Heat and gravity: why clocks drifted

A pendulum clock told the right time when it was adjusted. Then summer came, and it began to lose time. Winter came, and it gained. Nothing was broken; the rod had changed length.

Most solids expand when heated. A rod of length L warms by ΔT and grows by ΔL = α L ΔT, where α is the coefficient of thermal expansion of the material. Because the period depends on √L, a rod that is longer by a fraction ΔL/L makes the clock slower by half that fraction:

change in rate ≈ ½ α ΔT

Take the numbers. Over one day, with 86 400 s:

So a steel-rod clock in a room that is 10 K warmer in summer than in winter loses about 5 s a day more. That seems small, but a precision clock is judged on fractions of a second, so a serious clockmaker could not accept it.

Compensation means building a pendulum whose effective length stays the same as the temperature changes. Two classic ideas:

• The mercury pendulum (George Graham, around 1721). The bob is a jar of mercury. When the steel rod grows longer and lowers the bob, the mercury also expands, and its level rises in the jar, raising the centre of the weight. If the amounts are chosen well, the two effects cancel.
• The gridiron pendulum (John Harrison, around 1726). Rods of two metals, steel and brass, are arranged in a frame so that the expansion of some rods lowers the bob while the expansion of the others raises it. Brass expands more than steel, so it needs fewer or shorter rods for the same cancellation.

A different cure was to change the material. In 1896 the Swiss physicist Charles-Édouard Guillaume discovered Invar, an iron-nickel alloy (about 36 % nickel) that hardly expands at all near room temperature. A rod made of it needs little or no compensation. Guillaume received the 1920 Nobel Prize in Physics for work on such alloys. Invar rods were used in the best observatory clocks in the early 1900s, and the same material appears in precise instruments today.

The other cause of drift was gravity itself. In 1671 to 1673 the French astronomer Jean Richer took a pendulum clock from Paris to Cayenne in South America, close to the equator. He found that the clock, adjusted to perfect time in Paris, lost a few minutes every day (accounts say about two and a half minutes). The pendulum's length had not changed enough to explain it. The conclusion was that gravity is slightly weaker near the equator.

We now know why. The Earth spins, so it bulges at the equator: the equator is about 21 km further from the centre than the poles. A point on the equator is farther from the centre, so gravity pulls a little less, and the spin also flings things outward a little. The result is g ≈ 9.780 m/s² at the equator and 9.832 m/s² at the poles. That small difference changes a pendulum clock's rate by about 230 s a day, which is an enormous effect for a timekeeper. A pendulum clock adjusted in London will not keep correct time in Quito, Ecuador, without being re-adjusted.

Richer's observation helped to show that the Earth is not a perfect sphere, and the same idea of "g depends on where you are" is why pendulum measurements were used to explore the shape of our planet.