We know that, in 1762, in a voyage to Cayenne, near the line, undertaken by order of Louis XIV., under the auspices of Colbert, the patron of all the arts, Richer, among many other observations, found that the oscillations or vibrations of his timepiece did not continue so frequent as in the latitude of Paris, and that it was absolutely necessary to shorten the pendulum one line and something more than a quarter. Physics and geometry were at that time not nearly so much cultivated as they now are; what man would have believed that an observation so trivial in appearance, a line more or less, could lead to the knowledge of the greatest physical truths? It was first of all discovered that the weight must necessarily be less on the equator than in our latitudes, since weight alone causes the oscillation of a pendulum. Consequently, the weight of bodies being the less the farther they are from the centre of the earth, it was inferred that the region of the equator must be much more elevated than our own--much more remote from the centre; so the earth could not be an exact sphere.
Many philosophers acted, on the occasion of these discoveries, as all men act when an opinion is to be changed--they disputed on Richer's experiment; they pretended that our pendulums made their vibrations more slowly about the equator only because the metal was lengthened by the heat; but it was seen that the heat of the most burning summer lengthens it but one line in thirty feet; and here was an elongation of a line and a quarter, a line and a half, or even two lines, in an iron rod, only three feet and eight lines long.
Some years after MM. Varin, Deshayes, Feuillée, and Couplet, repeated the same experiment on the pendulum, near the equator; and it was always found necessary to shorten it, although the heat was very often less on the line than fifteen or twenty degrees from it. This experiment was again confirmed by the academicians whom Louis XV. sent to Peru; and who were obliged, on the mountains about Quito, where it froze, to shorten the second pendulum about two lines.
About the same time, the academicians who went to measure an arc of the meridian in the north, found that at Pello, within the Polar circle, it was necessary to lengthen the pendulum, in order to have the same oscillations as at Paris: consequently weight is greater at the polar circle than in the latitude of France, as it is greater in our latitude than at the equator. Weight being greater in the north, the north was therefore nearer the centre of the earth than the equator; therefore the earth was flattened at the poles.