may occasion from a force proportional to the angular distance from the middle point, must bear a great proportion to the whole force.

The common recoiling escapement of the old clocks still holds its place in the ordinary pocket watches, and answers all the common purposes of a watch very well. A well finished watch, with a recoiling escapement, will

will keep time within a minute in the day. This is enough for the ordinary affairs of life. But such watches are subject to great variation in their rate of going, by any change in the power of the wheels. This is evident; for if the watch be held back, or pressed forward, by the key applied to the fusée square, we hear the beating greatly retarded or accelerated. The maintaining power, in the best of such watches, is never less than one-fifth of the regulating power of the spring. For, if we take off the balance spring, and allow the balance to vibrate by the impulse of the wheels alone, we shall find the minute hand to go forward from 25 to 30 minutes per hour. Suppose it 30. Then, since the wheels act through equal spaces with or without a spring, the forces are as the squares of the acquired velocities. (DYNAMICS, Suppl. n° 95.) The velocity in this case is double; therefore the accelerating force is quadruple, and the force of the spring is three times that of the wheels. If the hand goes forward 25 minutes, the force of the wheels is about one-fifth of that of the spring. This great proportion is necessary, as already observed, that the watch may go as soon as unstopped.

We have but little to say on this escapement; its principle and manner of action, and its good and bad qualities, being the same with those of the similar escapement for pendulums. It is evident that the maintaining power being applied in the most direct manner, and during the whole of the vibration, it will have the greatest possible influence to move the balance. A given main-spring and train will keep in motion a heavier balance by means of this escapement than by any other. But, on the other hand, and for the same reason, the balance has less dominion over the wheel-work, and its vibrations are more affected by any irregularities of the wheel-work. Moreover, the chief action of the wheel being at the very extremities of the vibrations, and being very abrupt, the variations in its force are most hurtful to the isochronism of the vibrations.

Although this escapement is extremely simple, it is susceptible of more degrees of goodness or imperfection than almost any other, by the variation of the few particulars of its construction. We shall therefore briefly describe that construction which long experience has sanctioned as approaching near to the best performance that can be obtained from the common escapement. Fig. 11. represents it in what are thought its best proportions, as it appears when looking straight down on the end of the balance arbor. C is the centre of the balance and verge. CA and CB are the two pallets; CA being the upper pallet, or the one next to the balance, and CB being the lower one. F and D are two teeth of the crown wheel, moving from left to right; and E, G, are two teeth on the lower part of the circumference, moving from right to left. The tooth D is represented as just escaped from the point of CA, and the lower tooth E as just come in contact with the lower pallet. The escapement should not, however, be quite so close, because an inequality on the teeth might prevent D from escaping at all. For if E touch the pallet CB before D has quitted CA, all will stand still. This fault will be corrected by withdrawing the wheel a little from the verge, or by shortening the pallets.

The proportions are as follow. The distance between the front of the teeth (that is, of G, F, E, D) and

the axis C of the balance is one-fifth of FA, the distance between the points of the teeth. The length CA, CB of the pallets is three-fifths of the same distance. The pallets make an angle ACB of 95 degrees, and the front DH or FK of the teeth make 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.

From these proportions it appears that the pallet A can throw out, by the action of the tooth D, till it reaches a, 120 degrees from CL, the line of the crown-wheel axis. For it can throw out till the pallet B strike against the front of E, which is inclined 25° to CL. To this add BCA, = 95°, and we have LCa = 120°. In like manner B will throw out as far on the other side. From 240°, the sum of these angles, take the angle of the pallets 95°, and there remains 145° for the greatest vibration which the balance can make without striking the front of the teeth. This extent of vibration suppose the teeth to terminate in points, and the acting surfaces of the pallets to be planes directed to the very axis of the verge. But the points of the teeth must be rounded off a little for strength, and to diminish friction on the face of the pallets. This diminishes the angle of escapement very considerably, by shortening the teeth. Moreover, we must by no means allow the point of the pallet to bank or strike on the foreside of a tooth. This would greatly derange the vibration by the violence and abruptness of the check which the wheel would give to the pallet. This circumstance makes it improper to continue the vibrations much beyond the angle of escapement. One-third of a circle, or 120°, is therefore reckoned a very proper vibration for a escapement made in these proportions. The impulse of the wheels, or the angle of escapement, may be increased by making the face of the pallets a little concave (preserving the same angle at the centre). The vibration may also be widened by pushing the wheel nearer to the verge. This would also diminish the recoil. Indeed this may be entirely removed by bringing the front of the wheel up to C, and making the face of the pallet not a radius, but parallel to a radius and behind it, i. e. by placing the pallet CA so that its acting face may be where its back is just now. In this case, the tooth D would drop on it at the centre, and lie there at rest, while the balance completes its vibration. But this would make the banking (as the stroke is called) on the teeth almost unavoidable. In short, after varying every circumstance in every possible manner, the best makers have settled on a escapement very nearly such as we have described. Precise rules can scarcely be given; because the law by which the force acting on the pallets varies in its intensity, deviates so widely from the action of the balance spring, especially near the limits of the excursions.

