# How two Trinity reverends let the great world spin

## When two men in Dublin replicated Foucault’s pendulum experiment, the results were impressive

Engraving in ‘L’Illustration’ of the first pendulum installed in the Panthéon in Paris by Foucault in 1851

Spectators gathered in Paris in March 1851 were astonished to witness evidence of the Earth’s rotation.

With a simple apparatus comprising a heavy ball swinging on a wire, Léon Foucault showed how the Earth rotates on its axis. His demonstration caused a sensation, and Foucault achieved instant and lasting fame. The announcement of the experiment read: “You are invited to see the Earth spinning. ”

A bob of mass 28kg was suspended from the dome of the Panthéon by a 67m wire. The pendulum swung through a diameter of about 6m, and the position was indicated on a large circular scale. Demonstrations were held daily, and attracted large crowds.

#### Pendulum mania

Following the demonstration, pendulum mania raged in Europe and the US, and the experiment was repeated hundreds of times. Many of these attempts were done without due care. The London Literary Gazette reported on several cases in which, “to the horror of the spectators, the Earth has been shown to turn the wrong way”. These errors probably resulted from elliptical bob trajectories due to incorrect starting conditions, or to stray air currents disturbing the movement of the bob.

The observed change in the swing plane of the pendulum is often said to be due to the Earth turning beneath it. This is roughly correct, but it is an oversimplification. The turning rate for a pendulum swinging at the North Pole is one revolution per day. At other locations the rate depends on the latitude, and at the equator there is no turning at all. Thus, after one day, the swing plane does not return to its original position. In Paris, the turning period is about 31 hours. The mathematical term for this phenomenon is “anholonomy”, and it has been a source of confusion ever since Foucault’s demonstration.

In September 1851, the American Journal of Science surveyed several pendulum demonstrations in Europe and America. It included details of the experiments carried out in Dublin by two reverends, Joseph Galbraith and Samuel Haughton. They were close contemporaries and life-long collaborators, both fellows of Trinity College. They were well-known for their many mathematical textbooks, which were widely used and earned them handsome royalties. They replicated the pendulum experiment shortly after Foucault had reported his findings. Their experiment was done at the engine factory of the Dublin and Kingstown Railway, where Samuel’s cousin Wilfred Haughton was chief engineer. They also analysed the effects of ellipticity of the trajectory, and derived a mathematical expression for the precession due to this effect.

#### Surprisingly accurate

The pendulum length for the experiments of Galbraith and Haughton was 35ft and its swing length 4ft. The bob was an iron sphere, 30lb in weight, with a downward-pointing spike to indicate its position on a scale. The theoretical precession rate at the latitude of Dublin is 12.07 degrees per hour. The mean rate observed in the experiments was 11.9 degrees per hour, which is surprisingly accurate considering the many possible sources of error.

According to an article in the Philosophical Magazine, “Messrs Galbraith and Haughton . . . have pursued their research with all imaginable precautions”. Their impressive results confirm this view.

Peter Lynch is professor of meteorology at University College Dublin. He blogs at thatsmaths.com

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