Under this title are usually comprehended such machines only as are moved by weights or springs, and regulated by a pendulum or balance for the purpose of measuring the lapse of time, or indicating or announcing its progress; but other machines also, when they resemble these, sometimes get the same name. It is however of the former sort for measuring time that we propose to treat at present, in a manner suited rather to the general reader than those engaged in the manual practice of the art. Such of these machines as are not portable, and especially if they strike or publish the hours, are called clocks, while the term watch applies to the smaller sort carried in the pocket. Those which are of a more refined and accurate construction are sometimes called timekeepers or chronometers, the latter being generally portable. But it is to be observed, that the term clock work or clock part is often used with reference to the striking part alone, particularly among the artists; while to the going part, which moves the hands, they give the name of the watch work or watch part, even in a clock. We shall first consider what principally belongs to the construction of clocks, and then what more properly relates to watches, though we cannot always adhere to this distinction.

I.—Clock Work.

Clocks, such as we at present use, seem to have been unknown to the ancients; but it is believed that at an Clock and Watch Work.

Clock and early period a train of toothed wheels leading round an index; and regulated by a fly, as in a kitchen jack, had been employed to measure time; which is the more probable, considering the great antiquity of wheel and pinion work. Unfortunately, terms which had at first been used to denote dials and clepsydrae came at length to be applied to other contrivances for measuring time; a circumstance which renders the hints of the early writers very ambiguous. Indeed almost all the accounts we can find of any thing of the sort earlier than the middle of the fourteenth century, seem either to relate to dials and clepsydrae, or are at least so vague and indistinct that we are left in the dark as to the nature of the instruments intended to be described. We are as little informed respecting the inventors, or the dates at which the several parts were invented, of those clocks which have been described to us as existing at that period. For, as Berthoud observes, we can hardly suppose that a clock, imperfect as it then was, could be wholly the invention of any one man, but that it consisted of an assemblage of separate inventions, each of them perhaps having been made by a different person, and probably all at very different periods. The earliest clock with a balance, of which we have any distinct account, was made by Henry de Wyck or de Vick, a German artist, for Charles V., king of France, and set up in the tower of his palace about the year 1364. As some account of so ancient a machine is likely to be interesting, and will supersede a minute description of the like parts of clocks of a more perfect construction, we shall now begin with it.

Fig. 4, Plate CLXIII., represents this huge machine in profile. ABCD is the frame, consisting of two iron plates joined together, and seen edgewise. The top AB, front AC, and bottom CD, form but one plate, kned or bent at right angles at A and C, and having studs or pins formed on its corners, which come through the back plate BD, where they are secured by having nuts screwed upon them. The weight W, of more than 500 lbs., is suspended by a rope wound upon the barrel E, which is fixed on the axle or arbor qq. The ends of this axle turn in holes in the frame plates, and the action of the weight would turn it rapidly round, were there not on the end of the barrel E a small wheel X called a ratchet, with sloping teeth. But a similar ratchet, &c. with the same letters of reference, are better seen in a drawing of a different machine in fig. 10. The axis qq passes through and turns freely in the centre of the first wheel N; and upon a stud fixed in the side of that wheel there turns a click m, which is pressed into the teeth of the ratchet by its spring n. This click permits the sloping backs of the teeth of the ratchet to push it aside and pass it easily without moving the wheel N, when the barrel is turning in the direction which winds up the weight; but the click catches so securely on the faces of the teeth that it will allow none of them to pass in the other direction, or the barrel to turn by the force of the weight, without carrying round with it the first wheel N. This is called click and ratchet work, and probably was a separate invention. The wheel N is thus made to act by means of its teeth upon those of the pinion f. But upon the axis of f, which likewise turns in the frame, is the wheel G, which again impels a pinion g on the axis of the crown wheel H. One end of this axis turns in the front plate AC, and the other in the stud O, which is screwed to the back plate. The crown wheel H has on the edge of its rim teeth like those of a saw, and leaning forward in the direction of its motion. These teeth act alternately on the two teeth or pallets ii of the upright axis II, which carries the cross bar RR called the balance. But this sort of action, which most probably was a separate invention, being indeed the most important thing in this clock, will be particularly explained afterwards. Suffice it at present to say, that it causes the balance loaded with two weights vv, to vibrate or turn alternately backward and forward for each tooth of the wheel H that scopes or passes these pallets. The ends of the axis II turned in holes in the pieces Q, t, but the balance being very heavy was suspended from the cock w by a cord attached to the axle; and no doubt the twisting and untwisting of this cord by alternately raising and lowering the balance accelerated its motion. The balance was for regulating the motion of the machine, which was made to go faster or slower by shifting the weights vv nearer or farther from the axis; there being a set of notches for this purpose on the upper side of the horizontal bar RR.

The first wheel N turns just once round in an hour; its axis qq prolonged through the front plate, carries a pinion p of eight teeth or leaves, which leads round a wheel PP of ninety-six teeth. Now since each tooth of the pinion just lays hold of one tooth of the wheel, the pinion p, which turns in one hour, will lead round the wheel PP with twelve times as many teeth in twelve hours. This wheel therefore carries upon its axis the hour hand h, and twelve pins project from its side for discharging the striking apparatus. The first wheel N has sixty-four teeth acting on a pinion f of eight leaves, which it therefore turns eight times in an hour, or once round in seven minutes and a half. But the wheel G being fixed on the axis of f, also turns in seven minutes and a half; it has sixty teeth acting on the eight leaves of the pinion g, which it therefore turns seven times and a half in seven minutes and a half, or once round in one minute. On the same axis with g is the crown wheel H, which therefore turns in one minute. It has thirty teeth; but since each of these teeth in every revolution acts on both the pallets ii in succession, or meets a pallet in every half revolution, the balance must make just twice as many vibrations in a minute as there are teeth in that wheel, that is, sixty in a minute, or one in a second.

It has been objected, particularly by Mr Reid, that this part of the history of Vick's clock must be erroneous, on the ground, as he supposes with artists in general, that a crown wheel can only work with an odd number of teeth. But we shall afterwards see, that though the odd number is preferable, it is by no means indispensable. Indeed we should think it could make very little difference whether the crown wheel in such a clock had twenty-nine or thirty teeth, provided proper care were taken to place the axis of the balance out of the centre line of the axis of the wheel, by only the 120th part of its circumference, a quantity which the teeth themselves would readily point out. But where so small numbers as nine, eleven, or thirteen teeth are used, as in a common watch, it is very likely the intermediate even numbers ten or twelve could scarcely be made to work at all.

To wind up this clock, a key was put on the squared end s of the axis of the pinion k. By turning the key in the proper direction, the pinion k led round the large wheel K, together with the barrel E, and of course raised or wound up the weight W. The share which the click m and ratchet X have in this operation has been already explained. This method of winding, as it were by a windlass, was well contrived, considering the greatness of the weight, which could scarcely have been wound up in the ordinary way. A similar method is still used, though not on account of a heavy weight, in some of the most refined astronomical clocks; but in these the pinion differs less from the wheel, or sometimes k exceeds K, and is withdrawn from it so soon as the winding is finished.

As already mentioned, this clock had likewise a striking part, which differed little except in size from that still We shall now return to the history, particularly of the pendulum, and then proceed to explain a variety of methods by which the wheel work acts on the pendulum or balance. When a weight or spring is applied to the wheels of a clock or watch, the machine would run down with a rapidly-accelerating motion, till friction and resistance of the air induced a sort of uniformity, as is the case with a kitchen-jack. To check this, and to regulate the movement, a pendulum or balance is applied in such a manner that only one tooth can pass at a vibration. The rate at which the wheels revolve must therefore depend on the duration of the vibrations. Now it had been long known that, within moderate limits, the width of the vibrations of the same pendulum does not much affect their frequency. This has been often, although very incorrectly, reckoned among the discoveries of the justly celebrated Galileo; for the ancient astronomers of the East employed pendulums in measuring the times of their observations, patiently counting their vibrations during the phases of an eclipse or the transits of the stars, and renewing them by a little push with the finger when they languished. Gassendi, Riccioli, and others, in more recent times, followed their example. The alternate motion of a suspended body, and its seeming uniformity, are among the most familiar observations of common life, and it is surprising it was not at an early period thought of as a regulator; whereas the alternate motion of the old balance is one of the least likely means to be hit upon that can be imagined, and might pass for the invention of a very reflecting mind. A pendulum only requires to be drawn aside and let go, that it may vibrate regularly; whereas the old balance being without a spring, must be put in motion by the clock, then stopped by it; next set in motion by the clock in the opposite direction, then stopped, and so on. This must have been known, as also that like checks and like forces will produce uniform oscillations, before the balance could have been thought of as a regulator. Yet so it is, that clocks regulated by a balance had been long used and become very common over Europe, before any thing like the pendulum was proposed as a regulator. Some say Galileo proposed it about the year 1600, others that he did not do so till thirty years after, by which time it had certainly been applied.

But it is not agreed when or by whom the pendulum was first applied. Sanctarius, in his Commentaries on Avicenna, published in 1625, says he had done so thirteen years before, or in 1612. Some put in as early a claim for Caspar Dorn. According to Mr Thomas Grignon, watchmaker in London, who died at an advanced age in 1784, Richard Harris had in 1644 constructed a turret-clock in London, for the church of St Paul's, Covent-Garden, which had not only a pendulum, but a long pendulum. It is, however, to be wished, that some farther light were thrown on this statement. Galileo's son, Vincenzo Galilei, seems to have applied the pendulum in 1649, Hooke in 1656, Huygens in 1657; and to this elegant geometer belongs the honour of being the first who succeeded in explaining the motions of the pendulum. By the most refined and ingenious application of geometry to mechanical problems, he demonstrated that the wider vibrations of a pendulum employ rather more time than the narrower, and that the time of a semicircular vibration is to that of a very small one nearly as 34 to 29; and, aided by a new department of geometrical science, invented by himself, namely, the evolution of curves, he showed how to make a pendulum swing in a cycloid, and that its vibrations in this curve are all performed in equal times, whatever be their extent. But long before 1673, the year in which Huygens published these investigations, Dr Hooke, the most ingenious and inventive mechanician of his age, had discovered the great accuracy of pendulum clocks, having found that the real merit of pendulums had been obscured, from their having been made to vibrate in very large arcs—a fault almost inseparable from the only method then known of giving them motion. He therefore, in 1656, as appears from astronomical observations made at Oxford, invented another method, and made a clock which moved with astonishing uniformity. Using a long and heavy pendulum, and making it swing in very small arcs, which implies his having then used the anchor pallets, the clocks so constructed were found to excel the cycloidal pendulums of Huygens; and those who were unfriendly to this philosopher had a sort of triumph on the occasion. But perhaps, after all, Huygens was the first who explained this, and showed that the error of an hundredth of an inch in the formation of the parts which produced the cycloidal motion, would cause a greater irregularity than a circular vibration of even $10^\circ$ or $12^\circ$ could do. The unavoidable inaccuracies even of the best artists, in the cycloidal construction, make the performance much inferior to that of a common pendulum vibrating in arcs not exceeding $6^\circ$ or $7^\circ$.

As already observed, a pendulum need only be drawn aside and let go, that it may vibrate and measure time. Hence it might seem that nothing is wanted but machinery so connected with the pendulum as to keep a register, as it were, of the vibrations. It would not be difficult to contrive a method of doing this; but more is wanted. The air must be displaced by the pendulum. This requires some force, and must therefore employ some part of the momentum. If the pendulum swing on pivots, they occasion friction. If hung by a thread or thin piece of metal to avoid such friction, some force is lost from want of perfect flexibility or elasticity. These and other causes make the vibrations gradually languish till the pendulum is brought to rest. It is therefore necessary to have a contrivance in the wheel work, which will restore to the pendulum the small portion of force lost in every vibration. Hence, the action of the wheels may be called a maintaining power, because it keeps up the vibrations; but we now see that this may affect the regularity of vibration. If it be supposed that the action of gravity renders all the vibrations isochronous, or of equal duration, we must grant that the additional impulsion by the wheels will destroy that isochronism, unless it be so applied that the sum total of this impulsion, and the force of gravity, may vary so with the situation of the pendulum, as still to give a series of forces, or a law of variation, perfectly similar to that of gravity. We cannot expect to effect this, unless we know both the law which regulates the action of gravity, producing isochronism of vibration, and the intensity of the force to be derived from the wheels, in every situation of the pendulum.

From the principles of dynamics, it appears necessary for the isochronous motion of the pendulum, that the force which urges it towards the perpendicular be everywhere proportional to its distance from it; and therefore, since pendulums swinging in small circular arcs are sensibly isochronous, we must infer that such is the law by which the accelerating action of gravity on them is really accommodated to every situation in those arcs. The effect of the maintaining power will be better understood by keeping in view the chief circumstances attending a motion of this kind. Therefore, let ACa, fig. 1, Plate CLXI., represent the arc passed over by the pendulum, and as if stretched out into a straight line. Let C be its middle point when the pendulum hangs perpendicularly, and Aa the extremities of the oscillation. Let Clock and AD be drawn perpendicular to AC, to represent the accelerating action of gravity on the pendulum at A, and parallel to AD draw the equal line ad; join Dd. About C, as a centre, describe the semicircle AFHo. Through any points B, K, k, b, &c. of AA draw the perpendiculars BFE, KLM, &c. cutting both the straight line and semicircle. Then,

1. The actions of gravity on the pendulum, when in the situations B, K, &c., by which it is urged toward C, are proportional to, and may be represented by, the ordinates BE, KL, be, kl, &c.

2. The velocities acquired at B, K, &c., by the acceleration along AB, AK, &c., are proportional to the ordinates BF, KM, &c. of the semicircle AHa; and therefore the velocity at C is to that at any other point B, as CH to BF.

3. The times of describing the parts AB, BK, &c. of the whole arc of oscillation, are proportional to, and may be represented by, the arcs AF, FM, MH, &c.

4. If one pendulum describe the arc represented by ACa, and another that represented by KCk, they will describe them in equal times, and their maximum velocities in passing C are proportional to AC and KC; that is, to the width of the oscillations.

The same propositions are true with respect to the outward motions from C. That is, when the pendulum describes CA with the initial velocity CH, its velocity at K is reduced to KM by the retarding action of gravity. It is reduced to BF at B, and to nothing at A; and the times of describing CK, KB, BA, CA, are as HM, MF, FA, HA. Another pendulum setting out from C, with the initial velocity CO, reaches only to K, CK being equal to CO. The times of their vibrations are likewise equal. If we consider the whole oscillation as performed in the direction Ao, the forces AD, BE, KL accelerate the pendulum; and the similar forces ad, be, kl, on the other side retard it. The contrary happens in the next oscillation, oCA.

5. The areas DABE, DAKL, &c., are proportional to the squares of the velocities acquired by moving along AB, AK, &c.; or to the diminution of the squares of the velocities sustained by moving outwards, along BA or KA, &c.

The consideration of this figure will enable us to form some notion of the effect of any proposed application of a maintaining power by means of wheel work; for, knowing the weight of the pendulum, we know the accelerating action of gravity upon it in any particular situation A. We also know how much we aid or counteract the motion of the pendulum in that situation by the wheel work. Suppose it is aided by an addition of pressure equal to a certain number of grains. We can make AD to Dd as the previous force to the increase, and then Ad will be the whole force urging the pendulum toward C. Doing the same for every point of AC, we obtain a line or curve dAc, which is a new scale of forces, and the space DCd comprehended between the two scales CD and Cd will express the addition made to the square of the velocity in passing along AC by the joint action of gravity and the maintaining power. Also by drawing a line ps perpendicular to AC, making the area Cps equal CAD, the point p will be the limit of the oscillation outward from C where the initial velocity HC is extinguished. If the line ps cut the semicircle in q, one half of the arc qa will nearly express the contraction made in the time of the outward oscillation by the maintaining power. An accurate determination of it is operose, and even difficult; but this solution is not far from the truth, and will assist us in judging of the effect of any proposal, even though pq be drawn by estimation of the eye, making the area left out as nearly equal to what is taken in as we can estimate by inspection.

Since the motion of a pendulum or balance is alternate, while the pressure of the wheels is constantly in one direction, some art must be used to accommodate the one to the other. When a tooth of the wheel has given the balance a motion in one direction, it must quit it that it may return, and perhaps get an impulsion in the opposite direction, though that is not always the case. The balance or pendulum thus escaping from the tooth of the wheel, or the tooth from it, has given to all contrivances for this purpose the general name of escapement or scape-

ment.

The oldest escapement known is the one still used in common watches. It was employed in the earliest balance clocks and watches on record, and was for ages after the only one in use, even in pendulum clocks, till Hooke introduced the long heavy pendulum. It is very simple, and its mode of operation is too obvious to need much explanation. In fig. 2, Plate CLXL, XY represents a horizontal axis, to which the ball of the pendulum P is attached by a slender rod or otherwise. This axis has two leaves C and D attached to it, one near each end, and not in the same plane, but so that, when the pendulum hangs perpendicularly, or at rest, the piece C spreads 40° or 50° to the right hand, and D as much to the left. These two pieces are called pallets, and the axis XY which carries them the verge, though some writers apply this term to any small rod or axis, as the French do. AFB represents a wheel turning on an upright axis EO in the order of the letters AFEB. Its rim resembles a hoop with one edge cut into teeth like those of a saw, and leaning forward in the direction of its motion. It is sometimes called the crown wheel, from the teeth a little resembling the points of an antique royal diadem. The number of teeth should be odd; so that when one of them B is pressing on a pallet D, the opposite pallet C may be in the space between two teeth A and L. But it is evident that, if the verge do not pass exactly over the centre of the wheel, which seems to have been the case in some of the old watches, particularly those of Huygens, a large even number of teeth might work, because by this means the arrangement just mentioned could readily be given to the pallets and teeth. Hence Le Roy and Berthoud may not, as some suppose, be in any mistake when they say the crown wheel in Vick's ancient clock had thirty teeth. In Howell's escapement, described in vol. x. Trans. Soc. of Arts, &c. the verge passes quite past the side of the common axis of the two crown wheels; the eccentricity must therefore have much exceeded the 120th part of the circumference, which we mentioned above as just sufficient for Vick's escapement with thirty teeth.

The figure represents the pendulum at the extremity of its excursion to the right, the tooth A having just escaped from the pallet C, and the tooth B having just dropped on the pallet D. It is plain that while the pendulum now moves over to the left, in the arc PG, the tooth B continues to press on the pallet D, and thus accelerates the pendulum, both during its descent along the arc PHI, and in its ascent along the arc HG. It is no less evident that, when the pallet D, by turning the axis XY, raises its point above the plane of the wheel, the tooth B escapes from it, and I drops on the pallet C, which is now nearly perpendicular. I presses C to the right; and accelerates the motion of the pendulum along the arc GP. Nothing can be more obvious than this action of the wheel in maintaining the vibrations of the pendulum. We can easily perceive also that, when the pendulum is hanging perpendicularly in the line XH, the tooth B, by pressing on the pallet D, will force the pendulum a little way to the left of the perpendicular, and the more so as the pendulum is lighter; and if it be sufficiently light, it will be forced so far from the perpendicular that the tooth B will escape, and then I will catch on C, and force the pendulum back to P, where the whole operation will be repeated. The same effect will be produced in a more remarkable degree if the rod of the pendulum be continued through the axis XY, and a ball Q put on the other end to balance P; and indeed this is the contrivance which was first applied to clocks all over Europe before the application of the pendulum. They were balance clocks, nearly allied to that of Vick, already described. The force of the wheel was of a certain magnitude, and therefore able, during its action on a pallet, to communicate a certain quantity of motion and velocity to the balls or weights of the balance. When the tooth B escapes from the pallet D, the balls are moving with a certain velocity and momentum. In this condition, the balance is checked by the tooth I catching on the pallet C; but it is not instantly stopped. It continues its motion a little to the left, and the pallet C forces the tooth I a little backward, but not so far as to escape over it; because all the momentum of the balance was generated by the force of the tooth B, and that of I is equally powerful. Besides, when I catches on C, and C continues its motion to the left, its lower point applies to the face of the tooth I, which now acts on the balance by a longer and more powerful lever, and soon stops its farther motion in that direction, but continuing to press on C, it turns back the balance in the opposite direction. We thus see how, in a scapement of this kind, the motion of the wheel must be very hobbling and unequal, making a great step forward and a short step backward at every beat, from which it is sometimes called the recoiling scapement or the recoiling pallets. This hobbling motion is very observable in the wheel of an alarm, and indeed wherever this scapement is employed with wide vibrations.

Of the two principles of regulation which have been noticed above, the most obvious and by far the most perfect is the natural and nearly isochronous vibrations of a pendulum. The only use of the wheel work here, besides registering the vibrations, is to give a gentle impulse to the pendulum by means of the pallets, in order to compensate friction, &c. But in a balance there is no such native motion to which that of the wheels must accommodate itself; the wheels, urged by a determinate pressure, and acting through an assigned space, must generate a certain velocity in the balance; and therefore the time of the oscillation is also determined, both during the progressive and the retrograde motion of the wheel. Hence a balance moved in this manner would be isochronous, and fit for regulating a time-keeper, did the action of the wheels upon the pallets continue always the same; but as this is not exactly the case, other contrivances have been employed where greater exactness is required, as will be noticed hereafter.

The verge XY does not require to be in a horizontal position when a balance is employed. Accordingly, in the old clocks this axis was vertical; so that the whole weight of the balance rested on one pivot, which, if of hard steel and small size, greatly diminished friction. Indeed friction was sometimes nearly annihilated, as in the case of Vick's clock, by suspending the balance by a thread. But perhaps it was the want of, or to avoid a contrate wheel, which caused the verge at first be placed upright. As the balance admits of every position of the machine, balance clocks were made in an infinite variety of forms and sizes. The substitution of a spring in place of a weight as a first mover was a most ingenious thought, but was only brought to its present state very gradually. There was lately to be seen at Brussels an old clock, having for a mainspring a sword blade, with a string attached to the point of it, and wound round the barrel of the first wheel. The spiral clock and mainspring is supposed to have originated in Germany. It takes less room, and produces more revolutions of the barrel. Clocks thus far advanced only needed to be reduced in size to be portable. This was accomplished very early, though the exact date is unknown.

As already observed, it is doubtful who first substituted Anchor the pendulum instead of the balance in clocks. But many years elapsed before the pendulum was applied in anything like a proper form. Being light, short, and vibrating in wide arcs, it formed but a very imperfect regulator. Hooke saw these defects, which were not easily avoidable with the crown wheel; and so early as 1656 he, as already mentioned, contrived another scapement, with a long heavy pendulum, and very nearly allied to that which is still in most general use. In this scapement we ordinarily employ teeth moving in not very different directions, whereas in the crown wheel opposite teeth were employed moving in contrary directions. Yet even here we communicate an alternate motion to the verge or axis of the pallets, in the following manner. On that axis A, fig. 3, Plate CLXI., which is the same, or in a line with that of the pendulum, is fixed a piece of metal BAC, which we call the crutch, and the French tancre. Its extremities Bb, Cc, are in this case the pallets, upon which the teeth of the swinging wheel BC act, in pressing forward in the direction BC. The faces Bb, Cc, are set in such positions that the teeth push them out of the way. Thus they push B to the left, and C to the right. Both pallets are pushed sidewise outward from the centre of the wheel. The pendulum rod AS is placed as if at rest. Suppose it drawn aside to the right at Q, and then let go. It is plain that the tooth B, pressing on the face of the pallet SBb, all the way from β to b, thrusts it aside outwards, and thus, by the connection of the crutch with the pendulum rod, aids the motion of the pendulum along the arc QPR. When the pendulum reaches R, the point of the tooth B has reached the angle b of the pallet, and escapes from it; then another tooth drops on the pallet face Cc, and by pressing it outward, aids the pendulum to move from R to P. The tooth escapes from this pallet at the angle c, and now a tooth B' drops on the first pallet, and again aids the pendulum, and so on.

The mechanism of this communication of motion is explained by several elementary writers as follows:—The tooth B, fig. 4, is urged forward in the direction BD, perpendicular to the radius MB of the swinging wheel. It therefore presses on the pallet, which is movable only in the direction BE, perpendicular to BA, the radius of the pallet. Wherefore the force BD must be resolved into two, viz. BE in the direction in which alone the pallet can move, and ED or BF perpendicular to it. The latter only presses the pallet and crutch against the pivot hole A. BE is the only useful force, or the force communicated to the pallet enabling it to maintain the pendulum's motion by restoring the momentum lost by friction and other causes.

But this is a very erroneous account of the modus operandi, as may at once be seen by supposing the radius of the pallet to be a tangent to the wheel; which is a position most frequently given to them, and is the very position in fig. 3. In this case MB is perpendicular to BA, and therefore BD will coincide with BA, and there will be no such force as BE to move the pendulum. It is a truth deducible from what we know of the constitution of solid bodies, that when two of them press on each other, the direction in which the mutual pressure is exerted is always perpendicular to the touching surfaces. Whatever be the shapes of the faces of the tooth and pallet, we can draw a plane BN, to be a common tangent to both sur- faces, and a line HBI, through the point of contact perpendicular to BN. It is farther demonstrable, that the action of the wheel on the pendulum is the same as if the whole crutch were annihilated, and in its stead there were two rigid lines AH, MI, from the centres of the crutch and wheel, perpendicular to, and connected by, a third rigid line or rod HI.

