The French Geodesic Mission to the Equator (Expédition géodésique française en Équateur), also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission, was an 18th-century expedition to what is now Ecuador carried out for the purpose of performing an arc measurement, measuring the length of a degree of latitude near the Equator, by which the Earth radius can be inferred. The mission was one of the first geodesic (or geodetic) missions carried out under modern scientific principles, and the first major international scientific expedition.
In the 18th century, there was significant debate in the scientific community, specifically in the French Academy of Sciences (Académie des sciences), as to whether the circumference of the Earth was greater around the Equator or around the poles. French astronomer Jacques Cassini held to the view that the polar circumference was greater. Louis XV of France and the academy sent two expeditions to determine the answer: one was sent to Meänmaa in Lapland, close to the Arctic Circle, under Swedish physicist Anders Celsius and French mathematician Pierre Maupertuis. The other mission was sent to Ecuador, at the Equator. Previous accurate measurements had been taken in Paris by Cassini and others.
The equatorial mission was led by French astronomers Charles Marie de La Condamine, Pierre Bouguer, Louis Godin and Spanish geographers Jorge Juan and Antonio de Ulloa. They were accompanied by several assistants, including the naturalist Joseph de Jussieu and Louis's cousin Jean Godin. La Condamine was joined in his journey down the Amazon by Ecuadoran geographer and topographer Pedro Maldonado. (Maldonado later traveled to Europe to continue his scientific work.)
The Ecuadoran expedition
left France in May 1735. They landed on the Caribbean coast in Colombia, sailed to Panama where they traveled overland to the Pacific, and continued by sail to Ecuador, then called the Territory of Quito by Spain. In Ecuador, they split into two groups, traveling overland through rain forests, arriving in Quito in June 1736.
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In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to determine a figure of the Earth. One or more measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements.
Antonio de Ulloa (12 January 1716 – 3 July 1795) was a Spanish naval officer, scientist, and administrator. At the age of nineteen, he joined the French Geodesic Mission to what is now the country of Ecuador. That mission took more than eight years to complete its work, during which time Ulloa made many astronomical, natural, and social observations in South America. The reports of Ulloa's findings earned him an international reputation as a leading savant.
Charles Marie de La Condamine (28 January 1701 – 4 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in territory which is now Ecuador, measuring the length of a degree of latitude at the equator and preparing the first map of the Amazon region based on astro-geodetic observations. Furthermore he was a contributor to the Encyclopédie. Charles Marie de La Condamine was born in Paris as a son of well-to-do parents, Charles de La Condamine and Louise Marguerite Chourses.
This paper introduces a subgradient descent algorithm to compute a Riemannian metric that minimizes an energy involving geodesic distances. The heart of the method is the Subgradient Marching Algorithm to compute the derivative of the geodesic distance wit ...