The pendulum and the shape of the planet

The 'researchers' of the Internet, the climate clowns who cherry-pick data to prove their dopey obstructionist theories, commonly demonstrate how little they know of the ways that scientists can measure and discover things.

With the exception of the Flat-Earthers (and even climate clowns hate it when they are treated as latterday Flat-Earthers!), we all believe that the Earth is pretty much a sphere, but pretty much leaves wiggle room, and strange as it may seem, it was an upgraded version of a playground swing that revealed the precise shape of our globe, which some people likened to a watermelon stood on end, while others thought was more like a pumpkin.

This is the story of how they did it, almost three centuries ago.

*

In some parts here, the main measurements have been converted to their modern equivalents. The unconverted unit called the ‘line’ is 1/4 of a barleycorn, a twelfth of an inch, or about 2 millimetres.

The barleycorn measurement turns up in the oddest of places. Edward I, King of England, decreed in 1305 that “three grains of barley, dry and round, make an inch”, and if you change from a size 7 shoe to a size 8 shoe, the difference in length is one barleycorn.

*

Now to our story:

In 1672 Jean Richer reported that the period of a pendulum varied with latitude, and Isaac Newton said that Richer’s variation of pendulum was due to equatorial bulge, a comment offended the French. By this time, nobody thought the world was a perfect sphere any more, but France and England disagreed, and national honour was at stake.

Isaac Newton had proposed that the Earth was an oblate spheroid. If this were so, argued Newton, the precession of the equinoxes (we may or may not come to those later) could be explained. French scientists had taken some sloppy measurements, getting results which suggested that the Earth was more like a watermelon on its end than a pumpkin.

The French Académie set out to determine the truth of the matter by experiment, measuring a degree of latitude in Lapland and in Central America. Among those who went to Lapland was Pierre de Maupertuis, while the American group included Pierre Bouguer and Charles La Condamine.

Richer’s pendulum clock had been accurate in Paris but it lost two and a half minutes each day at Cayenne in Africa, closer to the equator. Clearly, more data were needed, and scientists were rushed to different places in 1735, mainly in South America, a mere 63 years after the comment. Newton had died in 1727, but the French still wanted to show him up, the insolent upstart!

We know Pierre Bouguer’s name today mainly in the form of Bouguer anomalies. This name commemorates his pioneering work in the Americas. When the acceleration due to gravity is measured very accurately, small local fluctuations can indicate equally local deposits of high or low density mineralisation — these fluctuations are the Bouguer anomalies.

Bouguer spent much of his life studying gravitational effects. In 1740, he estimated the value of G, the universal gravitational constant, using a mountain as an attracting mass. A method such as this can only be as accurate as the information the enquirer has about the interior of the mountain, and there were other problems which Bouguer could not have known about. We will ignore those for now, but the key word is isostasy, if you want to know more.

The French work in Central and South America between 1735 and 1743 was to measure the length of an arc of one degree of latitude at the Equator. Other scientists went to Lapland to measure a close-to-polar degree. Any difference in the lengths would reveal whether France or Britain had the right shape.

Inserted without comment.

Here, from the French Académie des Sciences Memoirs, is part of a letter from Bouguer to René de Réaumur in 1735, followed by part of Bouguer’s 1749 report of his findings.

I have made here [in San Domingo] a simple pendulum of steel which I have made as invariant as possible. It has a bob of [12 kilograms], about [12 centimetres] in diameter and [3 centimetres] deep. To keep it swinging true, I have put on the rod a crossbar of iron to serve as an axis, at right-angles to the rod. The instrument is mounted on a tempered steel knife-edge on two steel springs. These two springs are mounted on a copper plate in which there is a hole for the rod. The plate rests on a stool [1.5 metres] high, and is levelled by three screws…

We used the barometer that we set up to study the balance between the weight of the mercury and the air in all the accessible parts of the atmosphere. We saw how many feet we had to rise or descend to make the mercury change height by one line. It is then necessary to find the specific weight of air that balances other bodies. In this way, I have found by comparison with copper that on the top of Pichincha, there is a loss from unity of 1/11 000. Now it follows that the weight of my simple pendulum also loses 1/11 000 part of its weight. This loss produces a similar reduction in the restoring force, and naturally, I found the pendulum to be slow by 1/11 000. To correct this loss, it was necessary to adjust the pendulum’s length by 4/100 of a line…

Translation of the translation: Bouguer had an accurate pendulum, mounted on a wooden stand (the stool) and it was adjustable. He used a barometer as a way of measuring altitude. By timing the pendulum, he could get a measure of g at different heights above sea level.

The degree-measuring expeditions succeeded in proving Newton correct, but one of the more lasting effects came from La Condamine’s explorations while he was there, travelling over a large part of South America, and then 5000 km down the Amazon.

When he returned to Europe, La Condamine brought with him what the locals called cauchu, and the French still call caoutchouc. Thanks to Joseph Priestley, we still call it ‘rubber’, because it can be used to rub out pencil marks, and what is an eraser in some English-speaking countries is still called a rubber in others.