clocks, as accurate measurers of time. Mathematicians saw that their vibrations had some regular dependence on uniform gravity, and in their writ ings we meet with many attempts to determine the time and demonstrate the isochronism of the vibrations. Riccioli, Gassendus, and Galileo, made similar attempts to explain the motion of pendulums, but without success. This honor was reserved for Mr. Huyghens, the most elegant of modern geometers. He had succeeded in 1656 or 1657 in adapting the machinery of a clock to the maintaining of the vibrations of a pendulum. Charmed with the accuracy of its performance, he began to investigate with scrupulous attention the theory of its motion. By the most ingenious and elegant application of geometry to mechanical problems, he demonstrated that the wider vibrations of a pendulum employed more time than the narrower, and that the time of a semicircular vibration is to that of a very small one nearly as thirty-four to twenty nine; and aided by a new department of geometrical science invented by himself, viz. 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 before this time Dr. Hooke, the most ingenious and inventive mechanician of his age, had discovered the great accuracy of pendulum clocks, having found that the manner in which they had been employed had obscured their real merit. They had been made to vibrate in very large arches, the only motion that could be given them by the contrivances then known; and in 1656 he invented another method, and made a clock which moved with astonishing regularity. Using a heavy pendulum, and making it swing in very small arches, the clocks so constructed were found to excel Mr. Huyghens's cycloidal pendulums. It has been found that 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 arches which do not exceed three or four degrees from the perpendicular. Such clocks alone are now made, and they exceed all expectation. We have said that a pendulum needed only to be removed from the perpendicular, and then let go, in order to vibrate and measure time. Hence it might seem that nothing is wanted but a machinery so connected with the pendulum as to keep a register, as it were, of the vibration. It could 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 of the pendulum. The pivot on which it swings occasions friction-the thread or thin piece of metal by which it is hung, in order to avoid this friction, occasions some expenditure of force by its want of perfect flexibility or elasticity. These, and other causes, make the vibrations grow more and more narrow by degrees, till at last the pendulum is brought to rest. We must therefore have a contrivance in the wheel-work which will restore to the pendulum the small portion of force which it loses in every vibration. The action of the wheels therefore 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, 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. This cannot be effected, 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. The necessary requisite for the isochronous motion of the pendulum is, that the force which urges it toward the perpendicular, be proportional to its distance from it; and therefore, since pendulums swinging in small circular arches 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 these arches.

Under the head of CLOCK-MAKING we have entered very fully into the construction of those large horological machines that are intended to measure the time by means of a weight and pendulum. In watches, on the contrary, a spring is the usual maintaining power.

From what we have already seen of the nature of the pendulum, it will be apparent that its oscillations can only approach to a true measure of time when the point of support is fixed and immoveable. An approximation, however, to this desideratum may be obtained by a pocket watch regulated by a balance. This useful machine, in its most perfect form, contains within itself a colection of inventions which have exercised the skill of some of the most ingenious mechanics for the three last centuries, and it is gratifying to know that we are indebted to our countrymen Hooke, Graham, Earnshaw, Arnold, and Harrison, for its invention and present improved form.

To explain the mechanism of a watch it is necessary to refer to the figs. 1, 2, 3, plate WATCHES, as they contain engravings of a sunk pocket-watch of the best construction. Fig. 1 is a plan of the wheelwork all exhibited at one view, for which purpose the upper plate of the watch is removed. Fig. 2 is a plan of the balance, and the work situated upon the upper plate. Fig. 3 is an elevation of all the movements together, the works being supposed to be opened out into a straight line, to exhibit them all at once.

The principal frame for supporting the acting parts of the watch consists of two circular plates, marked C and D in the figures; of these the former is called the upper plate, and D is called the pillar plate, from the circumstance of the four pillars, E, E, which unite the two plates and keep them a proper distance asunder, being fastened firmly into the lower plate; the other ends pass through holes made in the upper plate, C, and small pins, being put through the ends of the pillars, keep all together; but, by drawing out these pins, the whole watch may be taken to pieces; and the pivots of the several wheels being received in small holes made in these plates, they of course fall to pieces as soon as the plates are separated.

