With the decline of classical antiquity, the doctrine of the spherical shape of the earth was lost, and only one investigation, that by the Arabs under Calif Al-Mamun in A.D. 827, is recorded until the 16th century. In 1525, the French mathematician Fernel measured the length of a degree of latitude between Paris and Amiens by the revolutions of the wheels of his carriage, the circumference of which he had determined. In England, Norwood in 1635 measured the length of an arc between London and York with a chain. An important forward step in geodesy was the measurement of distance by triangulation, first by Tycho Brahe, in Denmark, and later, in 1615, by Willebrord Snell, in Holland.
Of historic importance, was the use of telescopes in the triangulation for the measurement of a degree of arc by the Abbé Jean Picard in 1669. [6] He had been commissioned by the newly established Academy of Sciences to measure an arc corresponding to an angle of 1°, 22′, 55″ of the meridian between Amiens and Malvoisine, near Paris. Picard proposed to the Academy the measurement of the meridian of Paris through all of France, and this project was supported by Colbert, who obtained the approval of the King. In 1684, Giovanni-Domenico Cassini and De la Hire commenced a trigonometrical measure of an arc south of Paris; subsequently, Jacques Cassini, the son of Giovanni-Domenico, added the arc to the north of Paris. The project was completed in 1718. The length of a degree of arc south of Paris was found to be greater than the length north of Paris. From the difference, 57,097 toises [7] minus 56,960 toises, it was concluded that the polar diameter of the earth is larger than the equatorial diameter, i.e., that the earth is a prolate spheroid ([fig. 3]).
Figure 3.—Measurements of the length of a degree of latitude which were completed in different parts of France in 1669 and 1718 gave differing results which suggested that the shape of the earth is not a sphere but a prolate spheroid (1). But Richer’s pendulum observation of 1672, as explained by Huygens and Newton, indicated that its shape is that of an oblate spheroid (2). The disagreement is reflected in this drawing. In the 1730’s it was resolved in favor of the latter view by two French geodetic expeditions for the measurement of degrees of latitude in the equatorial and polar regions (Ecuador—then part of Peru—and Lapland).
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 11/4 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.