The discoveries of Huyghens and Newton in rational mechanics engaged all the mathematical philosophers of Europe in the solution of mechanical problems, about the end of the last century. The vibrations of elastic plates or wires, and their influence on watch balances, became familiar to every body. The great requisites for producing isochronous vibrations were well understood, and the artists were prompted by the speculativists to attempt constructions of escapements proper for this purpose. It appeared clearly, that the most effectual means for

for this purpose was to leave the balance unconnected with the wheels, especially near the extremities of the vibration, where the motion is languid, and where every inequality of maintaining power must act for a longer time, and therefore have a great effect on the whole duration of the vibrations. The maxim of construction that naturally arises from these reflections is to confine, if possible, the action of the wheels to the middle of the vibration, where the motion is rapid, and where the chief effect of an increase or diminution of the maintaining power will be to enlarge or contract the angular motions, but will make little change on their duration; because the greatest part of the motion will be effected by the balance spring alone. This maxim was inculcated in express terms by John Bernoulli, in his Recherches Mécaniques et Physiques; but it had been suggested by common sense to several unlettered artists before that time. About the beginning of this century watches were made in London, where the verge had a portion $edb$ (fig. 12.) of a small cylinder, having its centre $e$ in the axis, and a radial pallet $ba$ proceeding from it. Suppose a tooth just escaped from the point of the pallet, moving in the direction $bde$, the cylindrical part was so situated that the next tooth dropped on it at a small distance from its termination. While the verge continues turning in the direction $bde$, the tooth continues resting on the cylinder, and the balance sustains no action from the wheels, and has only to overcome the minute frictions on the polished surface of a hard steel cylinder. This motion may perhaps continue till the pallet acquires the position $f$, almost touching the tooth. It then stops, its motion being extinguished by the increasing force of the spring. It now returns, moving in the direction $edb$; and when the pallet has acquired the position $ci$, the tooth $g$ quits the circumference of the cylinder, and drops in on the pallet at the very centre. The crooked form of the tooth allows the pallet to proceed still farther, before there is any danger of banking on the tooth. This vibration being also ended, the balance resumes its first direction, and the tooth now acts on the face of the pallet, and restores to the balance all the motion which it had lost by friction, &c. during the two preceding vibrations.

It is evident that this construction obviates all the objections to the former recoiling escapement, and that, by sufficiently diminishing the diameter of the cylindrical part, the friction may be reduced to a very small quantity, and the balance be made to move by the action of the spring during the whole of the excursion, and of the returning vibration. Yet this construction does not seem to have come much into use, owing, in all probability, to the great difficulty of making the drop so accurate in all the teeth. The smallest inequality in the length of a tooth would occasion it to drop sooner or later; and if the cylinder was made very small, to diminish friction, the formation of the notch was almost a microscopical operation, and the smallest shake in the axis of the verge or the balance wheel would make the tooth slip past the cylinder, and the watch run down amain.

About the same time, a French artist in London (then the school of this art) formed another escapement, with the same views. We have not any distinct account of it, but are only informed (in the 7th volume of the Machines approuvées par l'Acad. des Sciences) that the

tooth rested on the surface of a hollow cylinder, and then escaped by acting on the inclined edge of it. But we may presume that it had merit, being there told that Sir Isaac Newton wore a watch of this kind.

A much superior escapement, on the same principle, was invented by Mr Geo. Graham, at the same time that he changed the recoiling escapement for pendulums into the dead beat. Indeed it is the same escapement, accommodated to the large vibrations of a balance. In fig. 13. DE represents part of the rim of the balance-wheel. A and C are two of its teeth, having their faces $be$ formed into planes, inclined to the circumference of the wheel, in an angle of about 15 degrees; so that the length $be$ of the face is nearly quadruple of its height $em$. Suppose a circular arch ABC described round the centre of the wheel, and through the middle of the faces of the teeth. The axis of the balance passes thro' some point B of this arch, and we may say that the mean circumference of the teeth passes through the centre of the verge. On this axis is fixed a portion of a thin hollow cylinder $bcd$, made of hard tempered steel, or of some hard and tough stone, such as ruby or sapphire. Agates, though very hard, are brittle. Chalcedony and corneian are tough, but inferior in hardness. This cylinder is so placed on the verge, that when the balance is in its quiescent position, the two edges $b$ and $d$ are in the circumference which passes through the points of the teeth. By this construction the portion of the cylinder will occupy 210° of the circumference, or 30° more than a semicircle. 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 the balance round in the direction $bcd$. The heel $e$ of the tooth will escape from this edge when it is in the position $b$, and $e$ is in the position $f$. The point $b$ of the tooth is now at $d$, but the edge of the cylinder has now got to $i$. The tooth, therefore, rests on the inside of the cylinder, while the balance continues its vibration a little way, in consequence of the shove which it has received from the action of the inclined plane pushing it out of the way, as the mould board of a plough shoves a stone aside. When this vibration is ended, by the opposition of the balance-spring, the balance returns, the tooth (now in the position $h$) rubbing all the while on the inside of the cylinder. The balance comes back into its natural position $bcd$, with an accelerated motion, by the action of its spring, and would, of itself, vibrate as far, at least, on the other side. But it is aided again by the tooth, which, pressing on the edge $d$, pushes it aside, till it come into the position $k$, when the tooth escapes from the cylinder altogether. At this moment the other edge of the cylinder is in the position $l$, and therefore is in the way of the next tooth, now in the position A. The balance continues its vibration, the tooth all the while resting, and rubbing on the outside of the cylinder. When this vibration, in the direction $dce$, is finished, the balance resumes its first motion $bcd$, by the action of the spring, and the tooth begins to act on the first edge $b$, as soon as the balance gets into its natural position, shoves it aside, escapes from it, and drops on the inside of the cylinder. In this manner are

the vibrations produced, gradually increased to their maximum, and maintained in that state. Every succeeding tooth of the wheel acts first on the edge $b$, and then on the edge $d$; resting first on the outside, and then on the inside of the cylinder. The balance is under the influence of the wheels while the edge $b$ passes to $b$, and while $d$ passes to $d$; and the rest of the vibration is performed without any action on the part of the wheels, but is a little obstructed by friction, and by the clamminess of the oil. In the construction now described, the arch of action or scapement is evidently $30^\backslash circ$, being twice the angle which the face of a tooth makes with the circumference.

