Clocks

This page has been revised under the stimulus of making a Nixie Clock


I have tried to understand how mechanical clocks worked, and this paper is a conversation with myself on the subject. I discovered that most books on clocks treated them as objets d'art (which they indeed were) and not as mechanisms, the 'works' being accessory. There are excellent references on the history of clocks and time, but the technical explanations are not satisfying. Books on the history of technology described clocks, but were deficient in explanation, or gave bad explanations. There must be good treatments of mechanical clocks somewhere, and perhaps I will find one eventually. The references below show the sources I have found most enlightening.

I wear on my wrist daily a clock that shows the time with hands, does not require winding, and is at least as accurate as the best clocks available up to about 1900, varying less than a second per day. The amazing thing is that it costs less than 20. There exist clocks now that measure time directly in terms of the definition of the second as 9 192 631 770 periods of a certain radiative transition in the Cs133 atom, varying less than one second in 30,000 years. These are not mechanical clocks, and I thoroughly understand how they work.

The passage of time can be marked by natural processes, the most useful of which are the steady and reliable motions of the heavens. The daily passage of the sun, the wheeling of the stars at night, the monthly excursion of the moon and the yearly journey of the sun are the basic movements by which time and date are reckoned. The planets are too unreliable and inconstant for this purpose, but are an amusing accompaniment. Few people these days can read these clocks.

One can also contrive processes that proceed at a constant rate, such as the flow of liquid or sand through an orifice, or the combustion of a lamp or candle. These processes served at night, satisfactory to mark the progress of the hours of darkness, and easier to read than the stars. In China, a wheel was driven by water filling buckets one by one, each bucket tipping and emptying as it was filled to its capacity, and releasing the wheel to rotate the next bucket into position. This escapement drove an elaborate astronomical display, so that the portents of the heavens could be interpreted without seeing the sky. Clepsydras in the West indicated the hours appropriate to every day in the year, and operated delicate mechanisms to ring alarms and move automata. Clepsydra, incidentally, is from the Greek for water-stealer, referring to the surreptitious disappearance of the liquid.

Clocks were much better-developed in antiquity than is commonly recognized, often with associated mechanisms of great ingenuity. They were all based on the regular flow of liquids, as in the clepsydra, or on the regular rate of burning of oil. I cannot determine the orgin of the sand-glass, which was so frequently used on shipboard to measure the passage of time. Ships are very unfriendly to clocks of most classical types (including sundials!) because of their constant motion. Fortunately, unless you are navigating by time, the exact time is of little consequence aboard ship. If you are navigating by time, then you need the exact time, not some rough approximation, which is worthless.

The origin of the mechanical clock is traced by one writer to the necessity of knowing when to make Christian religious observances, which took place at arbitrary hours, as well as at easily-recognized times such as dawn and dusk, which were sufficient for most religions. This argument is specious and cannot be supported. Monasteries did not lack for labour to sit up with a clepsydra or sandglass and bang on the bells as required. Precision was totally unnecessary and labour was cheap.

The silent clepsydra could be arranged to issue an audible alarm at the proper season, something that had been done already in antiquity. One ingenious way to do this was to use a falling weight to drive a hammer that struck the bell repeatedly. The ingenious contrivance for this purpose consisted of a crown wheel, rotated by the falling weight, whose teeth drove the pallets of a verge backwards and forwards. This verge was connected to an arm with a hammer on the end that struck the bell. When the mechanism was released by a trip, the bell sounded until it received attention.

There is, of course, no evidence for this at all: it is merely a plausible story, like so many that are taken to be history of technology. Nevertheless, it gives a motive for the creation of such a mechanism, and such mechanisms have indeed been used to strike bells. The interesting thing is that this application could have come first, before its use as an escapement. Our word clock is from a Latin word for bell (glocca), so there is a very close connection. This mechanism, the verge and foliot, is a mechanical relaxation oscillator, the balance beam or foliot being positively driven in one direction, brought to a stand, and impelled in the other direction at the end of each half-period. The mechanism is illustrated in the Figure on the right.

The clock resulted from the observation that the crown wheel rotated at a constant rate that could be adjusted by moving the weights on the foliot towards or away from the axis of rotation, and that this regular rotation could be transmitted through a chain of spur gears to give any rate of rotation of a hand or other indicator that was desired, and even to trigger the ringing of the bell. The ingenuity sufficient for this advance was certainly equal to the problem of making the bell ring a certain number of times depending on the hour each time it was triggered, and so we have the tower clock that strikes the hours. Such clocks are recorded from around 1300, which is a good date for the introduction of clocks showing equal hours (whether water or mechanical). If adjusted daily, perhaps at local noon, they would give good service and indicate the time to within a few minutes all day. The mechanisms originated earlier, since it is improbable that everything burst on the scene fully developed. The desire for an impressive public display of the hours is a better motive for the development of mechanical clocks.