For if a weight V be hung at v, the extremity of the horizontal radius Me of the wheel, it will act on the lever eMI, pressing its point I upwards in the direction HI perpendicular to MI; the upper end of this rod HI will in like manner press the extremity H of the rod HA, and this will urge the pendulum from P towards R. To withstand this, the pendulum AP may be withheld by a weight Z hanging by a thread on the extremity of the horizontal lever Az equal Mr, and connected with the crutch and pendulum. The weights V and Z may be so proportioned to each other, that by acting perpendicularly on the crooked levers eMI, zAH, the pressures at H and I shall be equal, and just balance each other by the intervention of the rod HI. When this is the case, we have put things into the same mechanical state, in respect of mutual action, as if effected by the crutch, pallets, and wheel, which in like manner produce equal pressures at B, the point of contact in the direction BH and BI. The weight V may be such as produces the very same effect at B as does the previous train of wheel work. The weight Z, therefore, must be just equal the force produced by the wheel work on the point z connected with the pendulum rod, because by acting in the opposite direction it just balances it.

To determine the force communicated to the pendulum by the wheels: Let x be the upward pressure excited at I, and y the equal opposite pressure excited at H. Then by the property of the lever, MI : Mr :: V : x, and x × MI = V × Mr. In like manner, y × AH = Z × Az. Therefore, since x = y and Az = Mr, we have V : Z :: MI : AH. That is, the force exerted by the tooth of the wheel in the direction of its motion, is to the force impressed on the pendulum rod at a distance equal to the radius of the wheel, as MI to AH. The force impressed on the ball of the pendulum is less than this in the ratio of AP to Az, or Mr.

Cor. 1. If the perpendiculars MN, AO, be drawn on the tangent plane, the forces at B and z will be as BN to BO. For these lines are respectively equal to MI and AH.

Cor. 2. If HI meet the line of the centres AM in S, the forces will be as SM to SA; that is, V : Z :: SM : SA.

Cor. 3. If the face βBb of the pallet be the involute of a circle described with the radius AH, and the face of the tooth be the involute of a circle described with the radius MI, the force impressed on the pendulum by the wheels will be constant during the whole vibration. But these are not the only forms which produce such constancy. The forms of teeth described by De Lahire, Camus, and others, for producing a constant force in the trains of wheel work, will have the same effect here. It is also easy to see that the force impressed on the pendulum may be varied according to almost any law, by making these faces of a proper form. Therefore the face, from B outwards, may be so formed that the force communicated to the pendulum by the wheels during its descent from Q to P, may be in one constant proportion to the acceleration of gravity, and then the sum of the forces will be such as produce isochronous vibrations. If the inner part Bb of the face be formed on the same principle, the difference of the forces will have the same law of variation. If the face βb be the involute of a circle, and the tooth B terminate in a point, gently rounded, or quite angular, the force on the pendulum will continually increase as the tooth slides from β to b. For the line AH continues of the same magnitude, and MI diminishes. The contrary will happen if the pallet be a point, either sharp or rounded, and the face of the tooth be the involute now mentioned; for MI will remain the same, while AH diminishes. If the tooth be pointed, and Bb be a straight line, the force communicated to the pendulum will diminish, while the tooth slides from β to b. For in this case AH diminishes, and MI increases.

Cor. 4. In general, the force on the pendulum is greater, as the angle MBb increases, and as ABB diminishes.

Cor. 5. The angular velocity of the wheel is to that of the pendulum, in any part of its vibration, as AH to MI. This is evident; because the rod IH moving (in the moment under consideration) in its own direction, the points H and I move through equal spaces; and therefore the angles at A and M must be inversely as the radii.

All that has been said of the first pallet AB, may be applied to the second AC. If the perpendicular Cs be drawn to the touching plane oCn, cutting AM in s, we have V : Z :: SM : SA, as in Cor. 2. And if the perpendiculars Ms Ak be drawn on Cs, we have V : Z :: Ms : Ak, as in the general theorem. The only difference in the action on the two pallets is, that if the faces of both are plain, the force on the pendulum increases during the whole action on the pallet C; whereas it diminishes during the progress of the tooth along the other pallet.

Since each tooth of the wheel acts on both pallets in succession, and since during its action on each of them the pendulum makes one vibration, the number of vibrations during one turn of the wheel must be double the number of its teeth; consequently, while a tooth slides along one of the pallets, it advances half the space between two successive teeth; and when it escapes from the pallet, the other tooth may be just in contact with the other pallet. We say it may be so; in which case there will be no dropping of the teeth from pallet to pallet. This, however, requires very nice workmanship; the teeth must be precisely equal, and at equal distance from each other. Should the tooth which is just going to apply to a pallet, chance to be a little too far advanced on the wheel, it would touch the pallet before the other had escaped. Thus, suppose that before B escapes from the point b of the pallet, a tooth is in contact with the pallet C, B cannot escape. Therefore, when the pendulum returns from R toward Q, the pallet Bb returning along with it, will push back the tooth B in opposition to the force of the wheel, so that whatever motion the wheel had communicated to the pendulum, during its swing from P to Q, will now be taken from it again. The pendulum will not reach Q, because it had been aided in its motion from Q, and had proceeded farther than it would have done without this help. Its motion toward Q is farther diminished by the friction of the pallet. Therefore it will now return from some nearer point q, and will not go so far as in the last vibration, but will return through a still shorter arc. It will be more contracted in the next vibration, and so on. Thus it appears, that if a tooth chance to touch the pallet before the escape of the other, the wheel will advance no further; and soon after, the pendulum will be brought to rest.

For such reasons it is necessary to allow one tooth to escape a little before the other reaches the pallet on which it is to act, and to allow a small drop of the teeth from pallet to pallet. But it is accounted bad workmanship to let the drop be considerable, and close scapement is accounted a mark of care and good workmanship. It is evidently an advantage, because it gives a longer time of action on each pallet. From all that has been said, it appears that the interval between the pallets should comprehend a certain number of teeth, and half a space more. In contriving a escapement, the first circumstance to be considered is the angular motion that is intended to be given to the pendulum during the action of the wheel. This is usually called the angle of escapement, or the angle of action. Having fixed on an angle \(a\), which we think proper, we must secure it by the position and form of the face of the pallets. Dividing \(180^\circ\) by the number of teeth in the swing wheel, the quotient is evidently the angle \(b\) of the wheel's motion during one vibration of the pendulum. In the line \(AM\), joining the centres of the crutch and wheel, make \(SM\) to \(SA\), and \(SM\) to \(TA\), as \(a\) to \(b\); and then having determined how many teeth shall be comprehended between the pallets, call this number \(n\). Set off \(\frac{1}{2} b (n + 1)\) in the extreme circumference of the wheel on each side of the line \(AM\), as at \(TB\) and \(TC\). Join \(SB, SC\); draw \(BB'\) perpendicular to \(SB\), for the medium position of the face of the first pallet, when the pendulum hangs perpendicularly. In like manner, drawing \(OC\) perpendicular to \(SC\), we have the medium position of the second pallet. The demonstration of this is very evident from what has been said above.

We have hitherto supposed that the pendulum finishes a vibration at the instant a tooth escapes from a pallet, and another drops on the other pallet. But this should never be the case; for if, when the clock is clean and in good order, the pendulum do not go beyond the angle of escapement, but stop precisely at the drop of a tooth, then by the time it gets foul and the vibration shortens, the teeth will not escape at all, and the clock will immediately stop. This remark applies to most other escapements, and to those in watches as well as clocks. Therefore the force communicated by the wheels during the vibration within the limits of escapement, must be increased so as to make the pendulum throw farther out, as the artists term it; and a clock is more valued the more it throws out beyond the angle of escapement, with the same moving power. For this there are good reasons: the momentum of the pendulum, and its power to regulate the clock, which Mr Harrison significantly calls its dominion, are within proper limits very nearly proportional to the width of its vibrations. It is easy to see that, when the face \(BB'\) of the leading pallet is a plane, if the pendulum continue its motion to the right from \(P\) toward \(Q\), after the tooth \(B\) has dropped on it, the pallet will push the wheel back again, while the tooth slides outward on the pallet toward \(B'\). Such pallets, therefore, will make a recoiling escapement, resembling, in this respect, the old pallet employed with the crown wheel, and having the properties attached to it; in particular that of being much affected by any inequalities in the maintaining power. It is well known that a common watch goes slower when very near run down, in consequence of the mainspring not pulling by a radius of the fusee. Also, by pressing forward the wheel work by means of the key, we immediately hear the beating accelerated, and vice versa. The reason of this is pretty plain; the balance, in consequence of the acceleration in the angle of escapement when aided by the key, would have gone much farther, employing nearly its usual time in the excursion; but by being checked abruptly, both the vibration and the time employed in it are shortened. In the return of the balance, the motion is accelerated the whole way along an arch, which is shorter than what corresponds to its velocity in the middle point; for it is again checked on the other side, and does not make its full excursion. Besides, all this irregularity of force, or the great deviation from forming a resistance to the excursion proportional to the distance from the middle point, is exerted on the balance when it is near the end of the excursion, where the velocity being small, this irregular force acts long upon it at the very time when it has little force wherewith to resist it. All temporary inequalities of force, therefore, will be more felt in this situation of the balance, than if they had occurred in the middle of its motion. Now, although the regulating power of a pendulum greatly exceeds that of the light balances used in pocket watches, something of the same kind may be expected even in pendulum clocks. Accordingly, this appears by a series of experiments made by Berthoud. A clock with a half-second pendulum, weighing five drachms, was furnished with a recoiling escapement whose pallets were planes. The angle of escapement was \(5^\circ 5\). When actuated by a weight of two pounds, it swung eight degrees, and lost fifteen seconds per hour; with four pounds it swung ten degrees, and lost six seconds. Thus it appears, that by doubling the maintaining power, although the vibration was increased, the time was lessened nine seconds per hour, viz. about \(\frac{1}{10}\). But long before this, Dr Halley had made similar experiments, and obtained like results, which it is believed led Graham to invent the escapement shortly to be noticed. It is plain, from what was said when we described the first escapement, that an increase of maintaining power must render the vibrations more frequent. We saw, that even when the gravity of the pendulum is balanced by a weight on the other end of the rod, the force of the wheels will produce a vibratory motion, and that an augmentation of this force will increase it, or make the vibrations more rapid. The precise effect of any particular form of teeth can be learned only by computing the force on the pendulum in every position, and then constructing the curve \(BB'\) of fig. I. The rapid increase of the ordinates beyond those of the triangle \(ADC\), forms a considerable area \(DAPr\), to compensate the area \(SCr\), and thus makes a considerable contraction \(pA\) of the vibration, and a sensible contraction \(\frac{Ag}{2}\) of the time.

For astronomical and other purposes, where a steady or Harrison's at least a direct movement of the seconds hand is wanted, the preference undoubtedly is to be given to escapements which have no recoil; but in other respects the recoiling anchor escapement is scarcely behind any of them. This is owing to the great dominion which a heavy seconds pendulum has over the wheel work. We shall now adduce a striking proof of this. 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 this escapement, in so far as it respects 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 those which we have described, both in form and principle, that we must not omit some account of it.

In fig. II, Plate CLXL, GD represents the swing wheel, whose centre is M. A is the verge or axis of the pendulum, having 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 right to 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, is brought back to it again by a slender spring. The arm AE is furnished with a detent EF, which turns on pivots in the joint E, and which also, when at liberty, maintains its position on the arm by means of a very slender spring.

Let us now suppose the tooth D presses on the claw C, Clock and 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 wheel, 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. The pendulum having finished its excursion to the right (in which it causes the wheel to recoil by means of the detent F), returns towards 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 arc of a circle round A, and approaches the wheel till it takes hold of another tooth 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, and so on.

It is obvious that the pressure of the tooth G on the detent is transferred to the joint E, by the intervention of the shank FE, and from the joint E to the pendulum rod by the intervention of the arm EA. This communication of pressure is precisely similar to what we used in explaining the common scapement. MG, FE, and EA, in this fig. 11, 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; but in his scapement the motion is given to the pendulum by a fair pull or push, and the teeth of the wheel apply themselves to the detents or pallets, without sliding or rubbing. There is no drop, and the scapement makes no noise, being what the artists call a silent scapement. The mechanician will readily perceive, that by properly disposing the arms AB, AE, as also 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 at least with the action of gravity as the nature of a scapement alternately pushing and pulling will admit.

Harrison, however, sometimes poised and otherwise checked his pallets, so that they required no springs; but the principle of the scapement is more easily perceived in the very simple form under which it has been here represented. It is obvious, that were a click or catch, placed on a fixed stud, to fall behind the teeth, the recoil of the wheel might be prevented altogether. Such an obstacle would no doubt tend to check the motion of the pendulum abruptly; yet this could be avoided by contriving some part so as to give way to the pendulum. But the scapement, so modified, would still be nearly allied to a recoiling one; for the action between the teeth and pendulum would be greatest at the extremity of the vibration, where every disturbance of the regular cycloidal vibration occasions the greatest disturbance to the motion. Yet Harrison's clock kept time with most unexampled precision, far excelling all that had been made before, and equal to any that have been contrived since. The want of friction is a great recommendation, but its keeping time so well is chiefly owing to the sovereign control which a long heavy pendulum has over the maintaining power.

The following was the origin of this scapement. Mr Harrison was at first a carpenter in a country place. Being extremely ingenious and inventive, he had made a variety of curious wooden clocks, 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, more than any other part, required some such alteration. After various other projects, he contrived those above described, where there was no friction, and where no oil is wanted. The turret-clock, thus improved, continued to go without being touched till Mr Harrison left the country.

A little prior to the year 1700, the celebrated Mr Graham contrived the following scapement, with the view of leaving the pendulum almost in its natural state. The acting face of the pallet abe, fig. 5, is a plane. The tooth drops on a, and escapes from c, and is on the middle point b, when the pendulum is perpendicular; but beyond a the face of the pallet is an arch ad, whose centre is A, the centre of the crutch. The maintaining power is made so great as to produce a much wider vibration than the angle of active scapement aAc. The consequence is, that when the tooth drops on the angle a, the pendulum, continuing its motion to the right, carries the crutch along with it, and causes the tooth to slide from a to d. But the tooth, by pressing on the arch ad, in a direction passing through the centre of the crutch, can neither accelerate nor retard the motion of the crutch and pendulum. The acting face gh of the other pallet is also a plane; and the remaining part hi of its inner surface is an arch, having the same radius and centre A, as the exterior arch ad has. As the pendulum, after passing the perpendicular, was accelerated by the other pallet gh, it would, if quite unobstructed, throw out farther than what corresponds to the velocity which it had had in the middle of its vibration; perhaps till the tooth passed from a to c on the circular arch of the pallet. But although it sustains no contrary action from the wheels during this excursion, beyond the angle of scapement, it will not proceed so far, but will stop when the tooth reaches some intermediate point d; because there must be some resistance from the friction of the tooth in sliding along the arch of repose ad, and from the clamminess of the oil employed to lubricate it; but this resistance, though rather variable and uncertain, does not amount to an eighth of the pressure on the arch, and generally will be much less.

The chief cause of irregularity seems to be removed in this scapement, viz. the inequality in the action of the wheels in the extremity of the vibration, where the pendulum, having little force, is long exposed to their action in the same little space. The derangement produced by any force depends on the time of its action, and therefore must be greatest when the motion is slowest. The pendulum gets its impulse in the middle of its vibration, where its velocity is the greatest; and, therefore, the inequalities of the maintaining power act on it only for a short time, and make a very trifling alteration in the time of describing the arc of scapement. Beyond this arc it is nearly in the state of a free pendulum; nay, even though it be affected by an inequality of the maintaining power, and be accelerated beyond its usual rate in that arc, the chief effect of this will be to cause it to describe a larger arc of excursion, while the wheel rests on the cylindric... The shortening of the time of this description by the friction will be the same as before, happening at the end of the excursion; but the return will be more retarded by the friction on a longer arch; and by this a compensation may be made for the trifling contraction of the time of describing the arc of scapement.

It is of the greatest importance in all scapements that the impulse be given in the middle of the vibration, where its time of action is the smallest possible, and whereby the pendulum is so long left free from the action of the wheels. When this is adhered to, the form of the face \( abe \) is of less moment. Much has been written on this form, and many attempts have been made to make it such, that the action of the wheels might be proportional to that of gravity. Mr Graham made them planes, not only because these were of easiest execution, but because a plane really conspires pretty well with the change of gravity. While the pendulum moves from \( Q \) to \( P \), fig. 3, the force of gravity acting in the direction \( QP \) is continually diminishing; so is the accelerating power of the pallet from \( a \) to \( b \), fig. 5. While the pendulum rises from \( P \) to \( R \), fig. 3, a force in the opposite direction \( RP \) continually increases. This is analogous to the continual diminution of a force in the direction \( PR \). Now we have such a diminution of such a force in the action of the pallet from \( b \) to \( e \), fig. 5, and such an augmentation in the action of the other pallet.

This scapement fully realized Mr Graham's expectations, and has given great satisfaction in many nice clocks. Mr Graham, however, did not think it prudent to cause a tooth drop on the very corner \( a \) of the pallet, but on a point \( f \) of the arch of excursion. This has also the advantage of diminishing the angle of action, which we have seen to be of service. It requires, indeed, a greater maintaining power, which can easily be procured, and is less affected by changes, to which it is liable from the effect of heat and cold on the oil. Such effects, however, are almost entirely avoided by making the rubbing parts of materials which require no oil. In a clock of this sort long used in the transit room of the Royal Observatory at Greenwich, the pallets were of Oriental ruby, and the wheel of hard-tempered steel. The angle of action seldom exceeded one third the swing of the pendulum. This clock never varied a whole second from equable motion in the course of five days.

This contrivance is known by the name of the dead beat, the dead scapement, the scapement of repose; because the seconds index stands still after each drop, whereas the index of a clock with a recoiling scapement is always in motion hobbling backward and forward.

These scapements, both recoiling and dead beat, have been made in many different forms; but any person acquainted with mechanics will be able to recognise them though under a different shape, or varied in some other unimportant circumstance. A convenient form is given in fig. 6, where the shaded part is the crutch made of brass or iron, and \( A, B \) are two pieces of agate, flint, or other hard stone, cut into the requisite form for pallets of either kind, and firmly fixed in proper sockets. They project half an inch or so in front of the crutch, so that the swing wheel is also before the crutch. Pallets of ruby, with a swing wheel of hard steel, need no oil, but only to be rubbed clean at first with an oily cloth.

Sometimes instead of teeth the wheel has pins ranged round the rim, and perpendicular to its plane. When the pallets are placed on two arms, which, as in fig. 7, overlap each other, and are on the opposite sides of the wheel, the alternate pins are also on the opposite sides. This, which has likewise been adapted to watches, is called Lepaute's scapement. But if the pins be all on one side of the wheel, the pallets may either be on two arms as in fig. 6, or on one as in fig. 8, which is called Amant's scapement.

By the motion of the pendulum to the right, a pin, after resting on the concave arch \( da \), fig. 8, acts on the face \( ae \), and drops from \( c \) on the other concave arch \( hi \), which continues to move a little to the right. It then returns; the pin slides and acts on the face \( gh \), and escapes at \( g \). The next pin is then on the arch of repose \( ad \), and so on. It is to be observed, that if when pallets such as those in fig. 7 and 8 are used, the verge be placed directly above the axis of the swing wheel, it would need a counterpoise, especially if the pallets have an axis separate from that of the pendulum.

It being evident that the recoiling scapement accelerates the vibrations beyond the rate of a free pendulum, and it also appearing to many of the first artists that the dead scapement retards them, they have attempted to form a scapement which might avoid both of these defects, by forming the arches \( ad, hi \), fig. 5 and 8, so as to produce a very small recoil. Berthoud does this in a very simple manner, by placing the centre of \( ad \) at a small distance from that of the crutch, so as to make the rise of the pallet above the concentric arch about one third of the arch itself. Applying such a crutch to his light pendulum which we mentioned above, he found that doubling, and even trebling the maintaining power produced no change on the time of vibration, though it increased the arc from \( 8^\circ \) to \( 12^\circ \) and \( 14^\circ \). We have no doubt of the efficacy of this contrivance, and think it very proper for all clocks requiring much oil. But we apprehend no rule can be given for the angle which the recoiling arch should make with the concentric one, because it seems to depend principally on the share which friction and oil have in producing the retardation in the dead beat; and these are causes of very variable and uncertain amount, even in the same clock.

It has been attempted to avoid the inconveniences of friction and oil on the arch of repose in another way. Instead of allowing the tooth of the wheel to drop on a cylindric surface on the pallet which is called the arch of excursion or arch of repose, it drops on a stop or detent of \( a \), fig. 9, of which the part \( ta \) is an arch whose centre is \( A \), the centre of the crutch, and \( ta \) is in the direction of a radius. This piece \( ota \) does not adhere to the pallet, though it is on the end of an arm \( oA \), which turns round the same axis \( A \) on fine pivots; but it is made to apply itself to the back of the pallet by means of a slender spring attached to the pallet, and pressing inward on a pin fixed in the arm of the detent. When so applied, its arch \( ta \) makes the repose, and its point \( a \) forms a small portion of the face \( abe \) of the pallet. When a tooth escapes from the second pallet by the motion of the pendulum from left to right, another tooth drops on this pallet (which the figure shows to be the first or leading one) at the angle \( t \), and rests on the small portion \( ta \) of an arch of repose. But the crutch continuing its motion to the right, immediately quits the arm \( oA \), carrying the pallet \( be \) along with it, and leaving the wheel locked or detained by the detent \( ota \). By and by the pendulum finishes its excursion to the right, and returns. When it enters the arch of action, the pallet has applied itself to the detent \( ota \), and withdraws it from the tooth. The tooth immediately acts on the united face \( abe \) of the pallet and detent, and restores the motion lost during the last vibration. The use of the spring is merely to keep the detent to the pallet without shaking. It is a little bent during their separation, and adds something of an opposing force to the ascent of the pendulum on the other side of the wheel, and accelerates its return. A similar detent on the back of the second pallet performs a similar office, detaining the wheel while the pendulum is beyond the arch of scapement, and quitting it when the pendulum enters that arch. It is uncertain with whom this invention originated, but it was put in practice by Mudge as early as 1753 or 1754. Contrivances of the same nature were noticed, though obscurely, by Berthoud, Le Roy, and Lepaute. Friction is greatly diminished by being transferred to the pivots at A, so that in the excursion beyond the angle of escapement, the pendulum seems almost free. The detents, however, are not always made to turn on an axis in that of the crutch, but frequently on axes placed without, or at a considerable distance from the verge. Indeed the friction of pivots is sometimes avoided altogether by making the arm of the detent a spring of considerable thickness, except near the top, where it is thin and broad. But a part of the friction still remains, and cannot be obviated; namely, that on the arch ta while it is being drawn from the tooth. Nay, we apprehend that something more than friction must be overcome here. The tooth is apt to force the detent outward unless the part ta be a little elevated at its point α, like a claw above the concentric arch, and the face of the tooth be made to fit such a shape of detent. This will consume some force, when the momentum of the pendulum is by no means at its maximum. Should the clock be foul, and the excursions beyond escapement be very small, this disturbance must be exceedingly pernicious. But we have a much greater objection. During the whole excursion beyond escapement there is a new force of a spring acting on the pendulum which deviates considerably from the proportions of the accelerating power of gravity. This does not commence its action till the detent separate from the arm of the crutch. Then the spring of the detent acts as a retarding force against the excursion of the pendulum now on the other side, bringing it sooner to rest, and then accelerating it in its way back to the beginning of the arch of escapement. In short, this construction should partake of the properties of a recoiling escapement. There is, however, a circumstance in the sort of detached escapements now described, which tends to compensate one of the defects. For if, when the power of the wheels is from some cause augmented, more force is required from the pendulum to unlock the tooth, it should be observed, that the moment the tooth is set free it co-operates with the pendulum in raising the pallet through the remainder of the requisite height; and when the power of the tooth is greater, it acts with greater energy, so that the pendulum must then have so much the less to do. On the contrary, when the force of the wheels happens to relax, the tooth is more easily unlocked, and the pendulum gets and needs less aid in raising the pallet.

In the escapements last described, the pallets were fixed to the crutch and pendulum; and the maintaining power, during its action, was applied to the pendulum by means of the pallets, in the same way as in ordinary escapements. The detents were unconnected with the pendulum, and it was free during the whole excursion. We shall now describe a few of a different class, which are called remontoirs or rewinders; because at short intervals a small force is as it were wound up by the wheels, and afterwards let go upon the pendulum. We shall begin with a escapement executed by Mr. Cumming, in which the manner of applying the maintaining power is extremely different from any yet mentioned. The pallets as well as detents are detached from the pendulum, except in the moment of unlocking the wheel; so that the pendulum is quite free from the wheels in its whole course, except during this short moment, which unfortunately is at the extremity of the vibration.

Cummings's In fig. 10, Plate CLXI., ABC represents a portion of escapement, the swing wheel, of which O is the centre. Z is the centre of the crutch, pallets, and pendulum. The crutch or detents are represented in a form resembling the letter A, having in the circular cross piece a slit ik, also circular, Z being the centre. This form, though somewhat different from Mr. Cumming's, is essentially the same, but is adopted here 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, movable round Z, independently of the detents, and of the second pallet E, which also turns about Z on the arm ZE independently of D. The arm DZ to which the pallet D is attached, lies behind the arm ZF of the detent, being fixed to an axis which has pivots turning concentric with the axis of the pendulum. With the arm ZD is connected the horizontal arm eH, carrying at its extremity the ball H, of such a weight that the action of the tooth A on the pallet D is just able to raise it to the position here drawn. The arm ZE is in like manner connected with an equal ball I on the opposite side. PB represents the fork or pendulum rod behind both detent and pallet. A pin p in that rod projects forward, coming through the slit ik without touching the upper or under margin of it. There is also fixed upon the fork the cross bar mn, of such a length that when the pin of the pendulum rod has unlocked the detent F, the end n of the bar just strikes the arm ZD of the pallet connected with the ball H; and the other end m does the like with the opposite arm EZ. The ball M is connected with the crutch EZF, and of such a weight as just to balance or counterpoise the two detents.

