CHAPTER XIII.

THE CLOCK AND CHRONOMETER.

I. THE RISE AND PROGRESS OF TIME-KEEPING.

When we dealt with the astronomical instruments of Hipparchus, we saw that although the astrolabe which that great observer used was the germ of our modern instruments, the time recorded by Hipparchus and those who lived after him down to the later times of the Roman Empire was, as they measured it, a time which would be entirely useless for us.

The ancients contented themselves with dividing the interval between sunrise and sunset, regardless whether this was in summer or winter, into twelve equal hours. Now, as in summer the sun is longer above the horizon than in winter in these northern latitudes, we have more time during which the sun is above the horizon in summer than in winter, and if that period of time is to be divided into twelve hours, the hours would be much longer in summer than in other seasons.

As we are informed by Herodotus, tables were made by which these varying lengths of hours might be indicated by the shadows of a pole, which they called a gnomon or style. This was placed in a given locality, and the hour of the day was determined by the position of the shadow of the gnomon; and we need scarcely say that as Hipparchus observed he was compelled to find the position of the sun in order to determine the absolute longitude of a star at night. The ancients were limited to such ideas of time as could be got from slaves, who watched the risings and settings of the constellations, and who tried to bring to their own minds and those of their masters some idea of the lapse of time; and this even a few centuries ago was ordinarily depended upon in several countries.

Then, a little later, we come to the time being measured by monks repeating psalms—a certain number perhaps in the hour; and there were the water and sand clocks dating from Aristophanes, which were the predecessors of our sand-glasses. Candles were also at one time used with divisions on them to show how long they had been burning. But when we come to clocks proper, the history of which is very imperfectly known, we find an enormous improvement upon this state of things; because the clock, being dependent upon a constant mechanical action produced by the fall of a weight, could not be got to imitate these varying hours.

Still the clock had to fight its own battle for all that; and the first clocks were altered from week to week, or from month to month, so that the time-keeper, which did its best to be constant, was made inconstant to represent the ever-varying hours.

Doubtless the history of the first clocks—by which we do not mean the sand clocks or water clocks of the ancients, but such as those used by Archimedes when he attached wheels together—is lost in obscurity; and whether clocks, as we have them, were suggested in the sixth (Boethius, A.D. 525) or ninth century matters little for our inquiry; but beyond all doubt the first clock of considerable importance that was put up in England was the one erected in Old Palace Yard in the year 1288, as the result of a fine imposed upon the Lord Chief Justice of that time.

If we have a falling weight as a time-measurer we must also have some opposing force—a regulator in fact, so that the weight becomes the source of power, and the regulator the time-measurer; therefore, in addition to the fall of the weight, we find in the earliest clocks a regulating power to prevent the weight falling too fast. So we have the two contending powers, first the weight causing the motion and then the regulator.

The first thing which was introduced as a regulator was a fly-wheel. There was a fly-wheel of a certain weight, and the force which was applied to the clock had to turn the wheel against the resistance of the air; but that did not answer well, and the first tolerable arrangement was suggested by Henry de Wyck, who constructed a bell and a clock in 1364, in which the fall of the weight was prevented by an oscillating balance, similar to that shown in Fig. 85.

Here we see what is called the crown wheel (S S, shown in plan, Fig. 86), on which the escapement depends, and into the teeth of which work two pallets, P_{1} P_{2}, which are placed on a vertical axis pivoted above and below. Now if we suppose a weight attached to the cord passing over a drum, so as to propel the intermediate wheels and pull them round, the crown wheel tends to rotate, but is prevented from moving until the pallets give way. Let us see how the clock goes. When the bottom tooth, presses against the pallet P_{1}, in order to make it get out of the way and enable the wheel to go on, it twists the rod and moves the horizontal bar M M, on which are several saw-like teeth, on the intervals of which, as in the modern steelyard, weights are placed, so that the wheel pushes away the pallet and makes the horizontal beam describe a part of a circle. And what happens is this:—the upper pallet is turned out of its position and driven into the upper teeth of the wheel, and driven out by the further revolution of the wheel, so that the fall of the weight depends on the oscillations of the horizontal beam which carries the weights. The clock was regulated by the distance of the weights from the pivots on which the balance swung. Such was the form of clock used by Tycho Brahe, but with little success, for it was extremely irregular in its action, and Tycho still had to compare the position of one star with another instead of trusting to his clock.

