COUNTING SECONDS

YOU CAN measure civilization by its timepieces. The higher the civilization of a community the more it appreciates the value of time and the more minutely does it measure the passage of time. The savage divides his day into but two periods: the period of light and that of darkness; the early Romans divided their day into eight watches, four watches of daylight and four of night, but the higher and more complex civilization became, the smaller became the subdivisions of time. People began to feel the need of carrying the time with them, and about 1500 A. D. watches came into use, but it was not until 1665 that watches began to be equipped with minute hands, and it was almost exactly a century later that they were equipped with a second hand. To-day time means so much to us that we will fight our way into a subway express, instead of riding more comfortably in a local train, merely for the sake of saving five minutes. The tiny second hands of our watches divide the day into eighty-six thousand four hundred parts, and in some operations we measure time intervals down to the thousandth part of a second. Only among the most highly civilized nations are timepieces carried by the common people.

It used to be that time was made for slaves, but now time has made slaves of us. Shift the hands of the clock and the whole nation is forced to change its habits.

Time-measuring mechanism is given early prominence in this book because clocks were among the earliest machines invented, and they furnish an example of the wonderful ingenuity of inventors before the dawn of the modern era of machinery. Naturally this chapter must be largely historical.

The first thought of measuring time came from the ancient astronomers and astrologers, who, in watching the motions of heavenly bodies, the sun by day and the moon by day and night, found it necessary to keep a record of these motions and sought about for some mechanical means of doing so. The studies of the old astrologers were closely associated with religion, and as a consequence the most advanced intellects were centered upon astronomical matters and incidentally upon horology. Fortunately the design and construction of mechanisms for measuring time were not considered beneath the dignity of the scientists of those early days. Mathematicians felt free to record their investigations in this branch of mechanics, and as a consequence of the early cooperation of science and mechanics in this field much real progress was made, and the development of timepieces was more rapid than that of any other machine.

TELLING TIME WITH A LEAKY BUCKET

The ancient Egyptians early felt the need of a better clock than the sundial, because it operated only on cloudless days and was absolutely worthless to tell off the hours of darkness. Realizing that time is a measure of motion, they sought for some slowly moving body whose motion could be used to measure time, and naturally they turned to water. The earliest form of clock consisted merely of a leaking bucket. Either the bucket was filled with water which was allowed to escape through a very tiny orifice, or else the heavily loaded bucket was placed in water and the water was allowed to leak into the bucket until it sank. The period it took for a bucket to run dry or for a bucket to fill and sink indicated a lapse of an hour or some other standard of time.

The idea of subdividing this period was a later development. As the water leaked out of a bucket, the water level descended, but unfortunately not at a uniform rate. The weight of water in a full bucket made the drops come faster than when the bucket was nearly empty. Consequently the time graduations on the side of the bucket had to be set farther apart at the top of the bucket than at the bottom. Various ingenious schemes were devised for maintaining a uniform discharge. In one type of water clock or clepsydra a conical bucket was used so that there would be a constant relation between the head of water and the volume in the bucket and the time graduations could be spaced uniformly.

THE REMARKABLE WATER CLOCK OF CTESIBIUS

The most remarkable clepsydrÆ were those invented by an old Alexandrian mathematician, Ctesibius, who lived about 250 years before Christ. Ctesibius introduced the siphon principle into his clocks, and also employed gear wheels and even a cord and pulley. Furthermore, he was the first man to employ jeweled bearings in a timepiece. The use of jewels in timepieces was reinvented in 1704 A. D. However, Ctesibius used his jewels in a very different way from that in which they are used now, as will be described below.

Figure 25 illustrates the most interesting clock he built and it was arranged to run year in and year out. The clock had a cylindrical face mounted on a hollow pedestal in which the mechanism was concealed. The column was divided off into twenty-four hours and a pointer that rose vertically marked off the lapse of time. But here he was faced with a serious complication. Hours in those days varied with the time of the year. A day from sunrise to sunset consisted of twelve hours. In summer, when the days were long, the hours were long, and in the short days of winter the hours were correspondingly shortened. To be sure, the variations in the length of the day are not so great in Egypt as they are in our latitude, because it is nearer to the equator; nevertheless there is a difference which the precise old mathematician had to take into account. In order to provide for variations in the hours, Ctesibius ran the lines spirally around the column and arranged his cylindrical clockface to turn slightly each day, so that in the winter months the clock hand or pointer moved over that part of the face where the daylight hour lines were closer together and the hours of night were farther apart, while in summer, the reverse would obtain. At the bottom of the column were two little cherubs. The cherub on the left was a sad little fellow who was constantly weeping. Tears trickled from his eyes and dropped into a basin. The tears passed into the hollow pedestal of the clock and gradually filled a cylinder formed in the base of the clock. A piston in this cylinder supported the other cherub. As the water gradually filled the cylinder this cherub was slowly raised and a wand he held in his hand pointed off the hours on the clockface. When the twenty-fourth hour was reached, a siphon came into play, which suddenly emptied the cylinder, permitting the pointer to drop. The siphon discharged its water into a small water wheel, which, by means of the system of gears, turned the column slightly to bring the hour lines in proper positions for measuring the time intervals of the next day. The column made one complete turn in 365 days. The jeweled bearings, referred to above, were placed in the eyes of the weeping boy, so that the holes that pierced them would not be enlarged by the constant wear of the water and thereby increase the rate of flow.

