It was a row that split scientists, launched globe-trotting expeditions and for one man, ended in murder: was the Earth shaped like an orange or a lemon?The 18th-century debate – and the endeavours that settled it –can now be relived by visitors to this year’s Royal Society summer science exhibition, in a display called “Figuring the Earth”.Opening to the public on Tuesday, and remaining on show in London until October, the exhibition – which is presented in English and French – celebrates the importance of international competition and collaboration.The citrus fruit conundrum, it seems, is a case in point.“The debate comes from ways of measuring and ways of thinking about the Earth,” said Dr Louisiane Ferlier, curator of the exhibition.Some members of the French Academy of Sciences interpreted measurements taken in Paris by scientists including Jacques Cassini as supporting the idea that the Earth was elongated at the poles, resembling a lemon or a melon.By contrast, Isaac Newton had proposed that the centrifugal force caused by the Earth’s rotation would result in the planet being flattened at its poles, thus having a similar shape to an orange.As Voltaire wrote in 1724: “In Paris you see the Earth shaped like a melon; in London it is flattened on two sides.”The French Academy of Sciences has loaned mathematical observations made by scientists for the exhibition. Photograph: Academie des sciencesWith scientists split as to which view was correct, the French Academy of Sciences launched two international expeditions, funded by Louis XV, to settle the question of whether the circumference of the Earth was larger around the equator or around the poles.Celebrating the debate, and its resolution, Figuring the Earth will showcase a host of objects. Among them is Isaac Newton’s Principia Mathematica, which contains his theory on the shape of the Earth.Alongside it is the translation from Latin into French by Marquise Émilie du Châtelet – an 18th-century French noblewoman who became a mathematician and physicist – which is on loan from the French Academy of Sciences.“They’ve never been shown side by side,” said Ferlier.Other objects include dividers, a two-legged measuring instrument that was used during the French geodesic mission to the equator – one of the two research endeavours backed by the academy.The other expedition, Ferlier noted, went to Lapland and involved a team that included the French mathematician and philosopher Pierre Louis Maupertuis, and the Swedish scientist Anders Celsius.In both cases the teams used an approach known as triangulation to determine the shape of the Earth.skip past newsletter promotionOur morning email breaks down the key stories of the day, telling you what’s happening and why it mattersPrivacy Notice: Newsletters may contain info about charities, online ads, and content funded by outside parties. For more information see our Privacy Policy. We use Google reCaptcha to protect our website and the Google Privacy Policy and Terms of Service apply.after newsletter promotionUnfortunately for those who backed the idea of a lemon-shaped Earth, including Cassini himself, the results supported Newton’s theory.But the work did not only shed light on the Earth’s form: the scientists who headed to the equator also documented how to tap rubber from trees, studied the bark of the tree from which quinine is derived, and experienced myriad adventures – including the murder of the expedition’s surgeon by a mob in Ecuador, apparently after he became romantically entangled with a local woman.“It’s a lot of drama,” said Ferlier.The exhibition also considers more recent efforts to map and survey the Earth. Among the items on display are instruments and results relating to the great trigonometrical survey of India, begun in 1802, as well as a model of the first artificial satellite, Sputnik 1.“[In the 20th century] satellites completely revolutionised the way the shape of the Earth is calculated, and mapped,” said Ferlier.But the spirit of international competition and collaboration epitomised by the historical debate continues today: among the research being showcased in the wider summer exhibition is an international endeavour known as the Deep Underground Neutrino Experiment, as well as results from the James Webb space telescope, which has involved teams from around the world.Ferlier said Figuring the Earth highlighted fundamental aspects of science.“Science has to be collaborative, and it has to be responsive,” she said. “And you have to get things wrong to get things right.”