The mode of action is very simple. The natural position of the pallet D is at δ, represented by the dotted lines. It is naturally brought into this position by its own weight, and still more by that of the ball H. The pallet D being set on the foreside of the arm DZ, comes into the same plane with the detent F and the swing wheel. The tooth C of the wheel is supposed to have escaped from the second pallet, immediately after which the tooth A engages with the pallet D, situated at δ, forces it out, and then rests on the detent F, the pallet D leaning on the top of the tooth. It will presently appear how F is brought into this situation. After the escape of C, the pendulum, moving down the arc 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 bar n touches the arm ZD. The pendulum proceeding a hair's breadth farther, 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 thus unlocked, the tooth following C on the other side acts on its pallet E, pushes it off, and rests on its detent G, 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 G 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 n, opposed by the weight of the ball H and the pallet connected with 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 lost during the last vibration. When by moving to the right, the pin p reaches the end k of the slit, 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 another tooth on the pallet D.

The prominent feature of this 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 pendu- It has been supposed that if in this escapement each pallet had still a little way to fall after it ceased to impel the pendulum, it might be made to communicate the remaining force to the opposite detent and unlock it; which would render the pendulum independent of the unlocking. But unless the fall of the pallets were much more considerable, the force of the one could not unlock the other. However, when the detents are separate from the pallets, as in Cumming's escapement, and also separate from each other, the residual force of the loaded pallet may be made to unlock the light detent on the opposite side.

Sometimes pallets like those of Mudge, instead of being fixed near the point from which the pendulum is suspended, are carried by slender spring arms pallets. These are called spring pallets, and have been applied to a variety of escapements. One of the most elaborate is that of the distinguished artist Mr Hardy, in the timekeeper which he made for the Royal Observatory at Greenwich, and described in the Transactions of the Society of Arts, vol. xxxvii. It is, however, to be observed, that in all remontoirs which act by means of springs, the force is affected by the temperature, even supposing the pendulum entirely relieved from the unlocking of the detents; and the same remark applies to similar escapements in watches.

In the Histoire de l'Academie for 1752, mention is made of M. Gallonde having perfected the anchor escapement by applying to it rollers to act as pallets; and in the Machines Approuées, tome vii., we find a figure of this escapement, with a description, in which we are told, that when applied to a clock it only required half the moving power, and had almost no recoil. But the figure surely does not give a very correct representation of this machine. To us, at least, it appears not a little paradoxical. For since, during one vibration of the pendulum, the swing wheel only advances through an arc equal to half the interval between the points of two teeth, it is plain that the largest roller, in the form of an entire cylinder, which can be employed as a pallet, must be somewhat less in diameter than the half interval just mentioned. But the diameter of Gallonde's rollers seems much greater than the half interval. Two views are given of one of them, which to all appearance must have been an entire cylinder. In his swing wheel, the sides of the teeth are concave, though not hooked; the intervals between the teeth being nearly semicircular to a diameter barely exceeding that of the rollers. The depth of these intervals seems equal to the radius of the rollers, so that the half of a roller almost fills up one of them. The engraving represents one roller as being close to the round bottom of the space between two teeth, while the other roller is scarcely free to escape over the top of a tooth. Of course there is no room for the pendulum moving one hair's-breadth beyond the angle of escapement, if even so far.

We are not aware of anything further having been done in this way till 1817, when the Society for the Encouragement of Arts presented Mr William Wynn with their gold Isis medal and twenty guineas for a timekeeper, in which he had managed to introduce rollers whose diameter was at least equal to the entire interval between the points of two teeth. This is effected by employing rollers which are not entire cylinders, that is, by cutting out a part from the side of each roller, to make room for its returning clear of the tooth from which it had last escaped. More recently, Mr David Whitelaw, not being aware of what Wynn had done, has described a similar escapement in the Transactions of the Royal Society of Edinburgh. The following will give some idea of the manner in which these artists have applied the rollers. In fig. 12, Plate CLXII., ABC is the crutch, having at its extremities B, C, rollers to act as pallets. The dotted parts of the small circles represent the parts which are cut out from...

To those acquainted with the anchor pallets or dead beat the mode of action must be quite obvious; but in order that the rollers may always present only their cylindric parts, to be acted on by the teeth, they are so poised or counterpoised, that each, after being moved round a little way by a tooth, naturally resumes the position given it in the figure.

Such scapements display considerable ingenuity; but we rather incline to think that using a large scape wheel with the rollers entire would still be found the preferable mode of constructing a scapement with rollers. That the wheel may have no recoil, the faces of its teeth would need to be concave to suit the one roller, and convex for the other, which could only be accomplished by giving a separate scape wheel to each roller. But when we use only one scape wheel, we must endeavour as much as possible to avoid the recoil, by taking a medium between concave and convex, namely, by making the faces of the teeth planes; and it is easily shown, that the pressure upon the rollers will be least when these planes are directed to the centre of the wheel. Consequently, when a tooth presses on a roller, its face should be as nearly as possible at right angles to a line joining the centres of the roller and crutch. The obvious intention of rollers is the diminution of friction, and that the teeth of the scape wheel may need no oil. In Mr Wynn's timekeeper above mentioned, the leaves of the pinions are also rollers, and the teeth of the wheels of course need no oil. Could pinions with such rollers be readily made with as great exactness as those with teeth, they might in some cases be an acquisition; but we fear that, in the hands of most workmen, they would only furnish a fertile source of great inaccuracy. We are not certain who first applied rollers to the pinions of clocks. Harrison did so more than a century ago. It is, however, to be observed, that wherever there is room to change teeth into rollers of a sufficient thickness to be useful in diminishing friction, the teeth would admit of being made of a smaller size, and consequently a greater number of them could be put in the same pinion, and likewise in its wheel, which in our opinion would be greatly preferable to any rollers, and more easily achieved. For in respect of the bad shape of the teeth, and the small number of them in the pinions, the greater part of clock work is a century behind other machinery.

In 1824, the Society of Arts rewarded Mr J. Aitkin, watchmaker in London, for a very ingenious method of applying a remontoir to the dead beat scapement of a clock. Fig. 1, Plate CLXIII., is a profile of the remontoir, and fig. 3 a front view of it and the scapement, both figures having the same letters of reference. F is the third wheel which works into or drives the equal pinions g and h. G is the scape wheel, and H the crutch, having pallets of the dead beat. The pinion h is fixed on the axis ii, as also eight arms or spring detents j, k, l, m, n, o, p, q, whose ends, after resting in succession upon the cylindric sides of the axle rr of the scape wheel, escape in their turns through the notches 1, 2, 3, 4, 5, 6, 7, 8, as the axis rr revolves. The angular position of the eight notches in the axis is represented in fig. 2 by the same numbers. The axis or arbor rr, on which the scape wheel G is fixed, passes through, and is at liberty to turn freely within, a cylindric hole in a socket, on which is fixed the pinion g and the collet s. The pinion g, therefore, is not fixed on the axis rr, but the helical spring t connects it with the scape wheel G by means of a screw r, which pinches the collet c against the axis; the collet c not being fixed to the socket of the collet s. When the clock has been wound up, the pendulum put in motion, and the axis rr of the scape wheel has turned one eighth round, the detent j will be at liberty to pass through the notch 8, then the wheel F will cause the pinion h, together with the detents, turn one eighth round, and consequently the detent k will be turned till it rest against the cylindric surface of the axis rr opposite the notch 7. The wheel F will at same time have turned the pinion g, together with the collet s, one eighth round, which will rewind the helical spring t, and give sufficient power to the scape wheel G to make one eighth of a revolution during the unwinding of that spring. The detent k will then be at liberty to escape, the wheel F will turn the pinions g and h one eighth round, and at same time the spring t will be again wound up, and so on. This sort of remontoir, it is obvious, may be applied to various other scapements, as well as the dead beat.

The foregoing scapements have been all applied near the top of the pendulum rod; but there are some which act quite at its lower end, with the wheel work below the pendulum. We shall now describe a detached scapement of this sort, which has been known for a considerable time both here and on the Continent; but we have not been able to learn who was its inventor. In fig. 7, Plate CLXIII., ABCD is the scape wheel, represented as locked by the detent DL, which is one of the limbs of the three-legged figure DIK, movable upon a stud or axis at L. K is a counterpoise, which makes the leg LI tend to bear against the fixed stud P. The piece EFG is fixed or united at E to the lower end of the pendulum rod, and the point of the pallet G vibrates along with the pendulum in the arc MN. To the extremity B is attached, by means of a joint, the horizontal lever FH, which is movable upward on that joint, but cannot descend lower than it is represented in the figure. It has a hook at H for catching the claw I of the leg LI while the pendulum is returning from N towards M. But, in the contrary vibration, the sloping back of the hook H, on meeting the slant side of the claw I, rises and passes easily over it, without disturbing the detent, which at any rate cannot turn in that direction. The mode of action will now be evident. While the pendulum returns from N, the hook H, catching the claw I, withdraws the detent DL, and unlocks the tooth D. The wheel immediately springs forward, causing the tooth A to overtake the pallet G, and consequently impel the pendulum in the middle of its vibration. In the mean time, the detent having resumed its former position by means of the counterpoise K, has detained the tooth C. The succeeding vibrations are just repetitions of the same actions.

Among the scapements which the Society of Arts have rewarded of late years, there is in vol. xlviii. of their Transactions a description of one for a turret clock by Mr James Harrison, a descendant of the celebrated John Harrison. It is of the remontoir kind, somewhat allied to Cuming's; but it is rather complex, and has rollers on the pallets. In the same volume, Mr J. Chancellor describes a scapement which has two scape wheels on one axis. The pallets are formed on the ends of a bar fixed across the pendulum rod, and vibrate in a plane perpendicular to those of the scape wheels. It is essentially the same with a scapement which Sully applied in a more simple form to watches early in the last century. But since our limits will not admit of a farther description of scapements, we beg to refer those who may wish to see other contrivances of the sort, to the numerous works of Berthoud; the Transactions of the Society of Arts, &c.; the Repertory of Arts, &c.; Reid's Treatise on Clock and Watch Making, which contains a list of works on the subject; Rees's Cyclopaedia; Nicholson's and other scientific Journals.

Preparatory to the description of a few clocks, &c. it may be of service briefly to enunciate what will be more fully treated of in an after-part of the work, namely, the Clock and Watch Work

general rule for computing the effect of a train of wheels, that if we multiply the several numbers of teeth in each of the wheels or pinions which move or drive, into one product, and the several numbers in those that are moved or driven, into another product, the quotient of the first product by the second is the number of turns or parts of a turn which the last wheel or pinion in the train makes for one turn of the first of the train.

Thus, in the case of Vick's clock, already described, the first wheel N had sixty-four teeth, and turned the pinion f of eight leaves; the second wheel G had sixty teeth, and turned the pinion g of eight leaves. Here 64 times 60 are 3840; and 8 times 8 are 64, by which, if we divide 3840, we have sixty turns of g for one of N, as formerly. Or more systematically thus:

\[ \frac{N \times G}{f \times g} = \frac{64 \times 60}{8 \times 8} = 60. \]

It is almost needless to observe, that when the same factors occur in both numerator and denominator, they should first be thrown out to simplify the process. But it was an excellent rule of the old millwrights, and one which should never be departed from, unless in the case of absolute necessity, that the number of teeth in a wheel should be prime relatively to the number in the wheel or pinion which works or pitches with it; that is, their numbers of teeth should admit of no common divisor. The design of this was, that each tooth of the one wheel might come alike into contact with every tooth of the other wheel or pinion, which would tend to wear them all equally, or to correct any inequalities in their size or form. This would be attained in the above case by giving seventy teeth to N, eleven to f, sixty-six to G, and seven to g.

\[ 70 \times 66 = 60. \]

Thus,

\[ 11 \times 7 = 60. \]

But in cases where numbers exactly prime to each other would not suit the train, the nearest approach to such numbers should be attempted. It is alleged that clock teeth, being cut by an engine, are so exact as to need no such precaution; but that exactness surely does not prevent softer teeth from wearing more quickly than harder ones, or those having accidentally hard particles stuck in them from cutting those teeth only which they act upon, and consequently it does not prevent the teeth becoming unequal, especially where the teeth in the pinion are so few that but one can be acted on at a time. We have, however, some little doubt regarding the great exactness of clock wheels. Sometimes, to be sure, they are cut and finished by an engine, and may not for all that have a good shape, but more commonly the engine is only employed to make slits between the teeth, which are afterwards rounded off by guess with a file; so that it is by mere chance if such a wheel contain two teeth exactly equal, or in their proper places.

Judging from the general and long established practice of making the number of teeth in a wheel an exact multiple of those in its pinion, one is apt to suppose that to be the best possible arrangement, whereas it is just the very worst. In heavy machinery there is at present less regard than there was formerly to the employment of relatively prime numbers; but the superior shape and largeness of the numbers of teeth in mills, &c., render that of less importance in them than in clock work, where the teeth are numerous, and several have hold at the same time, which tends greatly to equalize the action and wear; whereas a wheel acting on a pinion of six teeth can never have a proper hold of more than one, and the unavoidable obliquity of the greater part of the action has a constant tendency to thrust the pinion and wheel asunder, which greatly augments the strain and wear on the pivots. Indeed it is well known to such mathematicians as have carefully studied the forms of wheel teeth, that if wear and friction be kept in view, no form can be given to a pinion of few teeth which will make a wheel act on it smoothly or uniformly, and that it is necessarily attended with a great loss of the moving power. Experience soon convinces the most backward, that a wheel cannot be employed to give a powerful and rapid motion to a pinion of six leaves, without waste of power, and some part very soon giving way. Of all the forms of teeth having something like the sanction of mathematical investigation, we cannot help regarding those formed by the involute of the circle as the worst. Indeed any sorts of teeth which, like these, taper much, occasion an irresistible repulsion between the axes of the wheels or pinions, the pernicious effects of which speedily manifest themselves in heavy machinery, though they may not be so soon observable in clocks or watches.

About the middle of last century a number of artists, clocks with particularly on the Continent, were much occupied in contriving clocks with few wheels, and publishing descriptions of them. It would seem, however, that neither Dr Franklin nor Mr Ferguson was aware of this, at least for a long time after; for when Ferguson published his Select Exercises, he described as quite new a clock of this sort by Franklin, and another by himself, each having three wheels and two pinions. Of these, which have both their merits and defects, we shall now give some account, beginning with that of Dr Franklin.

Fig. I, Plate CLXIV., shows the dial-plate, having the hours engraved in spiral spaces, such that in one hour the clock index A, which is both the hour and minute hand, describes a right angle, or the fourth part of a revolution, and consequently goes quite round in four hours. The hours are encompassed by a graduated circle, containing four times sixty divisions, upon which the same index counts the minutes from any hour it has passed to the next following hour. The time, as shown by the figure, is either 39½ minutes past XII., or past III., or past VIII., and so on in each quarter of the circle. The small hand B at top goes round in a minute, and shows the seconds as in a common clock. There is evidently no ambiguity here respecting the minutes and seconds, but it might happen that such a clock would leave an uncertainty of four whole hours, though this we should think would seldom occur.

The wheel work is as follows. On the axis of the large index A, is a wheel of 160 teeth turning a pinion of ten leaves, on whose axis is a wheel of 120 teeth turning a pinion of eight leaves. The arbor of this last pinion carries the scape wheel of thirty teeth, and the small index B. This clock was intended to be wound up by merely putting the cord of the weight over a notched pulley, and pulling the opposite end, which is stretched by a small weight. This is the usual way with wooden thirty-hour clocks; but it is not even the most simple method, and it besides creates a great deal of dust by the partial slipping and consequent wearing of the cord in the groove of the pulley. A far better way, where room can be had, is either to give the cord several turns on the barrel, both ends still hanging down, or to have two cords, the one winding on while the other winds off, as in Prior's striking part, to be afterwards described.

To obviate the ambiguity of four hours in Franklin's Ferguson's clock, and also the inconvenience of frequent winding, clock Ferguson contrived the following clock, of which fig. 2 shows the dial-plate, having an opening ab below the centre, through which part of a circular plate appears, having the twelve hours engraven upon it and divided into quarters. This plate turns round behind the dial-plate in twelve hours; and the true hour, or part of the hour, appears in Clock and the middle of the opening, at the point of an index A engraved on the dial-plate. B is the minute hand, which goes round in an hour, showing the minutes on the large circle in the usual way. Near the top of the dial is another opening, through which the seconds are seen on a movable plate, at the point of an index C, in the same way as the hours. On the axis of the hour-plate is a wheel of 120 teeth turning a pinion of ten leaves, on whose axis is the minute hand B, and another wheel of 120 teeth turning a pinion of six leaves. The axis of the last pinion carries the scape wheel of ninety teeth, and the flat ring or circle for the seconds, on which is engraven three times sixty divisions, because it only turns in three minutes. This clock is quite free from ambiguity, and will go a week with one winding. But the swing wheel being large, and its axis being besides loaded with the plate for seconds, will have considerable friction on its pivots, as Ferguson himself admitted. Nay, he even supposed his clock had another defect. He imagined, that since the scape wheel had three times the usual number of teeth, the pendulum would necessarily be confined in its vibrations. This he thought a defect, and no less a man than Harrison held a similar opinion. Others again have been good enough to insinuate, that if Ferguson had been better versed in the principles of clocks, he would have seen that narrow vibrations were preferable to wide ones. But, we presume, the question admits of a different solution; for, if we apply to this case the rules laid down at page 771, for computing the proportions in the anchor escapement, it will be found that neither a large wheel nor small teeth necessarily restrict the pendulum to narrow vibrations. With different scape-ments the results would be different, but there seems little doubt the common scape-motion was intended by Ferguson. We indeed see little need for employing the movable circles at all. Had the wheels been made to turn in the other direction, an hour hand, and likewise a seconds hand, could have been applied in the usual way; and we know no reason why a minute-hand might not have been used, turning backward, or contrary to the common direction, especially where the greatest possible simplicity was aimed at.

In the Transactions of the Society of Arts, vol. xxxvii., page 138, there is a description of a clock by M. Fayrer, which is something intermediate between the two last. The central hand goes round in six hours, and might have shown both hours and minutes, as in Franklin's; but there is also a ring within, which shows the hours through a hole, as in Ferguson's. The seconds hand goes round in one minute. This clock is called three wheeled in the title, but a fourth wheel and pinion are employed in moving the hour ring.

Berthoud, in his Essai sur l'Horlogerie, describes a clock in which an ordinary hour hand going round in twelve hours shows every third minute on a very large dial-plate. A seconds hand at top goes round in two minutes. The minutes are of course a little ambiguous, but had he employed a seconds hand going round in three minutes, as Ferguson has done, all ambiguity might have been avoided.

Mr Ferguson also contrived the following very simple clock for showing the apparent motions of the sun and moon, with her age, southing, and phases, as also the times of high and low water, by having only two wheels and one pinion added to the common movement. The dial-plate, fig. 3, Plate CLXIV., contains the whole twenty-four hours of the day and night. The sun S, which is also the hour hand, is fixed to and carried round by a circular plate, fig. 3, upon which the twenty-four hours are engraven; and within them is a circle divided into twenty-nine and a half equal parts, for the days of the moon's age from one new moon to the next. Each day stands directly under the time of the moon's southing or coming to the meridian; the XII. under the sun standing for noon, and the opposite XII. for midnight. Thus, when the moon is eight days old she comes to the meridian at half past six in the afternoon, and when sixteen days old she does so at one in the morning. The moon M, fig. 3, is fixed to another plate of the same diameter with that which carries the sun, and this lunar plate turns round in twenty-four hours 50'52 minutes. It has an opening to show some of the hours, and days of the moon's age, on the plate behind it, which carries the sun. Across this opening, at a, is a piece of wire, which shows on the plate just mentioned the day of the moon's age, and time of coming to the meridian; and if another wire were placed at a point, b, as far from the wire a as the moon's southing differs from the time of high water at the place for which the clock is made, it would show upon the same plate the time of high water for that place. At London Bridge it is high water two hours and a half after the moon passes the meridian. Above the moon-plate there is a fixed plate N, supported by a wire A, the lower end of which is kned and fixed in the dial-plate at XII. This plate may represent the earth, and the dot over L London, or the place for which the clock is made. Around this plate is an elliptical shade upon the plate that carries the moon M, the highest points of which are marked high water, and the lowest low water. While this plate turns behind the fixed plate N, the high and low water points come successively even with L, and stand just over it at the times when it is high and low water at the given place; which times are pointed out by the sun S, among the twenty-four hours. Above the dial-plate is a figure of London Bridge with a plate H, which rises and falls to represent the tide. When it is high water there, one of the highest points of the elliptical shade stands just over L, and the plate H is at its greatest height; and at low water, one of the lowest points of the ellipse is over L, and the tide-plate has gone down quite behind the dial-plate.

While the sun makes twenty-nine and a half revolutions, the moon makes only twenty-eight and a half; so that the moon-plate moves so much slower than the sun-plate as to cause the wire a shift over one day of the moon's age on the sun-plate in twenty-four hours. In the moon-plate is a round hole m, through which the phases or appearance of the moon may be seen on the sun-plate. At the new moon, the hole m is all of it black, at the full it is all white, and is equally well represented at the quarters, &c. All this is obviously produced by the hole m being opposite different parts of the eccentric ring NRF, in fig. 5, at the new moon N, full moon F, first quarter f, and last quarter l.

The mechanism is represented in fig. 4, where A is a wheel of fifty-seven teeth; its axis is hollow, and comes through the dial-plate, carrying the sun-plate. B is a wheel of the same diameter as A, and has fifty-nine teeth; its axis is solid, and turns within that of A, carrying the moon-plate. Pinion C of nineteen leaves pitches into both wheels, and is itself turned round by the clock in eight hours; but as eight is to twenty-four, so is nineteen to fifty-seven, consequently the wheel A carries round the sun in twenty-four hours. Since fifty-seven teeth are to fifty-nine, as twenty-four to twenty-four hours fifty and a half minutes, this last is the time of the revolution of the wheel B carrying the moon-plate. On the back of the wheel C is fixed an elliptic ring D, which, as it turns round, raises and lets down a lever EF, turning on a fixed stud F, and this, by means of the bar G, raises and lowers the tide-plate H moving between the rollers R, R, R, R.

If the thick pinion C be made for working with a wheel of fifty-eight teeth, it may fit both A and B well enough; but independently of this, the numbers are not the most correct, for in about thirty-two lunations they would lead to an error of one day's motion. To obviate this, Dr Pearson has proposed the following numbers, which would come extremely near the truth. Let the wheel A, which belongs to the sun-plate, have seventy-four teeth, and drive another, C, of forty-three, turning on a fixed stud. Then if a wheel C', of thirty-two teeth, be pinned on the side of C, and drive the wheel B, which belongs to the moon plate, and is in this case to have fifty-seven teeth, we shall have the relative motions of the sun and moon with surprising exactness, considering the simplicity of the numbers. We cannot here move the solar wheel by one turn in eight hours, because seventy-four is not divisible by three; but it is perhaps better that it is divisible by two, for then it admits of being moved by a wheel of thirty-seven teeth turning round in twelve hours.

In 1825, the Society for the Encouragement of Arts, &c., rewarded Mr J. Aitkin for very much simplifying and improving the dial work, or work between the dial-plate and frame, of a quarter or chime clock. Of this a description is given in their Transactions, but which is rather too diffuse for our limits, and therefore we shall describe it more briefly, in our own way, supplying some omissions. In Plate CLXV., the same letters and numbers refer to the same parts in all the figures. The front plate of the frame is denoted by a a. The wheel work is nearly the same as usual. The dial-plate is omitted, and the dotted circles supposed to be seen through the plate a a, are the pitch-lines of the wheels and pinions within the frame; the number of teeth in each being put close after its letter of reference.

The circles B, C, D, may therefore denote the first, second, and third wheels of the going train, which respectively turn the pinions b, c, d. But in the original, through some inadvertence, the pinions c and d have each only seven teeth, which we have here increased to eight, because the train requires it. Still the numbers in this clock are just of the sort to which we so strongly objected above. Upon the axis of d is fixed the scape wheel E, which by acting on the pallets e, maintains the motion of the pendulum. The circles G, H, I, J, represent the first, second, &c., wheels of the quarter and chime part. They respectively turn the pinions g, h, i, j. Upon the axis of j is the fly, which regulates the striking of the quarters and chimes. The second wheel H also turns the wheel P, on whose axis is fixed a barrel f, having on its cylindrical surface a number of short pins k, k, which act upon the tail of the quarter hammer p, or upon the tails of any number of hammers p, p, p, &c., striking as many bells Q, Q, Q, &c., if the clock is intended to chime. The circles L, M, N, O, denote the wheels of the striking train, respectively turning the pinions l, m, n, o. Upon the axis of o is the fly for regulating the striking of the hours. According as the clock is to be moved by weights or springs, the wheels B, G, L, have each a barrel or fusee on its arbor. The use of the fusee will be explained when treating of watches.

