In 1735 the French Academy of Sciences did something no scientific body had done before. It sent two expeditions to opposite ends of the world, at enormous expense, to settle a disagreement about a number that nobody could see and that had no obvious practical use: whether a degree of latitude is longer near the pole than near the equator.
One team went to Lapland, above the Arctic Circle. The other went to the Viceroyalty of Peru, in what is now Ecuador, and spent ten years there. The question they were sent to answer was whether the Earth is squashed or stretched, and behind that lay a larger one, which was whether the physics in Newton’s Principia described the real world or only an elegant possible one.
Two Predictions, Two Countries
Newton’s argument, set out in Book III of the Principia, is a thought experiment about a rotating fluid. Imagine two channels of water bored to the centre of the Earth, one from the pole and one from the equator, meeting in the middle. For the planet to be in equilibrium, the two columns must balance. The equatorial column is carried around by the rotation and is therefore effectively lighter, so it has to be longer. The Earth must bulge at the equator and be flattened at the poles, and he estimated the flattening at about one part in 230.
The French position came from Descartes, whose physics explained gravity as the effect of vortices of subtle matter swirling around the Earth. Vortex reasoning suggested a body elongated towards the poles, like an egg standing on end.
This was not merely a difference of opinion. It was a national division. Cartesian physics was the establishment view in France, Newtonian physics was English, and the two systems disagreed about what gravity was, not just about the answer.
Worse for the Newtonians, the available measurements supported the other side. Jean Dominique Cassini and his son Jacques had surveyed the meridian through Paris from Dunkirk to the Pyrenees and concluded that a degree of latitude got shorter as you went north, which implies a prolate Earth. Their instruments were good. Their errors, over the short north to south span available inside France, were bigger than the effect they were trying to measure.
The Clock That Went Slow
There was already a clue, sixty years old, from an entirely different kind of measurement.
In 1672 the astronomer Jean Richer was sent to Cayenne, in French Guiana, near the equator. He took a pendulum clock that kept accurate time in Paris and found that it lost about two and a half minutes a day. To keep correct time he had to shorten the pendulum by roughly a millimetre and a half.
A pendulum’s period depends on the local strength of gravity, so his clock was reporting that gravity is weaker at the equator. Two things contribute: the centrifugal effect of rotation, and being further from the centre of the Earth because of the bulge. Newton used Richer’s result as evidence.
Cassini’s response was that the clock was probably affected by heat and humidity, which was not an unreasonable objection to a single instrument in a tropical colony.
Sending Men to the Ends of the Earth
The way to settle it was to measure a degree of latitude in two places as far apart as possible. The method, triangulation, was the same one Gauss would later use to map the Kingdom of Hanover, and it was already well established: lay out a base line and measure it with extreme care, build a chain of triangles from it across the landscape, measuring every angle, and then determine the latitudes of the two ends astronomically. Compare the ground distance with the difference in latitude and you have the length of a degree.
On an oblate Earth, the surface curves less sharply near the poles, so a degree of latitude is longer there. On a prolate one, the reverse.
The Peru expedition sailed in 1735: Charles Marie de La Condamine, Pierre Bouguer and Louis Godin, with a Spanish escort including the naval officers Jorge Juan and Antonio de Ulloa, since the territory was Spanish.
The Lapland expedition left in 1736 under Pierre Louis Moreau de Maupertuis, with Alexis Clairaut, the Abbé Outhier, and the Swedish astronomer Anders Celsius, whose temperature scale was still eight years away.
Lapland Was Hard and Quick
Maupertuis chose to work along the frozen valley of the Tornio river, using the river ice as a base line, which is the kind of decision that separates a successful expedition from a long one. The team endured mosquitoes in summer and temperatures that froze brandy in winter, hauled a heavy zenith sector up hills, and finished the survey in about a year.
The result was unambiguous. A degree of latitude at the Arctic Circle was longer than a degree in France by roughly a kilometre, which meant the Earth is flattened at the poles.
They returned to Paris in August 1737 to a reception that was not entirely friendly, since they had proved a Frenchman wrong and an Englishman right. Maupertuis had himself painted with his hand resting on a globe, pressing it flat. Voltaire, an enthusiastic Newtonian, wrote that he had flattened both the poles and the Cassinis.
Voltaire’s collaborator Émilie du Châtelet had studied under both Maupertuis and Clairaut, and her French translation of the Principia, still the standard one, was produced in exactly this intellectual climate: Newton being tested, in French, by French instruments, against a French orthodoxy.
Peru Took Ten Years
The southern expedition is one of the great disasters of eighteenth century science, and it produced more knowledge than the northern one.
They measured their base line on a plain near Quito at altitude, in thin air, and then carried instruments up volcanoes to occupy stations that were snowbound and frequently invisible in cloud for weeks. The survey took nearly eight years rather than the planned three.
The human cost was severe. The expedition’s surgeon, Jean Seniergues, was killed by a crowd during a bullfight in Cuenca after a local dispute. The botanist Joseph de Jussieu suffered a breakdown after years of collecting and lost his specimens. Godin married locally and stayed. One assistant died in a fall, another of fever. When they finally had the result, they learned that Maupertuis had already settled the question years earlier.
What they brought back went well beyond the degree measurement. La Condamine descended the Amazon by canoe and produced the first scientific map of the river, along with the first serious European account of caoutchouc, rubber, and of curare. Bouguer studied how the pull of gravity is altered near a mountain mass, work that survives as the Bouguer correction in geophysics, and effectively founded gravimetry. Ulloa described platinum. The expedition also brought back detailed information on cinchona bark, the source of quinine.
There is a postscript. Isabel Godin des Odonais, Jean Godin’s wife, set out in 1769 to rejoin her husband and travel down the Amazon. Her entire party of more than forty people died. She survived alone in the forest for days and reached the coast, and the story became one of the most widely read travel accounts of the century.
What Was Actually Settled
The Earth is an oblate spheroid, flattened by about one part in 298, which is close to Newton’s estimate and in the direction he predicted. The equatorial diameter exceeds the polar by about 43 kilometres.
The consequences went beyond winning an argument.
- Newtonian physics was accepted in France, which removed the last major national holdout and made gravitation the common framework of European science
- Geodesy became a discipline, with the recognition that the Earth’s figure is a measurable object rather than an assumption, and that gravity varies from place to place in ways that reveal what is underneath
- The metre was defined from it. When France sought a natural unit of length in 1791, it chose one ten millionth of the quadrant of the meridian from the pole to the equator, and sent Delambre and Méchain out to measure the arc from Dunkirk to Barcelona through the Revolution and its wars
The shape is still in daily use. Every satellite navigation fix is computed against a reference ellipsoid, WGS 84, whose flattening is specified as 1/298.257223563. That number is the direct descendant of a chain of triangles laid out on a frozen river in 1736 and another laid across the Andes by men who took a decade to come home.
The Point of the Story
A theory that predicts something already known is cheap. Newton’s flattening was a prediction about a quantity nobody had measured, derived from a general principle, in a direction opposite to the available data.
The Academy could have argued about it indefinitely. Instead it spent a fortune sending people to two of the least convenient places on Earth to find out, and accepted the answer when it went against the home team. That is a more impressive thing than the result.
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