The reader will perceive, that when this scapement is executed in such a manner that the succeeding tooth is in contact with the cylinder at the instant that the preceding one escapes from it, the face of the tooth must be equal to the inside diameter of the cylinder, and that the distance between the heel of one tooth and the point of the following one must be equal to the outside diameter. When the scapement is so close there is no drop. A good artist approaches as near to this adjustment as possible; because, while a tooth is dropping, but not yet in contact, it is not acting on the balance, and some force is lost. The execution is accounted very good, if the distance between the centres of two teeth is twice the external diameter of the cylinder. This allows a drop equal to the thickness of the cylinder, which is about $\backslash frac\{1\}\{4\}$th of its diameter.

We must also explain how this cylinder is so connected with the verge 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 or pin fixed into the extremity of the piece of brass $m\; D$ formed on the rim of the wheel. Thus the wedge-tooth has its plane parallel to the plane of the wheel, but at a small distance above it. Fig. B represents the verge, a long hollow cylinder of hard steel. A great portion of the metal is cut out. If it were spread out flat, it would have the shape of fig. C. Suppose this rolled up till the edges $G\; H$ and $G\; H\text{'}$ are joined, and we have the exact form. The part acted on by the point of the tooth is the dotted line $b\; d$. The part $D\; I\; F\; E\text{'}$ serves to connect the two ends. Thus it appears to be a very slender and delicate piece; but being of tempered steel, it is strong enough to resist moderate jolts. The ruby cylinders are much more delicate.

Such is the cylinder scapement of Mr Graham, called also the HORIZONTAL SCAPEMENT, because the balance wheel is parallel to the others. Let us see how far it may be expected to answer the intended purposes. If the excursions of the balance beyond the angle of impulsion were made altogether unconnected with the wheels, the whole vibration would be quicker than one of the same extent, made by the action of the balance-spring alone, because the middle part of it is accelerated by the wheels. But the excursions are obstructed by friction and the clamminess of oil. The effect of this in obstructing the motion is very considerable. Mr I. E. Roy placed the balance so, that it rested when the point of the tooth was on the middle of the cylindric surface. When the wheel was allowed to press on it, and it was drawn $85^\backslash circ$ from this position, it vibrated only during $4\backslash frac\{1\}\{2\}$ seconds. When the wheel was not allowed to touch the cylinder, it vibrated 90 seconds, or 20 times as

long; so much did the friction on the cylinder exceed that of the pivots. We are not sufficiently acquainted with the laws of either of these obstructions to pronounce decidedly whether they will increase or diminish the time of the whole vibrations. We observe distinctly, in motions with considerable friction, that it does not increase nearly so fast as the velocity of the motion; nay, it is often less when the velocity is very great. In all cases it is observed to terminate motions abruptly. The friction requires a certain force to overcome it, and if the body has any less it will stop. Now this will not only contract the excursion of the balance, but will shorten the time. But the return to the angle of impulsion will undoubtedly be of longer duration than the excursion; for the arch of return, from the extremity of the excursion to its beginning, where the angle of impulsion ends, is the same with the arch of excursion. The velocity which the balance has in any point of the return is less than what it had in the same point of the excursion; because, in the excursion, it had velocity enough to carry it to the extremity, and also to overcome the friction. In the return, it could, even without friction, only have the velocity which would have carried it to the extremity; and this smaller velocity is diminished by friction during the return. The velocity being less through the whole return than during the excursion, the time must be greater. It may therefore happen that this retardation of the return may compensate the contraction of the excursion and the diminution of its duration. In this case the vibration will occupy the same time as if the balance had been free from the wheels. But it may more than compensate, and the vibrations will then be slower; or it may not fully compensate, and they will be quicker. We cannot therefore say, a priori, which of the two will happen: but we may venture to say that an increase of the force of the wheels will make the watch go slower: for this will exert a greater pressure, give a greater impulsion, produce a wider excursion, and increase the friction during that greater excursion, making the wide vibrations slower than the narrow ones; because the angle of impulsion remaining the same, the pressures exerted must be quadrupled, in order to double the excursion (see Dynamics, n^o 95. Suppl.), and therefore the friction will be increased in a greater proportion than the momentum which is to overcome it. But, with respect to the obstruction arising from the viscosity of the oil, we know that it follows a very different law. It bears a manifest relation to the velocity, and is nearly proportional to it. But still it is difficult to say how this will affect the whole vibration. The duration of the excursion will not be so much contracted as by an equal obstruction from friction, because it will not terminate the motion abruptly. There are therefore more chances of the increased duration of the return exceeding the diminution of it in the excursion. All that we can say, therefore, is, that there will be a compensation in both cases. The time of excursion will be contracted, and that of return augmented.

Now, as the friction may be greatly diminished by fine polish, fine oil, and a small diameter of the cylinder, we may reasonably expect that the vibrations of such a balance will not vary nearly so much from isochronism as with a recoiling scapement, and will be little affected by changes in the force of the wheels.

Accordingly, Graham's cylindrical escapement supplanted all others as soon as it was generally known. We cannot compare the vibrations with those of a free balance, because we have no way of making a free balance vibrate for some hours. But we find that doubling or trebling the force of the wheels makes very little alteration in the rate of the watch, though it greatly enlarges the angular motion. Any one may perceive the immense superiority of this escapement over the common recoil escapement, by pressing forward the movement of a horizontal watch with the key, or by keeping it back. No great change can be observed in the frequency of the beats, however hard we press. But a more careful examination shews that an increase of the power of the wheels generally causes the watch to go slower; and that this is more remarkable as the watch has been long going without being cleaned. This shews that the cause is to be ascribed to the friction and oil operating on the wide arches of excursion. But when this escapement is well executed, in the best proportions of the parts, the performance is extremely good. We know such watches, which have continued for several weeks without ever varying more than 7^th in one day from equable motion. We have seen one whose cylinder was not concentric with the balance, but so placed on the verge that the axis of the verge was at $o$ (fig. 13.), between the centre $B$ of the cylinder and the entering edge $b$, and $Bb$ was equal to the thickness of the cylinder. The watch was made by Emery of London, and was said to go with astonishing regularity, so as to equal any time piece while the temperature of the air did not vary; and when clean, was said to be less affected by the temperature than a watch with a free escapement, but unprovided with a compensation piece. It is evident that this watch must have a minute recoil. This was said to be the aim of the artist, in order to compensate for the obstruction caused by friction during the return of the balance from its excursions. It indeed promises to have this effect; but we should fear that it subjects the excursions to the influence of the wheels. We suspect that the indifferent performance of cylinder watches may often arise from the cylinder being off the centre in some disadvantageous manner.