The axis of the centre wheel C, prolonged in front of the plate aa, carries upon a socket or cannon the minute hand u, and a wheel R, which pitches into an equal wheel S, turning on a fixed stud. These revolve once in an hour. On the face of the minute wheel S are fixed four pins, r r' r'' r''', to be noticed after; and on its socket q is a small pinion s, of six teeth, leading round the hour wheel T, of seventy-two teeth, in twelve hours. The socket of T carries the hour hand t, and embraces and turns upon the cannon or socket of the wheel R. The axis of the scape wheel E revolves in one minute; and, being prolonged through the dial-plate, carries the seconds hand.

Upon the face of the wheel R is fixed the quarter snail v, clock and the edges of which are formed of five concentric arcs, v v' v'' v''' v''', the use of which will be noticed after. When the snail is turned round, a pin w on its side acts on one of the twelve teeth of the star wheel U, and first moves it slowly, till the point of a tooth gets over the angle of the bent spring or jumper, xx; then all at once the wheel, aided by the jumper pressing behind, jumps forward through what remains of the twelfth part of a revolution, and there rests till the pin w return. The use of this will be seen afterwards. On the face of the star wheel U is fixed the hour snail V, so called from its resembling the shell of a snail: it is formed of twelve concentric arcs, marked 1, 2, 3, &c. The star and snail turn together on a fixed stud y. On another fixed stud W turns the hour rack X, in the lower tail of which is fixed a pin z, which tends to drop against the edge of the snail V by a spring a acting on the inside of one of the arms of the rack. The rack has on its upper edge fourteen notches or teeth, into which drops a catch or detent Y, turning on a fixed stud 13. Projecting from the back of the lower tail of the catch is a pin 14; and from the back of its opposite end there projects a piece or detent 15, which passes through an oblong hole 16 in the plate aa, and against which buts or rests a pin 17 in the rim of the wheel O. But the detent 15 can only get low enough to catch and detain the pin 17 when the catch Y is got fully into the notch 1, which is cut deeper than the rest.

On the axis of the wheel N, which turns once round for each stroke of the hammer, is fixed the gathering pallet 18, which at each turn lays hold of a tooth of the rack X, moving it through the space of one notch, when it will be detained by the catch Y dropping into a notch before the pallet quits the point of the tooth. If the catch Y be raised till the detent 15 reach the upper end of the hole 16, the wheel O will also be prevented from turning round, by a pin 19 in one of its arms coming against the detent 15, as is the case when a clock warns. Z is the quarter rack turning on a fixed stud 20. It is pressed towards the left by the spring 21; on its upper edge are six notches, in which acts the detent 22, turning on the fixed stud 23. On the socket and front side of the catch 22 is fixed an arm 24, having in its extremity a slit, in which a trigger 25 is inserted, and forms a joint by means of a pin or screw passing through them. The motion of this joint is limited by the shoulder of the trigger coming against the end of the slit, when its point has moved through an arc equal a'a', fig. 5. On the upper side of the arm 24 is attached a spring 26, which acts on the trigger, and tends to keep it straight with the arm 24. From the tail or lower branch of the quarter rack Z there projects behind a pin 27, which, by the action of the spring 21, drops against the edge of the quarter snail v, when the catch 22 is raised above the teeth of the rack Z. On the axis of the wheel I is the pallet 28, fig. 5, which gathers up the rack Z, in the same way as the pallet 18 gathered the other rack X; only the pallet 28 has a tail 29 which locks against a pin 30 in the rack, so soon as the catch 22 has hold of the last notch. When the pallet 28 is in that position, it is acting on the slant end of a lever 31, which turns on a fixed stud behind the catch 22, and by means of a pin 33 assists in lifting that catch; but the pallet only does so in commencing its first revolution, when the detent 30 has just been removed; for no sooner has the lever 31 been quitted by the pallet 28, than it drops out of the reach of that pallet, and its side 34 rests on the fixed stud 35 till the pallet 28 begins to act on the fourth tooth of the rack Z; then, as the rack advances, a pin 36 in its side acts on the sloping edge 37 of the lever 31, and raises it to its first posi- So that when the pallet has just cleared the fourth tooth of the rack Z, the lever 31 will again be within its reach.

On the fixed stud 39 turns the tumbler 38, which is pressed against the pin 14 in the tail of the catch Y by the spring 40. In the rack Z is a pin 42, fig. 4, which acts on the tail 43 of the tumbler. Suppose the notch e to be opposite the pin 27 in the tail of the quarter rack, and the catch 22 to be lifted out of the notch, the spring 21 will cause the end 44 of the rack Z strike against the tail 45 of the catch Y, and depress it till the detent 15 in its opposite end reach the upper end of the hole 16. By this time the tumbler having escaped the pin 14, will be resting against the fixed stud 46, while the pin 14 will rest on the end 47 of the tumbler, and prevent the catch Y from dropping into the rack X till the pallet 28 begin to act on the fourth tooth of the rack Z. The pin 42 will then be drawn against the edge 43 of the tumbler, and will bring it back to its former position, which will allow the catch Y to drop into the rack X.

The wheel N turns eight times round for each revolution of the wheel M. In the rim of the latter are fixed eight pins 48, which, as the wheel turns round, act successively in lifting the tail 49 of the hammer 51, and upon quitting it the spring 50 makes it strike the hour bell 52, once for each turn of the pallet 18; so that for every tooth of the rack X which the pallet gathers up, the hammer gives a stroke. The snail V, an ingenious contrivance, first used in the repeating clocks and watches of Barlow, has the radii of its several steps so proportioned, that if, when the catch Y has been lifted, the pin z in the tail of the rack come against the step 1 of the snail, the rack will only have gone back one notch; consequently one turn of the pallet gathers it up, and the hammer strikes once. In like manner, when the pin z falls on the step 5, there are five notches to gather up, the clock strikes five, and so on for all the other steps. The like explanation applies to the quarter snail, except that it has only four steps beside the part r, which passes close by the pin 27.

Two levers, 53 and 54, turn upon the fixed studs 55 and 56. They are connected by the jointed rod 57, and pressed to the left by the spring 58; but their motion is limited by the fixed studs 59 and 60. When moved to the right, they act against the tails 61 and 62 of the catches 22 and Y respectively; so that, if to either of the screws 63 or 64 in the ends of the levers we attach a cord or wire, the pulling of this will raise the catches 22 and Y, and cause the clock repeat, or strike over again, first the quarters and then the hour. The design of making the star and snail shift suddenly from one hour to another, as was before described, is to avoid the chance of the pin z falling on the wrong step, and consequently the clock striking a wrong hour when the repeating cord happens to be pulled near the end of an hour. In a great many clocks the snail V is just fixed on the side of the hour wheel, which does very well if no repeating is intended.

When the clock has just struck twelve, the minute and hour hands will be together; and if at any time before the minute hand advance another quarter, the cord 65 be pulled, there will be no quarter to strike, but the hour twelve will be repeated; for the step 12 of the hour snail will then be turned toward the pin z; but the highest step e of the quarter snail will be sliding close by the pin 27, so that the quarter rack cannot drop at all, and no quarters can be struck. When the minute hand reaches the tenth minute, the pin r in the wheel S, which revolves in an hour, will just begin to act on the trigger 25; and when the pin r reaches its first dotted position, fig. 5, the trigger will be bent into its first dotted position a', but its shoulder being then come against the end of the slit in the arm 24, will prevent its bending farther. Again, when the pin r has reached its second dotted position, the minute hand will have completed the first quarter; the point of the trigger will have got to its second dotted position a", the arm 24 to its first dotted position; and the catch 22, being also at its first dotted position, will clear the teeth of the rack Z. The highest arc of the quarter snail having quite passed the pin 27, that pin can now drop on the next stop, and the rack go back one notch with the detent 30, which will release the pallet tail 29. The pallet 28 beginning to turn, raises the lever 31 with its pin 33; and when the pallet just clears that lever, the catch 22 and arm 24 will be at their second dotted position, and the trigger at its third. As soon as the trigger is clear of the pin r, it is pressed inward by its spring 26; and when the pallet 28 is half round, the catch drops into the fifth notch. The pallet then gathers up the fourth tooth, during which the wheel P turning one fifth round, one of its five pins k acts on the hammer tail p, making it strike one quarter; but the hour will not be repeated, unless the cord 65 has been pulled. The use of the joint of the trigger is, that after being lifted clear of the pin r by the action of the pin 33, its spring 26 bends it inwards; and therefore, while the catch 22 descends, the point of the trigger clears or falls behind the pin r. Were there no joint, the point would drop again on the pin r, as represented in the second dotted position, which would keep the catch from dropping into a notch, and of course the clock would continue striking till the pin r had passed the point of the trigger, which would be more than a minute.

At the half hour the step e' of the quarter snail will be next the pin 27, which will allow the rack Z to drop two notches, and two quarters will be struck; and in like manner, when the minute hand is at three quarters, the step e" being next the pin 27, will allow three quarters to be struck. But at the fifty-second minute, the pin r in the side of the quarter snail will begin to act on a tooth of the star wheel U; and in six minutes more will have moved it with a start one tooth forward, as was before explained. The step 1 of the hour snail V will then be next the pin z in the tail of the rack X; and the step e"m of the quarter snail next the pin 27; and at the hour's end the pin r"m will have raised the trigger 25, along with the catch 22. The pin 27 will next drop to the bottom of the notch r", and the end 44 of the rack Z, by striking the tail of the hour catch Y, will raise it out of the notch 1 of the rack X. While the detent 15 is being raised to the top of the hole 16, it will first let go the pin 17 and wheel O; but, by catching the pin 19, will again arrest that wheel. The pin z will then drop against the step 1 of the hour snail V, and the rack X fall back one notch. During this the rack Z will have dropped back four notches. The clock will next strike four quarters; then the pin 42 drawing up the tail of the tumbler, will allow the pin 14 to escape, and the catch Y to fall into the notch 17, which will clear the detent 15 of the pins 17 and 19. The pallet 18 will then gather up the tooth of the rack X; the hammer 51 will strike one o'clock; and so on for the other hours, &c.

Fig. 5 is a front view of the detent or catch 22, &c. in several different positions. Fig. 2 is a view of the upper edges of the lever 31, and of the parts in fig. 5, without the spring 26. Fig. 3 is the spring 26. Fig. 8 shows the front, and fig. 4 the upper side, of the quarter rack Z, its tail 27, and the stud 20. Fig. 6 shows the star wheel U and hour snail V. Fig. 7 is the quarter snail r and the minute wheel R.

When a clock is to show the day of the month, the hour, Day one wheel, or a wheel on its socket, turns a wheel of double moon.

The number of teeth round in twenty-four hours. The latter carries a pin which daily lays hold of a star wheel of thirty-one teeth, and shifts it forward one tooth. The axis of the last carries either a day-of-the-month hand outside the dial-plate, or a ring with the days engraven on it behind the dial-plate, and the day of the month is seen through a hole, as the hours are, in Ferguson's clock. Sometimes, instead of a wheel with thirty-one teeth, there is a flat ring movable between three or four pulleys, and having 365 notches on its inner edge, into one of which the foresaid pin enters daily, and shifts it forward one notch, the days being seen on this ring through the hole. A similar contrivance is used for the twenty-nine and a half days of the moon's age. The hour wheel carries a pin, which twice in twenty-four hours enters the teeth of a star wheel of fifty-nine teeth, or of a flat ring of fifty-nine teeth, movable between pulleys.

The merit of being the first who applied a pendulum to regulate the striking part of a clock, is by most English writers ascribed to Mr Masey; probably because, in 1803, the Society of Arts voted him twenty guineas for it. But long before his time, the same thing had been done, and published too, by Le Roy, Berthoud, and others. As a regulator for striking work, the pendulum is greatly preferable to the fly and train of wheels; yet custom, it seems, has in this instance, as in many others, given the latter method a prescriptive right to maintain its place, perhaps for an indefinite period. This arises, in a great measure, from the circumstance that the majority of workmen never think for themselves, or inquire into the reason of what they are doing. They content themselves with being mere machines, working by imitation or by old traditional rules. In short, the rational faculties never being called into action, remain torpid all their days. Striking parts have sometimes been regulated by being connected, while in action, with the going part; and it is a considerable time since Mr Ward contrived a striking part which derived its motion entirely from the pendulum of the going part. This, however, requires a very heavy pendulum, having rather wide vibrations.

Mr John Prior has laboured much to simplify the striking mechanism of clocks; and various devices of his for that purpose have at different times been rewarded by the Society of Arts, and published in their Transactions. Two of them were regulated by a fly with a screw on its axis, like a kitchen jack. The third was regulated by a pendulum, and could repeat, without expending any part of the ordinary winding thereon. The fourth, which we shall now describe, might also have been made to repeat in the same way; but it has the advantage of all the rest, in being regulated by a pendulum, which is likewise the striking hammer. Fig. 6, Plate CLXVIII., is a side view of this machine, which is meant to be in an upright position; and fig. 7 is a plan or view on the top of the machine. a is the weight, suspended by a cord wound on the barrel b, which acts on the scape wheel d, by means of the ratchet c. These, of course, are all on the same axis. The wheel d has seventy-eight teeth, because the sum of all the strokes in the twelve hours is seventy-eight. It has likewise a set of pins e, projecting from the side of its rim, and dividing it into twelve unequal arches. The smallest of these segments contains one tooth, or a space equal to one notch between the teeth, the second two, and so on, till we come to the twelfth, which contains twelve. From its being thus divided, to count or regulate the number of strokes for the different hours, it is called the count wheel, and is a much more ancient contrivance than the snail, which originated with the repeating clocks of Barlow. Formerly, however, the unequal divisions of the count wheel were not marked by pins, but by cuts or notches in a hoop fixed on its side. The two closest notches generally left nothing between them. There is a catch or detent h, which detains the wheel, by holding some one of the twelve pins. On this catch being lifted, the wheel advances, and during that act on the pallets f, causing the pendulum gh to vibrate and give as many strokes to the bell i as there are teeth or notches in the arch between that and the next following pin, which is stopped by the detent h. The bell is placed a little obliquely, to let the hammer clear it on one side, and only strike it on the other at every alternate vibration.

We have now described as much of this apparatus as is sufficient for being applied in the usual way as the striking part of a clock; but it is provided with some small additional parts, by which it may be adapted to a common watch thus:—Take off the outer case, if the watch has any, throw back the glass, and lay the watch with its face upward upon the brass plate zz of the watch holder, in front of the instrument, and which may be raised or lowered, to suit the thickness of the watch, and there fixed by the screw l. The watch being in this position, and having the axis of its minute hand directly under and in a line with the small vertical axis w of the machine, which carries a small plate e, of sixty divisions or minutes, screw the sliders fast which inclose the watch; then raise or lower the plate zz with the watch, till the notch in the ivory piece x, on the lower end of the axis, embrace the minute hand, and there fix the plate zz by the screw; then holding the upright axis w, turn the minute plate to suit the position of the minute hand. So very little force is necessary to move the axis w, that it will be easily turned round by the watch, which will cause the machine to strike the hours at the proper times, as indicated by the watch. But it remains to be explained how the axis w, in turning, can unlock the count wheel; and before we have done, we must not, like the inventor, omit to observe, that if the position of the divisions of the count wheel do not suit the hour hand of the watch, the wheel must be set or turned round till they correspond. Upon the upright axis w is an eccentric plate q, better seen in fig. 8, which, in every revolution of that axis, presses upon the arm n of the spring l, pushing this spring back from the frame-plate pp. So soon as the beak of the plate q passes the arm n, the spring l, aided by the momentum of its weight r, flies beyond its place of rest, causing its tooth o raise the sloping end m, fig. 9, of an arm, which, being on the same axis with the detent h, lifts that detent, and unlocks the wheel. The pin s prevents the arm m from rising too high, and t is a guide-pin fixed in the plate pp, and standing through the forked end of the spring l. Under the plate q is the minute plate e, which has a spring beneath, bearing upon the axis w, so as to be carried round with that axis, or to admit of being readily set with the watch, according to the index y. The counter string 2 being pulled, winds up the machine; for it winds upon the barrel while the other winds off; and vice versa. If the pendulum is wanted to strike slower, the ball 3 may be screwed upon its top.

Under the article CLOCK, in Rees's Cyclopaedia, there is a description and engraving of a striking part which has without fly neither fly nor pendulum. On the axis of the hammer is or pendu fixed a pinion, which an enormous wheel with 300 teeth turns quite round for each stroke. The shank of the hammer has a knee joint, which enables it to stretch out by means of the centrifugal force, so as to reach the inside of the bell placed over it; and of course the more rapidly the hammer revolves, the greater is the resistance it meets from the bell. This, which is represented as the masterpiece of a singular character long since deceased, we cannot help regarding as a very far-fetched contrivance. We Clock and a scape ment of repose nearly allied to the duplex, properly applied to a hammer, we have no doubt it would effectually control the striking both in clocks and watches, and would perhaps be the easiest mode of doing so. We mean that the wheel should rest on an arch or cylinder of repose during the coming on of the stroke; and that what is the pallet of impulsion in the duplex should here be the hammer tail. This last, we presume, ought to be a little flexible, or a spring. A description of the duplex scape ment will be found among those of watches, farther on.

Alarm clocks or watches are such as, being previously set, can give a very audible notice of the arrival of some particular point of time, such as awakening a person at a certain hour, and the like. Clocks and watches of this sort have been made in a great variety of forms. In 1819, the Society for the Encouragement of Arts rewarded Mr Thomas Taylor for an alarm clock, so contrived that, with only one setting, it can give several alarms succeeding each other at almost any intervals we please during the twenty-four hours after being so set. Of this we shall now give a description.

Fig. 1, Plate CLXVI., represents the dial-plate, which turns round in the course of twenty-four hours, and has an index fixed over it at top. Having been made for the Royal Observatory at Greenwich, the dial contains the whole twenty-four hours, as is usual with many clocks for astronomical purposes. But that does not unfit it for other purposes; and indeed a clock of this sort might have twice twelve hours put on it; or, when not intended for astronomers, the wheels might be calculated for any other number. The hours are placed in an inverted order when compared with other dial-plates; but that is quite arbitrary, because it might as well turn in the other direction. Each hour is divided into twelve equal parts, a division answering to five minutes. Fig. 2 is a front view of the work when the dial and front plates have been removed. Fig. 3 is a plan or view on the upper side. Fig. 4 is a side view of the alarm part only. The same letters refer to the same parts in all the figures. With the exception of the dial-plate moving, the going part of this clock differs little from that of a common clock. The dial-plate is keyed to the arbor of the first wheel B, but only tight enough to turn with it, that it may be moved at pleasure to any point. The time is shown by an index fixed to the top of the frame or front plate CC. This plate is fixed and kept parallel to the second plate DD by four pillars and screws bbb. The plate CC has a large opening, to show the dial-plate. The back plate EE is fixed to the second plate DD by the pillars ccc. To the side of the wheel B is fixed a spring and catch acting on the ratchet wheel F. The ratchet is fixed to the pulley G, over which the cord H of the weight passes. While the weight is being raised, the ratchet and pulley are free to turn on the arbor, but the weight in descending turns the wheel B, and the dial-plate along with it. I is the second wheel, J the third wheel, K the scape wheel, and L the pallets of the going part.

The first wheel M of the alarm part has a ratchet, pulley, cord, and weight, similar to those in the going part. On the back of this wheel is fixed a rim or wheel N, represented by the dotted circle within the rim of M. It has two gaps or notches x, y, on its periphery. The wheel M turns the pinion O, on whose axis is fixed the escape wheel P, having a pin or stud e in the side of the rim. Q is the crutch or pallets, R the alarm hammer, the shank of which is fixed to the back of the verge or pallet arbor at f; and by this means the hammer R is made to vibrate within, and strike the bell S when the alarm part is put in motion. T is a hammer or lever turning on a pin or fulcrum at g, fixed on the front side of the plate DD. The shorter end or tail h of this hammer is acted on by a pin i screwed into the dial-plate on purpose. As the dial-plate turns, the pin i depresses the tail h of the hammer, as seen in fig. 2 and 3, till the pin pass over it and allow the end of the hammer T to fall on the pin j in the end of the arm fixed on the arbor kk. This arm being depressed by the momentum of the hammer, lifts at the same time the two detents l, m, also fixed on the arbor kk. The pin e in the escape wheel being now free, and the detent m being lifted out of the notch y in the rim or wheel N, the alarm is set in motion, and the rim N sustains the detent till the great wheel M has made half a revolution. At the same time the detent l has been kept up sufficiently for the pin e in the scape wheel P to pass under it, whereby the alarm has been kept in motion about twenty-four seconds, and during half a revolution of the first wheel M. When the notch z comes round to the place of y, the detent l stops the pin e in the scape wheel P, which immediately stops the alarm.

For the purpose of discharging the alarm at various times, the dial-plate is pierced with a ring of screwed holes, on the inside of the divisions for hours, at every ten minutes distance, so as to admit such a pin as t, which is screwed next XXIV. A number of these pins being prepared, one of them is screwed into each of the holes in the dial-plate nearest to the times when the alarm is required to be discharged; but though the holes are ten minutes apart, the discharge may often be regulated to within four minutes of the time.

When the clock is intended to give notice of the daily transits of fixed stars, as was the case in the one at Greenwich, it is farther provided with the following contrivance:—On the end of the arbor U is fixed the hammer V, and at the other end an arm or lever n, which is acted on by a number of pins projecting from the inside of the dial-plate near its edge. When one of these pins comes in contact with the arm n, it elevates the hammer V, which on falling gives the bell one blow. These pins are inserted in such places that the hammer may strike five minutes previous to the passage over the meridian of each of twenty-five principal fixed stars. If this is not sufficient to awaken the observer, an alarm may likewise be set so as to discharge at the same time. When the hammer V is not wanted to give notice of these stars, a pin o is fixed in the upper end of a lever, which projects over the front of the top plate at S, p being the fulcrum and q a stud fixed in the lower end of the lever. When the pin o is turned to N, the stud q acts against the arm n, and depresses it, as shown by the dotted line; so that the pins on the inside of the dial-plate will pass over the arm n, and the bell will remain silent. The outer ends of these pins are shown on the dial-plate.

For astronomical purposes, especially transits over the meridian, such a clock should be regulated according to sidereal time; but since that makes one day more in the year than common clocks or sun-dials do, the common reckoning will be found much more convenient for all sublunary affairs, and only requires the pendulum to be a very little longer.

An equation clock is one which is furnished with a contrivance for indicating the equation of time; that is, the difference between the time shown by a good clock, called mean time, and the time shown by a sun-dial, called apparent time; or it is a clock which with one set of hands or circles shows mean time, and with another apparent time. The first clock of this sort was made about the year 1699, by Mr Joseph Williamson, an English artist, then working for Mr Daniel Quare, watchmaker in London, who sold it to go to Charles II., king of Spain, about the year 1699. It went 400 days with one winding, and and had two fixed and two movable circles for the hands to mark the time upon: the former giving the hours and minutes of mean time; and the latter, which were concentric with the former, apparent time. The same artist tells us in the Phil. Trans. for 1719, that he had made other clocks which showed apparent time, including a general correction for temperature, by raising and lowering the pendulum so that its vibrations made the clock keep pace with the sun throughout the year. Father Alexandre, a Benedictine, had laid a project of this sort before the Academy of Sciences in 1698, which is mentioned in their Memoirs for 1725; but nothing of the kind seems to have been practised in France, till a clock, the equation work of which scarcely differed from Williamson's, was made by Lebon in 1717. This was soon after followed by another by Leroy. That of Lebon had two concentric circles, one of which was movable, and regulated by an equation-plate which revolved once in a year. Clocks and watches with movable circles have since been made with some improvements by various artists; and, so far as simplicity is concerned, they are perhaps preferable to any that had been made during the last century.

The celebrated Mr George Graham had a much more elegant mode of showing mean and apparent time by using two concentric minute hands, one of which carried a figure of the sun, to distinguish it from the other or ordinary minute hand. The same thing has been done by several eminent French artists; but all these are so complex and expensive, that they have in a great measure been laid aside. They have not only an annual motion in common with all others of the kind, but the minute work has several additional wheels, which render them extremely difficult of execution, and, without great care, liable to considerable error.

A very simple equation part, having the two minute hands, has been contrived by Mr Henry Ward, for which he was rewarded by the Society of Arts in 1814. It has no real annual movement, but only a relative one, and may be made by any ordinary workman who comprehends the use of its parts.

In fig. 3, Plate CLXVIII., AA is a steel arbor which carries the apparent time hand 1, and on which is fixed a pinion B of twenty-four teeth. But it may be proper here to observe, that through some inadvertence the letters are sadly misplaced and transposed in the original engraving of this figure in the Society's Transactions. We mean misplaced for the description there given. C is the minute wheel of 111 teeth, screwed to a brass socket ee, which turns on the arbor AA; the end of this socket is the fore pivot to the arbor, and carries the mean time hand 2. The minute wheel C drives a wheel D of sixty-four teeth on the arbor EE, the fore pivot of which is squared to receive a key for setting right the equation work if the clock has been standing or out of order. On the same arbor is fixed another wheel F of the same diameter, but containing seventy-nine teeth. It drives a wheel G of 137 teeth, screwed to the socket gg, which turns freely on the arbor AA, and to which is also fixed the equation plate H. In the rim of the minute wheel C is fixed a stud s, upon which turns the toothed quadrant I, pitching into the pinion B. In one extremity of the quadrant is fastened a pin i, which, by the revolving of the equation plate, is moved backward and forward, and is made to bear on the edge of that plate by means of a slender spring, which connects it with and pulls it towards the arbor AA. Fig. 4 shows in perspective the equation work more distinctly, with the same letters of reference; and fig. 5 is a front view of the rack I, its pinion B, the equation plate H, &c.

