known, and we cannot doubt that bodies attract each other in a direct ratio of their masses, and in an inverted ratio, at the squares of their distances; so likewise we cannot doubt, that the general action of any body is not composed of all the particular actions of its parts. Thus each part of matter mutually attracts in a direct ratio of its mass and an inverted ratio of its distance, and from all these attractions there results a sphere when there is no rotatory motion, and a spheroid when there is one. This spheroid is longer or shorter at the two extremities of the axis of rotation, in proportion to the velocity of its diurnal motion, and the earth has then, by virtue of its rotative velocity, and of the mutual attraction of all its parts, the figure of a spheroid, the two axes of which are as 229 to 230 to one another.
Thus, by its original constituent, by its homogeneousness, and independent of every hypothesis from the direction of gravity, the earth has taken this figure of a spheroid at its formation, and agreeable to mechanical laws: its equatorial diameter was raised about 6-1/2 leagues higher than under the poles.
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.
Let us now proceed to examine whether the matter of which the terrestrial globe is composed be homogeneous. I admit, that if it is supposed the globe is more dense in some parts than in others, the direction of gravity must be different from what we have just assigned, and that the figure of the Earth would also differ agreeable to those suppositions. But what reason have we to make these suppositions? Why, for example, should we suppose that the parts near the centre are denser than those which are more remote? Are not all the particles which compose the globe collected together by their mutual attraction?
hence, each particle is a centre, and there is no reason to believe, that the parts which surround the centre are denser than those which are about any other point. Besides, if one considerable part of the globe was denser than another, the axis of rotation would be found near the dense parts, and an inequality would ensue in the diurnal revolution; we should remark an inequality in the apparent motion of the fixed stars; they would appear to move more quick or slow in the zenith, or horizon, according as we should be placed on the denser or lighter parts of the earth; and the axis of the globe no longer passing through the centre of gravity, would also very sensibly change its position: but nothing like this ever happens; on the contrary, the diurnal motion of the earth is equal and uniform. At all parts of the Earth's surface, the stars appear to move with the same velocity at all heights, and if there be any rotation in its axis, it is so trifling as to have escaped observation: it must therefore be concluded, that the globe is homogeneous, or nearly so in all its parts.
If the earth was a hollow and void globe, and the crust of which, for example, not more than two or three miles thick; it would
produce these effects. 1. The mountains would be such considerable parts of the whole thickness of the crust, that great irregularities in the motions of the Earth would be occasioned by the attraction of the Moon and Sun: for when the highest parts of the globe, as the Cordeliers, should have the Moon at noon, the attraction would be much stronger on the whole globe than when she was in the meridian of the lowest parts. 2. The attraction of mountains would be much more considerable than it is in comparison with the attraction of the whole globe, and experiments made at the mountain of Chimboraco, in Peru, would in this case give more degrees than they have given seconds for the deviation of the plumb line. 3. The weight of bodies would be greater on the tops of high mountains than on the planes; so that we should feel ourselves considerably heavier, and should walk with more difficulty in high than in low places. These observations, with many others that might be added, must convince us, that the inner parts of the globe is not void, but filled with a dense matter.