The maintaining power is a spiral steel spring which is coiled up close by a tool used for the purpose, and put into a brass box called the barrel, it is marked A in all the figures; the pivots of its arbor pass through the top and bottom of the barrel, and one of them is filed square to hold a ratcher wheel, which has a click, and retains the arbor

from turning round except in one direction; the two pivots of the arbor are received in pivot holes in the plates C, D, of the watch, and the pivot which has the ratchet wheel upon it passes through the plate, and the wheel marked 6, with its click, is therefore on the outside of the pillar plate D of the watch; the top of the barrel has a cover or lid fitted into it, through which the upper pivot of the arbor projects; thus the arbor of the barrel is to be considered as a fixture, the click of the ratchet wheel preventing it from turning round, and the interior end of the spiral spring being hooked, this arbor is stationary likewise. The barrel thus mounted has a small steel chain, d, coiled round its circumference, and attached to it by a small hook of the chain which enters a little hole, made in the circumference of the barrel at its upper end; the other extremity of this chain is hooked to the lower part of the fusee, marked F, and the chain is disposed either upon the circumference of the barrel, or in the spiral groove cut round the fusee for its reception, the arbor of which has pivots at the ends, which are received into pivot holes made in the plates of the watch; one pivot is formed square and projects through the plate, to adapt the key by which the watch is wound up.

It is evident that, when the fusee is turned by the watch-key, it will wind the chain off the circumference of the barrel on itself; and as the outer end of the spring is fastened to the barrel, and the other is hooked to the barrel arbor, which, as before mentioned, is prevented from turning by the click of the ratchet wheel, a b, beneath, the spring will be coiled up into a smaller compass than before, and, by its reaction, will, when the key is taken off, turn the barrel, and by the chain turn the fusee and give motion to the wheels of the watch, which will be hereafter described. The fusee has a spiral groove cut round it, in which the chain lies; this groove is cut by an engine, in such a form that the chain shall pull from the smallest part or radius of the fusee, when the spring is quite wound up, and therefore acts with its greatest force on the chain; from this point the groove gradually increases in diameter, as the spring unwinds and so acts with less power, the chain operates on a larger radius of the fusee, so that the effect upon the arbor of the fusee, or the cog-wheel attached to it, may always be the same, and cause the watch to go with regularity.

To prevent too much chain being wound upon the fusee, and by that means breaking the chain or overstraining the spring, a contrivance called a guard gut is added; it is a small lever, e, moving on a stud fixed to the upper plate, C, of the watch, and pressed downwards by a small spring, f; as the chain is wound upon the fusee, it rises in the spiral groove, and lifts up the lever until it touches the upper plate, and it is then in a position to intercept the edge or tooth, g, of the spiral piece of metal seen on the top of the fusee, and thus stops it from being wound up any further.

The power of the spring is transmitted to the balance by means of several toothed wheels, which multiply the number of revolutions that the chain makes on the fusee, to such a number, that though the last or balance wheel turns nine times and a half every minute, the fusee will at the same time turn so slowly that the chain will not be all drawn off from it in less than twenty-eight or thirty hours, and it makes one turn in about four hours; this VOL. XXII.

