I have thus described the principal features of ordinary clocks. For the details many treatises must be studied, and knowledge acquired which is not in any books at all.

I now, however, pass to watches. It will be remembered that a verge escapement consists of a crown wheel with teeth, engaging two pallets fixed upon a verge, furnished with balls at its extremities.

As the crown wheel was urged forwards each pallet in succession was pushed till it slipped over the tooth which was engaging it. Then a tooth on the other side came into sharp collision with the other pallet, and drove the verge the other way, and so on.

Now here we have a driving force, and a sort of pendulum. But how did the verge act as a pendulum to measure time? It is not a body rocking under the action of gravity, nor under the acceleration of a spring. How then can it act as a regulator of time, and what is the period of its swing?

The answer to this is, that it is under the acceleration of gravity, but that gravity does not act freely on the bobs or weights, but only through the driving weight and teeth. The impulse that drives the verge is really also the accelerating force upon it, and the only accelerating force upon it.

And the worst feature about the movement is, that as the teeth and pallets move, the leverage of the teeth on the pallets alters, and thus the bobs on the verge are under the influence not of a uniform or duly regulated force, but of a constantly varying one, and one that varies in a very complicated and erratic way. It would be hopeless to expect much time-keeping from such a contrivance. The most that could be expected would be by putting on a very big weight to reduce to comparative insignificance the friction, and then hope that the swings would be uniform, so that whatever went on in one swing would go on in the next, and thus the time-keeping be regular.

But any course tending to diminish the driving force, such as the thickening of the oil, would greatly affect the going. It was for this reason that Huygens turned the verge into a pendulum by removing one of the bobs, and letting gravity thus act on the other.

For watches, however, a different plan was contrived. One end of a slender spiral spring was affixed to the verge. The other end of the spring was made fast to the clock frame. The verge was now, therefore, chiefly under the action of the acceleration of the spring. To make the acceleration of the teeth of the ’scape wheel less embarrassing, the teeth were so shaped as only to give a short push at stated intervals, and not interfere with the free swing of the verge under the alternate to-and-fro accelerations and retardations of the spring. By this means the verge became in every way an excellent pendulum, not dependent on gravity, and permitting the watch to be held in any position.

The verge thus fitted was turned into a wheel, and became a “balance wheel.” It was compensated for heat expansion by a cunning use of the unequal expansion of brass and steel, in a manner analogous to the way this unequal expansion of metals had been employed to compensate the pendulum, and became the beautiful and accurate time-measurer that we see to-day, with its pivots mounted in jewels to diminish friction, and with screws round the rims of the balance wheel to enable the centre of gravity to be exactly adjusted to its centre of rotation, and with a delicate hair-spring of tempered steel that is a marvel of microscopic work.

But the escapement of the early watches left much to be desired. In order to make it clear how imperfect that early escapement was, we have to turn back and remember what has been said about the dead beat escapement.

It will then be remembered that it was shown that for small arcs the pendulum would keep good time provided you let it have as much swing as it wanted to use up the force which the escapement had applied to it, but not otherwise, so the pendulums only acted really well when the impulse was given about the middle of the swing, and they were free to go on and stop when they pleased, and turn back at the end of it.

This essential condition was fairly approximated to in the dead beat escapement of clocks which left them at the end of their swing with only a very slight friction to impede their free motion.

But when you come to deal with a watch the case is quite different. Here the escapement is of a great size compared with the balance wheel, and the friction even of the most dead beat watch escapement that could be contrived was so big compared with the forces acting on the balance wheel as seriously to derange its motion, and render it far from a perfect time-keeper.

Now about this time—I am speaking of the early part of the eighteenth century—a demand of a very exceptional character arose for a really perfect watch. The demand did not arise from gentlemen who wanted to keep appointments to play at ombre at their clubs, or even from merchants to time their counting house hours. For these the old-fashioned watch did very well. The demand came from mariners. But the seamen did not want to know the time merely to arrange the hours for meals on the ship or to determine when the watch was to be relieved, but for a far more important purpose, namely, to find out by observation of the heavens their place upon the ocean when far out of sight of the land. It will be very interesting to see how this problem arose, and how the patient industry and ingenuity of man has solved it.