It is obvious, that when the parts are arranged in the manner now described, the minute wheel C cannot be put on the axis of the centre wheel of the clock. But that might be done by making the wheel G and plate H change places with C, and by putting the pinion B on a socket, which should include that of C. The former arrangement will, however, be found more simple, and there will be no difficulty in getting motion to the minute wheel without putting it on the axis of the centre wheel.

The rationale of the contrivance is this: If the wheel C be made to revolve just once in an hour, it will cause the wheel G make one turn more than itself does in the course of a year; so that relatively to the wheel C, the equation plate turns once round in a year. It indeed takes fully two hours more than a year; for $137 \times 64 = 8768$ turns of C or hours, $= 365$ days 8 hours; and in this time G makes $111 \times 79 = 8769$, which is just one complete turn more. But this inaccuracy is of no moment; for any error arising from it in the equation of time can accumulate to no sensible quantity during the interval between the times of cleaning the clock. After almost every thing else had been made and put together, the figure of the equation plate was obtained by finding successively, by trial, the points in its periphery which corresponded to the relative annual positions of the several teeth of the wheel G, in respect of C, and which likewise corresponded to the equation of time, or difference between the hands for these relative positions. To facilitate this, Mr Ward had previously constructed a table of the equation of time for each 137th part of the year, setting out from where the equation is nothing. After these points had been marked on the side of the plate, the rest of it was cut away. It will now be obvious how the extent which the quadrant I moves the pinion B and the hand I backward and forward, in respect of C and the ordinary minute hand, is always equal to the equation of time; and it will be found that no similar construction can come nearer the exact length of the year without employing wheels with greater numbers of teeth.

Although the equation work first applied to clocks was much more complicated than that now described, it was shortly afterwards adapted occasionally to watches. Equation work however has now gone almost entirely into disuse in watches.

There are various machines for measuring minute intervals of time, with wheel work like that of a clock or watch, and regulated by a escapement or a conical pendulum. The general mode of using such an instrument is to set it in motion, or rather to let it go at the beginning of the interval, to stop it at the end, and then see how far it has gone during the interval. But we cannot help thinking the merits of these machines have been greatly overrated, and that they can scarcely be depended on to a tenth of a second. For, when several of these instruments are employed by different persons to measure the same interval of time, the results rarely agree, nay often differ by three, four, and five tenths of a second, as was the case with very nice instruments used in the experiments made in France on the velocity of sound in 1822; and the like discordance was observed in the less perfect experiments afterwards made at Port Bowen, as noticed more particularly in the Edinburgh Phil. Journ. for October 1828. It is indeed difficult to conceive how such a machine can either be let go or stopped by the finger of a person taken in some degree by surprise, without an uncertainty of much more than a hundredth of a second attaching to each of the instants of doing so. Mr Hardy's instrument, described in Trans. Soc. of Arts, vol. xliii., is accounted one of the most refined. In perusing that description we were much surprised to find so intelligent an artist putting an index on such a vague moving thing as Clock and Watch Work.

the axis of a balance with the common escapement; and still more did we wonder that he should have made that index vibrate over an arc graduated with equal divisions; as if the motion of the balance were perfectly uniform, or the same in every part of a vibration. But since the length of the vibrations, especially in this machine, which has no fusee, is variable and uncertain, no mode of graduation could suit such an index. Besides, the first vibration after starting will generally be much slower than the rest. From such considerations, we question if this instrument can be depended on to a tenth of a second, instead of a six hundredth. Indeed, no machine is likely ever to be invented which shall measure with the certainty of a sufficient exactness, and separately by itself, the time which sound takes to pass over a few hundred feet. A different method of accomplishing this to almost any degree of exactness has therefore been proposed by Mr Meikle, in the Edinburgh Phil. Journ. for October 1827. Suppose a hammer moved by clock work to strike a bell at equal short intervals, as seconds, and that an observer sees the hammer just touch the bell always at the very instant he first hears the sound. It is evident that he must be either quite near the bell, or at such a distance as requires exactly one second or a whole number of seconds for the sound to reach him. By removing himself a very little farther off, the sound will arrive too late, and by approaching rather nearer, the report will precede the visible stroke. In short, a very small variation on the distance will sensibly disturb the coincidence; and since this experiment might be often repeated in the course of a few minutes, ample opportunity would be afforded for determining the exact distance which should make the two sensations perfectly harmonize. But instead of watching the motions of the hammer itself, a more precise and conspicuous signal might easily be contrived; such as a long index, completing a revolution during each interval between the strokes, and then passing or covering some conspicuous mark or line. For experiments in the dark, a small hole might be opened and instantly shut by the clock work, at the very nick of time to allow a lamp placed behind a screen sending a momentary ray to the observer; so that in proper hands such a machine would, in a great measure, obviate the uncertainty inseparable from hurriedly measuring in a direct manner the short interval of time which elapses during the passing of sound over a small distance. For, if the visible signal be ascertained exactly to agree with the sound, we are sure of the true elapsed time to almost any degree of exactness, from the rate of the clock, without fluttering ourselves about measuring it at the moment. The observer, instead of hurriedly moving his fingers, when taken no doubt in some degree by surprise, would merely need to walk a very little backward and forward with perfect deliberation till he found himself at the precise distance. But since neither eyes nor ears are in all persons equally acute, several observers might be employed at the same time; and if they did not quite agree about the distance, this might lead to a more minute investigation of the circumstances. This method obviously possesses, and even in a greater degree, the same sort of advantages over the former method, that Hadley's quadrant does in measuring angles at sea, over the old instruments. See Edinburgh Phil. Journ. for June 1828.

Sometimes a contrivance similar to those for measuring small intervals of time is employed by astronomers, with the view of enabling them to note the time of observation with extreme precision. Such an instrument having been previously set or compared with a clock, is to be suddenly stopped at the instant of observation. But the exactness is just as illusory here as in the other case, except that this requires accuracy at one instant only, whereas the other required it at two. When several of these instruments are used simultaneously, as in the above case in France, the discordance in the results shows clearly that the defect lies principally with the observer; his movements being too slow and uncertain for co-operating with his senses with the requisite precision. There is therefore little probability of this defect ever being obviated by accuracy of instruments, or indeed by any other means. The remedy proposed in the case of sound is not applicable here.

A novel use of clock work has lately been made by Mr Rutherford, in applying it to locks, so as to render it impossible to open them, even with the proper keys, during a certain interval, or except at a certain hour. By this ingenious method, for which he has obtained a patent, great security may be given to various sorts of repositories; but a description of it scarcely belongs to this article.

The first contrivance for keeping a clock going during the time of winding was that of Huygens. In fig. 11, Plate CLXII., the pulley A, with a notched groove, is fixed upon the arbor of the first wheel. H is a similar pulley pinned on the side of a ratchet R, and movable on a stud fixed in the frame. An endless cord is put over these two pulleys, and under the pulleys B and C, which carry the weights P, p. It is evident that half of the large weight P is sustained by the pulley H, and the other half by the pulley A; and that half the weight will continue to bear upon A, although we turn the pulley H so as to raise the weight P. Now this is just what occurs in time of winding; for Huygens, by pulling the part of the cord next B, turned the pulley H, and raised or wound up the weight P, which all the while acted with half its weight on A, and consequently kept the clock going. The ratchet R only turns in time of winding, and is prevented by a click from going back. The method is perfect enough in theory, but it does not after all answer very well unless a chain be used instead of the cord; for the pulleys A and H wear the cord so fast as to create a great deal of dust, which soon renders the clock foul. The chain again is objectionable on account of its weight, which sometimes aids and at other times counteracts the moving power.

The method most commonly used for keeping both clocks and watches going in time of winding, is that of the celebrated Harrison. In fig. 12, ABC is a ratchet, placed but not fixed upon the first wheel DE, and prevented from going back by the click HG, which turns on a stud fixed to the frame at H. To the side of the ratchet ABC is attached at B the click of the fusee-ratchet or barrel-ratchet LM, which operates in the usual way during the winding. In a cavity between the ratchet ABC and the first wheel there is a circular spring of considerable length, which is represented by two dotted arcs, almost entire circles. One end of this spring is fixed to the wheel at A, and the other to the ratchet at C. When, therefore, we turn forward the ratchet ABC, it acts by means of the spring upon the wheel DE, and presses it forward. But since the ratchet ABC cannot get backward for the click H, it is evident that if, when the spring is thus in a state of tension, we cease to urge forward the ratchet, the spring will continue for some time to impel the wheel. Now this is just what takes place in time of winding. For during the ordinary going of the machine, the smaller ratchet, by means of its click, urges forward the larger one, and it again impels the wheel through the medium of the spring; and although, by applying the key to the arbor K, we withdraw the force of the smaller ratchet from the larger, the auxiliary spring can continue the motion of the wheel, at least during an interval amply sufficient for the winding. This contrivance Harrison called the perpetual ratchet.

It is, however, to be observed, that in this method other forms of springs are often used; and sometimes two or more springs are applied to the same wheel, especially in clocks.

There are various other contrivances for going in time of winding; but all of them with which we are acquainted are either inferior to the last or more complicated, except when a mainspring is used without a fusee; for if, in that case, the click of the ratchet turn on a fixed stud, the tension of the mainspring, whatever that may be, is as fully exerted on the wheels during winding as at any other time. But the want of the fusee is a great defect, and is not in the least supplied by anything of this sort.

Clocks have sometimes been provided with a contrivance on which the changes in the pressure or temperature of the air operated so as to wind them up continually, and keep them going so long as everything was in order or repair. The like has been done by a current of air. It is considerably above a century since such devices were applied to clocks.

We have already had occasion to mention some properties of pendulums, particularly the cycloidal sort; under the articles PENDULUM, and CENTRE OF OSCILLATION, will be found the theory and properties of the pendulum more at length. We confine ourselves here to its use as a regulator for clocks, and shall be so much the more brief on account of what has already been said on that head. Pendulums are suspended in several ways; sometimes by an axis turning on fine pivots, or on friction wheels, or on pieces called knife-edges, though more like very thick and short wedges. These are made of hardened steel, or of some hard stone. The most usual suspension is by a slender spring, which no doubt is very durable, and obviates friction; but as it tends to shorten the time of vibration in a variable and rather uncertain degree, depending on the temperature, it is not always used in nice clocks. A small silk cord is sometimes employed as a suspension for the lighter sort of pendulums.

In speaking of the length of a pendulum as a regulator, we mean the distance of a point called its centre of oscillation, from the axis of suspension about which it vibrates; the time of vibration being the same as that in which one particle would vibrate, if at the same distance from the axis, and suspended by a rod having neither weight nor inertia. The time of vibration through a given angle is as the square root of the pendulum's length. Thus, if a pendulum 39·2 inches in length vibrate in one second, another of 156·8 inches, or four times the length, requires only double the time, or two seconds. In unequal but very small arcs, the vibrations of the same pendulum are very nearly isochronous, or of equal duration; but when the arc becomes considerable, the duration is sensibly increased. The time in a very small arc is to that in a semicircle as 29 to 34 nearly; but within the limits of ten degrees, a change in the arc of a second's pendulum will occasion a daily variation, in seconds, of 1·644 times the difference between the square of the degrees in the arc which gives seconds, and the square of the degrees when the arc is different. Thus, if the clock keep time when the pendulum vibrates in an arc of 3°, it will lose 11·5 daily in an arc of 4°. For 4°—3° = 7°, and 7 × 1·644 = 11·508.

Huygens indeed showed, that to make the vibrations isochronous in different arcs, it would require the centre of oscillation to vibrate, not in a circular arc, but in the arc of a cycloid. However, it was found so difficult, or rather impossible, to make the centre of oscillation accurately describe any considerable portion of this curve, that the preference is now given to long and heavy pendulums vibrating in small circular arcs; which make a much nearer approach to isochronism than has yet been attained by any cycloidal pendulum in a larger arc.

Since the squares of the times of vibration of two pendulums are proportional to their lengths, a change of 100th part in the length will alter the time of vibration about a 200th. But since all bodies expand by heat, the variable temperature of the atmosphere must necessarily affect the lengths, and consequently the motions, of pendulums. Accordingly, clocks are found to move slower in summer and faster in winter. There is, however, a great difference in the expansibilities of different substances. Dry deal, being one of the least expansible, is often used for pendulum rods. Brass expands about one part in 100,000 for a degree of Fahrenheit, glass and platinum not quite half so much, iron about two thirds, and mercury three times as much, we mean in one dimension. A pendulum with a brass rod would therefore make one vibration less in 10,000 at 70° than at 50°, and lose 6½ seconds daily.

With an iron or steel rod the alteration will be much less, yet the daily variation of the rate of the clock from summer to winter will be considerable. Most pendulums, it is true, have a nut or regulator at the lower end, by which the bob or weight may be raised or lowered at pleasure by a very minute quantity; but since the state of the weather is ever variable, and as it is impossible to be raising or lowering the bob at every change of temperature, several contrivances have been proposed for avoiding it altogether. The method most commonly followed is to construct a pendulum of different materials, and dispose them in such a manner that their expansions or contractions may take place in opposite directions, and thereby counterbalance each other. If this is accomplished, the pendulum will continue of the same length. But for such contrivances we must refer to the article PENDULUM.

It contributes not a little to the accurate performance of a good clock that it be firmly fixed to a solid support, none of a Any unsteadiness in the support causes the point of suspension to follow the motion of the pendulum, and enlarges the radius of the arc described by the pendulum; it must therefore tend in general to retard the clock, which might, after all, be of little consequence, could we be sure its effects were always the same. Sometimes, however, an unsteady support may be of such a nature as to accelerate the motion; and an observation of this kind, made by Berthoud, has suggested to Bernoulli a theory of compound vibrations, which may perhaps be true in some cases, but is by no means universally applicable. From some circumstances of this kind it happens, as was first observed by Huygens, that when two clocks are placed near each other, with their faces looking the same way, and both resting in a great measure on the same support, or having their cases connected by a wooden rod, they have often a remarkable effect on each other's motions, so as to continue going for several days without varying a single second, even when they would have differed considerably if otherwise situated; and it sometimes happens that the clock which goes the more slowly of the two will set the other in motion, and then stop itself. This has been explained from the greater frequency of the vibrations of a pendulum, when confined to a smaller arc; the tendency of the pendulums to vibrate in the same time causing the shorter to describe an arc continually increasing, and the longer to contract its vibrations, till at last its motion entirely ceases. But a shorter pendulum does not set a longer one in motion; for as the vibrations of the latter increase, they become still slower. See Ellicott, in Phil. Trans. for 1739.

This sympathy of clocks, as it is called, has some resemblance to the alternate vibrations of two weighing scales hanging on the same beam, one of which may often be Clock and observed to stop its vibrations when the other begins to move, and to resume its motion when the latter ceases; but it is still more analogous to the mutual influence of two strings, or even two organ pipes, which, though not separately tuned to a perfect unison, still influence each other's vibrations in such a manner as to produce exactly the same note when they sound together. It is probably owing to a like cause that the notes of a tune, when heard at a distance, succeed each other quite in their proper order; and if so, we have no right to infer from this, as is usually done, that sounds of every tone and intensity travel at precisely the same rate.

A very ingenious instrument has been invented by Mr Hardy's instrument Hardy, for trying the stability of any thing on which it may be set. It is a sort of inverted pendulum, having its lower end, which is a spring, fixed in a portable pedestal, and carrying a weight on the upper part of its rod. When this instrument is set on any unsteady support, it is sure to be set a nodding, especially if we have known the probable frequency of the oscillations of the support, and adjusted the position of the weight on the rod of the instrument, so as it may vibrate nearly in the same time, should it be set in motion by such oscillations.

II.—WATCH WORK.

It was formerly observed, that after balance clocks had attained a certain degree of perfection, they only needed to be reduced in size to be portable. The next step, therefore, to making them watches, evidently was to reduce them still further in size. This must have been accomplished at an early period, but the precise date is far from being ascertained. Between forty and fifty years ago there was a great noise about the discovery of a watch, which, from an inscription on the dial-plate, was supposed to have belonged to King Robert Bruce, and which, after passing through several hands, and attaining a high price, was said to have reached King George III. Some learned antiquaries were perfectly satisfied of its authenticity, particularly the Honourable Daines Barrington, who expressed his convictions at great length and in strong terms. But on this ancient watch being shown to the Rev. Dr Jamieson, he pronounced it to be an imposture, from the inscription, "Robertus B. Rex Scotorum," being in Roman characters; whereas had it really belonged to the age of that prince, the letters behoved to have been Saxon. It in short turned out to be an old watch from America, and, therefore, very likely several centuries more recent than the days of Robert Bruce. Watches are said to have been made at Nuremberg in 1477; but if such was the case, they no doubt fell far short of that perfection to which they were brought by Hooke and Huygens, about two centuries later, as will be noticed more particularly afterwards. Some of the early ones were very small, in the shape of a pear, and sometimes sunk or fitted into the top of a walking cane. But anything further in the way of history will be noticed as we proceed, after explaining the construction of the common watch in its simplest form.

Structure of the common watch

Fig. 10, Plate CLXIII., exhibits at one view the several acting parts of a small portable timepiece, in their connection with each other, and therefore forms perhaps the simplest introduction to the structure of watches, especially since these parts are essentially the same with the corresponding ones in the common watch. A few things which, for the sake of simplicity, are omitted, shall be described separately. The frame DEFG needs no explanation, and as little does the dial-plate RS, which it carries upon two pillars. A is the balance, which only differs from those formerly described in having its weight principally accumulated in its ring or rim. Its axis or verge carries two pallets r, upon which the crown wheel C acts, as was particularly explained before for clocks, and will be farther considered after for watches. The axis of the crown wheel turns with one end in a branch r of the potance I, and the other in the counterpoise H. Its pinion d is moved by the fourth or contrate wheel K, on the axis of which is the pinion e, moved by the third wheel L; and on the axis of L is the pinion b, which is turned by the second or centre wheel M, which again derives its motion from the action of the first wheel N on the pinion a. The axis of the centre wheel M is prolonged through the dial-plate, and upon it is put spring-tight the tube or cannon of the cannon pinion Q. The upper end of this cannon is squared for receiving the minute hand. The pinion Q leads the minute wheel T, whose pinion q leads the hour wheel V, fixed on a socket t, which embraces the cannon of Q, and carries the hour hand. To the lower end of the arbor qq of the first wheel N is hooked or fixed one end of the mainspring OP, which is coiled in the form of a spiral, and has its other end fixed to the pillar p of the frame. This spring is here represented as being in a great measure in its natural relaxed state. But when we put the key on the upper end o of the arbor qq, and turn it round in the direction in which the hands f i turn, the spring is gradually wrapped closer upon the arbor; and when this is done sufficiently, the spring is in a state of tension, and is said to be wound up. During this operation the arbor carries round with it the ratchet X, but turns freely in the wheel N, which remains at rest. When the key is withdrawn, the spring endeavours to unwind itself, and turn the arbor in the other direction; but this it cannot do suddenly, because the small spring n makes the click m catch into the hooked teeth of the ratchet X, and prevent it from turning without taking with it the wheel N, which impels the whole train.

The reason why the minute hand ef is not put on the bare arbor itself of the centre wheel M, but on a tube or cannon holding somewhat stiffly upon it, is, that we may be at liberty to shift the minute hand at pleasure without all interfering with the position of any thing else except the three dial wheels T, q, and V, which move the hour hand hi.

The chief design of this figure is to exhibit the working parts of a common watch in the plainest possible manner, without regard to the form or position of the fixtures; for in a watch neither pivot of the balance runs in the frame plates. The one turns in a branch of the potance, and the balance itself being outside the frame, has its other pivot running in a piece called the cock, which formerly used to be very much ornamented. Besides, the balance in fig. 10 is without a spring; but fig. 11 shows a balance A having one end of a small spiral spring, which is extremely slender, fixed in a collet which is spring-tight on the verge at p, and the other end pinned into a fixed stud s. This is a flat spiral; but not unfrequently such springs are coiled in the form of a cylindric spiral, similar to the spring tc in fig. 1. Both these figures of balances will be further described afterwards.

The mainspring is here placed upon the axis of the first wheel, and so it is in many French watches and clocks; but since the force of a spring is greater the more it is wound up, it does not, when so applied, act uniformly on the watch; and therefore, to obviate this, the spring is commonly put on a separate axis, and inclosed in such a barrel as B in fig. 9. In that case, the axis of the spring continues at rest, while the barrel turns with the outer end of the spring fixed to the inside of its rim. One end of a gut or chain being attached to and wound upon this barrel, the other end is hooked to and coiled upon the somewhat conical piece ebh called the fusee, which is to be fixed upon the axis of the first wheel N. The axis of the spring or barrel B has on its lower end a small ratchet, not seen in the figure, which holds against a click, and keeps the axis from turning. By means of this ratchet, too, we can give a greater or less degree of tension to the mainspring; but this must not be done after the fusee has been adjusted to it. To the fusee is fixed the ratchet X, and the beak of the plate O is to prevent overwinding, as will be explained in describing the horizontal watch. By turning the fusee so as to coil the chain upon it, we uncoil it from the barrel, and in so turning the barrel we wind up the spring. But it will be observed, that the barrel and fusee in fig. 9 must be inverted when applied to fig. 10.

It is generally supposed that, to equalize the action of the spring, the radius of the fusee at any point to which the chain is a tangent should be inversely as the tension of the chain in that position. Within moderate limits this is nearly true; but we shall afterwards see that, if adopted as a datum, it may lead to an erroneous determination of the figure of the fusee, because the radius of the chain's curvature does not pass through the axis of the fusee, or coincide with its radius.

The motions of the spring barrel and fusee are different in different watches. For an ordinary thirty hours' winding, the barrel may make from three to four turns, the fusee from five to seven. When the axis of the fourth or contrate wheel carries a seconds hand, it revolves in one minute, or makes sixty turns for one of the centre wheel; but in the more common sorts of watches, which have no seconds hand, it usually makes more than sixty turns in a minute. The scape wheel again commonly moves so as to make the balance give from four to five vibrations in a second. But chronometers, and watches of peculiar constructions, differ widely in these particulars.

The action of watch springs is treated of at considerable length in the Berlin Memoirs for 1769, by Lagrange, a mathematician of uncommon reputation, who is usually looked up to as an authority on the subject. But the greatest efforts of talents or learning are only thrown away when applied to mistaken or erroneous data. For unfortunately this great man, not having previously acquainted himself sufficiently with springs, conducts his investigations upon principles so very different from those on which spiral springs are actually employed, or indeed could be employed, that whatever might have been his results, we could not regard them as throwing any light on the structure of watches. Thus the mainsprings whose action he investigates are supposed to become perfectly straight when left to themselves. He seems to have known that this is not the case with those employed in watches or clocks; but he surely was not aware of the importance of the difference, or that a spring which would admit of so great a change of figure without breaking must be so extremely thin that it would scarcely bear to be touched, much less could it have strength or force to move a watch or anything else. But, which is still more objectionable, he did not proceed as if aware that a mainspring properly applied has its outer end fixed to the barrel, and that this lessens the rubbing of the coils on one another, while it may occasion a considerable strain and flexure near that end, and almost none at some distance from it, if not rather a tendency to straighten it there. Nay, he seems to have had no idea that the coils, however well shaped when free, are prone to lean and rub on one another when in action, and that they would be far more prone to this, nay would bear all to one side of the arbor, forming a most distorted spiral, were the outer end of the spring only pulled or pushed round as he assumed, and as would be the case were it simply attached but not fixed to the barrel. He ought likewise to have known that one end of the balance spring being fixed to the balance, and the other to a stud in the frame, neither end is simply pushed or pulled round as he assumed. Similar objections attach to all the investigations on spiral springs with which we are acquainted; so that we are led to suspect that this subject is still in its infancy, with the exception of what light has been thrown on it by practice and experiment.

The case of mainsprings is usually regarded as the same with that of a flat spiral spring having only its inner end fixed, while a simple force acts on the other extremity. It is, however, a great mistake to suppose that such a spring, under the action of a simple force, or rather of a change of such force, will preserve anything like the original spiral figure, only varied in size. For if we pull a thread attached to the outer end of the spring, we shall find that, in place of being able to bend it regularly round, we drag all the coils towards one side of the arbor, making them crowd together at one side and widen at the opposite, in such a manner that the figure of the spring will no longer deserve the name of a spiral. Neither this fact, which lies at the very foundation of the research, nor the real circumstances of a mainspring strongly compressed in, and having its outer end fixed to the barrel, have, so far as we know, been attended to by our learned theorists.

