Pendulum and Precision

The History of Timekeeping

Course 2 · Chapter 5 · Pendulum and Precision

A well-known story says that a young Galileo, sitting in the cathedral at Pisa, watched a lamp swinging from the ceiling and timed its swings against his own pulse, noticing that they took the same time whether the swing was wide or narrow (check; the tale is probably embroidered). Whatever the truth of the story, the idea behind it changed timekeeping. A pendulum has a natural rhythm of its own, set by its length. Harnessing that rhythm took the best clocks from losing a quarter of an hour a day to losing a few seconds. This chapter follows that leap in accuracy, and the people and the mechanisms that brought it about.

The Idea of the Pendulum

A weight on a string or rod swings back and forth at a rate that depends almost entirely on its length, not on its weight or, for small swings, on how far it swings. This property, called isochronism, is only approximately true, but for small swings it is true enough to be very useful (check the details of the physics).

The pendulum rule The time of one swing grows with the square root of the length. A pendulum about one metre long takes roughly one second to swing from one side to the other (check), which is why the "seconds pendulum" became a standard idea. A shorter pendulum swings faster; a longer one more slowly. To adjust a pendulum clock, you move the bob up or down.

Huygens and the First Pendulum Clock

Galileo studied the pendulum and, late in life, is said to have designed a clock using one, but the first working pendulum clock is credited to the Dutch scientist Christiaan Huygens, who built one around 1656 and published a description soon after (check the dates). Huygens' early clocks were reported to keep time to within about a minute a day, and later versions did better (check the figure). It was an enormous improvement on the verge and foliot of Chapter 4. Huygens also worked out the mathematics of the pendulum in detail, in a book published in 1673 (check).

StageTypical accuracyNotes
Verge and foliotPerhaps a quarter of an hour a day or worseSet against a sundial
Early pendulum clocksAbout a minute a dayWide swings; verge escapement
Anchor escapement and long caseA few seconds a dayNarrow swings; seconds pendulum
Best observatory clocksA fraction of a second a dayTemperature-compensated pendulums

All figures are rough guides only (check).

The Anchor Escapement and the Long-Case Clock

The early pendulum clocks still used the verge escapement, which forced the pendulum to swing through a wide arc, undermining the accuracy gain. In England in the later seventeenth century, an escapement shaped like a ship's anchor, now called the anchor or recoil escapement, was introduced, and the credit is often given to the English clockmaker William Clement or to Robert Hooke, though the matter is disputed (check). It let the pendulum swing through a small arc, where the rule of isochronism holds best.

A small arc allows a long pendulum, and a long pendulum needs a tall case. The result was the long-case clock, the grandfather clock of the popular name, which became a status piece of the British home. The name "grandfather clock" itself is said to come from a nineteenth-century American song (check).

Weights

Two or three weights hang inside the case, driving the movement and the striking. Long-case clocks run for a day, eight days or a month between windings.

Bob and rod

The pendulum hangs from a thin spring at the top. A nut under the bob lets the owner adjust the rate with a turn of the key.

Dial and hands

With the accuracy came the minute hand, and then the seconds hand, as clocks became precise enough to make them worth reading.

Fighting the Weather

A metal pendulum rod lengthens a little in warm weather and shortens in cold, so a clock runs slow in summer and fast in winter. The best makers devised compensation to cancel this. Two famous designs are the mercury pendulum, in which the expansion of liquid mercury balances the rod, and the gridiron, which uses rods of different metals (check the makers and dates). Changes in air pressure and humidity also have an effect, and observatory clocks were sometimes kept in sealed chambers.

Why accuracy mattered Better clocks did not simply make life tidier. Astronomers needed them to time the passage of stars across the sky, and navigators needed them to find a ship's position at sea. The question of longitude, in Chapter 6, is where accurate timekeeping changed history most plainly.

Clockmakers in Britain

From the seventeenth century, London was one of the leading centres of clockmaking, and the Worshipful Company of Clockmakers received its charter in 1631 (check the date). Names such as Thomas Tompion and George Graham are often cited among the finest makers of the following century (check). Edinburgh had its own guild of craftsmen, and clockmakers in Scotland made long-case clocks that survive in museums and houses (check the guild details).

Who invented what Disputes over priority were common in the age of the pendulum clock, with Hooke, Huygens and others each claiming credit for various devices. Historians still weigh the evidence, so treat any single-name attribution in popular accounts with caution.

Exercises

Exercise 1

A pendulum clock runs 30 seconds fast each day. Should you raise or lower the bob, and why? Explain in three sentences.

Exercise 2

Explain why a long-case clock is tall, and why a pendulum clock cannot easily be used on a ship.

Exercise 3

Make a pendulum from a string and a small weight. Time 20 swings with a short string and with one twice as long, and write two sentences on how the timing changed.

Quick Reference

  • Pendulum: swing time depends on length; small swings are nearly equal in time
  • Huygens: first working pendulum clock, around 1656
  • Seconds pendulum: about one metre long, one second per swing
  • Anchor escapement: small arc, better accuracy, tall case
  • Accuracy: from minutes a day to seconds a day
  • Temperature: compensated by mercury or gridiron pendulums
  • Guilds: London Clockmakers' Company, 1631
  • Check: the Galileo story, dates and attributions, accuracy figures and the origin of the name

Next chapter: Longitude and the Marine Chronometer, which covers why finding a ship's position needed an accurate clock, and the story of John Harrison.