The ancient navigators never went very far from the shore, for, once out of sight of land, a ship was out of all means of knowing where she was. On clear days and nights the compass, and the sun and stars would tell the mariner the direction he was sailing in, but it was quite a problem to determine where he was on the surface of the earth.

Let us consider the problem. Suppose for convenience that the earth is divided up into “squares,” as nearly, at least, as you can consider a globe to be so marked out. Let us suppose that it has been agreed to draw on it from pole to pole 360 lines of longitude, commencing with one through say Greenwich Observatory as a starting-point, and going right round the earth till you come back to Greenwich again. Also suppose that there have been drawn a series of circles parallel to the equator, but going up at equal distances apart towards the poles. Let us have 179 of these circles, so as to leave 180 spaces, a to b, b to c, etc., from pole to pole. This will divide the earth up like a bird-cage into squares, as if we had robed it in a well-fitting Scotch plaid. The length measured along the equator of the side p q of each square at the equator is taken as exactly sixty nautical miles (apart from a small error of measurement, which makes it in actual practice 59·96). This is equal to sixty-nine and a quarter English statute miles. The side of the square leading towards the poles q s would also be sixty nautical miles were it not that the earth is not truly spherical, which introduces a slight error. We may, however, roughly say that at the equator each square measures sixty nautical miles each way.

As we get towards the poles the squares become rectangular figures, with the heights of latitude still sixty nautical miles, but the widths becoming smaller. Thus in England our squares measure p q = 37 nautical miles and q s = 60 nautical miles.

Now of course we can see at once that it is easy at any place on the earth’s surface to find your latitude by a simple observation of the sun at noon, if you know the day of the year, and have got a nautical almanac. For by an instrument called a sextant you can measure the angle he appears to be above the horizon, and then, as you know from a nautical almanac the angle he is above the equator, you can soon determine your place A on the globe. Or at night, if you measure the angular distance that the polar star P is from the zenith, or point exactly over your head—that is, the angle P O Z—you can subtract it from a right angle and get your latitude, A O E, at once.

But how are you to determine your longitude? The pole-star, or sun, or any other star won’t help you, for as the earth is moving they keep shifting, and at one time or another appear exactly in the same position to everyone on the same parallel of latitude, as it is easy to see. The fact is that you are on a ball turning round. You know easily what latitude you are on, but you cannot tell your longitude unless you can tell how many hours and minutes you get to a position before Greenwich gets to the same position. If when a particular star got to Greenwich a gong were sounded which could be heard all over the earth, then of course, by seeing what stars were overhead, everyone would know their longitude at once. Perhaps by means of the new electric waves this will before long be done, and the Greenwich hours will be sounded all over the world for the use of mariners. But till this is accomplished all that can be done is to keep an accurate clock on board, so as always to give you Greenwich time.

Early attempts were made to take a pendulum clock to sea, suspending it so as to avoid disturbance to its motion by the rocking of the ship. These proved vain.

It therefore became desirable that a watch with a balance wheel should be contrived to go with a degree of accuracy in some respects comparable with the accuracy of a pendulum clock. To encourage inventors an Act of Parliament was passed in the thirteenth year of Queen Anne’s reign (chapter xv.) (1713) promising a reward of £20,000 to anyone who would invent a method of finding the longitude at sea true to half a degree—that is, true to thirty geographical miles.

If the finding of the longitude were to be accomplished by the invention of an accurate watch, then this involved the use of a watch that should not, in several months’ going, have an error of more than two minutes, which is the time which the earth takes to turn through half a degree of longitude.

This was the problem which John Harrison, a carpenter, of Yorkshire, made it his life business to solve. His efforts lasted over forty years, but at the end he succeeded in winning the prize.

These instruments have been much improved by subsequent inventors, and have resulted in the construction of the modern ship’s chronometer, a large watch about six inches in diameter, mounted on axles, in a mahogany box. Several of these are taken to sea by every ship.