TIMING ANCIENT ORATORS

We have dwelt at considerable length upon this old clock of the pre-Christian era to show the ingenuity of inventors of that day, and also the careful study that was made of time by ancient mathematicians and astronomers. Of course water clocks were used before the time of Ctesibius. In fact, we read of them in the comedies of Aristophanes, written 400 B. C. Water clocks were used to limit the long speeches of orators at court, and in one place we find Demosthenes accusing a man of “talking in my water,” while at another time, when he was interrupted, he called to the officer to stop the water, showing that he valued every moment of time allotted to him for his speech.

In 807 Charlemagne was presented with a clock by the King of Persia. This consisted of an elaborate mechanism in which were all manner of wheels, and the clock would actually strike the hours. The driving power, however, was water.

But there were serious disadvantages in the use of water for the measurement of time. No great accuracy was ever obtainable with it, owing to the fact that its volume varied considerably with the temperature, and also with the dryness or moisture in the surrounding atmosphere. The idea of using a weight instead of water is claimed to have originated as far back as 990 A. D. The next important advance in the motive power of clocks was in 1500, when Peter Hele of Nuremberg invented the mainspring.

That was long before the pendulum made its appearance. The clock mechanism was slowed down and kept under control by what was known as a balance lever. (See Figure 26.) This was a horizontal lever mounted to oscillate in a horizontal plane. The lever was fitted with sliding weights, so that it could be carefully adjusted. The last wheel of the train of gears was provided with escapement teeth, somewhat similar to those used on our clocks and watches, but which would alternately move the lever this way and that. The inertia of the lever with the heavy weights on it was sufficient to prevent the mechanism from racing, and by this means, the motion was governed and slowed down, so that it measured time with a fair degree of accuracy.

DISCOVERY OF THE PENDULUM

The pendulum had an interesting origin. Galileo, while a student in Pisa in 1581, was attending a service in the cathedral one day when his attention was drawn to the swinging of a large hanging lamp. One of the attendants had drawn the lamp toward him, so that he could reach it more readily to light it. When he let go the lamp began to swing slowly back and forth, and the observant young student noticed that although the oscillations gradually slowed down the period of oscillation was constant. He had no watch with which to measure the length of the period, but being a medical student he knew that he had a fair timepiece in his own heartbeats, and so by counting his pulse he proved that it took the lamp just as long to complete each oscillation when it swept through a long arc as when it died down to but a few inches. He made note of this peculiar action and began experimenting with pendulums of different lengths. Then it occurred to him that if he could time the pendulum with his pulse he could time his pulse with a pendulum. So he devised a pendulum whose length could be adjusted until its oscillation would coincide with the throb of a patient’s pulse, and then the length of the pendulum would give him the rate of the pulse beat. The invention was seized upon by the medical profession of that day, and the pulsilogia, as it was called, became an indispensable instrument for physicians.

The idea of using the pendulum to control the action of the clock also occurred to Galileo, and in later years, after he had lost his sight, he passed the idea down to his son, Vincent. However, it is generally conceded that the credit for introducing the pendulum and doing away with the balance lever belongs to Christian Huygens, the Dutch mathematician, whose first pendulum clock dates back to 1659.

About the same time Dr. Robert Hooke invented the balance spring which made it unnecessary to use the pendulum in portable timepieces. Prior to that watches were fitted with balance levers and they gave a great deal of trouble, because the time varied with the position in which they were carried. But the balance wheel overcame all these difficulties and made it possible for a person to carry an accurate timepiece in his vest pocket, although the early watches were very bulky mechanisms.

THE FIRST SHIP’S CHRONOMETER

The importance of having accurate timepieces aboard ship was felt as far back as the time of Columbus. When ships began to go out beyond the sight of land, it was highly important that they be equipped with some means of locating their position at sea. By noting the elevation of the sun at noon with a sextant it was possible to determine the latitude of the ship, but there was no means of determining its longitude, except by dead reckoning, that is, using a log to measure the speed of a ship, and estimating its position by calculating the number of miles it had traveled since leaving port. If ships could be provided with an accurate timepiece which would keep the same time as that of some fixed observatory, it would be possible definitely to locate the position of the ship east or west by noting how fast or slow the sun was at noon on the particular day on which the observation was taken. This use of the chronometer is common in these days, but up to 150 years ago there was no timepiece sufficiently accurate to permit a navigator to tell with any certainty just where he was.

