677. There is thus no recoil, and the pendulum is allowed to reach the extremity of its swing to the right unretarded; but when the pendulum is returning, the crutch moves until the tooth passes from the circular arc d on to the pallet b: instantly the tooth slides down the pallet, giving the crutch an impulse, and escaping when the point has traversed b. The next tooth that comes into action falls upon the circular arc c, of which the centre is also at o; this tooth likewise remains at rest until the pendulum has finished its swing, and has commenced its return; then the tooth slides down a, and the process recommences as before.
Fig. 100.
678. The operations are so timed that the pendulum receives its impulse (which takes place when a tooth slides down a pallet) precisely when the oscillation is at the point of greatest velocity; the pendulum is then unacted upon till it reaches a similar position in the next vibration. This impulse at the middle of the swing does not affect the time of vibration.
679. There is still a small frictional force acting to retard the pendulum. This arises from the pressure of the teeth upon the circular arcs, for there is a certain amount of friction, no matter how carefully the surfaces may be polished. It is not however found practically to be a source of appreciable irregularity.
In a clock furnished with a dead-beat escapement and a mercurial pendulum, we have a superb time-keeper.
THE TRAIN OF WHEELS.
680. We have next to consider the manner in which the supply of energy is communicated to the escapement-wheel, and also the mode in which the vibrations of the pendulum are counted. A train of wheels for this purpose is shown in [Fig. 99]. The same remark may be made about this train that we have already made about the escapement,—namely, that it is more designed to explain the principle clearly than to show the actual construction of a clock.
681. The weight a which animates the whole machine is attached to a rope, which is wound around a barrel b; the process of winding up the clock consists in raising this weight. On the same axle as the barrel b is a large tooth-wheel c; this wheel contains 200 teeth. The wheel c works into a pinion d, containing 20 teeth; consequently, when the wheel c has turned round once, the pinion d has turned round ten times. The large wheel e is on the same axle with the pinion d, and turns with d; the wheel e contains 180 teeth, and works into the pinion f, containing 30 teeth: consequently when e has gone round once, f will have turned round six times; and therefore, when the wheel c and the barrel b have made one revolution, the pinion f will have gone round sixty times; but the wheel g is on the same shaft as the pinion f, and therefore, for every sixty revolutions of the escapement-wheel, the wheel c will have gone round once. We have already shown that the escapement-wheel goes round once a minute, and hence the wheel c must go round once in an hour. If therefore a hand be placed on the same axle with c, in front of a clock dial, the hand will go completely round once an hour; that is, it will be the minute-hand of the clock.
682. The train of wheels serves to transmit the power of the descending weight and thus supply energy to the pendulum. In the clock model you see before you, the weight sustaining the motion is 56 lbs. The diameter of the escapement-wheel is about double that of the barrel, and the wheel turns round sixty times as fast as the barrel; therefore for every inch the weight descends, the circumference of the escapement-wheel must move through 120 inches. From the principle of work it follows that the energy applied at one end of a machine equals that obtained from the other, friction being neglected. The force of 56 lbs. is therefore, reduced to the one hundred-and-twentieth part of its amount at the circumference of the escapement-wheel. And as the friction is considerable; the actual force with which each tooth acts upon the pallet is only a few ounces.