There is no necessity to say much regarding the train of wheels between the weight or spring and the escapement. Their office is simply to create a great difference in velocity of rotation between the wheel turned by the weight or spring and the escape wheel, so that a slow motion with great force may be transformed into a quick motion with small force. The train of wheels is so arranged, by the consideration of the number of teeth in the wheels, that one wheel shall go round once an hour, and another once a minute, so that the first may carry the minute-hand and the other the second-hand. The hour-hand wheel is also geared to the minute-wheel, so that it shall turn once in twelve hours or twenty-four hours, according to the purposes for which the clock is required. Weights are usually used when space is no object, being more regular in their action than springs; but the latter are used for chronometers and watches, and other portable time-keepers.

The general arrangement of the clock train is shown in Fig. 87, where W is the weight, hung by a cord passing over the barrel B, on the axis of wheel G. The teeth of the wheel G gear into the pinion P_{1}, which again is carried on the axis of the wheel C, and so on up the last wheel—the escape-wheel, which generally is cut to thirty teeth, so that it goes round once a minute and carries a second-hand. The pinion P_{1} is so arranged by the number of teeth between it and the escape-wheel that it goes round once an hour or to sixty turns of the escape-wheel.

To wind up the clock the barrel B, Fig. 88, is turned round by the key on the square; the pawl L fastened to the wheel G allows the barrel to be turned in one direction without turning the wheel. It is obvious, however that directly we begin to wind up, the pressure on the pawl tending to turn the wheel G is removed, and the clock stops—a very objectionable thing in astronomical and other clocks supposed to keep good time. The following is one of the devices for keeping the clock going during winding,—in this case everything is the same as before, with the exception of an additional rachet-wheel R_{2}, Fig. 88, carrying the pawl L; this wheel is loose on the axis but attached to the wheel G through the spring S. The weight therefore acts on the pawl L, and tends to drive the wheel R_{2}, which again presses round the wheel G by means of the spring S, and, as the whole moves round, the teeth of the wheel R_{2} pass the pawl K K fixed to some part of the clock-frame. When now we commence to wind, the pressure on the pawl L and wheel R_{2} is removed, and the spring S S, which is always kept bent by the action of the weight, endeavours to open; and since the wheel R_{2} is prevented from going backwards by the pawl K, the wheel G is continually urged onwards by the spring, and the clock kept going for the short period of winding.

II. THE PENDULUM.

The clock, as left by Henry de Wyck, was only an exceedingly irregular time-keeper, and some mechanical contrivance that should beat or mark correct intervals of time was urgently required. The contrivance for beating correct intervals of time—the pendulum—was thought of by Galileo, who showed that its oscillations were isochronous, although their lengths might vary within small limits. The pendulum then was just the very thing required, and Huyghens, in 1658, applied it to clocks.

In the next form of clock, therefore, we find the pendulum introduced as a regulator. There was a crown wheel like the one in the balance clock, only instead of being vertical it was horizontal. This wheel was allowed to go round and the weight was allowed to fall by means of alternating pallets; it was in fact like that shown in Fig. 86, with the balance weights and the rod carrying them removed, and instead thereof there was a rod, attached at right angles to the end of that carrying the pallets, and hanging downwards, which, by means of a fork at its lower end, swung a pendulum to an extent equal to the go of the balance first used. Thus the pendulum was adapted by Huyghens. We have here something extremely different from the rough arrangement in which the weight was controlled by the horizontal oscillating bar carrying the weights, for the balance would go faster or slower as the crown wheel pressed harder or softer against the pallets, and so, if the weight acted at all irregularly the clock would go badly. But with the pendulum the control of the weight over it is small, for the bob can be made of considerable weight, because it swings from its suspending spring without friction, and such a heavy weight at the end of a long rod is scarcely altered in its rate by variations of pressure on the pallets.

