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. Never did reasoning and experiment so fully concur to establish a truth. The celebrated Huygens, by calculating centrifugal forces, had proved that the consequent diminution of weight on the surface of a sphere was not great enough to explain the phenomena, and that therefore the earth must be a spheroid flattened at the poles. Newton, by the principles of attraction, had found nearly the same relations: only it must be observed, that Huygens believed this force inherent in bodies determining them towards the centre of the globe, to be everywhere the same. He had not yet seen the discoveries of Newton; so that he considered the diminution of weight by the theory of centrifugal forces only. The effect of centrifugal forces diminishes the primitive gravity on the equator. The smaller the circles in which this centrifugal force is exercised become, the more it yields to the force of gravity; thus, at the pole itself the centrifugal force being null, must leave the primitive gravity in full action. But this principle of a gravity always equal, falls to nothing before the discovery made by Newton, that a body transported, for instance, to the distance of ten diameters from the centre of the earth, would weigh one hundred times less than at the distance of one diameter.