The watch from which the proportions here stated were taken, is a very fine one made by Graham for Archibald Duke of Argyle, which has kept time with the regularity now mentioned. We believe that there are but few watches which have so large a portion of the cylinder; few indeed have more than one half, or 180° of the circumference. But this is too little. The tooth of the wheel does not begin to act on the resting cylinder till its middle point $A$ or $B$ touch one of the edges. To obtain the same angle of escapement, the inclination of the face of the tooth must be increased (it must be doubled); and this requires the maintaining power to be increased in the same proportion. Besides, in such a escapement it may happen that the tooth will never rest on the cylinder; because the instant that it quits one edge it falls on the other, and pushes it aside, so that the balance acquires no wider vibration than the angle of escapement, and is continually under the influence of the wheels. The escapement is in its best state when the portion of the cylinder exceeds 180° by twice the inclination of the teeth to the circumference of the wheel.

It would employ volumes to describe all the escapements which have been contrived by different artists, aiming at the same points which Graham had in view. We shall only take notice of such as have some essential difference in principle.

Fig. 14. represents a escapement invented in France, and called the Escapement à Virgule, because the pallet resembles a comma. The teeth $A$, $B$, $C$, of the balance wheel are set very oblique to the radius, and there is formed on the point of each a pin, standing up perpendicular to the plane of the wheel. This greatly resembles the wheel of Graham's escapement, when the triangular wedge is cut off from the top of the pin on which it stands. The axis $c$ of the verge is placed in the circumference passing through the pins. The pallet is a plate of hard steel $aefdb$, having its plane parallel to the plane of the wheel. The inner edge of this plate is formed into a concave cylindrical surface between $a$ and $b$, whose axis $e$ coincides with the axis of the verge. Adjoining to this is the resting face $bd$ of the pallet. This is either a straight line $bd$, making an angle of nearly 30° with a line $ebg$ drawn from the centre, or it is more generally curved, according to the nostrum of the artist. The back of the pallet $aef$ is also a cylindrical surface (convex) concentric with the other. This extends about 100° from $a$ to $f$. The part between $f$ and $d$ may have any shape. The interval $af$ is formed into a convex surface, in such a manner as to be everywhere intersected by the radius in an angle of 30° nearly; i. e. it is a portion of an equiangular spiral. The whole of this is connected with the verge by a crank, which passes perpendicularly through it between $f$ and $e$; and the plate is set at such height on the crank or verge, that it can turn round clear of the wheel, but not clear of the pins. The teeth of the wheel are set so obliquely, and made so slender, that the verge may turn almost quite round without the crank's banking on the teeth. The part $fdb$, called the horn, is of such a length, that when one pin $B$ rests on the outside cylinder at $a$, the point $d$ is just clear of the next pin $A$.

When the wheel is not acting, and the balance spring is in equilibrio, the position of the balance is such that the point $d$ of the horn is near $i$, about 30° from $d$. The figure represents it in the position which it has when the tooth $A$ has just escaped from the point $d$ of the horn. In this position the next tooth $B$ is applied to the convex cylinder, a very little way (about 5°) from its extremity $a$. This description will enable the reader to understand the operation of the virgule escapement.

Now suppose the pin $A$ just escaped from the horn. The succeeding pin $B$ is now in contact with the back of the cylinder; and the balance, having got an impulse by the action of $A$ along the concave pallet $bd$, continues its motion in the direction $dg$, till its force is spent, the point of the horn arriving perhaps at $h$, more than 90° from $d$. All this while the following tooth $B$ is resting on the back $ef$ of the cylinder. The balance now returns, by the action of its spring; and when the horn is at $i$, the pin gets over the edge $ao$, and drops on the opposite side of the concave cylinder, where it rests, while the horn moves from $i$ to $k$, where it stops, the force of the balance being again spent. The balance then returns; and when the horn comes within

300 of $d$, the pin gets out of the hollow cylinder, shoves the horn out of its way, and escapes at $d$. Besides the impulse which the balance receives by the action of the wheel on the horn $bd$, there is another, though smaller, action in the contrary direction, while the point of $B$ passes over the surface $ao$; for this surface being inclined to the radius, the pressure on it urges the balance round in the direction $bd$.

The chief difference of this escapement from the former is that the inclined plane is taken from the teeth of the wheel, and placed on the verge. This alone is a considerable improvement; for it is difficult to shape all the teeth alike; whereas the horn $bd$ is invariable. Moreover, the resting parts, although they be drawn large in this figure for the sake of distinctness, may be made vastly smaller than Graham's cylinder, which must be big enough to hold a tooth within it. By this change, the friction, during the repose of the wheel, that is, during the excursions of the balance, may be vastly diminished. The inside cylinder need be no bigger than to receive the pin. But although the performance of these escapements is excellent, they have not come into general use in this country. The cause seems to be the great nicety requisite in making the pins of the wheel pass exactly through the axis of the verge. The least shake in the pivots of the balance and balance-wheel must greatly change the action. A very minute increase of distance between the pivots will cause the pin $B$ to slide from the edge $a$ to the horn, without resting at all on the inside cylinder; and when it does so, it will stop the balance at once, and, immediately after, the watch will run down. The same irregularities will happen if all the pins be not at precisely the same distance from the axis of the wheel.