These clocks required frequent correction because the foliot does not have a natural frequency. Its rate of oscillation depends on the strength by which it is driven. Fortunately, the force provided by a falling weight is constant, and this made the clocks practical. Temperature and weather differences, the odd insect, and other influences made the timekeeping inaccurate, but it was close enough that the clocks were soon depended upon. At any rate, they could be made decorative, putting on hourly displays in the town square to astound the yokels. The ticking of a clock thereby entered human experience. Each time the verge released one tooth of the crown wheel, the wheel jumped by one tooth space until suddenly stopped by the other pallet, making a tick. This motion was transmitted to the hands.

Every discussion of clocks mentions Galileo and the pendulum, specifically that he found the period of oscillation to be approximately independent of the amplitude of vibration, and that somehow this was the key to the use of the pendulum in clocks. Sometimes they seem to believe that Galileo invented the pendulum. In fact, the important thing was that a pendulum has a natural frequency at all; that it is independent of amplitude is much less important. Also, the frequency does not depend on the weight of the pendulum, only on its length (and the acceleration of gravity). In fact, the period T = 2π(L/g)1/2, so a pendulum 39 inches long beats seconds; that is, its period is 2 seconds.

Although Galileo suggested how a pendulum could be used to control an escapement, Christiaan Huygens was the first to make a practical pendulum clock, by allowing the verge to drive a pendulum instead of a foliot. Huygens used the famous cycloidal cheeks on the pendulum suspension to render the pendulum isochronous at the large amplitudes of vibration that resulted, but this was futile, since the pendulum was forcibly stopped and reversed at each end of its travel. Its natural period did have considerable effect in making the rate of the clock more constant, however. A pendulum does not keep time well when it is ordered about so peremptorially.

Now that the verge did not have to drive a heavy foliot, and was only required to sustain the oscillations of a pendulum, which would naturally reverse itself at the ends of its path by the action of gravity, the escapement could be redesigned accordingly. The result was the recoil escapement, in which the verge was replaced by the anchor (named from its shape) and the crown wheel by the escape wheel, which looked more like a spur gear than a crown with rays. The travel of the pendulum could be greatly reduced, and the pendulum made longer and heavier so that its driving by the escape wheel had much less effect on its motion. The recoil was retained from the verge and foliot, giving the pendulum a little push at the ends of its motion. This made the clock run in spite of friction and other impediments, and apparently survived in inexpensive clocks for very many years, long after better escapements were available.

The next step was to eliminate the impulse at the end of the pendulum swing altogether, and to give the little push at a better part of the cycle, when it would influence the oscillation less. Graham's dead beat escapement of 1725 succeeded in this. The pallet simply slid on its dead face along the face of the escape wheel while the pendulum completed its swing and returned. These faces are concentric with the axis of the anchor. The impulse was given when the pallet left the wheel, the tip of the wheel tooth giving a push to the pallet. Then the pallet on the other side would hit the dead face on the next tooth, and so on. This is illustrated in the Figure, where the pallet on the left is about to leave a tooth and receive an impulse on the green face, while the pallet on the right will catch the next tooth on its red face, and allow the pendulum to continue without moving the escape wheel backwards. With this escapement, the pendulum could swing freely, except for a small push on each excursion, which was very constant in amount and timing. This finally resulted in clocks that varied by no more than a second a day by 1750.

The dead-beat escapment was accurate enough to reveal the effect of temperature on the length of the pendulum. Clocks ran fast in cold weather, slow in hot weather. The differential expansion of metals was used to make a pendulum that did not alter in length. Harrison used steel and brass, but mercury was also used, as well as zinc, which expands even more than brass. It is characteristic that each advance in the accuracy of clocks has revealed a new source of inaccuracy, which then was overcome, leading to still further improvement.

The pendulum clock is a stationary clock (the verge escapement could be arranged for portability). Some other suitable oscillator must be found if a clock is to be carried on the person or in a vehicle. Huygens discovered this when he attempted to make a clock that would work at sea. The question of the longitude was already of great importance. Robert Hooke invented the balance wheel and hairspring, which oscillated reliably even while being moved about (Huygens' invention of 1675 was probably independent). This was really a development of the foliot, rendered oscillatory by the spring.

A spring and mass also had a natural frequency, whose period is given by T = 2π(m/k)1/2, where m is the mass and k the spring constant (ratio of force to extension). It could drive, and be maintained by, a lever operating the anchor of a dead-beat escapement. Thomas Mudge developed this escapement in 1755. A peg on the axis of the balance wheel would drive the end of the lever one way or the other, where it would be maintained by the escapment until the wheel completed its oscillation and returned to drive the lever in the other direction. This, together with the spiral mainspring and jewelled bearings (1704), made accurate watches possible. It seems that among the first portable clocks were the famous Nürnberger Eierlein, appearing around 1450, with spring drive and verge escapement. They can have given only approximate time. In contrast, Harrison's No. 4 of 1762 was the first watch accurate enough to be used for navigation.

A weight-driven clock has the great advantage that the driving force is precisely constant. If a spring is substituted, the force decreases as the spring unwinds, causing the clock to run more slowly. This was countered by the fusée, a conical piece that equalized the force by varing the radius of action as the spring unwound. Lever-action watches are independent enough of the amount of the driving force to render this unnecessary.