The figure of the fusee has not yet been determined with anything like accuracy. It is treated, though rather in a preliminary way, by Lahire, in tome ix. p. 156 of the Mem. de l'Académie. It was afterwards considered somewhat more systematically by Varignon, who at different times communicated his ideas on the subject to the Académie; and at length a long article of his on the fusee was inserted in their Mémoires for 1702, p. 192. He there professes to treat the question in a very comprehensive manner, so as to suit various laws of elasticity; though indeed the law discovered by Hooke was the only one then known, and as yet no other seems to exist. Hooke contented himself with what experience taught him, viz. that within moderate limits the force of a spring is nearly in proportion to its distance from its resting position. This alone Lahire adopted, any other being superfluous. But Varignon's investigations are professedly so comprehensive as to allow of springs having their forces proportional to almost any power or function of their distances from rest. The result which he obtained when adopting Hooke's law amounts to this, that the radii of the fusee should be everywhere inversely as the square roots of their distances from a fixed point in the axis. Of course the fusee is not here generated by a common hyperbola revolving on one of its asymptotes; for in that curve the co-ordinates to the asymptotes are simply in a reciprocal proportion. But we shall afterwards see that even Varignon's investigations are not free from objection.

Notwithstanding all that had been done by Varignon, we find Mr B. Martin, a long time afterwards, taking up the subject, and treating it in a much more superficial manner, in his Mathematical Institutions. By entirely overlooking what Varignon had partly overlooked, and which is one of the most important elements in the problem, viz. the lengths of the parts of the chain or string coiled up on the fusee, he very readily gives a solution, in which he makes the fusee to be generated by a common equilateral hyperbola; and the worst of all is, that, ever since the publication of this result, almost every one in this country repeats the same thing on Martin's authority, without giving himself any further concern. Indeed, not only Martin's result, but the investigation of it, has been copied into Rees' Cyclopaedia, under the article Fusee. But allowing that the common hyperbola had been the generating curve, we are quite at a loss to see why its vertex must necessarily have described the circumference of the base or wide Clock and end of the fusee, as it is made to do in each of the various cases considered in that article. The consequence is, that the theory, as there laid down, is so cramped and restricted that it could scarcely have been applied in any case, even if it had had no other defect. It is, however, to be observed, that both under the article Clock, and also under that of Watch, in the Cyclopaedia, the fusee is always said to be generated by the revolution of a parabola, which is quite out of the question. The learned Dr Hutton, too, in his Dictionary, after stating that Varignon has investigated the figure of the fusee, and that it is generated by a hyperbola, just gives us Martin's solution, making the generating curve a common equilateral hyperbola: from which it would seem he was not aware how widely these authors differed in their results.

The figure of the fusee, it is well known, is not so much attended to in practice as it ought to be; and it is surely high time it were begun to be more correctly considered in theory. In his preliminary remarks, Varignon thought it was easy to show that the fusee must be a solid, generated by a curve, cmf, fig. 8, Plate CLXIII., of the hyperbolic sort, revolving about one asymptote ab, which is the axis of the fusee, and having another asymptote ac, at right angles to that axis. We suppose he would have reasoned thus: Let the mainspring be ever so much bent or wound up, its force being finite, must require a lever or radius to act upon; and hence neither the surface of the fusee nor the generating curve can meet the axis ab, which must therefore be one asymptote. On the other hand, suppose the spring were allowed to continue to act even till it approached the position in which it would rest if not confined by the barrel, the radius of the fusee upon which it acts would during this require to increase continually till it became infinite, and after that it could advance no farther laterally. Hence that radius, or at least the nearest parallel ac beyond it, would be another asymptote. This, however, implies that the axis of the fusee is at an infinite distance from that of the spring, which is as different from the actual state of the case as it is possible to imagine; for the greatest efficient radius, in place of being infinite, cannot exceed, if it so much as equal, the distance between those axes. A second asymptote is therefore entirely out of the question.

But the particular kind of curve has not yet been determined, even on the most simple hypothesis of elasticity. If we adopt Hooke's law, that the intensity of the spring is everywhere as its angular distance from its resting position, the parts of the chain or string which are wound off or on the barrel will be measures of, or proportional to, the corresponding parts of its angular motion. But it does not, therefore, follow, as Varignon has assumed, that the radius of the fusee should be everywhere inversely proportional to the tension of the chain, even abstracting from its thickness; because the angle which a radius of the fusee makes with the chain at the point to which it is a tangent, in place of being a right angle, as his assumption implies, is always acute; but since this angle diminishes continually as the radius increases, the radius of the fusee must observe a different ratio from that of the reciprocal of the chain's tension. Yet even this might not have been of so much importance, had Varignon's investigations not depended materially upon or involved that part of the curve which is near the supposed asymptote ac.

But we have not yet pointed out the most faulty part of the process; for Varignon in effect assumed, that when an inch of the chain is uncoiled from the spring barrel, no more than an inch is wound upon the fusee. Such, to be sure, is the case with a chain passing from one pulley to another, and may even be nearly true in our watches and clocks; but it can by no means be admitted as a datum for accurately investigating the figure of the fusee, unless we do what Varignon has not done, viz. prosecute such investigation without regard to that part of the curve which approaches the supposed asymptote ac. For while the spring, when near the resting position, parts with one inch of the chain, the fusee may gain, or at least come into contact with many, nay with an indefinite number of inches. Perhaps some may think it impossible that the surface of the fusee can acquire the chain faster than that of the barrel parts with it; but if any one thinks so he must be in a very great delusion. The radii of the fusee differ prodigiously one from another, especially on Varignon's supposition that they at length become infinite. For instance, the radius of an inch would differ by an infinite quantity from the infinite radius, and it would therefore take an infinite portion of the chain to reach from the extremity of the one radius round to that of the other; whereas during the corresponding turning of the spring, that is, while it was being turned from its resting position to that in which it has force enough to act on a radius of an inch, it can only have parted with a few inches of the chain. Varignon has therefore assumed quantities to be equal which differ in every possible degree.

To show to what an inconsistency these faulty principles have led that eminent mathematician, put \( ap = x \) \( pm = y \). Then, according to Varignon, \( xy^2 \) equals a constant quantity; but this, it is well known, is a property of a curve cmf in which the area \( apme \) is finite, and consequently the surface generated by the revolution of the arc cmf, being proportional to that area, must be finite also. But the same surface must likewise be infinite, that it may contain an infinite quantity of the chain, which is absurd. It is remarkable, that though a similar inconsistency attaches to each of the various cases to which Varignon supposed his investigations extended, he does not seem to have had the least suspicion of their being liable to any such objection. Still we are willing to admit that his result above quoted is by much the best we have yet met with, as an approximation to that part of the fusee which is usually employed. For since the increment of the chain coiled on the fusee is proportional to \( dy \), if that were also as the increment of the force of the spring, and this again as the variation \( \frac{dy}{y^2} \) of \( \frac{1}{y} \), we should obtain by integration \( xy^2 \), equal to a constant quantity.

A properly shaped fusee must no doubt owe something of its tapering form to the very considerable change which, during the motion of the barrel, the parallelism of the straight part of the chain undergoes in respect of a plane passing through the axes of the fusee and spring, and which is owing to the smallness of the distance between these axes. No notice seems ever to have been taken of this change of parallelism, the effect of which would increase so much as the radius of the fusee increased, that we suspect it would be found a very unmanageable ingredient in an accurate investigation, and yet it ought not to be neglected. Every one, we dare say, is aware that the thickness of the chain must not be overlooked; but we know no problem that has been handled more superficially than the figure of the fusee. Most authors who treat on it have, however, availed themselves of a very random-looking assertion, which seems to have been first made in the Hist. de l'Académie for 1702, page 123, viz. that the fusee would be a cone, did the force of the spring vary exactly as its distance from its resting position; which is exceedingly curious, considering that neither Lahire, Varignon, nor Martin, when they proceeded on that hypothesis, arrive at any such cone. But it would not be difficult to show, that if a cylindric barrel were put in the usual place of the fusee, a frustum of a cone would be nearly the figure of a fusee to clock and be formed upon the spring barrel or on its arbor. This would be much more easily executed, and might be conveniently employed in box chronometers and spring clocks, but there is scarcely room for it in pocket watches.

It is a far more delicate and difficult problem to execute a proper escapement for watches than for clocks, on account of the small size, which requires much more accurate workmanship, because the error of the hundredth part of an inch bears 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 means of accumulating such a control, or dominion as it is called, 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 risk of snapping its pivots at every jolt, is a mere trifle in comparison with the pendulum of an ordinary clock; from a dozen to twenty grains being the weight of the balance of a 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 as much as possible of 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 per second. Now when we reflect on the small momentum of this regulator, the inevitable inequalities of the maintaining power, the great proportion of the arc of vibration on which these inequalities will operate, and the comparative magnitude even of an almost insensible friction or clumsiness, it appears almost chimerical to expect any thing near to equability in the vibrations, and incredible that a watch can be made which will not vary more than one beat in 86,400. Yet such have been made, and must be considered as among the most masterly exertions of human art.

In treating on escapements for pendulums, we assumed as a leading principle that the natural vibrations of a pendulum are isochronous, or performed in equal times, whether wide or narrow. This is so nearly true when the arches of vibration do not exceed eight degrees, that the retardation of the wider arches within that limit will not become sensible, though accumulated for a long time. The common escapement, 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 Huygens. A similar principle is assumed in watches, namely, that the oscillations of a balance urged by its spring, and undisturbed by any foreign force, are performed in equal times, whether they are wide or narrow. This principle was assumed by the celebrated Dr 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 the space through which it is stretched or bent from its natural form, as we noticed when treating on the fusee. He expressed this in an anagram which he published about the year 1660, to establish his claim to the discovery, and yet conceal it till he had made some important application of it. When the anagram, namely, *ceitinossttav*, 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 towards it by a force proportional to its distance from it. He immediately (in 1658) applied a spring to the balance of an old watch, which he afterwards gave to Bishop Wilkins. So amazingly improved was its motion, that Hooke, persuaded thereby of the perfection of his principle, thought nothing further was wanting for making a watch of this kind a perfect chronometer, but the hand of a good workman; for, compared with former ones, his watch seemed almost perfect, though made in a small country town, in a very rough manner.

Mr Huygens also published a claim to this discovery about the year 1675, and proposed by means of it to make watches for discovering the longitude at sea. But there is the most unquestionable evidence of Dr Hooke's priority by at least fifteen years, and of his having made several watches of this kind. One of them having a double balance was presented to King Charles II. Upon it was engraved "Rob. Hooke, inven. 1658." Dr Hooke's first balance spring was straight, and acted on the balance in a very imperfect manner. But he soon saw this, and made several alterations; and, among others, he employed the cylindrical spiral, which he at length gave up for the flat spiral. The king's watch had one of this kind before Mr Huygens published his invention in 1675. Indeed, in his Horologium Oscillatorium, published two years before, there is not one word of it. But both Dr Hooke and Mr Huygens were too sanguine in their expectations. We have by no means 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 shown that it is sensibly true only within certain limits. The demonstrations by which Bernoulli supports the unqualified principle of Mr Huygens, proceed on hypothetical doctrines concerning the nature of elasticity. But even these show 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 Huygens. Besides, though this should be the true law of a spring in certain circumstances, it does not follow that this spring, applied in any way whatever to the axis of a balance, will urge it, agreeably to the same law; and if it did, it does not follow that the oscillations of the balance will be isochronous; for the force has not only to move the balance, but also to overcome the inertia of 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. The surplus, therefore, is all that is employed in actually moving the balance; and it is uncertain whether this surplus varies according to the same law, or be always proportional to the whole force of the spring. It is an extremely difficult problem to determine the law by which this surplus varies, even in the simplest form of the spring; nor is it easy to determine the law of oscillation for a spring free from any balance. There may be such forms of a spring, that although the velocity with which the different parts approach their quiescent position were exactly as their excursion from it, this might by no means be the law of velocity which such a spring would produce in a balance. When the spring is a simple and straight steel wire, suspending the balance in the direction of its axis, the motions, if not immoderate, agree remarkably well with Hooke and Huygens' rule. But the motion of a balance urged by a spring wound up into a flat or cylindrical spiral, as in common watches, deviates considerably 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 reverse takes place with a short spring. A certain taper or gradual diminution in the thickness of the spring is found to equalize the vibrations. There is also a great difference between the force with which a part of the Clock and 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, supposing these corrections, which are in a considerable degree in our power, to be applied, and the true motion, which we shall call the cycloidal, to be attained, we may then adapt the construction of the scapement to preserving this motion undisturbed. But here we may 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; but a viscosity which would never be felt by a pendulum of twenty pounds, will stop a balance of twenty 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, because 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.

In ordinary pocket watches, the original recoiling scapement, with the crown wheel, which was used in the older clocks, still holds its place, and answers very well for all common purposes in a watch. A well-finished watch, with that scapement, will keep time within a minute in the day, which is sufficient for ordinary affairs. But such watches are subject to great irregularities in their rate of going, by any change in the force of the wheels. This is evident; for, if the key be put on its square, and the watch be held back or pressed forward by it, we hear the beating greatly retarded or accelerated. The maintaining power in the best of such watches is supposed to be never less than one fifth of the regulating power of the spring, and the following is the argument by which this opinion is supported. If we take off the balance spring, and allow the balance to vibrate by the impulse of the wheels alone, the minute hand will only pass over from twenty-five to thirty minutes on the dial-plate per hour. Suppose it thirty; then, since the wheels act through equal spaces with or without the spring, the forces are as the squares of the acquired velocities. But the velocity is double when aided by the spring; therefore the accelerating force is quadruple, and so the force of the spring is three times that of the wheels. In the same way, if the hand go forward twenty-five minutes, the force of the wheels is about one fifth of that of the spring. So great a proportion is supposed necessary, that the watch may go so soon as unstopped.

Such is the usual mode of reasoning on this point; but we suspect it involves a very doubtful assumption, namely, that the balance receives exactly the same degree of force from the wheels when its spring is on as when it is off. But the principle and manner of action, as also the good and bad qualities of this scapement, are much the same as those of the like scapement for pendulums. The maintaining power being applied in a direct manner, and during the greater part of the vibration, will have great influence in moving the balance. A given mainspring and train will keep in motion a heavier balance by means of this scapement than by almost 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 train. Besides, the chief action of the scape wheel being at the very extremes of the vibrations, and being very abrupt, the variations in its force are most hurtful to the isochronism of the vibrations.

This scapement, though extremely simple, is, by the variation of the few particulars of its construction, susceptible of more degrees of excellence or imperfection than almost any other. We shall therefore briefly describe that construction which long experience has sanctioned, as the best for the common scapement. Fig. 4, Plate CLXII., represents it in what are thought its best proportions, as it appears when looking straight down on the end of the verge or balance arbor. C is the centre of the balance and verge, CA and CB are the two pallets; CA being the upper, or the one next the balance, and CB the lower one. F and D are two teeth of the crown wheel, moving from left to right; and E, G, are other 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 scapement should not, however, be quite so close, because an inequality in 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 may be obviated in some cases by withdrawing the wheel a little from the verge, in others by shortening the pallets.

The proportions are as follow:—The nearest approach of the teeth to the axis C of the balance is one fifth of AF, the interval between two teeth. The radius or length CA or CB of the pallets is three fifths of AF. The pallets make an angle ACB of 95°, 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 should be of an epicycloidal form, or 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° 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 ACB = 95°, and we have aCL = 120°. In like manner, B will throw out as far on the other side. From 240°, the sum of these angles, take the angle between 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 supposes the teeth to terminate in points, and the acting faces 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; for nothing can be more injudicious than to attempt, as some do, to lessen friction by making mere points scratch along surfaces. This rounding, however, lessens very considerably the angle of scapement, by shortening the teeth. Besides, 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; a circumstance which makes it improper to continue the vibrations much beyond the angle of scapement. One third of a circle, or 120°, is therefore reckoned a very proper vibration for a scapement made in these proportions. The impulse of the wheels, or the angle of scapement, may be increased by making the face of the pallets a little concave, preserving still the same angle at the centre. The vibration may also be widened by pushing the wheel nearer to the verge, which would likewise 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; that is, by placing the pallet CA so that its acting face may be where its back is The tooth would then drop on it at the centre, and lie there at rest, while the balance completes its vibration. But this would make the banking or striking on the teeth almost unavoidable. In short, the best makers, after varying every circumstance, 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 Huygens and Newton in rational mechanics engaged the mathematical philosophers in the solution of mechanical problems about the end of the seventeenth century. The vibrations of elastic blades or wires, and their influence on watch balances, became a subject of inquiry. The principal requisites for producing isochronous vibrations were pretty well understood, and the artists were prompted by the speculators to attempt constructions of escapements proper for this purpose. It appeared clearly that the most effectual means for this purpose was to leave the balance unconnected with the wheels, especially near the extremities of the vibrations, 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 naturally arising from these reflections is to confine, if possible, the action of the wheels to the middle of the vibrations, 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 motion, but will make little change in their duration, because the greatest part of the motion will be effected by the lance spring alone. This maxim was inculcated in express terms by John Bernoulli, in his Recherches Mécaniques et Physiques; but it had previously been suggested by common sense to several unlettered artists.

One of the methods first thought of for accomplishing this was to make the scape wheel rest upon a cylindric surface concentric with the verge, while the balance was in the exterior parts of its excursion, and only to impel the balance when near the middle of its vibrations. This was attempted with some degree of success by Tompion. He made a tooth fall upon a solid cylinder; and, after resting there till the cylinder turned a little round, it fell into a notch in the side of the cylinder. On escaping from the notch, the tooth slid along a pallet fixed to the cylinder, and, in so doing, gave an impulse to the balance when near the middle of its vibration.

This contrivance was materially improved upon by Graham, who, much about the time that he contrived his dead beat for clocks, succeeded in adapting the same sort of escapement to the wider vibrations of balances. The following is his construction:—In fig. 2, Plate CLXII., AA represents part of the rim of the scape wheel, which is to move from left to right. E and G are two of its teeth, having their faces nc, gp formed into planes inclined to the circumference of the wheel at an angle of about fifteen degrees. Suppose a circular arc, EFG, having the same centre as the wheel, to be described through E and G, the middles of the faces of the teeth. The axis of the balance passes through some point F of this arc, and we may say that the mean circumference of the teeth passes through that point, or the centre of the verge. On this axis is fixed a portion of a thin hollow cylinder, of which eb'd is a section. It is 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 carnelian 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 e and d are in the circumference which passes through the points of the teeth. By this construction the portion eb'd of the cylinder will occupy about 210° of the circumference, or 30° more than a semicircle. The edge e of the cylinder, to which the tooth E approaches from without, is rounded. The other edge d is formed into a plane inclined to the radius about 30°.

Now suppose the wheel pressing forward in the direction EG: the point e of the tooth, touching the rounded edge, will push it outwards, turning the balance round in the direction eb'd. The heel n of the tooth E will escape from this edge when it is in the position h, and E in the position F. The point e of the tooth has now got to r, and the edge of the cylinder 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 eb 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 F, rubbing all the while on the inside of the cylinder. The balance comes back into its natural position eb'd, 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 E. The balance continues its vibration, the tooth all the while resting and rubbing on the inside of the cylinder. When this vibration in the direction db'e is finished, the balance resumes its first motion eb'd by the action of the spring, and the tooth begins to act on the first edge e 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 e, 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 e passes to h, and while d passes to g; 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 escapement is evidently 30°, being twice the angle which the face of a tooth makes with the circumference.

It is evident that when this escapement is executed in such a manner that the succeeding tooth just reaches the cylinder at the instant 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 escapement 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 it allows a drop equal to the thickness of the cylinder, which is about the 20th part of its diameter.

Fig. 7 shows in perspective the entire wheel Λ, and cylinder BC. It will now be seen how the cylinder is connected with the verge, so as to make such a great part of a revolution round a tooth of the wheel. Each triangular tooth is placed upon the top of a little pillar, which connects it with a shank projecting from the rim of the wheel. The acting part \( cd \) of the cylinder should exceed 180° by the arc \( ir \); but to make room for the neck or shank of the tooth, the cylinder is farther cut away at \( e \) under the acting part, so that scarcely a fourth of the circle is left. Thus it appears to be a very slender and delicate piece, but when made of steel it is strong enough to resist moderate jolts. The ruby cylinders are much more delicate. From the scape wheel being here parallel to the others, this contrivance is frequently called the horizontal scape-

ment.

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 and motion are very considerably obstructed by friction, and the clamminess of the oil. M. Leroy placed the balance so that it rested when the point of the tooth was on the middle of the cylindric surface. When it was drawn 80° from this position, and the wheel allowed to press on it, it continued to vibrate only 4-5 seconds. When the wheel was not allowed to touch the cylinder, it vibrated ninety seconds, or twenty times as long; so much did the friction on the cylinder exceed that of the pivots. But we are not sufficiently acquainted with the laws of either of these obstructions, to decide whether they should increase or diminish the duration of single vibrations.

Since 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 scape ment, and that they will be less affected by changes in the force of the wheels. Accordingly, Graham's cylindrical scape ment 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 it is found that doubling or trebling the force of the wheels makes very little alteration in the rate of the watch, though it greatly enlarges the width of the vibrations. No great change can be observed in the frequency of the beats, whether we aid or relax the force by means of the key, provided we do not stop the watch altogether. But a more careful examination shows that an increase in the power of the wheels generally tends to make the watch go slower, and so much the more as the watch is in greater need of cleaning; which is no doubt owing to the friction and oil operating on the wider arches of excursion. But when the scape ment is well executed, in the best proportions of the parts, the performance is extremely good. It has been alleged, that by keeping the centre of the verge about the thickness of the cylinder from its centre \( F \) towards \( E \), the watches so constructed have gone with astonishing regularity. But it is evident that such watches must have a minute recoil, and are therefore likely to be affected by the irregularities 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. This scape ment is in its best state when the acting part \( cd \) of the cylinder exceeds 180° by twice the inclination of the faces of the teeth to the circumference of the wheel. There are, however, very few which have more than 180°. But this is too little; for in that case the tooth does not begin to act till its middle touch one of the edges of the cylinder in its resting position. Indeed it may happen that the tooth will never rest on the cylinder, because the instant 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

scapement, and is continually under the influence of the clock and wheels.

We formerly mentioned Lepaute's modification of Graham's dead beat, and that he adapted it to watches. In this he also used two inner cylindric surfaces, but much larger arches of them than in the pendulum scape ment. A tooth, in quitting one of these arches, acts, as in the former case, on the slant face of a pallet, though one which is much longer in proportion to the other parts. By this means the motion of the balance is very effectually maintained. Were it not very difficult of execution, and easily hurt or put out of order, it would be an excellent scape ment. The comma scape ment, or échappement à virgule, is of the same sort, but very inferior to that of Lepaute; in particular, that it has only one pallet and one cylindric arch.

The duplex scape ment, apparently so named from the Duplex scape wheel having two sets of teeth, is another in which a tooth of the scape wheel rests on a cylindric surface concentric with the verge, during the excursions of the balance beyond the angle of scapement; but it differs somewhat in the application of the maintaining power from all those already described. Fig. 5, Plate CLXII., represents the essential parts greatly magnified. \( AD \) is a portion of the scape wheel pressing from left to right, and having teeth \( f, b, g \), at the circumference, which are entirely for producing the repose of the wheel during the excursions of the balance. This is effected by means of a very small cylinder \( opq \), concentric with the verge, and made of hardened steel, or of some hard stone. This cylinder has an angular notch \( o \), which, while the cylinder turns in the direction \( opq \), easily passes the tooth \( B \), which is resting on the cylindric surface; but when it returns in the other direction, the tooth \( B \) gets into the notch and follows it, pressing on one side till the notch comes into the position \( a \). The tooth being then come to \( b \), escapes from the notch, and another tooth drops on the convex surface of the cylinder at \( B \).

The scape wheel is also furnished with another set of teeth standing upright on its rim, as represented by \( a, D \). There is also fixed on the verge, above the cylinder, and clear of the wheel, a pallet \( CF \), which is more distinctly seen in perspective in fig. 6. Its position with respect to the cylinder below it is such, that when the tooth \( b \) is just escaped from the notch, the point \( C \) has just passed the tooth \( a \), which was at \( A \) while \( B \) rested on the small cylinder, but moved from \( A \) to \( a \) while \( B \) moved to \( b \). The wheel being now at liberty, the tooth \( a \) exerts its pressure on the pallet \( C \) in the most direct and advantageous manner, following and accelerating it till another tooth stops against the little cylinder. When the balance is in its quiescent position, the pallet is at \( H \), quite out of the reach of the teeth \( a, D, \) etc.; and if in this state the mainspring is allowed to act, it can only press a tooth against the cylinder. Nay, although the tooth were getting into the notch, its action, being so near the centre, could not overcome the balance spring. Hence the force of the wheels cannot set the watch going; and therefore a watch with this scape ment may sometimes stop on receiving a sudden twirl or circular motion in the direction in which the balance happens to be moving at that instant. But every watch which cannot commence its own vibrations is liable to this, and some of them even more so than the duplex. In other respects the duplex scape ment gives great satisfaction. The cylinder of repose may be made very small, only care must be taken that the tooth get a sufficient hold of it, and the direct impulse on the pallet gives it a great superiority over those in which the action on the pallet is oblique; but since all the force with which the teeth strike against the The origin of the duplex is involved in some uncertainty, but it is supposed to have been derived from a more complex scapement of Dr Hooke, upon which Du Tertre made some improvements. This had two balances in the form of two toothed wheels pitching into each other, and consequently turning in opposite directions, with the view of obviating the effects of external motion, but only one of these balances had a spring. A part of the verge of each balance was formed into a semicylinder for the teeth of the scape wheel to rest on alternately. On the side of the scape wheel was fixed a smaller wheel with the same number of teeth, and each balance carried on one of its arms a stud or pallet to receive an impulse from the smaller wheel. As soon as the larger wheel had escaped from the cylinder of one balance, the smaller wheel gave an impulse to the pallet on the other balance. This was obviously just the duplex in a double form. It is long since Du Tertre and others applied it in the single form to clocks, though it is scarcely forty years since the duplex appeared, as applied to watches in its present shape, under the name of Tyrs' scapement.