This escapement was greatly improved, and, in appearance, totally changed, by Mr Lepaute of Paris in 1753. By placing the pins alternately on the two sides of the rim of the balance-wheel, he avoided the use of the outside cylinder altogether. The escapement is of such a singular form, that it is not easy to represent it by any drawing. We shall endeavour, however, to describe it in such a manner as that our readers, who are not artists, will understand its manner of acting. Artists by profession will easily comprehend how the parts may be united which we represent as separate.

Let $ABC$ (fig. 15.) represent 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, but the pins 2 and 4 on the farther 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, like a crank, that the rim of the wheel may not be interrupted by it. This will be more particularly described by and bye. There is attached to it a piece of hard tempered steel $abcd$, of which the part $abc$ is a concave arch of a circle, having $D$ for its centre. It wants about 30° of a semicircle. The rest of it $cd$ is also an arch of a circle, having the same radius with the balance-wheel. The natural position of the balance is such, that a line drawn from $D$, through the middle of the face $cd$, is a tangent to the circumference of the wheel. But, suppose the balance turned round till the point $d$ of the horn comes to $a$, and the point $c$ comes to 2, in the circumference in which the pins are placed. Then the

pin, pressing on the beginning of the horn or pallet, pushes it aside, slides along it, and escapes at $d$, after having generated a certain velocity in the balance. So far this escapement is like the virgule escapement described already. But now let another pallet, similar to the one 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 that the pin 1, on the upper side of the wheel, escapes from the pallet $cd$, the pin 4, on the under side of the wheel, falls on the end of the circular arch $efg$ of the other pallet. Let the two pallets be connected by means of 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 gotten an impulse from the action of 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 $b$ towards $k$. The pin 4 will therefore rest on the concave arch $gfe$ as the pallet turns round. When the force of the balance is spent, the pallet $cd$ returns towards its first position. The pallet $gh$ turns along 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 a little farther, this pin escapes from the concave arch $efg$, and slides along the pallet $gh$, pushing it aside, and therefore urging the pallet round the centre $E$, and consequently (by means of the connection of the pulleys) urging the balance on the axis $D$ round at the same time, and in the same direction. The pin 4 escapes from the pallet $gh$, when $b$ arrives at 3; but in the time that the pin 4 was sliding along the yielding pallet $gh$, the pin 3 is moving in the circumference $BDA$; and the instant that the pin 4 escapes from $b$ at 3, the pin 3 arrives at 2, and finds the beginning $e$ of the concave arch $cba$ ready to receive it. It therefore rests on this arch, while the balance continues its motion. This perhaps continues 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 $cd$, and when it escapes at 1, another pin on the under side of the wheel arrives at 4, and finds the arch $gfe$ ready to receive it. And in this manner will the vibration of the balance be continued.

This description of the mode of action at the same time points out the dimensions which must be given to the parts of the pallet. The length of the pallet $cd$ or $gh$ must be equal to the interval between two succeeding pins, and the distance of the centres $D$ and $E$ must be double of this. The radius $De$ or $Eg$ may be as small as we please. The concave arches $cba$ and $gfe$ must be continued far enough to keep a pin resting on them during the whole excursion of the balance. The angle of escapement, in which the balance is under the influence of the wheels, is had by drawing $De$ and $Dd$. This angle $eDd$ is about 30°, but may be made greater or less.

Fig. B will give some notion how the two pallets may be combined on one verge. $KL$ represents the verge with a pivot at each end. It is bent into a crank $MNO$, to admit the balance wheel between its branches. $BC$ represents this wheel, seen edgewise, with its pins, alternately on different sides. The pallets are also represented

presented edgewise by $bcd$ and $bgf$, fixed to the inside of the branches of the crank, fronting each other. The position of their acting faces may be seen in the preceding figure, on the verge $D$, where the pallet $gb$ is represented by the dotted line $2i$, as being situated behind the pallet $cd$. The remote pallet $2i$ is placed so, that when the point $d$ of the near pallet is just 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 under side of the rim. A little attention will make it plain, that the action will be precisely the same as when 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 is continuing its motion. When it returns, $2$ gets off the arch of rest, pushes aside the pallet $2i$, escapes from it when $i$ gets to $1$, and then the pin $3$ finds the point $c$ ready to receive it, &c. The vibrations may be increased by giving a sufficient impulse through the angle of scapement. But they cannot be more than a certain quantity, otherwise the top $N$ of the crank will strike the rim of the wheel. By placing the pins at the very edge of the wheel, the vibrations may easily be increased to a semicircle. By placing them at the points of long teeth, the crank may get in between them, and the vibrations extended still farther, perhaps to $240^\backslash circ$.

This scapement is unquestionably a very good one; and when equally well executed, should excel Graham's, both by having but two acting faces to form (and these of hard steel or of stone), and by allowing us to make the circle of rest exceedingly small without diminishing the acting face of the pallet. This will greatly diminish the friction and the influence of oil. But, on the other hand, we apprehend that it is of very difficult execution. The figure of the pallets, in a manner that shall be susceptible of adjustment and removal for repair, and yet sufficiently accurate and steady, seems to us a very delicate job.

Mr Cumming, in his Elements of Clock and Watch-work, describes (slightly) pallets of the very same construction, making what he conceives to be considerable improvements in the form of the acting faces and the curves of rest. He has also made some watches with this scapement; but they were so difficult, that few workmen can be found fit for the task; and they are exceedingly delicate, and apt to be put out of order. The connection of the pallets with each other, and with the verge, makes the whole such a contorted figure, that it is easily bent and twisted by any jolt or unskillful handling.

There remains another scapement of this kind, having the teeth of the balance-wheel resting on a cylindrical surface on the axis of the verge during the excursions of the balance beyond the angle of scapement, and which differs somewhat in the application of the maintaining power from all those already described.