assemblage of wheels is called the train of the watch. The great wheel, G, has forty-eight teeth on its circumference, which take into and turn a pinion of twelve teeth, fixed on the same arbor with the centre wheel H, so called from its situa tion in the centre of the watch; it has fifty-four teeth to turn a pinion of six leaves, on the arbor of the third wheel I, which has forty-eight teeth; it is sunk in a cavity formed in the pillar plate, and turns a pinion of six, on the arbor of the contrate wheel K, which has forty-eight teeth cut parallel with its axis, by which it turns a pinion of six leaves, fixed to the balance wheel L; one of the pivots of the arbor of this wheel turns in a frame, called the pottance, fixed to the upper plate, and the other pivot runs in a small piece fixed to the upper part, called the counter pottance (not shown in any of the figures), so that when the two plates are put together, the balance wheel pinion may work into the teeth of the contrate wheel, as is shown in fig. 4. The balance wheel, l, has fifteen teeth, by which it impels the balance op; the arbor of the balance, which is called the verge, has two small leaves or pallets projecting from it, nearly at right angles to each other; these are acted upon by the teeth of the balance wheel in such a manner that, at every vibration, the balance receives a slight impulse to continue its motion, and every vibration so made suffers a tooth of the wheel to escape or pass by; whence this part is called the escapement of the watch, and constitutes its most essential part. The wheel is sometimes called the scape wheel, or crown wheel. Suppose the pinion h on the arbor of the balance wheel, or crown wheel, i k, to be actuated by the main spring which forms the maintaining power, by means of the train of wheel-work in the direction of the arrow, while the pallets m and n, attached to the axis of the balance, and standing at right angles to each other, or very nearly so, are long enough to fall in the way of the ends of the sloped teeth of the wheel, when turned round at an angle at 45°, so as to point to opposite directions, as in the figure; then a tooth in the wheel below, for instance, meets with the pallet n (supposed to be at rest), and drives it before it a certain space, till the end of the tooth escapes; in the mean time the balance, o s pr, attached to the axis of the pallets, continues to move in the direction r o s p, and winds up the small spiral or pendulum spring q, one end of which is fast to the axis, and the other to a stud on the upper plate of the frame; in this operation the spring opposes the momentum given to the balance by this push of the tooth upon the pallet, and prevents the balance going quite round, but, the instant the tooth escapes, the upper pallet, m, meets with another tooth at the opposite side of the wheel's diameter, they therefore moving in an opposite direction to that below; here this pallet receives a push which carries the balance back again (having as yet but little power in the direction o s p r), and aids the spring, which now unbends itself till it comes to its equiescent position, but it swings beyond that point, partly by the impulse from the maintaining power on the pallet m, and partly by the acquired momentum of the moving balance, particularly when this pallet, m, has escaped; at length the pallet n again meets with the succeeding tooth, and is carried backward by it in the direction in which the balance is now moving, till the maintaining power and force of

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the unwo and spring together overcome the momentum of the balance, during which time the recoil of the balance wheel is apparent (for the seconds hand of the watch is usually put on the pivot of the arbor of the contrate wheel); at length the wheel brings the pallet n back again till it escapes, and the same process takes place with pallet m as has been described with respect to pallet n; thus two contrary excursions or oscillations of the balance take place before one tooth has completely escaped, which is the reason there must always be an odd number of teeth in this wheel, that a space on one side of the wheel may always be opposite to a tooth on the other, in order that one pallet may be out of action during the time the other is in action.

The upper pivot of the verge is supported in a cock screwed to the upper plate, as shown at N, which covers the balance, and protects it from violence, and the lower pivot works in the bottom of the pottance, M, at t. The socket for the pivot of the balance wheel is made in a small piece of brass, v, which slides in a groove made in the pottance, so that, by drawing the slide in and out, the teeth of the balance wheel shall just clear one pallet before it takes the other; and in the perfection of this adjustment, which is called the scaping of the watch, the performance of it very greatly depends. We shall speak more fully of this in another place. The banking of the watch is to prevent the balance from being turned round too far by accidental jerks, in which case one of the pallets would be pitched upon the point of a tooth of the balance wheel, and recoil it back too far, perhaps injuring its point; this is called being overthrown. Sometimes, if the balance gets turned round too far, the pallets are both turned away from the teeth of the wheel, which then runs down with inconceivable rapidity, and probably breaks the points of its teeth by striking against the pallets as they turn round; to avoid these accidents the banking is introduced; it is a pin fixed in the rim of the balance, and therefore describing a circular arc round the edge of the cock N, which covers the balance; but the proper extent of this arc is determined by the banking-pin meeting two projecting parts of the cock, which are extended out so far as to reach beyond the circle the banking pin moves in.

Having thus examined the various parts of a watch, it may now be advisable to revert more particularly to the movement; the mode of arranging the parts of which will be best understood by reference to a series of tables, calculated to produce any number of beats that may be required for practical purposes.

In the following tables the first column of figures gives the number of teeth in the centre, or second wheel, to the different trains; the second column the number of leaves in the third-wheel pinion; the third column the number of teeth in the thirdwheel; the fourth column the number of leaves in the counter, or fourth-wheel pinion; the fifth column the number of teeth in the counter-wheel; the sixth column the number of teeth in the escapement-wheel pinion; the seventh column the number of teeth in the escapement-wheel; the eighth column the number of beats in the hour; and the ninth column the time the fourth, or counterwheel, revolves in. These columns, if taken in the line from left to right, give each train in succession.