Photographs of the clock mechanism in , the face of the Houses of Parliament in London, show coins on a tray attached to the pendulum being used to tune the oscillation period. Since we all know that mass doesn鈥檛 affect the period of a pendulum, why is this done?
鈥� Your questioner is correct in saying that the mass of a pendulum does not affect its period. However, the length of the pendulum does, specifically the distance between the pivot and the pendulum鈥檚 centre of mass. Adding coins to the pendulum moves the centre of mass slightly, changing the period.
Gareth Shippen, Bromsgrove, Worcestershire, UK
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鈥� A pendulum swinging under the force of gravity is an example of simple harmonic motion. It is easy to work out that the period is proportional to the square root of its length but independent of the pendulum鈥檚 mass.
A clock pendulum is designed to have a period appropriate to the train of gears linking (in most cases) the minute hand with the 鈥渋mpulsing escapement鈥�, which converts the oscillations into rotational motion. This period is associated with a length between the pivot and the centre of oscillation, where all the pendulum鈥檚 mass is concentrated. Addition of mass above the centre of oscillation will raise this centre, shortening the period. The converse also applies.
In the 1990s I had the pleasure of working for the clock-making firm , then responsible for Big Ben鈥檚 maintenance. The clock鈥檚 actual name is the Great Westminster Clock; strictly speaking, 鈥淏ig Ben鈥� refers to the hour bell.
The clock鈥檚 pendulum has a 4-second period and its centre of oscillation can be calculated to be about 3.97 metres from the pivot. The addition of a penny to the tray on the pendulum raises the centre of oscillation by 0.0368 millimetres 鈥� enough to cause a gain of 0.4 seconds per day. Removing a penny has the opposite effect.
The pendulum is complex, comprising a steel suspension spring, a steel/zinc/steel temperature-compensating structure, and a cast-iron 鈥渂ob鈥� attached to the arm, with an adjustable rating nut at the bottom to regulate the swing. The bob swings 3 degrees (about 190 millimetres) to either side of the vertical. The pendulum鈥檚 length, including the spring, is about 4.5 metres and the whole construction weighs 322 kilograms. It is obvious that it is impractical, even dangerous, to stop the pendulum, make an adjustment to the rating nut and restart it. The disturbance to the pendulum, and to the clock鈥檚 timekeeping, would be intolerable.
Edward John Dent and his adopted son, Frederick, who built the clock in the 1850s, built their large clocks to run fractionally slow so they could easily be made to tick at the correct rate by adding weights to a top tray. Pennies were used because of their predictable response.
For small swings, a pendulum鈥檚 period is independent of the size of its swing, but in Big Ben鈥檚 case the pendulum has a big amplitude so this does not hold. Errors of up to 13 seconds a day could occur if the amplitude changes significantly for whatever reason.
That said, I analysed Big Ben鈥檚 performance over several years and found it is well able to maintain an accuracy better than 1 second in 1 day more than 95 per cent of the time. Accuracy is maintained by noting and acting upon the difference, if any, between the first strike of the hour bell and the time from the 鈥渟peaking clock鈥� service provided over the phone. Records show the clock does not appear sensitive to changes in temperature or atmospheric pressure, responding only to the addition or removal of pennies as the clock鈥檚 attendants correct random drifts in timekeeping.
鈥淏ig Ben鈥檚 accuracy is maintained by checking it against the speaking clock service on the phone鈥�
So what causes these drifts? Well, there is evidence the zinc core supporting the bob has been deformed under the load and the position of the bob is lower now than when the clock was built. This has been corrected over the years by increasing the mass on the tray. This stretching means the pendulum鈥檚 temperature compensation is not as good as it once was, but there have been no obvious effects. Any effects arising from changes in atmospheric pressure are likewise too small to observe.
The British Horological Journal (vol 151, p 437), describes a pendulum clock designed by horologist Philip Woodward and owned by a Californian, David Walter, that is sensitive to earth tremors imperceptible to humans, and probably to traffic on a nearby California freeway as well. In a similar spirit, I would speculate that Big Ben can feel the twice-daily ebb and flow of the Thames, as well as vibrations from the tube trains passing underneath, not to mention MPs moving in and out of the chamber of the House of Commons just to the south.
John Warner, Burgess Hill, West Sussex, UK