This is known by the name of Duplex's scapement, and is as follows: Fig. 16. represents the essential parts greatly magnified. $AD$ is a portion of the balance-wheel, having teeth $f,\; b,\; g$, at the circumference. These teeth are entirely for producing the rest of the wheel, while the balance is making excursions beyond the scapement. This is effected by means of an agate cylinder $opq$, on the verge. This cylinder has a notch

$o$. When the cylinder turns round in the direction $opq$, the notch easily passes the tooth $B$ which is resting on the cylindric surface; but when it returns in the direction $qpo$, 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 $b$, 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 stout flat-sided pins, standing upright on its rim, as represented by $a,\; D$. There is also fixed on the verge a larger cylinder $GFC$ above the smaller one $opq$, with its under surface clear of the wheel, and having a pallet $C$, of ruby or sapphire, firmly indented into it, and projecting so far as just 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, when the tooth $b$ is escaped from the notch, the pallet $C$ has just passed 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 and advantageous manner, and gives it a strong impulsion, following and accelerating it till another tooth stops on the little cylinder. The angle of scapement 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 scapement would be the whole arch of the large cylinder between $C$ and $a$. But $a$ stops before it is clear of the pallet, and the arch of impulsion is shortened by all the space that is described by the pin while a tooth moves from $B$ to $b$. It stops at $a$.

We are informed by the best artists, that this scapement gives great satisfaction, and equals, if it do not excel, Graham's cylindrical scapement. It is easier made, and requires very little oil on the small cylinder, and none at all on the pallet. They say that it is the best for pocket watches, and is coming every day more into repute. Theory seems to accord with this character. The resting cylinder may be made very small, and the direct impulse on the pallet gives it a great superiority over all those already described, where the action on the pallet is oblique, and therefore much force is lost by the influence of oil. But we fear that much force is lost by the tooth $B$ shifting its place, and thus shortening the arch of impulsion; for we cannot reckon much on the action of $B$ on the side of the notch, because the lever is so extremely short. Accordingly, all the watches which we have seen of this kind have a very strong main spring in proportion to the size and vibration of the balance. If we lessen this diminution of the angle of impulsion, by lessening the cylinder $opq$, and by not allowing $B$ to penetrate far into the notch, the smallest inequality of the teeth, or shake in the pivots of the balance or wheel, will cause irregularity, and even uncertainties in the locking and unlocking the wheel by this cylinder.

A scapement exceedingly like this was applied long ago by Dutertre, a French artist, to a pendulum. The only difference is, that in the pendulum scapement the small cylinder is cut through to the centre, half of it only being left; but the pendulum scapement gives a more effective employment of the maintaining power, because

the wheel acts on the pallet during the whole of the as-
sisted vibration. In a balance escapement, if we attempt
to diminish the inefficient motion of the pin from A to
a, by lessening the diameter of the small cylinder, the
hold given to the tooth in the notch will be so trifling,
that the tooth will be thrown out by the smallest play
in the pivot holes, or inequality in the length of the
teeth.

With this we conclude our account of escapements,
where the action of the maintaining power on the bal-
ance is suspended during the excursion beyond the angle
of impulsion, by making a tooth rest on the surface of
a small concentric cylinder. In such escapements, the
balance, during its excursions, is almost free from any
connection with the wheel, and its isochronism is dis-
turbed by nothing but the friction on this surface.—
We come now to escapements of more artful construc-
tion, in which the balance is really and completely free
during the whole of its excursion, being altogether dis-
engaged from the wheelwork. These are called DE-
TACHED ESCAPEMENTS. They are of more recent date.
We believe that Mr Le Roi was the first inventor of
them, about the year 1748. In the Memoirs of the
Academy of Paris for that year, and in the Collection
of approved Machines and Inventions, we have descrip-
tions of the contrivance. The balance-wheel rests on
a detent, while the balance is vibrating in perfect free-
dom. It has a pallet standing out from the centre,
which, in the course of vibration, passes close by the
point of a tooth of the wheel. At that instant a pin,
connected with this pallet, withdraws the detent from
the wheel, and the tooth just now mentioned follows the
pallet with rapidity, and gives it a smart push forward.
Immediately after, another tooth of the wheel meets the
other claw of the detent, and the wheel is again locked.
When the balance returns, the pin pushes the detent
back into its former place, where it again locks the
wheel. Then the balance, resuming its first direction,
unlocks the wheel, and receives another impulsion from
it. Thus the balance is unconnected with the wheels,
except while it gets the impulsion, and at the moments
of unlocking the wheels.

This contrivance has been reduced to the greatest
possible simplicity by the British artists, and seems
scarcely capable of farther improvement. The follow-
ing is one of the most approved constructions. In
fig. 17. abc represents the pallet, which is a cylinder
of hard steel or stone, having a notch ab. A portion
of the balance-wheel is represented by AB. It is placed
so near to the cylinder that the cylinder is no more
than clear of two adjoining teeth. DE is a long spring,
so fixed to the watch plate at E, as to press very gently
on the stop pin G. A small stud F is fixed to that
side of the spring that is next to the wheel. The tooth
of the wheel rests on this stud, in such a manner that
the tooth a is just about to touch the cylinder, and the
tooth f is just clear of it. Another spring, extremely
slender, is attached to the spring DE, on the side next
the balance-wheel, and claps close to it, but keeping
clear of the stud F, and having its point o projecting
about $\backslash frac\{1\}\{2\}$th of an inch beyond its extremity. When
the point o is pressed towards the wheel, it yields most
readily; but, when pressed in the opposite direction, it
carries the spring DE along with it. The cylinder be-
ing so placed on the verge that the edge a of the notch

is close by the tooth a, a hole is drilled at i, close by
the projecting point of the slender spring, and a small
pin is driven into this hole. This is the whole appa-
ratus; and this situation of the parts corresponds to the
quiescent position of the balance.