Galileo and Huyghens who followed him found that the oscillations of a simple pendulum are isochronous at all places where the force of gravity is equal, and that the time of oscillation depends on the length of the pendulum—the shorter the pendulum the shorter time of oscillation, and _vice versâ_. The time of oscillation varying as the square root of the length.

In 1658, then, the pendulum was applied to clocks, as the balance had been before that time. But Huyghens was not slow to perceive that the circular arc of a rigid pendulum would not be sufficiently accurate for an astronomical time-keeper, when used with a clock like that employed by Tycho Brahe and the Landgrave of Hesse for their astronomical observations. Huyghens next showed that with a clock of that kind, requiring a large swing of pendulum, the oscillations were not quite isochronous, but varied in time according as the arc increased or diminished. It was clear therefore that this simple form of pendulum would not do well for the large and varying arc required to be described, but that the theoretical requirements would be satisfied if the pendulum, instead of being suspended from a rigid rod, were suspended by a cord or spring or some elastic substance which would mould itself against two curved pieces of metal, C C, Fig. 89, attached one on either side of the suspending spring. In swinging, the spring would wrap, as it were, gradually round either curved surface, and so virtually alter the point of suspension, and with it, of course, the virtual length of the pendulum; so that the extreme point of the pendulum U, instead of describing a circular arc K B as before, would, by means of the portions of metal at the top, have a cycloidal motion D L, the pendulum becoming virtually shorter as the spring wrapped round the pieces of metal, so that it becomes isochronous for any length of swing. But it was very soon found that the theoretically perfect clock did not after all go as well as the clock it was to replace. And it would now be difficult to say what would have happened if a few years afterwards clocks had not been made much more simple and perfect by the introduction of an entirely new escapement which permitted a very small swing.

If we wish a clock to go perfectly well, we have only to consider a very few things—First, the weight should be as small as possible; secondly, within reason, the pendulum should be as solidly suspended and as heavy as possible; and, thirdly, the less connection there is between the pendulum which controls the clock, and the weight which drives the clock, the better.

The latter point is provided for in the dead beat arrangement of Graham, and in the “gravity” and other forms of escapement, about which more presently. At present we have been dealing with pendulums as if they were simple pendulums, which are almost mathematical abstractions.

Everything that we have said assumes that there is a mass depending from such a fine line that the mass of the line shall not be considered; but if we examine the pendulum of some clocks we see that the rod is of steel, and that its weight or bob is elongated, and consists of a long cylinder of glass filled with mercury, and carried in a sort of stirrup of steel; this is very different from our simple pendulum—it is a compound pendulum. In a compound pendulum we have first of all the axis of suspension, which is the axis where the pendulum is supported on the top, and below that, near the centre of gravity of the pendulum, we have what is called the centre of oscillation. It will at once be perceived that as the rate of the pendulum depends upon its length, the particles in the upper part of the pendulum will be trying to go more rapidly than they can go, seeing that they are connected in one series of particles, and that the particles at the lowest portion are carried with greater velocity than they would be if they were left to themselves, because they are connected rigidly with the upper ones. Therefore we have to find a point, which oscillates at the same rate as it would if all the other particles were absent.

This is called the centre of oscillation, and it is on the distance of this from the point of suspension that the rate depends.

What is the use of the mercury? It is to compensate for the expansion of the rod by temperature. We shall at once see the reason of this from the fact that the pendulum gets longer by being heated, and the rate of the pendulum depends on the square root of its length; that is, if we multiply the length by four, the square root of which is two, we shall only multiply the rate by two, or double the time of oscillation. Therefore, since temperature causes all metals to vary in length, and metals are the most useful things we can employ for the support of the weights, we find that we have to consider further the alteration of the length of the pendulum due to the variation of the length of the metal we employ. Hence, in addition to the necessity of an arrangement which gives the shortest possible swing, we require also a method for compensating for changes of temperature.

