b'Bouguer and the shape of the EarthFeatureFigure 1.Lengths of a degree of latitude for an oblate and a prolate Earth. For the case of an oblate Earth, the length at the pole (S 1 ) is greater than at the equator (S 2 ). From Ferreiro 2011, Figure 1.3, also crediting Eliecer Vilchez Ortega.The full human content of the expedition of 10 principals (notDespite all the difficulties experienced as a consequence of the counting the usual complement of attendants and slaves)remoteness, the intense tropical and energy-sapping heat, the included, as well as Bouguer, two other members of the Frenchconstant torrential rain and the hostility of the natives, Bouguer Academy, Charles-Marie de La Condamine and Louis Godin, thelaboured earnestly and diligently with deteriorating health for initial leader of the expedition, plus a doctor, surgeon, engineer,seven years. His work was later seen to be very accurate, despite draftsman and instrument maker, and, as added by the King ofthese trying conditions.Spain, two Spanish naval officers who were also astronomers6. However, from the first letters from home after being away for In May 1735 the expedition departed, expecting to be awayover a year, the expedition learnt that another expedition was three to four years. In fact Bouguer was away from France forplanned to the Arctic Circle to measure the length of a degree almost nine years. The voyage to their destination alone tookof latitude near the North Pole. The location was closer to Paris over one year, and another year to return. The long travel timethan Ecuador and a much easier site in which to work, so that was mainly due to having to wait, sometimes for two or threeexpedition returned with a result after little more than one months, for ships to be available at various places along theyear. In August 1737, as the distance calculated was longer than route. This was especially true at the Isthmus of Panama whereequivalent measurements at Paris, it was then official that the the Panama Canal would not be available for another 179 years.Earth was oblate. Newtonianism had won over Cartesianism.As a result, the 70 km crossing of the isthmus by all personnelDespite the great disappointment when this news was received and equipment had to be made by portage. by Bouguer and his party, Maurepas knew that both sets of As revealed by Milsom (2018), like a good field operator,data were needed to give a precise determination of the Earths Bouguer made some use of the two-month wait in Panamadimensions. So, the Ecuador expedition continued their task.to make a gravity observation. He also made a gravityFinally, the purpose of the expedition was achieved admirably, measurement at Manta, upon the first landfall of his journey tothanks to Bouguer being in charge at the end (Godin having Ecuador, and no doubt the first by anyone in that country. been found to be grossly inadequate as a leader). After almost Upon arrival in Quito, which was to be the base for thesix years on site, the final value of the length of a degree of entire mission, a particular area was chosen in the vicinity tolatitude was measured as 110.56 km. As it was shorter by perform the survey. It had the Andes Mountains to provide the1.29 km than the length at the Arctic Circle (111.85 km), it substantial relief needed for the triangulation, which was theproved conclusively that the Earth was indeed oblate, as generally accepted way to measure long distances accurately.Newton had postulated six decades earlier. Later, Bouguer used In this case a length of over 300 km was laid out, sufficient forthe three data points of the lengths of the degree of latitude at three degrees of latitude. Also the two chains of mountainsthe Arctic Circle, in France and at the equator, to mathematically were separated by a broad flat area, which was preferred fordefine the precise curve of the Earths shape.laying out the baselines for the triangulation where the utmost accuracy was required7. In addition to these achievements, Bouguer made use of spare time, while waiting for stages of triangulation to be completed, to conduct other geophysical experiments. To begin with he set 6The two Spanish members, Jorge Juan and Antonio de Ulloa, later wroteabout examining all the factors related to gravity that he thought their own account of the expedition as seen through their eyes. (Juan andwould influence his pendulum measurements (see Milsom de Ulloa 1765). 2018, Coda 4 for a mathematical formulation of these factors). 7The very flat area of the missions base line near Quito was recently used forWhen he was high in the Andes, he first considered the effect of the new Quito International Airport. elevation above sea level on gravity measurements if there was OCTOBER 2020 PREVIEW 40'