The peculiarity of the chronometer is its escapement.

Let A B be the scape wheel, and C D a small lever attached to C, the pivot on which the balance wheel and spring is fastened. Let E G be a lever, with a tooth F which engages the teeth of the scape wheel and prevents it moving round. Let H be a spring holding the lever E G up to its work.

The lever has a spring K E fastened to it at the point K. This spring is very delicate. If the lever C D is turned so that the little projection M on it strikes the spring E from left to right, then, as the spring rests on the lever, the whole lever is pushed over, and the teeth of the scape wheel set free. At that instant, however, the escapement is so arranged that the arm C D is just opposite the tooth D of the scape wheel, so that the scape wheel, instead of running away, leaps with its tooth D on to the lever C D and swings the balance wheel round. The balance wheel is free to twist as much as it pleases, but the moment it has twisted so much that the projection M passes the spring E, then the lever G E flies back to its place, and the scape wheel is again checked. Meanwhile the balance wheel flies round till at last it is brought to rest by the balance spring. It then recoils and sets out on its return path. This time, however, the projection M merely flips aside the spring E and the balance wheel goes back, till again it is brought to rest and returns. As soon as the lever comes opposite D the projection M then again hits the spring E, and releases the catch at F, and another tooth of the scape wheel goes by.

There then you have a completely free escapement, and consequently an accurate one. Many watches are made with these escapements, but they are more expensive than those in common use.

There is but little remaining in a watch that is not in a clock, for the wheel-trains and general arrangements are very similar.

It is possible to apply the chronometer’s detached escapement to a clock. This was done by several clock-makers in the eighteenth and early part of the nineteenth century. One method of doing it is as follows:

A is a block of metal fitted to the bottom of the pendulum, B a light lever pivoted on it. C is the scape wheel, with four teeth; D a tooth of the scape wheel, which hops on to the projection of the pendulum the moment that the impact of the point E of the lever B E has pushed aside the lever G F, and thus released the scape wheel. The advantage is that it is a very easy escapement to make. But it is in reality a detached (that is to say, a completely free) chronometer escapement, as can easily be seen.

Turret-clocks are open to considerable disadvantages, for the wind blowing on the hands gives rise to considerable pressure, so that the clocks are sometimes urging the hands against the wind, sometimes are being helped by the wind. And this inequality of driving force makes the pendulum at some times make a bigger arc of swing than at others.

But we saw above that though difference of arc of swing ought to make no difference in the time of swing of the pendulum, yet this was only strictly true if the arc of swing were a cycloid. But as for practical convenience we are obliged to make it a circle, it follows, as we saw, that for every tenth of an inch of increase of swing of an ordinary seconds pendulum about a second a day of error is introduced. To remove this difficulty a gravity escapement was invented by Mudge in the eighteenth century, improved by Bloxam, a barrister, and perfected by the late Lord Grimthorpe. The idea was to make the scape wheel, instead of directly driving the pendulum, lift a weight, which, being subsequently released, drove the pendulum. The consequence was, that inequalities in wind pressure, which affected the driving force of the scape wheel, would not act on the pendulum, which would be always driven by the uniform fall of a fixed and definite weight. A movement of this kind has been fixed in the great clock at Westminster, and has gone admirably. A description of its details will be found in the EncyclopÆdia Britannica, written by Lord Grimthorpe himself.

All sorts of eccentric clocks and watches have been proposed. For instance, it seems wonderful to see a pair of hands fitted to the centre of a transparent sheet of glass go round and keep time with apparently nothing to drive them.

But the mystery is simple. The seeming sheet of glass is not one sheet, but four. The two centre sheets move round invisibly, carrying the hour hand and minute hand with them, being urged by little rollers below on which they rest. When you touch the glass the outside sheets appear at rest, and you do not suspect that it is other than a single sheet. But beware of dust, for if dust gets on the inner plate you detect the trick. In this way a mechanical hand was made that wrote down answers to questions. This plan can be applied to all sorts of tricks.