We have not space to go through the history of compensating pendulums, but we may direct attention to some of the best results which have been obtained in this matter. We will first examine the mercurial pendulum, Fig. 90, which we have referred to. In this case the compensation is accomplished as follows: Mercury is inclosed in a glass cylinder M M; shown in the left hand side of the figure; and as the mercury expands more than the glass, it will rise to a higher level on being heated; and the lengthening of the steel rod R R will be counteracted by a similar lengthening due to the expansion of mercury, so that the centre of oscillation is carried down by the steel rod, and up by the mercury, and it is therefore not displaced if the proper ratio is maintained between the length of the steel rod and the column of mercury in the glass vessel. The mercury in the glass will lengthen fifteen times as much as the steel rod, if we have equal lengths of each, so that in order that they may expand equally the rod must be fifteen times as long as the mercury column. This would keep the top of the mercury at the same distance from the point of suspension, but we want to keep the centre of oscillation, which is about half way down the column, at the same distance, so we double the height of the mercury, making it two-fifteenths of the length of the steel rod, so that the surface is over-compensated, but the centre of oscillation is exactly corrected. An astronomer can alter the amount of mercury as he pleases, making it now more, now less, till the stars tell him he has done the right thing, and the pendulum is compensated, and the clock keeps correct time at all temperatures.

The little sliding cup C is to carry small weights for final delicate adjustment, the addition of a weight thus obviously tending to increase the rate of the pendulum.

This is Graham’s mercurial pendulum, invented by him in 1715. There is another compensating pendulum, called Harrison’s gridiron pendulum, from the bars of metal sustaining the pendulum being arranged gridiron fashion, Fig. 90. At the top is a knife edge or spring for the centre of suspension, and the pendulum bob is suspended by a system of rods, the five black ones being made of a less expansible metal than the other four; consequently, as the five black ones expand and tend to lower the bob, the intermediate ones expand also and tend to raise it; the length of the black rods exceeding that of the others, these latter must be made of a more expansible metal to make up for their smaller length. Thus the acting length of the shaded rods is two-thirds of the acting length of the black ones (each pair is considered as one rod because they act as such), so that a metal is used for the former which expands more than that used for the latter in the proportion of about three to two, and brass is found to answer for the most expansible metal, and steel for the less. These rods are packed side by side, and look very ornamental. If _l_ be the length of the brass rods, and _l´_ that of the steel rods, and _e_ the coefficient of expansion of the brass, and _e´_ that of the steel, then _l_: _l´_:: _e´_: _e_. The pendulum is then compensated, and the bob remains at the same distance from the centre of suspension at all temperatures.

For the pendulum of the clock at the Royal Observatory a modification of the gridiron form has been adopted; for it was found on trial with a mercurial pendulum that the steel rod gained in temperature more rapidly than the mercury, and lost heat quicker, so that the pendulum did not compensate immediately on a change of temperature. The form adopted is as follows (Fig. 90):—A steel rod is suspended as usual, and is encircled by a zinc tube resting on the nut for rating the pendulum; the zinc tube is again encircled by a steel tube resting on the top of the zinc tube and carrying at its lower end a cylindrical leaden bob attached at its centre to the steel tube; slots and holes are cut in the tubes to expose the inner parts to the air, so that each will experience the change of temperature at the same time. It is of course possible that the tubes forming the pendulum rod are not of exactly the right length to perfectly compensate; a final delicate adjustment is therefore added. On the crutch axis, and held by a collar to it, are two compound bars of brass and steel, _h_ and _i_, Fig. 96. The collar fits loosely on the axis, so that the rods, which carry small weights at their extremities, can be easily shifted to make any angle with the horizontal; then, since brass expands more than steel for the same degree of heat, the bars will bend on being heated or cooled, and if the brass be uppermost the weights at the ends of the rods will be lowered with an increase of temperature, and will tend to increase the rate of the pendulum, and _vice versâ_. So long as the rods are horizontal and in the same straight line their centre of gravity is in the crutch axis, and they are therefore balanced in every position; they therefore only retard the pendulum by their inertia; but when the ends are bent down the centre of gravity is lowered, and they have a tendency to come to a horizontal position and to balance each other like a scale beam, and so swing with the pendulum and overcome its retardation.

It is obvious that they would, if alone, swing in a shorter time than the pendulum and so, being connected, they increase its rate.

