I shall dwell on this article, because there are still geometricians who think that the figure of the earth depends upon theory, and this from a system of philosophy they have embraced, and from a supposed direction of gravity. The first thing we have to demonstrate is, the mutual attraction of every part of matter, and the second the homogeneousness of the terrestrial globe; if we clearly prove, that these two circumstances are really so, there will no longer be any hypothesis to be made on the direction of gravity: the earth will necessarily have the figure Newton decided in favour of, and every other figure given to it by virtue of vortexes or other hypotheses, will not be able to subsist. It cannot be doubted, that it is the force of gravity which retains the planets in their orbits; the satellites of Saturn gravitate towards Saturn, those of Jupiter towards Jupiter, the Moon gravitates towards the Earth: and Saturn, Jupiter, Mars, the Earth, Venus, and Mercury, gravitate towards the Sun: so likewise Saturn and Jupiter gravitate towards their satellites, the Earth gravitates towards the Moon, and the Sun towards the whole of the planets. Gravitation is therefore general and mutual in all the planetary system, for action cannot be exercised without a re-action; all the planets, therefore, act mutually one on the other. This mutual attraction serves as a foundation to the laws of their motion, and is demonstrated to exist by its effects. When Saturn and Jupiter are in conjunction, they act one on the other, and this attraction produces an irregularity in their motion round the Sun. It is the same with the Earth and the Moon, they also mutually attract each other; but the irregularities of the motion of the Moon, proceeds from the attraction of the Sun, so that the Earth, the Sun, and the Moon, mutually act one on the other. Now this mutual attraction of the planets, when the distances are equal, is proportional to their quantity of matter, and the same force of gravity which causes heavy matter to fall on the surface of the Earth, and which extends to the Moon, is also proportional to the quantity of matter; therefore the total gravity of a planet is composed of the gravity of each of its parts; from whence all the parts of the matter, either in the Earth or in the planets, mutually attract each other and the Earth, by its rotation round its own axis, has necessarily taken the figure of a spheroid, the axes of which are as 229 to 230. The direction of the weight must be perpendicular to the Earth's surface; consequently no hypothesis, drawn from the direction of gravity, can be sustained, unless the general attraction of the parts of matter be denied; but the existence of this mutual attraction is demonstrated by observations, and the experiment of pendulums prove, that its extension is general; therefore we cannot support an hypothesis on the direction of gravity without going against experience and reason.