Now, let the balance be turned out of this position
80 or 90 degrees, in the direction abc. When it is
let go, it returns to this position with an accelerated
motion. The pin i strikes on the projecting point of
the slender spring, and, pressing the strong spring DE
outward from the wheel, withdraws the stud F from
the tooth; and thus unlocks the wheel. The tooth a
engages in the notch, and urges round the balance.
The pin i quits the slender spring before the tooth quits
the notch; so that when it is clear of the pallet, the
wheel is locked again on the stud F, and another tooth
g is now in the place of a, ready to act in the same
manner. When the force of the balance is spent, it
flows, and then returns toward its quiescent position
with a motion continually accelerated. The pin i arrives
at the point o of the slender spring, raises it from the
strong spring without disturbing the latter, and almost
without being disturbed by this trifling obstacle; and it
goes on, turning in the direction abc, till its force is
again spent; it stops, returns, again unlocks the wheel,
and gets a new impulsion. And in this manner the
vibrations are continued. Thus we see a vibration, al-
most free, maintained in a manner even more simple than
the common crutch escapement. The impulse is given
direct, without any decomposition by oblique action,
and it is continued through the whole motion of the
wheel. No part of this motion is lost, as in Duplex's
escapement, by the gradual approach of the tooth to its
active position. Very little force is required for un-
locking the wheel, because the spring DE is made
slender at the remote end E, so that it turns round E
almost like a lever turning on pivots. A sudden twitch
of the watch, in the direction ba, might chance to un-
lock the wheel. But this will only derange one vibra-
tion, and even that not considerably, because the teeth
are so close to the cylinder that the wheel cannot ad-
vance till the notch comes round to the place of scape-
ment. A tooth will continue pressing on the cylinder,
and by its friction will change a little the extent and
duration of a single vibration. The greatest derange-
ment will happen if the wheel should thus unlock by a
jolt, while the notch passes through the arch of scape-
ment in the returning vibration. Even this will not
greatly derange it, when the watch is clean and vibra-
ting wide; because, in this position, the balance has its
greatest momentum, and the direction of the only jolt
that can unlock the wheel tends to increase this mo-
mentum relatively. In short, considering it theoretically,
it seems an almost perfect escapement; and the perfor-
mance of many of these watches abundantly confirms
that opinion. They are known to keep time for many
days together, without varying one second from day to
day; and this even under considerable variations of the
maintaining power. Other detached escapements may
equal this, but we scarcely expect any to exceed it; and
its simplicity is so much superior to any that we have
seen, that, on this account, we are disposed to give it
the preference. We do not mean to say that it is the
best for a pocket watch. Perhaps the escapement of
Duplex or Graham may be preferable, as being suf-
ceptible

ceptible of greater strength, and more able to withstand jolts. Yet it is a fact that some of the watches made in this form by Arnold and others have kept time in the wonderful manner abovementioned while carried about in the pocket.

Mr Mudge of London invented, about the year 1763, another detached escapement, of a still more ingenious construction. It is a counterpart of Mr Cuning's escapement for pendulums. The contrivance is to this effect. In fig. 18. abc represents the balance. Its axis is bent into a large crank EFGHIK, sufficiently roomy to admit within it two other axes M and L, with the proper cocks for receiving their pivots. The three axes form one straight line. About these smaller axes are coiled two auxiliary springs, in opposite directions, having their outer extremities fixed in the studs A and B. The balance has its spring also, as usual, and the three springs are so disposed that each of them alone would keep the balance at rest in the same position, which we may suppose to be that represented in the figure. The auxiliary springs A and B are connected with the balance only occasionally, by means of the arms m and n projecting from their respective axes. These arms are caught on opposite sides by the pins o, p, in the branches of the crank; so that when the balance turns round, it carries one or other of those arms round with it, and, during this motion, it is affected by the auxiliary spring connected with the arm so carried round by it.

Let us suppose that the balance vibrates $120^\backslash circ$ on each side of its quiescent position abc, so that the radius Ea acquires, alternately, the positions Eb and Ec. The auxiliary springs are connected with the wheels by a common dead-beat pendulum escapement, so that each can be separately wound up about $30^\backslash circ$, and retained in that position. Let us also suppose that the spring A has been wound up $30^\backslash circ$ in the direction ab, by the wheel-work, and that the point a of the rim of the balance, having come from c, is passing through a with its greatest velocity. When the radius Ea has passed $30^\backslash circ$ in its course toward b, the pin o finds the arm m in its way, and carries it along with it till a gets to b. But, by carrying away the arm m, it has unlocked the wheel-work, and the spring B is now wound up $30^\backslash circ$ in the other direction, but has no connection with the balance during this operation. Thus the balance finishes its semivibration ab of $120^\backslash circ$, opposed by its own spring the whole way, and by the auxiliary spring A through an angle of $90^\backslash circ$. It returns to the position Ea, aided by A and by the balance spring, through an angle of $120^\backslash circ$. In like manner, when Ea has moved $30^\backslash circ$ toward the position Ec, the pin p meets with the arm n, and carries it along with it through an angle of $90^\backslash circ$, opposed by the spring B, and then returns to the position Ea, assisted by the same spring through an arch of $120^\backslash circ$.

Thus it appears that the balance is opposed by each auxiliary spring through an angle of $90^\backslash circ$, and assisted through an angle of $120^\backslash circ$. This difference of action maintains the vibrations, and the necessary winding up of the auxiliary springs is performed by the wheel-work, at a time when they are totally disengaged from the balance. No irregularity of the wheel-work can have any influence on the force of the auxiliary springs,

and therefore the balance is completely disengaged from all these irregularities, except in the short moment of unlocking the wheel that winds up the springs.