When the rods are vertical they have no compensating action, for the centre of gravity is simply thrown sidewise, and acts as a continuous force tending to make the pendulum oscillate further on one side than on the other; and in the intermediate positions of the rods their action varies, and a consideration of the position of their centre of gravity will give the intensity of the compensating action. In order to make a small change in the rate of the clock without stopping it to turn the screw at the bottom of the pendulum, the following contrivance is adopted.

A weight _k_ slides freely on the crutch rod, but is tapped to receive the screw cut on the lower portion of the spindle _l_, the upper end of which terminates in a nut _m_ at the crutch axis. By turning this nut the position of the small weight on the crutch rod is altered, and the clock rate correspondingly changed. To make the clock lose, the weight must be raised.

There is also another method of compensation, depending on differential expansion. Attached to an ordinary pendulum just above the bob, and at right angles to it, is a composite rod, made of copper and iron, the lower half being copper; then, as the pendulum rod lengthens and lets down the bob, the copper expands more than the iron, and causes the rod to bend, like a piece of wood wetted on one side, and by this bending or warping the weights at either end are raised as the bob is lowered, so the centre of oscillation keeps at the same height at all temperatures.

We have dealt with clocks and pendulums somewhat in the order of their invention. We may add that the great majority of clocks of modern manufacture of any pretention to time-keepers are constructed with the dead beat escapement of Graham or a modification of it, combined with a mercurial or gridiron pendulum. For the best Observatory clocks of the more expensive kind other more elaborate forms of escapement are sometimes used, as, for example, that in the clock at the Royal Observatory, Greenwich, which we shall refer to in detail further on, on account of other new points in its construction.

Now, having a clock good enough to use with the transit instrument, it is necessary to take the utmost precautions with reference to it. The Russian astronomers have inclosed their clock in a stone case, and placed it many yards below the ground, endeavouring thus to get rid of the action of temperature, which changes the length of the steel pendulum rod. But that is not all; after we have corrected our clock as well as we can from the point of view of temperature, it is still found that there may be a variation, amounting to something considerable, due to another cause. If the barometer changes an inch or an inch and a half by change of pressure of the air, the rate of the pendulum will alter, and the cause of the variation it is impossible to prevent without putting the clock in a vacuum, so that changes of the barometer must be allowed for.

There are, however, methods of compensating the pendulum for changes of pressure if desirable: one way of doing this is to pass the suspending spring of the pendulum through a slit in a metal plate, which then becomes virtually the point of suspension; this plate is then raised or lowered by an aneroid barometer, or by a float in an ordinary cistern barometer so that the length of the pendulum is virtually altered with the pressure of the atmosphere. At Greenwich the Astronomer-Royal has adopted the following expedient: A magnet at the lower end of the pendulum passes at each swing near a magnet which is raised or lowered by means of a float in the cistern of a barometer. The magnet then has a greater or less influence on the pendulum magnet according as the pressure of the air varies, and so adds a variable amount to the effect of gravity and therefore to the rate of oscillation.

This principle is carried out as follows:—Two bar magnets, each about six inches long, are fixed vertically to the bob of the clock pendulum; one in front, _a_, Fig. 91, the other at the back. The lower pole of the front magnet is a north pole; the lower pole of the back magnet is a south pole. Below these a horse-shoe magnet, _b_, having its poles precisely under those of the pendulum magnets, is carried transversely at the end of the lever _c_, the extremity of the opposite arm of the lever being attached by the rod _d_, to the float _e_ in the lower leg of a syphon barometer. The lever turns on knife edges. A plan of the lever (on a smaller scale) is given, as well as a section through the point A. Weights can be added at _f_ to counterpoise the horse-shoe magnet. The rise or fall of the mercurial barometer correspondingly raises or depresses the horse shoe magnet, and, increasing or decreasing the magnetic action between its poles and those of the pendulum magnets, compensates, by the change of rate produced, for that arising from variation in the pressure of the atmosphere. The shorter leg of the barometer in which the float rests has an area of four times that of the barometer tube at the upper surface of the mercury, so that for a large change of barometric height the magnet is only moved a small distance, a change of one inch of the barometer lowering the surface in the short leg 2/10 inch; the distance between the pendulum magnets and the horse-shoe magnets is 3¾ inches.