It was John Harrison, the son of a Yorkshire carpenter, who was the first to build a chronometer worthy of the name. A prize of 10,000 pounds was offered by the British Parliament for anyone who could invent and sell a chronometer which would enable a ship to take a voyage from England to any of the West Indian islands and back and keep track of the longitude within one degree. If this could be defined within two-thirds of a degree, the prize would be 15,000 pounds. Harrison made a bid for this prize, and after years of effort and patient labor, he succeeded in being granted a trial. His son, William, was sent on a ship to Jamaica with the now celebrated chronometer, which was mounted on a large cushion. The instrument was constantly attended by the young man, its position being adjusted from time to time to suit the “lie” of the ship. When the ship was eighteen days out, the vessel was estimated by dead reckoning to be 13° 50' west of Portsmouth, but the chronometer indicated the position as 15° 19'. The timepiece was immediately condemned as worthless, but William Harrison had not lost faith in the instrument, and insisted that if the ship continued on the same course, a certain island, if properly marked on the chart, would be seen the following day. True to the prediction, the next morning at seven o’clock the island appeared. By means of his chronometer William Harrison was able to predict the appearance of the other islands, and at the end of the voyage, which occupied sixty-one days, the chronometer was only nine seconds slow. When he returned to Portsmouth, after an absence of five months, the error of the chronometer was only one minute and five seconds, giving an error in distance of only eighteen miles, whereas thirty miles was the margin of error allowed by the prize conditions. Such accuracy seemed so incredible that the chronometer had to be tested on a second voyage, during which it was kept under lock and key and when William Harrison had to wind the instrument he was obliged to do so in the presence of two witnesses, lest he move the hand of the chronometer surreptitiously. At the end of the second voyage there was no further doubt that Harrison was fully entitled to the prize. Chronometers soon came to be used extensively, until now they are one of the most perfect of machines made by man, and operate with an accuracy that is almost incredible. Usually a ship is provided with several chronometers, so that one may be used as a check upon another. They are mounted in ball sockets and gimbal joints, so that they are not affected by the roll of the ship, but always lie in a horizontal position.

MARVELOUS PRECISION OF MODERN WATCHES

While we may well marvel at the precision of the chronometer, it is equally marvelous, if not more so, that we may equip ourselves for a few dollars with a timepiece which is so wonderfully accurate as to vary little more than a second per day. If one took the pains to regulate his watch carefully, any of the better makes could be adjusted to such accuracy.

There is nothing very mysterious about the mechanism of a watch. It consists merely of a train of gears which slow down the motions of the mainspring to a convenient speed; and these gears moreover keep the proper relation between the hour and minute and second hands. But when we reflect that a small watch possesses a tiny second hand which travels something like ten miles in a year, and that if carefully regulated it will not vary from that of another watch in the whole journey by more than six or eight inches at the most, we certainly have a reason to marvel. There are 86,400 seconds in a day, and a watch is usually arranged to make five beats per second or 432,000 per day. The interval between beats must be adjusted with such minuteness that one beat must not differ from another by 1/86000 part of a second, else the watch will register more than a second fast or slow at the end of a day. And yet watches capable of such precision are being turned out daily by the thousands. Of course, such perfection would be absolutely impossible without the use of extremely accurate machine tools. It would have been impossible as long as we had to depend upon a watchmaker to make a watch by hand.

THE PACEMAKER OF A WATCH

If we look at the works of a clock the most conspicuous feature is the rapidly oscillating balance wheel which, by the way, is the most important part of the watch, for it governs the release of the power stored up in the spring.

It controls the escapement which brings the whole mechanism of the clock to a standstill five times each second—in fact it is the pacemaker of the watch, for it gives the watch a step-by-step movement and fixes the rate at which the steps are taken.