We shall now proceed to a different class of scapements, in which the balance is entirely free from the wheels in the greater part of its vibrations. These are called detached scapements, and are of more recent date. The first rude attempt of this sort, of which we have any distinct account, seems to be that noticed by Thibaut, vol. i., page 110, and the next that of Peter Le Roy, Mémoires de l'Académie for 1748; but it is said that Du Tertre had used something of the sort preferable to this long before, though no description of it is preserved. Since that time, the attention of artists, both here and on the Continent, has been very much occupied with this sort of scapements; but we can only notice here a few of these contrivances. The following is perhaps one of the simplest forms. In fig. 8, Plate CLXII., abc is a cylinder of hard steel or stone, having a notch ab, the side of which serves for the pallet. AB is part of the scape wheel pressing in the direction AB, and placed so near the verge that the cylinder is barely 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 stoppin G. A small stud or detent F is fixed to the spring on the side next the wheel. The tooth B rests on this detent in such a manner that the tooth a is just about to touch the cylinder, and the tooth f just clear of it. Another spring, extremely slender, is attached to the spring DE, and claps pretty close to it, on the side next the scape wheel. It should either not reach, or it should be clear of, the stud F, and its point projects a little beyond that of the long spring. When its point is pressed towards the wheel it yields readily; but when pressed in the opposite direction it carries the spring DE along with it. The cylinder is so placed on the verge, that, in the quiescent position of the balance, the edge a of the notch is close by the point of a tooth; and a pin i projecting from the end of the cylinder is then close by the projecting point of the slender spring.

When the balance is turned from this position 80° or 90° in the direction abc, and then 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 stronger 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 spring before the tooth quits the notch; so that when it is clear of the pallet, the wheel is locked again on the detent F, and another tooth comes in the place of a, ready to act in the same manner. When the force of the balance is spent, it stops, and then returns to its quiescent position with a motion continually accelerated. The pin i easily pushes aside the slender spring without disturbing the stronger one. The balance goes on, turning in the direction abc, till its force is again spent; it stops, returns, unlocks the wheel, gets a new impulsion, and so on. Thus we see a vibration almost free, maintained in a manner even more simple than the common crutch scapement. The impulse is given in an advantageous manner, and is continued through the whole motion of the wheel. Very little force is required for unlocking the wheel, because the spring DFE is very slender towards E. A sudden twitch of the watch in the direction ba might chance to unlock it. But this will only derange one vibration, and even that not considerably, because the teeth are so close to the cylinder that the wheel cannot advance till the notch come round to the place of scapement. A tooth may then continue pressing on the cylinder, and, by its friction, change a little the extent or duration of a single vibration. It is obvious that, on account of the weight of the springs and detent, the force required for the unlocking will not be exactly the same for every position of the watch. But if such a scapement be very little affected by great variation in the moving force, there is little room for alarm from this quarter.

So nearly allied to the last is Earnshaw's scapement, Earnshaw's fig. 10, that it will need little or no explanation. The scapement teeth of the scape wheel DF pass behind the long spring ICB, and would be quite clear of it, but for a pin which projects from it behind, and acts as a detent. The small pallet A fixed upon the verge passes clear of the long spring at B, but in ascending it catches the projecting point of the slender spring below, and thereby raises the long spring with its detent pin, which sets at liberty the tooth D. The wheel immediately advances till the next tooth G is locked against the pin. During this the tooth F has entered the notch of the cylinder, and given an impulse to the hooked pallet E. If it is a fixed stud, holding the point of a screw for regulating the distance of the spring from the wheel. The spring rests on the inside of the head of the screw, and is thereby prevented from going too close on the wheel. Sometimes, in place of a metallic pin, a piece of hard stone is fixed to the spring to act as a detent. Almost the only difference between this and the last is in the pallet E being considerably undercut, which is said to be an advantage. Unfortunately we have never been able to see it in that light. On the contrary, we should think it causes the teeth of the wheel to act at a needless disadvantage, and adds greatly to the sliding, and consequently to the friction and wear.

Fig. 9 shows Arnold's scapement, the same letters de-Arnold's noting the same things as in the last, except that each scapement-tooth has a heel projecting above the plane of the wheel, for the purpose of holding against the detent on the spring; and the unlocking is accomplished by the small pallet A pressing the spring inward, or toward the centre of the wheel. The regulating screw H passes through a fixed stud, and bears with its point against the spring. The acting faces of the teeth are epicycloidal, and some people fancy that therefore they only roll on the side E of the notch, and have no friction. All we have to say on this point is, that it is impossible to make epicycloidal teeth which shall act on a plane without sliding, and consequently these are attended with friction.

A great improvement upon the foregoing detached Robinson's scapements was made by Mr Owen Robinson, who introduced a double wheel, such as is used in the duplex. The extreme points of the long teeth, serving for the locking, obviously allow the unlocking to be effected with much Clock and less pressure and friction, while a powerful impulse can readily be given to the balance, by the side teeth acting on the side of the notch. It is remarkable that this excellent contrivance is scarcely ever employed.

A escapement very different from any of the last sort was invented by Mr Mudge, and applied to his marine timekeepers. It is of the remontoir class, but the balance is perfectly detached from the wheels, except during the extremely short interval of striking out the parts which serve the purpose of detents. In fig. 13, Plate CLXII., BEN is the balance vibrating by the joint action of two spiral springs, not here represented, on its axis CADH, which passes through the centre C. To make room for the other work, the axis is bent into a crank AXYD, for which there is a counterpoise I on the opposite arm of the balance. LM, ZW, are two rods fixed to the crank at the points L, Z, parallel to XY; and e, e, d, f, r, s, are fixed parts of the machine. TR is an axis concentric with that of the balance, and carrying an arm GO nearly at right angles to it, and a small auxiliary spring u, which is wound up whenever the arm GO is moved in the direction OQ. To the axis TR is fixed a curved pallet p, which receives the tooth l of the crown wheel near the verge. The tooth, proceeding along the curved surface by the force of the mainspring, turns the axis and its arm GO, and winds up the spring u. A small projection at the extremity of the curved surface of the pallet p prevents the farther progress of the tooth when the arm GO has been turned through an arc OQ of about 27°; and consequently, the spring u has been wound up through the same angle OGQ of 27°. There is another axis FS exactly similar to TR. It carries its arm Oi and spring v; and the tooth m of the crown wheel winds up the spring v, by acting on the pallet q, and is detained by a projection, after having carried it through an angle of 27°, as in the other case. The arcs passed through by the arms GO and Oi, and marked in the figure, are also denoted by the same letters on the rim of the balance. This figure is reduced from the large one which Pennington, who worked for Mudge, drew for Mr Attwood's paper in the Phil. Trans. for 1794. Though it differs from some drawings of this machine in which the backs of the scape-wheel teeth are nearly parallel to their faces, the acting surfaces are meant to be the same.

Suppose the balance in the quiescent state, the mainspring being unwound, and the branch or crank in the position represented in the figure. If the quiescent points of the auxiliary springs coincide with that of the balance springs, the arm GO will just touch the rod LM, and in like manner the arm Oi will just touch the rod WZ. The two arms GO, Oi, in this position are parallel to the line CO. This position of the balance and auxiliary springs remains as long as the mainspring is not wound up; but whenever the action of the mainspring sets the crown wheel in motion, a tooth thereof meeting with one or other of the pallets p or q, will wind up one of the auxiliary springs. Suppose it should be the spring u. The arm GO, being carried into the position GQ by the force of the crown wheel on the pallet p, remains in that position so long as the tooth of the wheel continues locked by the projection on that pallet; and the balance itself, not being at all affected by the motion of the arm GO, nor by the winding up of the spring u, remains in its quiescent position, consequently no vibration can take place except by the assistance of some external force to set the balance in motion.

But now suppose an impulse given to the balance sufficient to carry it through the semi-arc OB, which is about 135° in Mudge's construction, the balance during this motion carries with it the crank AXYD and the rods LM, WZ. When the balance has described an angle of 27° = Clock and OCh, or OGQ, the rod LM meets with the arm GQ, and, by turning the axis TR, and the pallet p, in the direction of the arch Oh, releases the tooth from the projecting point of the pallet p. The crown wheel advances, and a tooth below, meeting with the pallet q, winds up the auxiliary spring v, and carries the arm Oi through the angle Oik = 27°, where the arm Oi remains so long as the tooth is locked by the pallet q. During the winding up of the spring v through the arc Oh, the balance describes the rest of the semi-arc AB, and LM carries round the arm GQ, causing it to describe an angle hCB or hGB = 108° = arc hB. When the balance has arrived at the extremity of the semi-arc OB = 135°, the auxiliary spring u will have been wound up through the same angle of 135°; viz. 27° by the force of the wheel on the pallet p, and 108° by the balance itself carrying with it the arm GO, while it describes the arc AB. The balance therefore returns through the arc BO, by the joint action of the balance spring and the auxiliary spring u; the acceleration of both springs ceasing the instant the balance arrives at the quiescent position. When the balance has proceeded in its vibration about 27° beyond the point O to the position Ch, the rod WZ meets with the arm ik, and by carrying it forward releases the tooth of the crown wheel from the pallet q. The wheel again advances, and an upper tooth meeting the pallet p, winds up the spring u as before. The balance with the crank proceeding to describe the remaining semi-arc KE, winds up the spring v through the farther angle ACE = 108°, and returns through the semi-arc EO, by the joint action of the balance spring and the auxiliary spring v, both of which cease to accelerate the balance the instant it has arrived at O.

Thus it appears that the balance is opposed by each auxiliary spring through an angle of 108°, and assisted through an angle of 135°. This difference of action maintains the vibrations, and the necessary winding up of the auxiliary springs is performed by the wheel work while they are entirely 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. During this the balance describes an angle of about 8°.

The performance of Mudge's timekeeper, under the severest trials, equalled any that were compared with it, in so far as depended on escapement alone. But this escapement, though most simple in principle, must always be vastly more difficult to execute than any of the three or four last described. There is so little room, that the parts must be exceedingly small, requiring the nicest workmanship. But we do not see that it is superior to them even theoretically. The irregularities of the wheels affect those three escapements only in the act of impulsion, where the velocity is great, and the time of action very short. Besides, the chief effect of these irregularities is only upon the extent of the excursions of the balance, during the time the wheels are at rest. It is almost needless to observe, that room for such a escapement could never be found in a pocket watch of a moderate size.

In another detached escapement invented by Mr Mudge, Muskrat's crutch, the same as for a pendulum, is interposed between forked the scape wheel and balance. The crutch EDF; fig. 3, scape wheel has a third arm DG, standing outwards from the junction of the other two, and of twice their length. This arm exactly balances the other two, and 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 scape wheel of which IK is a part, by its action on Clock and 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 crutch EDF is not accurately a dead-beat scapement, but has a very small recoil, beyond the angle of impulsion, by which the branch A, now at B, is made to press very gently on the cylinder, while the wheel rests on the pallet F, and the balance turns in the direction BHA. The point A of the fork passes 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. When the balance returns from its excursion, the pallet C strikes on the branch A, still at B, and liberates the wheel, which 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 moves, making the balance describe a semi-vibration in the direction AHB. The fork is now in the situation Aga, similar to Bgb, and the wheel is again detained by the crutch pallet E.

This is evidently a very steady and effective scapement. The lockage of the wheel is procured in an ingenious manner; and, however powerful the action of the wheel, the pressure of the fork upon the cylinder may be made as small as we please, since it depends entirely on the degree of recoil caused by the pallets E, F. Pressure on the cylinder is not indeed absolutely necessary, and the crutch scapement might be a real dead beat. But a small recoil, by keeping the fork in contact with the cylinder, prevents any unsteadiness in the motion. This scapement has been variously modified by other artists. In particular, it has been found a considerable improvement to substitute a roller for the simple pallet C; and this again has sometimes been combined with Lepautre's modification of Graham's dead beat. In several of these modifications, the crutch is not balanced or counterpoised, which is apt to make the watch go differently in different positions. Some of their crutches, again, when counterpoised, are so heavy that much force is wasted in giving them motion.

A scapement resembling the last, but essentially different, was produced by Hautefeuille in 1722. Instead of the fork, the arm DG carried a circular rack or toothed segment, whose centre was D, and which we may suppose represented by the dotted arc aABb. Instead of the cylinder V, there was a pinion on the axis of the balance pitching into the rack. In Rree's Cyclopaedia, through some mistake, this scapement is ascribed to Berthoud, though it was well known before his time. Not long ago, a patent was taken out for this scapement; and the watches to which it was applied are known by the name of lever watches. It is true, that to save room, Hautefeuille arranged the parts a little differently. In particular, he put the scape wheel directly under the balance; but that did not in the least alter the principle. Indeed he seems to have borrowed this scapement in a great measure from one which Huygens had described in 1675, in tome x. of the Memoirs de l'Academie, and in Phil. Trans. for same year. Huygens put a pinion on the axis of the balance, and turned it by a vertical contrate wheel, fixed on an axis carrying pallets which were moved in the ordinary way by a crown wheel placed horizontally. By this means he could make the balance vibrate through as wide arcs as he pleased; but unfortunately in all such scapements the balance is too much under the influence of the wheels, and is particularly liable to be affected by the friction and irregularities in the action of the teeth upon its own pinion.

Descriptions of a variety of other scapements may be seen in the works already quoted, particularly the Transactions of the Society of Arts, and The Repertory of Arts and Patent Inventions. Some very judicious observations by Mr Haley on the wear of scapements will be found in Nicholson's Journal, vol. viii. The wearing of certain parts tends to accelerate the machine, of others to retard it. Mr Haley suggests that the parts should, if possible, be so contrived, that the opposite effects of their wearing may just balance each other.

Repeating watches are such as, by pushing in or turning round the pendant, &c. repeat or strike the hour or quarter at any time required. This repetition was the invention of Mr Barlow, and first put in practice by him in larger movements or clocks about the year 1676. "This ingenious contrivance," says Dr Derham, "soon took air, and being talked of among the London artists, set their heads to work, who presently contrived several ways to effect such a performance; and hence arose the divers ways of repeating-work which so early might be observed to be about the town, every man almost practising according to his own invention." About the latter end of King James II.'s reign, Mr Barlow contrived to put his invention into pocket watches, and endeavoured to get a patent for it; and in order to it, he set Mr Tompion, the famous artist, to work upon it, who made a piece according to his directions." The talk of a patent induced Mr Quare, watchmaker in London, to resume the thoughts of a like contrivance, which he had had in view some years before; and he now succeeded in putting it in practice. This being known among the other watchmakers, they pressed him to hinder Mr Barlow's patent. Applications were accordingly made at court, and a watch of each invention produced before the king and council, who were pleased to give the preference to Mr Quare's. The difference between them was, that Barlow's repeated the hour on pushing in a piece on one side of the watch, and the quarters on pushing in a second piece on the other side; whereas Quare's repeated both hours and quarters by pushing in only one piece. It is not agreed who this Mr Barlow was; some suppose him to have been a watchmaker, others think he was a clergyman, which would better agree with his employing Tompion to make his watch.

Plate CLXVII. shows the principal parts of a watch, having Graham's horizontal scapement, together with repeating mechanism. Fig. I exhibits the trains of the going watch part and of the repetition, as also all the parts which are put within the frame. The wheels B, C, D, E, F, are those of the movement or going part. The other train of smaller wheels a, b, c, d, e, f, belongs to the repetition. The barrel A contains the mainspring of the going part; B is the first or fusee wheel; C the centre or second wheel, whose axis, prolonged through the dial-plate, carries a pipe or cannon, fig. 9, upon which is put the cannon pinion e, and the minute hand; D is the third wheel; E the fourth; and F the scape wheel, whose teeth act on Graham's cylinder, which is not here represented, to avoid confusion, and because it was sufficiently explained when treating on that scapement. The fusee I acts upon the first wheel B, by means of a ratchet and click; and they are kept together by a spring-tight collet and pin. The mainspring and fusee are connected by the chain S, as formerly explained. The beak of the plate O is to prevent the watch being wound up too far. It catches against the end of the fusee-step, which is a short lever X, fig. 3, turning, between the cheeks of a fixed stud, upon the pin p. The stop is always kept clear of the plate O, by the action of the long spring s, except when the watch is fully wound up; for it is only then that the side of the chain has risen high enough to push the stop X within reach of the beak O. From a gut or string being sometimes used in place of a chain, especially in spring clocks, the fusee stop is also called the guard-gut.

The design of the runners, or train of small wheels, is Clock and to give a rapid motion to the fly, for the purpose of regulating the intervals between the strokes of the hammer in a manner similar to that in the ordinary striking part of a clock. If the wheels \(a, b, c, d, e\) have for the numbers of their teeth respectively 42, 36, 33, 30, and 25; and if each of their pinions has six leaves or teeth, then for every turn of the first wheel \(a\), the fly pinion \(f\) will make 4812.5 turns. But the ratchet \(R\), on whose axis the first wheel \(a\) turns freely, is never allowed to turn more than half round, and has twelve teeth on half its circumference, for the purpose of lifting the hammer \(M\) to strike twelve times. Hence the fly turns fully 200-5 times for each stroke of the hammer. Under the ratchet \(R\) is a smaller ratchet, with a click and spring similar to what connects the fusee and first wheel of the going part. The use of it is, that when we push in the pendant or pusher \(P\), fig. 2, we do not move the wheel \(a\); the ratchet \(R\) only goes back; and, by this means, the repeating mainspring, which is on the same axis, is wound up just as much as enables it to repeat or strike the hour and quarters last passed by the hands. But so soon as we cease to press in the pendant, the mainspring just mentioned, which is in the smaller barrel \(\beta\) of fig. 3, brings forward again the ratchet \(R\), to whose axis \(g\), the spring of the click is fixed, and the small ratchet, by acting on the click, turns the wheel \(a\), together with the rest of that train and the fly.

During this, the teeth of the ratchet \(R\), by acting successively on \(m\), the tail of the hammer \(M\), cause it to strike or repeat the hour. The hammer is brought back to the wheel by the long spring \(r\), fig. 2, acting on the pallet \(n\), which is on the axis of the hammer. But this repetition differs from that of the clock formerly described, in that it repeats the hours before the quarters, and never gives more than three quarters. It likewise differs in striking the quarters, by double blows of two hammers acting together.

Fig. 2 shows the dial work, or motion work, as such parts of a repeater, between the dial-plate and frame, are sometimes called. It is represented in the position it would have when the pendant has just been pushed home to make it repeat, and the dial-plate removed to let it be seen. This kind of repeating work is substantial, and has been long in very general use. Though commonly called the French repeater, by far the greater part of it was contrived by the English artists, particularly Barlow, who invented the first repeaters. \(Pp\) is the shank or pusher of the pendant, which enters in through the socket \(O\) of the watch-case. It is flat on the under side, to prevent its turning round. Its inner end \(p\) acts on the heel \(t\) of the rack \(CC\), whose centre of motion is \(y\), and at whose extremity \(c\) is fixed one end of the chain \(ss\). This chain passes over the pulley \(A\), and has its other end attached to the pulley \(A\), which is upon the axis of the wheel \(a\), as seen in fig. 6. When we press in the pusher \(P\), the end \(c\) of the rack will, by means of the chain, turn the pulleys \(A, B\), and make the ratchet \(R\) go back till the arm \(b\) of the rack come against the snail \(L\). Then having let go the pusher, the repeating mainspring will bring forward the ratchet \(R\), and the hour will be repeated as already described. The number of strokes depends on the step of the snail \(L\), which is presented to the arm \(b\) of the rack, as was explained when we described the striking parts of clocks.

Fig 6 shows in perspective some of the principal parts of the repetition, as if in action, and about to repeat two hours. They will be easily recognised, by having for the most part the same letters of reference as the like parts have either in fig. 1 or 2. The star \(E\) and snail \(L\) are screwed together, but are not attached to the frame; they only turn on the shank of the screw \(V\), fixed in the all or nothing piece \(TR\), which, therefore, carries the star and snail, and with them is movable on its centre \(T\). The all or nothing is supposed to have been invented by Julien Leroy, an eminent French artist, for the purpose of insuring that, according as the pendant is pushed quite home or not, the watch should either repeat the proper hour or not repeat at all; it having been found a sad defect in the first repeaters, that the number of hours struck depended on the length the pendant was pushed in,—a defect from which some more recent repeaters are not always free.

For repeating the quarters there is another hammer \(U\), fig. 1, movable on an axis which comes up within the motion work, and carries the piece \(s, 6\), fig 2. The axis of the hour hammer \(M\) is likewise prolonged within the motion work, and carries the small arm \(q\). These three pieces make the quarters be struck by double blows, in consequence of the quarter rack \(Q\) having teeth at the ends \(F\) and \(G\), which act on the pieces \(6\) and \(q\), and cause the hammers strike. The arm \(k\) is put on a square of the axis of the ratchet \(R\), above the pulley \(A\). When the hours are repeated, the arm \(k\) acts on the pin \(G\) in the quarter rack, and causes it to turn, and raise the arms \(6\) and \(q\), together with the hammers. The number of quarters to be struck is determined by the depth of the step \(h, i, 2, or 3\), which the quarter snail \(N\) presents. When not otherwise prevented, the quarter rack \(Q\) being pressed by the spring \(D\), retrogrades, and the teeth of the rack engage more or less with the arms \(q, 6\), which also recede, but are brought forward again by the springs 9 and 10. While the arm \(k\) brings forward the quarter rack from the snail, the arm \(m\) presses on the end \(R\) of the all or nothing \(TR\). In the end \(R\) is an opening \(x\), which, not being quite filled by the end of a stud fixed in the plate, allows the end \(R\) to traverse a little. So soon as the arm \(m\) comes to the extremity of \(R\), the spring \(ix\), by re-acting with its point on the fixed stud just mentioned, presses \(R\) past \(m\), which then rests on the end of \(R\); so that the quarter rack \(Q\) cannot now fall until the all or nothing is pushed aside. The other arm \(u\) of the quarter rack is for pushing aside the raising piece \(m\), fig. 1 and 6, which is upon the axis of the hour-hammer, by means of its pin \(11\), which comes up within the motion work; for after the repeating of the hours and quarters is completed, the rack \(Q\) is still moved by the arm \(k\) a little farther, and, by its arm \(u\) acting on the pin \(11\), turns aside the raising piece or hammer tail \(m\), and thus detaches it from the ratchet \(R\), until the piece \(TR\) allows the rack \(Q\) to drop on its snail, which only occurs when, the pendant having been pushed home, the arm \(b\) of the rack \(CC\) presses the hour snail \(L\), causing it, together with the all or nothing \(TR\), to describe a small arc about the centre \(T\); so that the extremity \(R\) of the all or nothing being thus pushed aside, will let go the arm \(m\) of the rack \(Q\), which will then be free to drop and disengage the lifting pieces; and first the hours, and then the quarters, will be struck, which correspond to the steps presented by the snails \(L\) and \(N\) respectively. The dial-work is drawn in fig. 2, as if ready to repeat eleven hours and one quarter.

The hour hammer \(M\), best seen in fig. 6, carries a pin 33, which comes up through an opening 33, fig. 2, till it meets the spring \(r\), which acts on it, and enables the hammer to strike. Another pin 22, belonging to this hammer, comes through an opening 22. Upon this pin the raising piece \(q\) acts, to enable the hammer \(M\) to join in striking the quarters. The smaller hammer \(U\) has likewise a pin, which comes through the opening 4. Upon this the spring \(7\) acts, and enables that hammer to strike the quarters in conjunction with the hammer \(M\). J is the spring jum-

Watch Work.

The clock and per which acts on the star E, as was explained when describing the striking parts of clocks. Fig. 9 represents in perspective the cannon pinion c, and quarter snail N, which are riveted together, and the square D is for putting the minute hand upon. These of course must revolve together in an hour. The snail N carries the surprise Z, the use of which is this: when the pin O of the surprise overtakes a tooth of the star wheel E, it continues to push it forward, till some other tooth, having got over the angle of the jumper, is aided by the inclined face of the jumper acting behind it, and by that means the wheel is made to start forward through the remaining half space between two teeth. While the wheel thus suddenly advances, the tooth next behind the pin O gives it and the surprise Z a push forward, without carrying with them the quarter snail; for though the plate Z, called the surprise, is attached to the quarter snail, it has freedom to turn upon it a little way; so that at the end of each hour the star E and snail L are suddenly shifted to the next step, which obviates the chance of the snail L presenting a wrong step; and the surprise, by being thrust forward upon the snail N, half way over step 3, prevents the arm of the quarter rack from dropping into step 3 of the quarter snail, and causing the watch strike, as it would otherwise do, the three quarters, should the pendant happen to be pushed in just at the end of an hour. By this means the watch strikes the precise hours indicated by the hands.

The socket or pipe cD of the cannon pinion fig. 9, is slit, that it may move spring-tight on the axis of the second wheel C, on which it enters with such stiffness as will just allow of the minute hand being easily set back or forward, as occasion may require. When turning the minute hand, we likewise set the hour hand, because the cannon pinion then moves the other three dial-wheels shown in figs. 4 and 7. Some imagine that a watch is injured by moving the hands, and especially by setting them back. To be convinced that this is not the case, we need only consider, that when we turn the minute hand, we neither move the axis of the centre wheel C, nor indeed any wheel at all within the frame. It is for this very purpose that the cannon pinion c is put on a cannon or pipe, which may slide round on the axis of the centre wheel, without interfering at all with the internal parts of the watch. But after having pushed in the pendant of a repeating watch, we should be careful not to move the hands till the watch has done repeating; because in that case the dial-wheels may be prevented from shifting, by being engaged with the repeating work.