III. ESCAPEMENTS.

The invention of the pendulum, its application, and the improvements thereon having been described, it remains to treat of the equally important improvements on the escapement. The first change for the better appears to have been due to Hooke, who in 1666 brought before the Royal Society the crutch, or anchor escapement, whereby the arc through which the pendulum vibrated was so much reduced that Huyghens’s cycloidal curves became unnecessary, and the power required to drive the clock was materially reduced.

This escapement, common in ordinary eight-day clocks, is different from that previously described in the way in which the crown wheel or escape wheel is regulated.

We have come back to a vertical escape wheel as it was in the clock used by Tycho; but instead of using two pallets on a rod which regulated the wheel, we have here an anchor escapement (Fig. 92) in connection with the pendulum; and what happens is this—when the pendulum is made to oscillate, these pallets P P gradually move in and out of the teeth of the wheel, and let a tooth pass at every swing; and it is obvious that when the wheel and anchor are nicely adjusted, an extremely small motion of the anchor, and consequently a small oscillation of the pendulum, allows the escape wheel to turn round, and the clock to go.

The greater regularity of this form of escapement is due to a smaller oscillation of the pendulum being required than with the form first described; for it is found that the motion of a pendulum when vibrating through not more than six degrees is practically cycloidal, and it is only with larger arcs that the circle materially differs from the theoretical curve required.

The pendulum is kept in vibration by the escape wheel, or rather by its teeth pressing against the inclined surfaces of the pallets, and forcing them outwards, and so giving the pendulum an impulse prior to each tick.

This anchor escapement, which was invented by “Clement, of London, clockmaker,” forms, as it were, the basis of our modern clocks, and, with the exception of the dead beat, which was due to Graham some years afterwards, is in almost exclusive use at the present date.

We see that as soon as a tooth has escaped on one side, a tooth on the other begins immediately to retard the action of the pendulum by pressing against the inclined surface of the other pallet, and as the pendulum swings on, the tooth gives way, and the motion of the wheel is reversed; then when the pendulum begins to return, it is assisted again by the tooth, so that the pendulum is always under the influence of the escape wheel, some times accelerated, and sometimes retarded. The principle of Graham’s dead beat is to get rid of the retarding action of the escape wheel, so that there should be no necessity for so much accelerating power, and the pendulum should be out of the influence of the escape wheel during a large portion of its vibration. This he accomplished by doing away with a large portion of the inclined surface of the pallet (Fig. 93), so that the teeth have no accelerating action on the pendulum until just as they leave the ends of the pallets where they are inclined; the greater portion of both the pallets on which the escape wheel works being at right angles to its direction of motion, the teeth have no tendency to force the pallet outwards. In Fig. 93 the tooth V has fallen on the pallet D, the tooth T having just been released, and as the pendulum still swings on in the direction of the arrow, the pallet D will be pushed further under the tooth C but without pressing the wheel backwards, and without retardation other than that of friction. When the pendulum returns and the pallet just gets past the position shown, it gets an impulse, and this is given as nearly as possible as much before the pendulum reaches its vertical position as after it passes it, its action is therefore neither to increase nor diminish the rate. In this escapement not only is the arc of oscillation considerably lessened and the motion of the pendulum brought near to the cycloidal form, but in addition to this there is this important point, that the weight is acting upon the pendulum for the least possible time.

