111. By considering the law of gravitation, which takes place throughout the Solar System, in another light, it will be evident that the Earth moves round the Sun in a year; and not the Sun round the Earth. It has been shewn (§ 106) that the power of gravity decreases as the square of the distance increases: and from this it follows with mathematical certainty, that when two or more bodies move round another as their centre of motion, the squares of their periodic times will be to one another in the same proportion as the cubes of their distances from the central body. This holds precisely with regard to the Planets round the Sun, and the Satellites round the Planets; the relative distances of all which, are well known. But, if we suppose the Sun to move round the Earth, and compare its period with the Moon’s by the above rule, it will be found that the Sun would take no less than 173,510 days to move round the Earth, in which case our year would be 475 times as long as it now is. To this we may add, that the aspects of increase and decrease of the Planets, the times of their seeming to stand still, and to move direct and retrograde, answer precisely to the Earth’s motion; but not at all to the Sun’s without introducing the most absurd and monstrous suppositions, which would destroy all harmony, order, and simplicity in the System. Moreover, if the Earth is supposed to stand still, and the Stars to revolve in free spaces about the Earth in 24 hours, it is certain that the forces by which the Stars revolve in their Orbits are not directed to the Earth, but to the centres of the several Orbits: that is, of the several parallel Circles which the Stars on different sides of the Equator describe every day: and the like inferences may be drawn from the supposed diurnal motion of the Planets, since they are never in the Equinoctial but twice, in their courses with regard to the starry Heavens. But, that forces should be directed to no central body, on which they physically depend, but to innumerable imaginary points in the axe of the Earth produced to the Poles of the Heavens, is an hypothesis too absurd to be allowed of by any rational creature. And it is still more absurd to imagine that these forces should increase exactly in proportion to the distances from this axe; for this is an indication of an increase to infinity: whereas the force of attraction is found to decrease in receding from the fountain from whence it flows. But, the farther that any Star is from the quiescent Pole the greater must be the Orbit which it describes; and yet it appears to go round in the same time as the nearest Star to the Pole does. And if we take into consideration the two-fold motion observed in the Stars, one diurnal round the Axis of the Earth in 24 hours, and the other round the Axis of the Ecliptic in 25920 years § 251, it would require an explication of such a perplexed composition of forces, as could by no means be reconciled with any physical Theory.