Sir William Congreve, an ingenious inventor, proposed to make a clock that measured time by letting a ball roll down an incline. When it got to the bottom it hit a lever, which released a spring and tipped the plane up again, so that the ball now ran down the other way. It is a poor time-keeper, and the idea was not original, for a ball had been previously designed for the same purpose.

Sometimes clocks are constructed by attaching pendulums to bronze figures, which have so small a movement that the eye is unable to detect it. The figure appears to be at rest, but is in reality slowly rocking to and fro. It is necessary to make the movement as small as about one four hundredth of an inch in half a second, if the movement is to escape human observation. For a movement of one two hundredth of an inch per second is about the largest that will certainly remain unperceived.

In mediÆval times clocks were constructed with all sorts of queer devices. The people of the upper town at Basle having quarrelled with those of the lower town, fought and beat them. To commemorate this victory they put on the old bridge at the upper town a clock provided with an iron head, that slowly put out and drew in a long tongue of derision. This clock may still be seen in the museum. It is as though the council of the city of London put a clock of derision at Temple Bar to put out its tongue at the County Council.

I do not propose here to describe the striking mechanism of clocks. There are several different ways of arranging it. They are rather complicated to follow out, but they all resolve themselves into a few simple principles. As the hour hand revolves it carries a cam so arranged as to be deeper cut away for the twelfth hour, less for the eleventh, and so on. When the minute hand comes to the hour it releases the striking mechanism, which, urged by a weight, begins to revolve, and, driving an arm carrying a pin, raises a hammer, which goes on striking away as the arm revolves. This would continue for ever if it were not that at the same moment an arm is liberated which falls against the cam. At each stroke the arm is (by the striking apparatus) raised a bit back into position. When it comes back into position it stops the striking. It thus acts as a counter, or reckoner of the blows given, stopping the movement when the clock has struck sufficiently. If the counting mechanism fails to act, we have the phenomenon which occasionally occurs of a “Grandfather” clock striking the whole of the hours for the week without stopping.

A chiming clock is simpler still. For here we have a barrel covered with pins, like the barrel in a musical box. As the pins go round they raise hammers which fall against bells. The barrel is wound up and driven by a spring or weight. When the clock comes to the hour, the barrel is released, and rotating, plays the tune.

If you want to make a clock wake you up in the morning it can be done by making the striking arrangement hammer away with no counting mechanism to stop it until the weight has run down. If, not content with that, you want the sheets pulled off the bed or the bed tilted up, or a can of water emptied over the person who will not rise, a mechanical device known as a relay must be used. It is very simple. What is wanted is that, after the lapse of a time which a clock must measure, a considerable force must be exerted to pull off the bedclothes. It would be absurd to make the clock exercise this pull. It is obviously better to attach the clothes by a hook to a rope which passes over a pulley, and from which hangs a weight. A pin secures the weight from falling, the pin being withdrawn by the clock. The work is thus done by the weight when released by the clock. In like manner, if you have a telegraph designed to print messages at a distance, you do not send along the wires the whole force necessary for doing the printing. You only send impulses, which, like triggers, release the forces by which the letters are to be stamped.

Electric clocks of many kinds have been invented. The principle of an electric escapement is similar to that of an ordinary escapement.

The reader no doubt knows that, when a circuit of wire is joined or completed leading to a source of electricity, electricity flows through the wire.

If the wire is wound round a piece of iron, then, whenever the circuit is joined, a current is set in motion, and the iron becomes an electro-magnet. When the circuit is severed the iron ceases to be a magnet.

If put at a proper position it would at each time an iron pendulum approached give it a small impulse provided that at that instant the current is turned on. This can easily be made to be done by the pendulum itself. For just as the pendulum is coming back to the central position a flipper P attached to the rod can be caused to make contact with a piece of metal fixed on its path. Then the electro-magnet, becoming magnetised, exerts a pull on the iron pendulum. On the return beat of the pendulum the other side of the flipper R strikes the obstruction. But if that side R is covered with ebonite or some non-conducting material no current will be set in motion, and the electro-magnet will not (as it would otherwise do) retard the pendulum. Such a pendulum has therefore an impulse given to it every second beat.