This is a most ingenious construction, and the nearest approach to a free vibration that has yet been thought of. It deserves particular remark that, during the whole of the returning or accelerated semivibration, the united force of the springs is proportional to the distance from the quiescent position. The same may be said of the retarded excursion beyond the angle of impulse: therefore the only deviation of the forces from the law of cycloidal vibration is during the motion from the quiescent position to the meeting with the auxiliary spring. Therefore, as the forces, on both sides, beyond this angle, are in their due proportion, and the balance always makes such excursions, there seems nothing to disturb the isochronism, whether the vibrations are wide or narrow. Accordingly, the performance of this escapement, under the severest trials, equalled any that were compared with it, in as far as it depended on escapement alone. But it is evident that the execution of this escapement, though most simple in principle, must always be vastly more difficult than the one described before. There is so little room, that the parts must be exceedingly small, requiring the most accurate workmanship. We think that it may be greatly simplified, preserving all its advantages, and that the parts may be made of more than twice their present size, with even less load on the balance from the inertia of matter. This improvement is now carrying into effect by a friend.

Still, however, we do not see that this escapement is, theoretically, superior to the last. The irregularities of maintaining power affect that escapement only in the arch of impulse, where the velocity is great, and the time of action very small. Moreover, the chief effect of the irregularities is only to enlarge the excursions; and in these the wheels have no concern.

Mr Mudge has also given another detached escapement, which he recommends for pocket watches, and executed entirely to his satisfaction in one made for the Queen. A dead beat pendulum escapement is interposed, as in the last, between the wheels and the balance. The crutch EDF (fig. 19.) has a third arm DG, standing outwards from the meeting of the other two, and of twice their length. This arm terminates in a fork AGB. The verge V has a pallet C, which, when all is at rest, would stand between the points A, B of the fork. But the wheel, by its action on the pallet E, forces the fork into the position Bgb, the point A of the fork being now where B was before, just touching the cylindrical surface of the verge. The escapement of the crutch EDF is not accurately a dead beat escapement, but has a very small recoil beyond the angle of impulse. By this circumstance the branch A (now at B) is made to press most gently on the cylinder, and keeps the wheel locked, while the balance is going round in the direction BHA. The point A gets moving from A to B by means of a notch in the cylinder, which turns round at the same time by the action of the branch AG on the pallet C; but A does not touch the cylinder during this motion, the notch leaving free room for its passage. When the balance returns from its excursion, the pallet C strikes on the branch A (still at B), and unlocks the wheel. This now acting on the

crutch pallet F, causes the branch b of the fork to follow the pallet C, and give it a strong impulse in the direction in which it is then moving, causing the balance to make a semivibration in the direction AHB. The fork is now in the situation A g a, similar to B g b, and the wheel is again locked on the crutch pallet E.

The intelligent reader will admit this to be a very steady and effective escapement. The lockage of the wheel is procured in a very ingenious manner; and the friction on the cylinder, necessary for effecting this, may be made as small as we please, notwithstanding a very strong action of the wheel: For the pressure of the fork on the cylinder depends entirely on the degree of recoil that is formed on the pallets E and F. Pres- sure on the cylinder is not indispensably necessary, and the crutch escapement might be a real dead beat. But a small recoil, by keeping the fork in contact with the cylinder, gives the most perfect steadiness to the motion. The ingenious inventor, a man of approved integrity and judgment, declares that her Majesty's watch was the best pocket watch he had ever seen. We are not disposed to question its excellency. We saw an experiment watch of this construction, made by a country artist, having a balance so heavy as to vibrate only twice in a second. Every vibration was sensibly beyond a turn and a half, or $540^\backslash circ$. The artist assured us, that when its proper balance was in, vibrating somewhat more than five times in a second, the vibrations even exceeded this. He had procured it this great mobility by substituting a roller with fine pivots in place of the simple pallet of Mudge. This great extent of detached vibration is an unquestionable excellence, and is peculiar to those two escapements of this ingenious artist.

Very ingenious escapements have been made by Erns- shaw, Howel, Hayley, and other British artists; and many by the artists of Paris and Geneva. But we must conclude the article, having described all that have any difference in principle.

The escapement having been brought to this degree of perfection, we have an opportunity of making experiments on the law of action of springs, which has been too readily assumed. We think it easy to demonstrate, that the figure of a spring, which must have a great extent of rapid motion, will have a considerable influence on the force which it impresses on a balance in actual motion. The accurate determination of this influence is not very difficult in some simple cases. It is the greatest of all in the plane spiral, and the least in the cylindrical; and, in this last form, it is so much less as the diameter is less, the length of the spring being the same. By employing many turns, in order to have the same ultimate force at the extremity of the excursion, this influence is increased. A particular length of spring, therefore, will make it equal to a given quantity; and it may thus compensate for a particular magnitude of friction, and other obstructions. This accounts for the observation of Le Roy, who found that every spring, when applied to a movement, had a certain length, which made the wide and narrow vibrations isochronous. His method of trial was so judicious, that there can be no doubt of the justness of his conclusion. His time-keeper had no fuzee; and when the last revolution of the main wheel was going on, the vibrations were but of half the extent of those made during the first revolution. Without minding the real rate of going, he only compared

the duration of the first and last revolution of the minute hand. An artist of our acquaintance repeated these experiments, and with the same result: But, unfortunately, could derive little benefit from them; because in one state of the oil, or with one balance, he found the lengths of the same spring, which produced isochronous vibrations, were different from those which had this effect in another state of the oil, or with another balance. He also observed another difference in the rate, arising from a difference of position, according as XII, VI, III, or IX, was uppermost; which difference plainly arises from the swagging of the spring by its weight, and, in that state, acting as a pendulum. This unluckily put a stop to his attempts to lessen this hurtful influence by employing a cylindrical spiral of small diameter and great length.