A less disturbing way to maintain the pendulum appeared in Shepherd's clock of 1852. A small weighted gravity lever was held up by a catch released by the pendulum when it moved in one direction past a certain limit. This lever fell and gave the pendulum an accurate push. In Shepherd's clock, the pendulum closed electrical contacts that drove an escapement wheel through electromagnets, and also reset the gravity lever. This was, indeed, an electrical clock and required no winding. The pendulum moved freely, except for operating the contacts, the gravity lever latch, and the impulse of the gravity lever, all of which were very reproducible. This clock was not more precise than other all-mechanical clocks, but the electrical signals were very useful, for correcting slave clocks, or for dropping time balls.

The ultimate in mechanical clocks was the Shortt free-pendulum clock, which appeared in 1925. The master pendulum vibrated completely freely in a low vacuum, except for once every thirty seconds, when a slave clock provided a pulse that allowed the master pendulum to release a gravity lever at a fixed point in its movement. The gravity lever maintained the master pendulum, and also closed a contact that sent a synchronizing pulse back to the slave clock. The master pendulum closed no contacts itself, only receiving a light impulse at a time where it would have the smallest influence on the period. The slave clock ran a little slow naturally, and its pendulum was stopped short by the effect of synchronizing pulse, so that it was jolted into the correct time. The slave pendulum itself also closed no contacts, but did ratchet the count wheel forward so that an impulse was sent to the master pendulum every thirty seconds by the falling of its own gravity lever. This clock was accurate to a few milliseconds a day, enough to reveal the seasonal variations in the earth's rate of rotation. The gravity lever of a slave clock is shown in the Figure. That of a master clock was similar, but there was no count wheel. When the lever fell, a contact was closed that moved the resetting lever, restoring the lever to its normal position latched up. On the slave clock, this also arrested the pendulum. The slave clock ticked every second, the master only twice a minute, though the pendulum swung constantly. The pendulums were made from Invar, an alloy with a zero thermal expansion coefficient.

In keeping time, clocks served as a kind of flywheel between astronomical observations, which were still made daily when possible, and used to correct the mechanical clocks. The Shortt clocks revealed that the earth was not a perfect timekeeper. Since the year is more constant than the rotation of the earth, the second was redefined in 1956 as 1/31 556 925.9747 of the tropical year 1900, instead of 1/86 400 of a mean solar day. This gave a constant second, but it was time-consuming to determine. Quartz oscillators were now used in place of pendulums, and were refined until they varied less than a second every 3 years or so. Atomic clocks were introduced in the 1950's, and achieved a great advance in accuracy, so much so that the second was again redefined in 1967 in terms of the Cs clock, finally losing its connection with astronomical observations. However, time still is arranged so that it is closely correlated with astronomical events.

When comparing a standard clock with a time signal or astronomical observation, the hands of the clock are not moved. It is simply recorded how fast or slow the clock is, and this information may be written on a card. If the clock steadily gains or loses, then it must be regulated by changing the effective length of the pendulum, usually by moving a threaded nut.

Since accurate time was important in American railway operation, reliable pocket watches were required for the employees concerned. These watches were inspected regularly by a watchmaker, who observed their condtion and rate of running. There were strict limits on the amount of time the watches could gain or lose in a month, and employees were not permitted to adjust the hands of the watches themselves, unless the watch stopped inadvertently. Typically, a watch had to run with less than 30 seconds variation in a week (50 ppm). A record was kept of the running of each watch. Among other requirements, hunting cases were not allowed, all numbers had to be Arabic and shown, and there were specifications of the quality of the movements, including number of jewels. Time was received by telegraph at the same hour each day, and watches had to be compared with a standard clock before going on duty each day.

A quartz clock is an electronic clock that is regulated by a piezoelectric quartz crystal. Typically, a 32,768 Hz oscillator is used, which divided by 215 gives a 1 Hz "tick." In a wristwatch, this "tick" drives the second hand directly through a small ratchet solenoid. The minutes and hour hands are driven by spur gears, as in a mechanical watch. Such a mechanism, made from off-the-shelf components, is accurate to better than 10 ppm, rivalling the best mechanical watches, which are very much more costly and troublesome.

A clock with a digital display simply counts the seconds ticks, 60 to each minute, 60 minutes to each hour, and 24 hours per day. It is easy to construct such a clock with available digital logic, displaying time from 1.00 to 12.59 hours, or from 00.00 to 23.59 hours. Electronic clocks are exactly analogous to mechanical clocks; each have an oscillator, dividing train, and display.

References

Derek Howse, Greenwich Time (Oxford: Oxford University Press, 1980). Highly recommended. Appendix III is on escapements.

D. S. Landes, Revolution in Time (Cambridge, MA: Harvard Univ. Press, 1983). A history of time measurement. Appendix A is on escapements.

Sigvard Strandh, A History of the Machine (New York: A&W Publishers, 1979). Chapter 2, pp. 48-52.

Anon., How Things Work, (London: Paladin Press, 1972), from the German original of 1963. pp. 214-219.


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Composed by J. B. Calvert
Created 8 July 2000
Last revised 7 July 2002