Such pendulums do not act very well, because it is difficult to keep metallic surfaces like Q clean, and therefore misses often occur. Besides, the strength of the current varies with the goodness of the contact and with other things.

What is now preferred is to make an arrangement by which an electric current winds the clock up every minute or so. By this means the impulse which drives the clock is not a varying electric one, but is a steady weight. The most successful clocks have been made on these principles.

The advantage of electricity is, that by means of the current that actuates the clock, or winds it up, you can at regular intervals set the hands in motion of a great number of clocks.

So that only one going clock with a pendulum is needed. The other clocks distributed over the building have only faces and hands, and a very few simple wheels, to which a slight push is given by an electro-magnet, say, every minute or so. The system is therefore well adapted for offices and hotels.

In America, by means of electric contacts, clocks have been arranged to put gramophones into action. You will remember that it was pointed out that if a wire were dragged over a file a sound would be produced due to the little taps made as the wire clicked against the rough cuts on the file, and that the tone of the note depended on the fineness of the cuts, and hence the rapidity of the little taps. You can imagine that, if the roughnesses were properly arranged, we might get the tones to vary, and thus imitate speech. This is the principle of the gramophone. The roughnesses are produced by a tool, which, vibrating under the influence of human speech, makes small cuts in a soft material. This is hardened, and then, when another wire is dragged over the cuts, the voice is reproduced.

In this way clocks are made to speak and tell the children when dinner is ready and when to go to bed. On this simple plan, too, dolls can be made to speak. The modern methods of clock and watch-making are very different from those in use in olden days. In former times the pivots were turned up by hand on small lathes, and even the teeth of the wheels were filed out. Each hole in the clock or watch frame was drilled out separately, and each wheel separately fitted in, so that the watch was gradually built up as one would build a house. Each wheel, of course, only fitted its own watch, and the parts of watches were not interchangeable.

This has now all been altered. By means of elaborate machinery the whole of the work of cutting out every wheel and the making of every single part is done by tools moved independently of the will of the workman, whose only duty is to sit still and see the things made. He is, as it were, the slave of the machine, watching it and answering to its calls. Or shall we rather say that he is the machine’s employer and master? He has here a servant who never tires nor ever disobeys him. All the machine requires is that its cutting edges should be exactly true and sharp and microscopically perfect; then it will cut away and make wheel after wheel. It oils itself. It only wants the man to act as superintendent, and stop it if any cutting edge gets unduly worn. For this purpose he measures the work it is doing from time to time with a microscope to see that it is good and true and exact. When all the parts have thus been made you have perhaps a hundred boxes, each with a thousand watch parts in it, each part exactly like its fellows. You take one wheel or bit from each box indiscriminately, and you then have the materials for a watch, screws, fittings, pins, and all. All you have now got to do is simply to screw them all together, like putting together a puzzle. Everything fits; there is no snipping or filing.

In such a watch if a bit gets broken you simply send for another bit of the same kind and fit it into its place.

Motor cars, bicycles, and many other machines are, or ought to be, made in this manner, so that if a driver at York breaks a part of the car he simply sends to London for another. It comes and fits into its place at once. But for this sort of plan you must do work true to much less than a thousandth of an inch, and, of course, no one must want to indulge his individual fancy as to the shape or appearance of the watch. The whole advantage consists in dead uniformity. But the cheapness is surprising. You can have a better watch now for 30s. than could have been got for £30 twenty years ago.

Artistic people are in the habit of condemning this uniformity as though it were inartistic and degrading. In truth, it is not degrading to get a machine to do what you want at the expense of as little labour as possible. You pay 30s. for the watch, but you have £28 10s. left to spend on pictures.

Only one ought not to confuse industry with art. Watches made in this way have no pretence to be artistic products. They are simply useful. To rule them all over with machine lines or to put hideous machine ornament on them is purely and simply base and degrading. Let your ornament be hand work, your utility machine work.

Thus then I have endeavoured to give a very brief sketch of the modes of measuring time, and incidentally to introduce my readers to those laws of motion which are the foundation of so large a part of modern science.