We will now describe the more elaborate forms of escapement, and we will take first the gravity escapement, as it is called. The principle of its action consists in there being a small impulse given to the pendulum at each oscillation, by means of two small rods hanging, one on each side of it, and tending by their own weight to force the pendulum into a vertical position; these rods are alternately pushed outwards by the escapement before the pendulum in its swing arrives at them, and then they are allowed to press against it on its return towards the vertical, so that the pendulum has a constant force acting on it at each oscillation, unconnected with the clock movement. This is carried out in the escapement invented by Mudge, as shown in Fig. 94. The pendulum rod is supposed to be hanging just in front of the rods hanging from the pivots Y_{1} Y_{2}, and on swinging it presses against the pins at the lower ends of the rods and so lifts the pallets S_{1} S_{2} out of the teeth of the escape wheel. In the position shown the pendulum is moving to the right, having been gently urged from the left by the weight of the pallet rod Y_{2} S_{2}, and the pallet S_{1} has been lifted outwards by the tooth acting on its inclined surface. On the pendulum rod reaching the pin the rod is moved outwards and the end of the pallet S_{1} pushed out of the tooth when the wheel moves on, at the same time pushing outwards the pallet S_{2}. As the pendulum returns towards the left again the rod Y_{1} follows it, giving it a gentle impulse by its own weight until it returns nearly to the vertical or to the corresponding position in which Y_{2} S_{2} is shown. On the pendulum swinging on and releasing T_{2} the pallet S_{1} is again pushed outwards by the inclined plane to the position shown in the diagram. In this escapement there was danger of the pallets being thrown too violently outwards so that the teeth were not caught by the flat surfaces at the ends, and Mr. Bloxam improved on it by letting the pallets be thrown outwards by a small wheel on the axis of the escape wheel so that the action was less rapid; he accomplished this in the following manner. On the end of the axis of the last wheel are a number of arms A A, Fig. 95, say nine, about 1½ inches long, which are prevented from revolving by studs L_{1} L_{2} on the inside of each hanging rod P_{1} P_{2}; then, as each rod is pushed outwards by the pendulum, an arm escapes from a stud and the clock goes on one second. Each rod is pushed outwards by the clock almost sufficiently far for the arm to escape, but not quite, so that the pendulum just releases the arm at the end of its swing in the same manner as in Mudge’s escapement, Fig. 94; but instead of the teeth of the escape wheel pushing the rods outwards there is the small wheel T_{1} T_{2}, having the same number of teeth as there are arms on the axis and close to them, and the projecting pieces H_{1} H_{2} at right angles to each swinging rod rest against the teeth of this wheel, one resting against the teeth at the top and the other at the bottom, so that they catch against the teeth after the manner of a ratchet, and the rods are pushed outwards by this wheel as it revolves. The arms and ratchet wheel are so set that, during the motion of an arm A, to a stud, a tooth of the ratchet wheel is pushing outwards the rod carrying that stud. The action is as follows:—The pendulum having just swung up to a rod and released the arm pressing against its stud, the arms and ratchet wheel revolve, and the tooth of the ratchet wheel, which had been pressing outwards the swinging rod, passes on free of the projecting piece, which can now move backwards to the next tooth; so the rod, being no longer supported, presses against the pendulum rod on its return oscillation. The arms and ratchet wheel revolve until an arm on the opposite side comes in contact with the stud on the other rod, and in revolving the ratchet wheel throws outwards this rod just so far that the arm is not released. The pendulum is assisted by the weight of the first rod to the vertical position, when the projecting piece of the rod comes in contact with the next tooth of the ratchet wheel where it rests until the oscillation is completed, and the second arm is released. It is then forced outwards, and the next arm on that side presses against the stud, when a repetition of the foregoing takes place. In this way the clock is kept going without any direct action of the clock train on the pendulum.

Another very beautiful escapement is that devised by the Astronomer-Royal and carried out in the clock erected in 1871 at Greenwich.[9] In this case the pendulum is free except during a portion of every alternate second, when it releases the escapement and receives an impulse, so that there is a tick only at every other second.

The details of the escapement may be seen in Fig. 96, which gives a general view of a portion of the back plate of the clock movement, supposing the pendulum removed; _a_ and _b_ are the front and back plates respectively of the clock train; _c_ is a cock supporting one end of the crutch axis; _d_ is the crutch rod carrying the pallets, and _e_ an arm carried by the crutch axis and fixed at _f_ to the left-hand pallet arm; _g_ is a cock supporting a detent projecting towards the left and curved at its extreme end; at a point near the top of the escape wheel this detent carries a pin (jewel) for locking the wheel, and at its extreme end there is a very light “passing spring.” The action of the escapement is as follows:—Suppose the pendulum to be swinging from the right hand. It swings quite freely until a pin at the end of the arm _e_ lifts the detent; the wheel escapes from the jewel before mentioned, and the tooth next above the left-hand pallet drops on the face of the pallet (the state shown in the figure), and gives impulse to the pendulum; the wheel is immediately locked again by the jewel, and the pendulum, now detached, passes on to the left; in returning to the right, the light passing spring, before spoken of, allows the pendulum to pass without disturbing the detent; on going again to the left, the pendulum again receives impulse as already described. The right-hand pallet forms no essential part of the escapement, but is simply a safety pallet, designed to catch the wheel in case of accident to the locking-stone during the time that the left-hand pallet is beyond the range of the wheel. The escape wheel carrying the seconds hand thus moves once only in each complete or double vibration of the pendulum, or every two seconds.