The last wheel of the watch train is what is known as an escape wheel. It is formed with teeth of an odd shape, such as shown at A in Figure 27. These teeth are engaged by a pair of pallets B and C, carried by a three-armed lever D. The pallets are usually bits of sapphire or similar hard stone to prevent wear. The third of the lever is slotted at its extremity to engage a sapphire pin E, carried by a disk F, which is mounted on the staff of the balance wheel. The escape wheel A revolves in the direction of the arrow, being impelled by the mainspring acting through the train of gears. One of the teeth of this wheel engages the pallet B, causing the lever D to swing on its axis and push the sapphire pin E toward the left, thereby giving the disk F an impulse in the same direction. Here a delicate coil spring, known as the hairspring, comes into play. Without the hairspring the parts would stand still, the escape wheel being blocked by the pallet B. The hairspring is attached at one end to the shaft or staff of the disk F and the other to the frame of the watch. It tries to hold the disk F in a fixed position, but is disturbed by the action of the escape wheel and is constantly oscillating the disk in its effort to bring it back to its normal position. When the disk swings over to the left the pallet B is clear of the teeth of the escape wheel. This releases the escape wheel and it springs forward in the direction of the arrow, but before it can move through an interval of one tooth it is arrested by the second pallet C, which has been projected into its path by the swing of the lever D. The lever swings back until the pallet C clears the escape wheel and the pallet B engages the next tooth. And so the action continues, the lever swinging back and forth and at each complete oscillation releasing one tooth of the escape wheel.

The hairspring takes up the shock of this intermittent motion and a balance wheel carried by the staff to which F is fastened steadies the oscillatory motion of the lever D. A watch is full of microscopic parts. In a small timepiece there are machine-made screws so small that without the aid of a magnifying glass one cannot see the screw threads cut upon them. But the most marvelous part of the whole watch is the delicate hairspring and the means of adjusting its tension and compensating for its expansion and contraction with changes of temperature.

INANIMATE MATTER IN CONTINUAL MOTION

When working with minute intervals of time many factors must be considered which are not even thought of in machines of grosser proportions. It never occurs to the man in the street that not only the animate world but the inanimate as well is in ceaseless and variable motion. If our eyes were capable of taking in minute microscopic details, we should see that everything is expanding or contracting, swelling or shriveling, twisting and warping in response to the atmospheric changes. Our steel bridges and skyscrapers are in constant motion; solid concrete dams must be provided with expansion joints; the Washington Monument goes through a diurnal gyration in response to the sun’s rays. Of course all this motion is almost immeasurably small. A bar of steel a mile long will expand ? of an inch for every increase of a degree Fahrenheit in temperature. The expansion of a hairspring, which may be nine or ten inches long, is infinitesimally small and yet this must be considered by the watchmaker. We must remember that the escapement mechanism divides the day into 432,000 parts, each of which contains some minute error, for absolute perfection is impossible, and if we add up all these 432,000 errors they must not foot up to more than a second per day. If the hairspring expands ever so slightly its power is weakened, but this loss of power is compensated by an ingenious form of balance wheel. The rim is in two parts, half of it being attached to one spoke of the wheel and the other half to the other, as shown in Figure 28. Each half rim is formed of two strips of metal, an inner strip of steel, and an outer strip of brass fused together. Brass expands and contracts almost twice as much as steel, and hence when there is a rise of temperature the rim sections tend to curl in, bringing their center of gravity nearer the center of the wheel and making less of a load for the weakened hairspring to move, while on the other hand, when the spring is contracted by cold, the rims spread out slightly, giving it a greater load to oscillate. The weight of the balance wheel is thus automatically adjusted against variations in power of the spring.

Aside from this automatic variable adjustment, the balance wheel must have a primary permanent adjustment. The rim of the wheel is loaded by means of small screws. Screws placed near the free ends of the rim sections will have a greater inward or outward play as the rim contracts and expands, and by their locations in different positions on the rims the balance wheel may be adjusted with great accuracy to compensate for temperature variation in the hairspring.

THE PENDULUM ESCAPEMENT

In the case of clocks such delicacy of adjustment is hardly necessary. Pendulum clocks, if they are to run accurately, must have their pendulums automatically adjustable for variations in temperature, because the longer the pendulum the more slowly it oscillates. Many years ago a grid type of pendulum was invented in which various alloys were used, which reacted one against the other and preserved the center of gravity always at the same distance from the center of oscillation. The action of a pendulum movement is similar to that of a balance-wheel movement described above. The pendulum operates a pallet lever similar to that shown in Figure 29. The teeth of an escape wheel, which are commonly somewhat different from those of the watch movement, strike the pallets of the pallet lever, and the escape wheel is intermittently stopped and permitted to proceed. The pressure of the escapement teeth against the pallets is just enough to keep the pendulum swinging and the speed of the clock is regulated by lengthening or shortening the pendulum.

We have added little to clock or watch movements in recent years. About the only conspicuous modern invention is the torsion pendulum. The pendulum in this case is a heavy horizontal disk suspended by a wire, and the disk rotates first in one direction and then in the other, twisting and untwisting the wire. The advantage of this pendulum is that the oscillations are very slow, and hence it is possible to keep the clock going for a year at a single winding.

The electric regulation of clocks is another important improvement. A clock need not be a very perfect timepiece, but if provided with an electric regulator its hands are brought up to the correct time every hour in response to an impulse sent from an accurate master clock which in turn has its time corrected daily from the National Observatory in Washington.

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