Meanwhile, Richer in 1672 had been sent to Cayenne, French Guiana, to make astronomical observations and to measure the length of the seconds pendulum.[8] He took with him a pendulum clock which had been adjusted to keep accurate time in Paris. At Cayenne, however, Richer found that the clock was retarded by 2 minutes and 28 seconds per day (fig. 1). He also fitted up a "simple" pendulum to vibrate in seconds and measured the length of this seconds pendulum several times every week for 10 months. Upon his return to Paris, he found that the length of the "simple" pendulum which beat seconds at Cayenne was 1-1/4 Paris lines[9] shorter than the length of the seconds pendulum at Paris. Huygens explained the reduction in the length of the seconds pendulum--and, therefore, the lesser intensity of gravity at the equator with respect to the value at Paris--in terms of his theory of centripetal force as applied to the rotation of the earth and pendulum.[10] A more complete theory was given by Newton in the _Principia_.[11] Newton showed that if the earth is assumed to be a homogeneous, mutually gravitating fluid globe, its rotation will result in a bulging at the equator. The earth will then have the form of an oblate spheroid, and the intensity of gravity as a form of universal gravitation will vary with position on the surface of the earth. Newton took into account gravitational attraction and centrifugal action, and he calculated the ratio of the axes of the spheroid to be 230:229. He calculated and prepared a table of the lengths of a degree of latitude and of the seconds pendulum for every 5° of latitude from the equator to the pole. A discrepancy between his predicted length of the seconds pendulum at the equator and Richer's measured length was explained by Newton in terms of the expansion of the scale with higher temperatures near the equator. Newton's theory that the earth is an oblate spheroid was confirmed by the measurements of Richer, but was rejected by the Paris Academy of Sciences, for it contradicted the results of the Cassinis, father and son, whose measurements of arcs to the south and north of Paris had led to the conclusion that the earth is a prolate spheroid. Thus, a controversy arose between the English scientists and the Paris Academy. The conflict was finally resolved by the results of expeditions sent by the Academy to Peru and Sweden. The first expedition, under Bouguer, La Condamine, and Godin in 1735, went to a region in Peru, and, with the help of the Spaniard Ullo, measured a meridian arc of about 3°7' near Quito, now in Ecuador.[12] The second expedition, with Maupertuis and Clairaut in 1736, went to Lapland within the Arctic Circle and measured an arc of about 1° in length.[13] The northern arc of 1° was found to be longer than the Peruvian arc of 1°, and thus it was confirmed that the earth is an oblate spheroid, that is, flattened at the poles, as predicted by the theory of Newton.