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:
| Rod material | α (per kelvin, approx.) | Clock changes by, per 1 K warmer |
|---|---|---|
| Steel | 12 × 10⁻⁶ | loses about 0.52 s per day |
| Brass | 19 × 10⁻⁶ | loses about 0.82 s per day |
| Invar (iron-nickel alloy) | about 1 × 10⁻⁶ | loses about 0.05 s per day |
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.