b'Bouguer and the shape of the EarthFeatureBouguers gravity corrections and the shape of the EarthIn terms of gravity readings, if the shape is oblate, values will increase with increasing latitude. Indeed, measurements of gravity by Jean Richer near the equator in French Guyana in 1672 (Richer 1679) had shown a reduction in values compared to those in Paris. Newton regarded this as further proof of oblateness. But still, many notable French physicists of the time considered the whole idea of gravitational attraction by an unseen force as suspect or even incomprehensible and continued to argue in favour of the shape being prolate. To support their beliefs, they adopted an alternative theory of vortices in an ether expounded by Ren Descartes, a French philosopher, in 1644 (Descartes 1644)3. His followers became known as the Cartesians. The debate between them and the Roger Henderson supporters of Newton, the Newtonians, ensued for decades. rogah@tpg.com.au Bouguer originally gave equal consideration to both schools so as not to harm his standing in the Academy.The sure way this debate could be settled was to accurately In the gravity method of exploration geophysics, Bouguer is themeasure the length of a degree of latitude in different parts of name of a specific correction to measurements, and also thethe earth, and especially at the equator and the poles where the name of the anomaly remaining after that correction and othervalues would be extreme, and compare them. Figure 1 shows corrections are made. For a full explanation of these two termsthe different lengths for the two types of shape. For an oblate see Sheriff (1991). The terms are named after Pierre Bouguershape, the length of one degree at the poles is more than the (1698-1758), a French mathematician and astronomer who alsolength of one degree at the equator.gave his name to a crater on Mars, another on the moon and anAt this time, a site at which to measure the length of one degree asteroid1. on the equator was not easy to find. The coastline of equatorial As a child prodigy, Pierre was taught mathematics, hydrographyAfrica was considered too dangerous, and relevant Asian and astronomy by his father, Jean Bouguer, who was Royalislands were too far away, especially given the available means Professor of Hydrography at Le Croisic in Brittany. When Jeanof transport. A somewhat more civilised place, due to strict died in 1714, Pierre applied for his fathers position and, withSpanish control, but still very far from France, was in what was his brilliance and knowledge of the subject, was appointedthen a part of the Viceroyalty of Peru, now Ecuador, centred on Professor of Hydrography at the age of sixteen. He proceededQuito the capital. Figure 2 is a map of colonial South America to win three Grand Prix at the French Acadmie Royale desas it was known in about 1740, with Quito on the western side Sciences: the first in 1727 on the masting of ships, the second innear the equator. Also shown on the north-eastern side of the 1729 on observing the altitudes of stars at sea, and the third incontinent is Cayenne in French Guyana, where Richer made his 1731 on observing magnetic declination at sea2. Thus, his stronggravity measurements.involvement in things nautical became apparent, and Pierre wasTo use this location required the cooperation of Spain, which soon a leading French authority on the subject. He was made awas negotiated by the Minister of the Navy of France (the Comte full member of the Academy in 1735. de Maurepas). In fact, an expedition would be undertaken However, Pierre was also interested in geodesy, which makeswith the agreement and protection of the King of Spain. As him more interesting to geophysicists and, indeed, they areFerreiro (2011) points out, this endeavour was unprecedented in especially interested in his involvement in the quest to measurebeing the first scientific expedition involving two nations with the shape of the Earth. In the 18th century, it was generallyparticipants from both countries4.accepted that the Earth was not flat (!), but it is hard to imagineThus in 1735 at the age of 38, while reluctant to travel outside that 300 years ago it was still being debated as to whether itof France because of suffering from sea-sickness and not in was an oblate spheroid (with a bulge at the equator) or a prolategood health generally, Bouguer was enticed by Maurepas, with spheroid (with a bulge at the poles). new astronomical instruments and other incentives, to join Isaac Newton believed the Earth to be oblate, as causedthe expedition sponsored by the French Academy to measure by rotation and resulting centrifugal forces. In his Principiathe length of a degree of latitude at the equator5. Bouguer was Mathematica (Newton 1687) he stated the earth is higherknown by Maurepas for his work on naval interests.under the equator than at the poles and he even put the excess at about 17 miles (27.4 km). This is amazingly close to the exact figure for someone working only theoretically, as the true number is close to 19 miles (30.6 km) (see Milsom 2018, 119). 3One reference specifically on the Vortex Theory in English is Aiton (1972).4Ferreiro (2011) also suggests that scientists in Europe saw it as a model for future scientific expeditions. One such international enterprise following it 1His name is variously pronounced bu-ger, bu-gai, or in Brittany where hein the 1760s was the coordination of four countries, Britain, France, Russia was born, bu- gawr. and Austria, to observe the transit of Venus around the world.2The above brief information on Bouguers career can be easily found on5This Geodesic Mission to the Equator as it was called then, is expertly told websites such as Wikipedia.org, Encyclopedia.com and mathshistory.st- in great and entertaining detail by Ferreiro (2011) and also, with more andrews.ac.uk. See References. emphasis on the science and mathematics, by Milsom (2018).39 PREVIEW OCTOBER 2020'