It only remains that I should shortly describe modern apparatus by means of which it is possible to measure with accuracy periods of time so short as to appear impossible. But when you see how it is done the method seems easy enough. It is still by means of a pendulum, only a pendulum beating time not once, but hundreds and even thousands of times in a second.

And such pendulums, instead of being difficult to make, are remarkably simple, and present no difficulty whatever. For we have only to use the tuning fork which has been previously described.

The tuning fork consists of a piece of steel bent into a U shape. The arms are set vibrating so as alternately to approach and recede from one another.

The reason why there are two arms is that, if they come together and recede, they balance, and hence the instrument as a whole does not shake on its base. This balance of moving parts of a rapidly moving machine is very important. Some motor cars are arranged so that the engines are “balanced,” and the moving parts come in and out simultaneously, leaving the centre of gravity unchanged whatever be the position of the motion. This makes the vibration of the car very small.

The tuning fork is therefore balanced. Being elastic, it obeys Hook’s law, “As the force, so the deflection.” And therefore, as we have seen, the vibrations of the fork are isochronous.

A fork with arms about six or seven inches long will make about fifty or sixty vibrations in a second. How are we to record those vibrations, and how keep the tuning fork vibrating?

A train of wheels is almost an impossibility, not perhaps so impossible as might be supposed, but still very difficult. So a different method is adopted. A little wire projects from one tuning fork arm. A piece of glazed paper is gently smoked by means of a wax taper, and is stretched round a well-made brass drum. The tuning fork is then put so that the little wire just touches the paper. The tuning fork is then made to vibrate by a blow, and while it is vibrating the drum is revolved. Thus a wavy line is formed on the drum by the wire on the tuning fork. If the tuning fork made fifty complete vibrations to and fro in a second there would be one hundred such indentations, fifty to the right and fifty to the left, and by these the time can be measured as you would measure a length upon a rule.

If an arm a b be fitted to move sideways when a little string c d is pulled, and be also provided with a small wire, so as to touch the drum, then it also will trace a straight line on the drum as the wire lightly scratches away the thin coating of smoke. Now, if it is suddenly jerked and flips back, then a little indentation will be made in the line, and if when we are to measure a rapid lapse of time a jerk is given at the beginning, and another jerk at the end of it, we should get a diagram like that in the adjoining figure, where a is the trace of the tuning fork, b that of the indicating arm. The time which has elapsed between the jerk which produced the indentation c and that which produced the indentation d will be about three and three-quarter double indentations of the tuning fork line, thus indicating three and three-quarter fiftieths of a second. It is easy to see how delicate this means of measurement can be made. With small tuning forks we can easily measure times to a thousandth part of a second, and much less if desired.

The jerk may be given by electricity if it is wished. When the current is joined a little electro-magnet pulls a bit of iron and gives a pull to the string. So extremely rapid is the flight of electricity that no appreciable time is lost in its transit through the wires, so that the impulse may be given from a distance. Thus we may arrange that when a cannon ball leaves a gun an electric impulse shall be given. When it reaches and hits a target another electric impulse is given. These make nicks in the tracing line on the drum from which we can easily compute the time that has elapsed between the leaving of the mouth of the gun and the arrival of the shot at its destination.

Such an apparatus is used in modern gunnery experiments. It is an elaborate one, but is based on the principle above described.

Drums are sometimes driven by clockwork, and tuning forks are also often kept vibrating by electricity, thus constituting very rapidly moving electric clocks. The arrangement is simple. An electro-magnet E is put in the vicinity of the arm of the tuning fork. A small piece of wire from the arm is in contact with a piece of metal Q, from which a wire runs to the electro-magnet, thence to a battery, and from the battery to the tuning fork, through which the current runs to the wire R. When the fork vibrates the arm, being bent outwards, makes the wire R touch Q. This at once causes the electro-magnet to give a small pull to the steel arm of the tuning fork, and thus assists the swing of the arm. The whole arrangement is exactly analogous to an electric clock, as may be seen by comparing Fig.71 with Fig.68.