IV. THE CHRONOMETER.

We have now given a description of the astronomical clock—the modern astronomical instrument which it was our duty to consider. There is another time-keeper—the chronometer—which we have to dwell upon. In the chronometer, instead of using the pendulum, we have a balance, the vibration of which is governed by a spiral spring, instead of by gravity, as the pendulum is. By such means we keep almost as accurate time as we do by employing a pendulum, the balance being corrected for temperature on principles, one of which we shall describe.

We must premise by saying that fully four-fifths of the compensation required by a chronometer or watch-balance is owing to the change in elasticity of the governing spiral spring, the remainder, comparatively insignificant, being due to the balance’s own expansion or contraction. The segments R_{1}, R_{2} of the balance (see Fig. 97) are composed of two metals, say copper and steel, the copper being exterior; then as the governing spiral spring loses its elasticity by heat, the segments R_{1}, R_{2} curve round and take up positions nearer the axis of motion, the curvature being produced by the greater expansion of copper over steel; and thus the loss of time due to the loss of elasticity of the spiral spring is compensated for.

This balance may be adjustable by placing on the arms small weights, W W, which may be moved along the arms, and so increase or diminish the effect of temperature at pleasure.

Of the number of watch and chronometer escapements we may mention the detached lever—the one most generally used for the best watches, the form is shown in Fig. 98. P P are the pallets working on a pin at S as in the dead-beat clock escapement; the pallets carry a lever L which can vibrate between two pins B B. R is a disc carried on the same axis with the balance, and it carries a pin I, which as the disc goes round in the direction of the arrow, falls into the fork of the lever, and moves it on and withdraws the pallet from the tooth D, which at once moves onwards and gives the lever an impulse as it passes the face of the pallet. This impulse is communicated to the balance through the pin I, the balance is kept vibrating in contrary directions under the influence of the hair-spring, gaining an impulse at each swing. On the same axis as R is a second disc O with a notch cut in it into which a tongue on the lever enters; this acts as a safety lock, as the lever can only move while the pin I is in the fork of the lever.

The escapement we next describe is that most generally used in chronometers. S S, Fig. 99, is the escape wheel which is kept from revolving by the detent D. On the axis of the balance are two discs, R_{1}, R_{2}, placed one under the other. As the balance revolves in the direction of the arrow, the pin P_{2} will come round and catch against the point of the detent, lifting it and releasing the escape-wheel, which will revolve, and the tooth T will hit against the stud P_{1}, giving the balance an impulse. The balance then swings on to the end of its course and returns, and the stud P_{2} passes the detent as follows: a light spring Y Y is fastened to the detent, projecting a little beyond it, and it is this spring, and not the detent itself, that the pin P_{2} touches: on the return of P_{2} it simply lifts the spring away from the detent and passes it, whereas in advancing the spring was supported by the point of the detent, and both were lifted together.

In watches and chronometers and in small clocks a coiled spring is used instead of a weight, but its action is irregular, since when it is fully wound up it exercises greater force than when nearly down. In order to compensate for this the cord or chain which is wound round the barrel containing the spring passes round a conical barrel called a _fusee_ (Fig. 100): B is the barrel containing the spring and A A the fusee. One end of the spring is fixed to the axis of the barrel, which is prevented from turning round, and the other end to the barrel, so that on winding up the clock by turning the fusee the cord becomes coiled on the latter, and the more the spring is wound the nearer the cord approaches the small end of the fusee, and has therefore less power over it; while as the clock goes and the spring becomes unwound, its power over the axis becomes greater. The power, therefore, acting to turn the fusee remains pretty constant.

Footnote 9:

By Messrs. E. Dent and Co. of the Strand.