The cannon pinion of ten leaves moves the returning wheel, fig. 7, which turns on the stud 12, fig. 2, and has forty teeth. Upon it is fixed a pinion of twelve teeth, which turns the hour wheel, fig. 4, of thirty-six teeth. The cannon pinion, therefore, turns twelve times for once of the hour wheel, which carries the wide socket of the hour hand. Fig. 5 shows the other side of the all or nothing, with the shanks of the screws T and V. The large hole e allows the squared end of the fuse arbor to come through to receive the key which winds up the watch in a hole of the dial-plate. W is the locking spring and bolt which keep the work in the case. Y is a small cock to steady the rack CC. The pieces 13 and 14 are for connecting the fixtures. Fig. 8 shows the star wheel.

In some repeaters the hammers strike on bells, in others on springs, and in some they strike on the case, or on a piece of metal fixed to the case. In the repeater just described, a large circular rack and pinion pitching into each other are sometimes substituted for the pulleys and chain. The rack is fixed on the piece CC, and its pinion is put in the place of the pulley A, on the arbor of the repeating mainspring. By such an arrangement there is supposed less risk of the action of the repetition being interrupted, as it might be by the breaking of the chain. In place of the fly, it is not uncommon for repeating work to be regulated by a escapement and balance, which renders it rather more simple.

Several repeaters of a very simple construction have been contrived by Mr J. M. Elliot, particularly the follow-repeatering one, for which he received from the Society of Arts a premium of thirty guineas. But the description of it in their Transactions is so very inexplicit and defective, that we are under the necessity of explaining it more fully in our own way. The dial-plate being removed, AB, in fig. 1, Plate CLXVIII., represents the upper side of the pillar plate. CD is a flat ring or circle of steel moving freely in the grooved edges of the pulleys or rollers E, F, G, H, in the same manner as the rings which show the days of the month, or the moon's age, in a common clock. The flat ring is put in motion by means of a pinion a fixed on the inner end of an axis which comes through the case, and has on its outer end the ring or handle of the pendant. The teeth of this pinion work into a set of teeth formed on the under side of almost one third of the ring CD. When, therefore, we turn round the pendant, we necessarily move the ring. I is the quarter snail, K the minute wheel, and the hour wheel may easily be supposed. L is the stud on which turns the hour snail, omitted here to avoid confusion, but shown in fig. 2 as fixed upon the star wheel 1, which is moved by means of the arm 2, on the cannon pinion. POQ and SRT are bent levers, movable respectively on studs fixed in the pillar-plate at O and R. The kned end P is for dropping on the steps of the hour snail; but in this it observes a rule the very reverse of any we have yet described, because the highest step of the snail answers to twelve hours, and the one nearest the centre to 1 hour. The like is the case with the end S, which drops on the quarter snail, neither of which circumstances are so much as hinted at in the inventor's own description. At X is a pin in the flat circle, to which is hooked a chain wound on the barrel V, containing a spiral spring. This chain, when the pendant is put in motion, unwinds from the barrel, and by acting on the rollers U and W, works both to the right and left. So soon, therefore, as we let go the pendant, this spring always brings back the large ring into the same position. The hour hammer, faintly represented by dotted lines, turns on the stud i, and has a small tail or pallet, which is acted on by a set of pins standing upright on the edge of the flat ring; so that, when we turn the ring in the direction in which the hands go, each pin which passes i causes the hour hammer to give one blow. But when the pins return in the other direction, they merely push aside the hammer tail, which is made to give way in that direction, and resumes its place by help of a small spring. The quarter hammer, which turns on the stud k, acts in a precisely similar manner by means of the same set of pins, when passing it in the direction contrary to that in which the hands go. To prevent the ring from turning too far, it has a circular slit ss, which plays or traverses upon a fixed stud p.

Fig. 1 represents the watch as having just struck one hour, and fig. 2 shows it just after repeating three quarters. When the large ring is quite in its resting-place, it bears upon the levers Q and T, so as to hold their other ends P and S as far up at least as the highest step of their respective snails. But when we begin to turn the ring in the direction of the hands, the angle of the broad part at C withdrawing from the arm Q, allows the end P to drop on the hour snail by the action of its spring. During this turning of the ring, the hour hammer being acted on by the pins, will continue striking till the end of the arm Q. Clock and arrest the motion of the ring by catching into one or other of the notches on its inner side. The spring V, if allowed, will now bring back the ring to its place; and to repeat the quarters we need only turn the pendant so as to move the ring CD in the other direction, which will allow the end S to drop on the quarter snail by help of its spring, and cause the quarter hammer to strike till the end T arrests the ring by catching one of the notches on its inner side at h. This repeater will obviously give either the hours or quarters first, as may be wished, or the one without the other; a property which, we should think, belonged to no repeaters prior to those of Mr Elliot.

Among the repeaters formerly in repute is the Stacden, Stockten, or Stogden repeater, of which drawings may be seen in the Encyclopédie Méthodique, and in Rees' Cyclopaedia. It is rather uncertain why it is so called, but there is a tradition that a person of some such name had worked with Graham, and possibly he may have invented it. For other forms of repeaters, and likewise for alarm watches and others of peculiar constructions, we must refer to the works already quoted.

We have already described Harrison's contrivance for keeping both clocks and watches going in time of winding; but watches have sometimes been contrived to need no winding, provided they were carried, a moderate external motion being sufficient to make a pendulum or balance vibrate so as to act upon a wheel which always contributes something towards winding up the machine, so long at least as that is not completed. The same principle has been often proposed for propelling a ship when violently tossed by wind or waves.

Having already had occasion to mention some particulars regarding the balance, we have now the less need to enlarge on it. From Mr Attwood's investigations on this subject in the Phil. Trans. for 1794, it appears that if \( w \) be the weight of a balance in grains, \( r \) its radius in inches, \( g \) the distance in inches of its centre of gyration from the axis, and \( p \) the force in grains which, acting at the circumference of the balance, can keep it 90° from the position in which its spring would allow it to rest, the time of one vibration in seconds will be

\[ \frac{g}{49898} \sqrt{\frac{w}{pr}}, \text{ or nearly } \frac{g}{5} \sqrt{\frac{w}{pr}}. \]

Owing to the difficulty of obtaining the dimensions with sufficient accuracy, this formula can scarcely be applied in a direct manner to determine either the duration of a vibration, or to compare the times of vibration in different balances; but it throws some light on the effects of temperature on the time. For when the radius of the balance varies with change of temperature, \( g \) will do so in the same ratio, and therefore the duration of a vibration is increased with heat and diminished with cold, which is conform to experience. But here again we cannot apply the formula, because the effect on the time is farther increased by the influence of heat in diminishing, and of cold in increasing, the force of the spring in a rather uncertain degree. Berthoud found a watch to be twenty-four times more affected by changes of temperature than a clock. This, however, will depend in some measure on the materials employed, we mean when there is no compensation, as also on the kind of escapement, state of the oil, &c.

Generally speaking, the time of vibration of a balance is increased by lengthening, and diminished by shortening its spring. On this depends the usual mode of adjusting or regulating the going of a watch. In fig. II, Plate CLXIII., \( mn \) is a circular-toothed rack, clear of the balance A, but movable in a groove concentric with it. The rack carries an arm \( r \), having a notch or clip, which slides upon the spring \( sp \). If the notch be so narrow as just to have room to slide upon the spring, it may be considered as forming one end of the spring, and \( p \) the other; and therefore, by putting the key upon the square of the pinion \( i \), and turning it a little, we shift the notch, and alter the length of the acting part of the spring. The notch, however, is generally far from being close upon the spring, which therefore sometimes moves from side to side of it; and this may be attended with both friction and wear. The index R shows upon a graduated plate how far the regulator, as this contrivance is called, may have been moved. This was wont to be almost the only mode of applying the regulator. Frequently, however, there is neither rack nor pinion. The notch or clip is in the arm of a lever, which has still a motion concentric with the balance, being attached to the cock or piece covering it. This regulator is moved by pushing its extremity about, which is not so precise and convenient as the old method, because it is apt to move by a start too far; but it is more easily made, and requires rather less room. It has another advantage; for the balance spring in this method being generally put above the balance, admits of being more easily adjusted and more readily taken off and on.

In some of the more common sorts of escapements, the Compensations in the fluidity, &c. of the oil compensate, though satirized in a very uncertain manner, for the effect of temperature on the vibrations of the balance; but the first scientific contrivances for this purpose were applied to the regulator, or at least to the balance spring, and are called compensation curbs. When Harrison explained the principles of his fourth timekeeper to the commissioners of longitude, he described a compensation which consisted of a slip of brass pinned upon another of steel. One end of this bar was fixed, and on the other was a notch or clip to receive the balance spring. The unequal expansions of the two metals made the compound bar bend and move the end with the clip, so as to equalize the going of the machine, on the principle of the common regulator. If, as is extremely probable, this remarkable genius used the same thing in his other three timekeepers or box chronometers, (for it is next to impossible they could have performed so well without compensation), he must have been by much the first who employed it, or indeed any compensation, in such a timekeeper; but not having published this in time, earlier claims have been put in for others. The first pocket watch with a compensation was made by Berthoud in 1764, and worn by King George III., who, it is well known, had a taste for nice machinery. In some compensations of this sort, the clip, as was the case with Harrison's, slides along the spring; in others, the width of the clip is made to vary, so as to give the spring more or less play. Various sorts of metals are used in the construction of these curbs. None of them, however, has yet given perfect satisfaction, which is in a great measure owing to the difficulty of interfering with the spring, without disturbing its isochronism. Le Roy attached two thermometers to the balance of his marine timekeeper. The bulbs, filled with alcohol, were near the verge; but the tubes were bent in such a manner that an increase of temperature drove a portion of mercury into parts of them which lay along the axis. The reverse took place with a fall of temperature; but such a contrivance could only be used in a large machine. It seems to have been this artist who first applied the compensation to the balance itself, nearly in the same form as it is still most commonly used, except that he pinned together the laminae of the different metals; whereas they are now united by fusion,—a mode of construction which was introduced by Brookbanks.

Compensation balances have been made in a great variety of forms; but some of them have such a parade of balance-tackling, and are otherwise so injudiciously contrived, as Clock and Watch Work

The following is perhaps less liable to this objection than the most of them. In fig. 14, Plate CLXII., the inner part of the rim is steel, which, after having been turned to the proper size, is immersed in melted brass till it becomes coated with that metal. The superfluous brass is then turned away, a ring of it only being left on the outer edge of the steel. This compound rim is next cut through in three places, A, B, C, which sets one end of each third part at liberty to move inwards when the temperature is increased, or outwards when it is diminished. D, E, F, are three equal weights, which admit of being fixed by screws upon any part of the compound circular bars. G, H, I, are three heavy headed screws, which serve as weights to adjust the centre of gravity of the balance to its axis of vibration, and likewise to adjust its mean rate of motion. When an increase of temperature tends to lengthen the arms of the balance, and to relax the force of its spring K, this would make it go slower; but the same cause, by expanding the brass more than the steel, must bend in the bars, so as to throw the weights D, E, F nearer the axis, and diminish the effect of the inertia of the balance, which, if the compensation is properly adjusted, will be as speedily carried through its course as before. The contrary compensation takes place with a fall of temperature. The exact adjustment of the weights is found by repeated trials of the going of the machine; if it gain by heat, the weights do more than compensate, and must be moved farther from the extreme ends of the compound bars; but if the gain be produced by cold, the weights must be set farther out.

A different form of compensation balance, in which the expansions and contractions of the metals are employed in a more direct manner, has been contrived by Mr Hardy, who objects to the sort just mentioned, that the two metals, united by fusion, are liable to partial separations; that the centrifugal force of the weights D, E, F, is apt to overpower or bend the compound bars; and that the adjustment for rate and temperature may affect the equilibrium of the balance, and consequently the rate of the machine in different positions. If the second and third objections are well founded, we are not very clear that Mr Hardy's balance is quite free from them, especially the third; for, unless the like parts of a compensation balance, of whatever sort, be every way equal, and equally affected by changes of temperature, there is a probability that its centre of gravity will not always be accurately in the axis of vibration; and, consequently, that the machine will go differently in different positions. Fig. 6, Plate CLXIII., shows Mr Hardy's balance in profile. DD is the verge, having a collet, to which is fixed a steel bar SS. There is no ring or rim; but in place of that, there are on the bar SS two upright rods, carrying the balls or weights AA; and CC are two heavy-headed screws, for adjusting the mean rate of the balance. The steel bar, when lengthening by heat, would throw the balls AA farther from the centre; but suppose two very short studs, projecting downwards from the ends of the bar SS, and that we connect these by a brass bar EE. It is evident that the brass, by its excess of expansion, must push out the studs below so much more than the steel does above, that the upright rods will be made to lean inward, and bring the balls AA nearer the verge; and so much the more as the balls are farther above the steel than the brass is below it. The contrary will take place with a fall of temperature.

We have stated the matter in this way for the purpose of more easily explaining the principle; but to increase the effects, the actual construction is a little different. Fig. 5 shows the under side of the compensation bars. The steel one occupies the whole length and breadth of this; but there are two bars, B, B, of brass, not quite so long as the steel, and each only about one third its breadth, except at the one end, where it a little exceeds a third. In the steel bar are two notches seen in fig. 6, which make it very thin and flexible near the ends. Each brass bar has one end pinned to the steel bar on the outside of one notch, and its other to the steel on the inside of the opposite notch. By this means the effect is nearly double of what it would be with a single brass bar. As the bars must necessarily bend, the design of the notches is to make the steel bend easily, and to form a short stud on the under side. The brass being more slender, and the bending taking place over its whole length, it has less need of any notch. Since the effects obviously vary with the heights of the balls above the compound bars, the balls admit of being shifted higher or lower upon the upright rods, as may be found necessary. But unless the balls be exactly at the same height above the bars, they will be unequally affected by change of temperature, which will of course disturb the centre of gravity. The like will happen if the similar parts are not equally flexible. At the same time it must be admitted, that the expansions being here employed in a more direct manner than in the other method, is a considerable recommendation to this balance, which, besides, may be made by a less skilful workman. But it is almost needless to observe, that room could scarcely ever be got for it in an ordinary-sized pocket watch.

As yet, compensation balances have succeeded better than curbs, but we are far from being persuaded that they must for that reason be preferable to every other device which may be fallen upon for obviating the effects of temperature. The rugged surface, which a compensation balance carries rapidly through the air, necessarily encounters a considerable, and, what is worse, a variable resistance; and we have already hinted at the difficulty and uncertainty of keeping the centre of gravity in the axis of motion. Of late years the French artists have directed their attention a good deal to the improvement of curbs; and we should not be surprised though at no distant day these should altogether supersede the use of the compensation balances: unless it be that some artists, having got into the habit of making or using such balances, must just continue to do so.

When a watch suddenly receives a circular motion, Banking especially in a direction contrary to that in which the balance is moving at the moment, it sometimes happens that the balance will be thrown so far round as to cripple its spring, and if put likewise beyond the reach of the scape wheel, or other parts maintaining its motion, it may be unable to return; or, though the watch do not stop, the balance spring may be permanently altered, so as to affect its rate of vibration. To prevent such occurrences, various devices have been adopted, which are known by the general name of banking the balance. This is easily effected where the vibration does not exceed an entire revolution. Thus, when the vibration is less than 120°, the balance A, Fig. 10, Plate CLXIII., carries on two of its arms the pins 1, 2, which, so soon as the vibration amounted to 120°, would strike against and be prevented from going farther by the fixed tongue z. Had there been but one pin, and that in the other arm of the balance, the vibration would have only been prevented from exceeding a revolution. However, unless the diameter of a balance be very small, or its vibrations of unusually long duration, we have some doubt whether they can ever exceed 360°, without encountering a hurtful resistance from the air. But to bank a balance having greater vibrations, Mr Hardy put upon its spring a small tongue or lever, which, by the motion of the spring, was thrown out close by the side of a fixed stud, just when a pin in the balance... Clock and arrived there. The lever, at the instant it was struck by Watch Work, the pin, came against the stud, which received the shock, and arrested the balance; but this method only banked or checked the motions of the balance on one side. A different method has more recently been employed by Mr Towson. Instead of using an immovable stud for holding the outer end of the balance spring, he forms that stud upon the end of a flexible spring-arm. In the stud is a notch, through which the turned-up end of a lever carried by the verge can pass quite clear of the sides when the vibrations are moderate; but as soon as a vibration in either direction exceeds a certain extent, the strain of the balance spring becomes sufficient to bend the elastic arm of the stud, so as to bring one of the cheeks of its notch in the way of the turned-up lever, by which the balance will be immediately arrested. This contrivance is free from friction, and has the advantage of Mr Hardy's in banking both ways. But we are not very clear that a sufficiently flexible spring-arm might not be disturbed by external motion, or yield to the action of gravity so as to make the machine go differently in different positions.

When, as is generally the case, balances are entirely or partly made of steel, it rarely happens that they are not more or less possessed of magnetic polarity, which inclines them to go differently in different positions, according as this force acts with or against the balance spring. The errors arising from this cause are often far greater than those from changes of temperature, as has been ascertained by direct experiments; and this is further confirmed from the circumstance that a common watch usually performs better with a brass balance than a steel one. Various attempts have been made to neutralize the magnetism of balances and other fine articles of steel or iron. The following method of Mr Abraham seems the most successful. Having dipped the article which is to have its magnetism neutralized, into fine steel filings, these will fall off when the polarity of the end of a magnet presented to them is of the same sort. But if the magnet be held too near, it may overdo the business, and communicate an opposite polarity. To ascertain this, as also whether polarity of any sort remain, the operation is to be repeated, dipping again the article in the filings, and only bringing the proper pole of the magnet near enough to make these filings all drop off, and so on till the article lift no more filings.

This mode of cure seems very plausible, but we are not quite persuaded of its being a permanent one. Since steel tools are generally magnetic, as also articles of steel which have undergone much work, it is evident that unless great precaution is used, a balance can scarcely be put in its place, or a tool applied to the watch, without a risk of the balance having polarity communicated to it from some such quarter. But since prevention is better than cure, we should think it would be preferable to abandon the use of steel altogether in the construction of balances. Platina, we presume, would be greatly preferable, especially where no compensation is to be used. It is scarcely, if at all, susceptible of polarity; it is much less affected by changes of temperature, and its great weight should be no small recommendation. Gold, though sometimes used, is much more expensive than platina, while it is inferior in hardness, and is affected in a far greater degree by changes of temperature.

Among the numerous devices for which patents have been taken out of late years, we may notice Mr Berrollas' Watch Keyless Watch. Within the loop of the pendant is a small knob, which, on being pulled, brings out a part of a chain; during which a piece connected with the inner end of the chain catches and turns round a small way the fusee, or the spring-barrel if there is no fusee. The chain being now let go, is drawn in by a small spring. Next the knob is pulled as before, and so on till the watch is wound up. The chain just mentioned comes through a larger knob or button, which, on being twisted round, sets the hands of the watch backward or forward as may be necessary. A different mode of winding without a key has been invented by Mr Brown, for which he likewise has a patent. It consists in twisting round a large circular part of the case, which acts by means of a toothed ring upon the fusee, or on the spring-barrel when there is no fusee. Mr Westwood, again, has taken out a patent for a spring-barrel of unusually large dimensions, being about three fourths the diameter of the frame plates. Such springs, he says, are as fit for making watches go eight days, as the ordinary springs are for thirty hours. But since Mr Westwood uses no fusee in these watches, they must be liable to much wear, because the force which impels the wheels is unnecessarily strong during the greater part of the eight days.

It is to be feared that, in clock work, as in other departments, many valuable inventions never see the light, owing to the influence of the law of patents. The most inventive men are not always the most opulent. It is no uncommon thing for a person to spend many years, and perhaps his all, in maturing an invention which may fully answer his expectations, and after he has brought it thus far he must make up his mind either to publish it and let others reap the benefit, or to conceal and probably consign it to oblivion. There is no alternative if he be unable to raise £500 or £600, which go principally into the pockets of official people who do nothing for it, and who do not need it. It is thus a lamentable fact, that the very laws intended for the protection of inventions, have in too many instances quite the contrary effect. Some allege, that were no needless or exorbitant expense heaped on patents, they would become too numerous, and even be obtained for all manner of nostrums. This certainly would be excellent logic, were the value of an invention in exact proportion to the wealth of the inventor, and his willingness to part with it; for then the prohibition would fall heaviest on the most worthless inventions. But since the case is far otherwise, we can see neither policy nor justice in the prohibitory system; for those only who choose to take out patents for nostrums are likely to feel the consequence. It were better surely to give free scope to a thousand nostrums, than that one useful invention should be stifled. The Society for the Encouragement of Arts certainly does a great deal of good in the way of promoting inventions; but all it can afford is quite inadequate to compensate individuals for the ruinous effects of the present system.

In addition to the various works mentioned in the course of this article, those who wish to pursue the subject further will find extensive catalogues in Berthoud's Histoire de la Mésure du Temps; Dr T. Young's Natural Philosophy; and Gregory's Mechanics.

END OF VOLUME SIXTH. CLOCK AND WATCH WORK.

Among the numerous devices for which patents have been taken out of late years, we may notice Mr. Horwood's Keyless Watch. Within the loop of the pendant is a small knob, which, on being pulled, brings out a part of a chain, during which a piece connected with the lower end of the chain catches and turns round a small way the pinion, or the spring-barrel if there is no fusee. The chain being now let go expands by a small spring. Next the knuckle is pulled as before, and so on till the watch is wound up. The chain just mentioned consists of a larger knob or button, which, as being twisted round, sets the hands of the watch backwards or forward, as may be necessary. A different mode of winding without a key has been invented by Mr. Brown, for which he was once has a patent. It consists in twisting round a large circular part of the case, which acts by means of a needle upon the fleur, or on the spring-barrel when the case is closed. Mr. Westwood, again, has taken out a patent for a spring-barrel of unusually large dimensions, being able to describe the diameter of the frame plates. Such springs, he says, are as fit for making watches go eight days, as the ordinary springs are for thirty hours. Since Mr. Westwood uses no fusee in these watches, they must be liable to much wear, because the force which pulls the wheels is unnecessarily strong during the greater part of the eight days.

It is to be feared that, in clock work, as in other pursuits, many valuable inventions never see the light owing to the influence of the law of patents. The inventors then are not always the most successful. In an arrangement where a person is obliged to spend many years and perhaps his all in sustaining an invention which only ensures his early fortune, and after he has brought them to the point where he has made either to publish or let others copy the patent, or to conceal and quietly escape into obscurity. There is no encouragement for the inventor to raise £200 or £300, which on principle is the pocket of official people who do nothing and who do not need it. It is thus a hazardous thing to rely upon the protection of patents; there have in too many instances quite the contrary. Some allege that were so needless or useless expense imposed on inventors, they might become more inventive, and even be obtained for all manner of useful things. This certainly would be excellent policy, were the value of an invention in exact proportion to the wealth of the inventor, and the willingness to part with it for the publication would fall likewise on the most valuable inventions. But since the case is the otherwise, we see neither policy nor justice in the prohibitory system for those only who choose to take out patents for inventions likely to lead to consequences. If were but one glass from script to a thousand notrones, than that real invention should be stifled. The Society for the encouragement of Arts certainly does a great deal in the way of promoting invention, but all its efforts is quite inadequate to compensate individuals for the loss caused by the present system.

In addition to the various works mentioned in the course of this article, those who wish to pursue the subject will find extensive catalogues in Berthoud's "Mechanics," in Messrs. the Taylor's, Dr. T. Young's, "Mechanical Essays," and Gregory's "Mechanics." ### Elements of Chinese Characters

#### Elements of 1 Stroke

| No. | Character | Meaning | |-----|-----------|---------| | 1 | 一 | one | | 2 | 二 | two | | 3 | 三 | three | | 4 | 四 | four | | 5 | 五 | five | | 6 | 六 | six | | 7 | 七 | seven | | 8 | 八 | eight | | 9 | 九 | nine | | 10 | 十 | ten |

#### Elements of 2 Strokes

| No. | Character | Meaning | |-----|-----------|---------| | 11 | 二 | two | | 12 | 三 | three | | 13 | 四 | four | | 14 | 五 | five | | 15 | 六 | six | | 16 | 七 | seven | | 17 | 八 | eight | | 18 | 九 | nine | | 19 | 十 | ten |

#### Elements of 3 Strokes

| No. | Character | Meaning | |-----|-----------|---------| | 20 | 二 | two | | 21 | 三 | three | | 22 | 四 | four | | 23 | 五 | five | | 24 | 六 | six | | 25 | 七 | seven | | 26 | 八 | eight | | 27 | 九 | nine | | 28 | 十 | ten |

#### Elements of 4 Strokes

| No. | Character | Meaning | |-----|-----------|---------| | 29 | 二 | two | | 30 | 三 | three | | 31 | 四 | four | | 32 | 五 | five | | 33 | 六 | six | | 34 | 七 | seven | | 35 | 八 | eight | | 36 | 九 | nine | | 37 | 十 | ten |

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This table provides a comprehensive list of Chinese characters categorized by the number of strokes they contain, along with their meanings.