There is another method of measuring rapid intervals of time which also merits attention. It is to let a body drop at the commencement of the period of time to be measured, and mark how far it falls in the time, and then find the time from the equation given previously,

S = 1/2 g t².

It is practically done by letting a piece of smoked glass fall and making a small pointer make two dots upon it, one at the beginning, another at the end, of the time to be measured.

An interesting adaptation of this method can serve as a basis of a curious toy.

Take a crossbow, with a bolt with a spike on it; fix it firmly in a vice so that the barrel points at a spot a on a wooden wall. On the spot a hang a cardboard figure of a cat on to a nail so contrived that when an electro-magnet acts the nail is pulled aside, and the cat drops. Thus let a be the cat, b the loop by which it is hung over the nail c, that is fixed to another piece of iron furnished with a hinge at c, so that when the electric current is turned on the nail c is withdrawn and the cat drops. Carry the wires from the electro-magnet and battery to the crossbow, and so arrange them that when the bolt leaves the muzzle one is pressed against the other, and contact made.

Now here you have an apparatus such that exactly as the bolt leaves the crossbow, the cat drops. Now what will happen?

When the bolt leaves the bow it is subject to two motions, one a motion of projection at a uniform pace in the direction of b a from the bow to the target.

But it is also subject to another force, namely that of gravity, which acts on it vertically, and deflects it in a vertical direction exactly as much and as fast as a body would do if dropped from rest at the same instant as the bolt leaves the bow. But the cat is such a body. Hence, then, since by the electric arrangement they are both let go together, they will both drop simultaneously, and thus will always be on the same level, and when the bolt reaches the wooden wall and has fallen vertically from a to c, the cat will also have fallen vertically from a to c, and the bolt will pin him to the wall. It does not matter how far you take the bow from the wall, nor how strong the bow is, nor how heavy the bolt is, nor how heavy the cat is, nor whether a b is horizontal or pointing upwards or downwards.

In every case, if only the barrel is pointed directly at the cat, then the bolt and cat fall simultaneously and at the same rate, and the bolt will pin the cat to the wall.

In trying the experiment the bolt should be pretty heavy, say half a pound, and have a good spike; but if carefully done the experiment will succeed every time. It enables you also to measure the speed of flight of the bolt. For if the distance of the bow from the wall be thirty feet, and the cat have fallen three feet when it is struck, then the time of fall is T² = v((2S)/g) = v(6/g) = ·43 seconds. But the bolt in this time went thirty feet; hence its velocity was thirty feet in ·43 seconds, or seventy feet per second.

Of course if you make the bolt heavier the velocity of projection will become slower, the time longer, and hence the cat will fall further before it is transfixed by the bolt.

My task is now at a close. I have endeavoured not merely to give a description of clocks and various apparatus for measuring time, but to explain the fundamental principles of mechanics which lie at the root of the subject.

May I end with a word of advice to parents?

There is a certain number of boys, but only a certain number, who have a real love for mechanical science. Such boys should be encouraged in every way by the possession of tools and apparatus, but in the selection of this apparatus the following principles should be borne in mind:—

First, that almost everything a boy wants can be made with wood, and metal, and wire, and string, if he has someone to give him a little instruction how to do it. A bent bit of steel jammed in a vice makes an excellent tuning fork.

Second, that he wants not toy tools, but good tools. If an expert wants a good tool, how much more a beginner.

Third, that he ought to have a reasonably dry and comfortable place to work in, and the help and advice of the village carpenter or blacksmith. Fourth, that he ought not to be allowed to potter with his tools, but to make something really sensible and useful, and not begin a dozen things and finish none.

Fifth, that the making of apparatus to show scientific facts is more useful than making bootjacks for his father or workboxes for his mother.

And, lastly, that a little money spent in this way will keep many a young rascal from worrying his sisters and stoning the cat; and when the inevitable time comes at which he must face the young man’s first trial, The Examiner, he will often thank his stars that he learned in play the fundamental formula S = 1/2 g t², and that he knows the nature of “harmonic motion,” the two most important principles in the measurement of time.

THE END.