1. In the first place, the system could not have subsisted, if the force had followed a _direct_ instead of an inverse law, with respect to the distance; that is, if it had increased when the distance increased. It has been sometimes said, that “all direct laws of force are excluded on account of the danger from perturbing forces;”[23] that if the planets had pulled at this earth, the harder the further off they were, they would have dragged it entirely out of its course. This is not an exact statement of what would happen: if the force were to be simply in the direct ratio of the distance, any number of planets might revolve in the most regular and orderly manner. Their mutual effects, which we may call perturbations if we please, would be considerable; but these perturbations would be so combined with the unperturbed motion, as to produce a new motion not less regular than the other. This curious result would follow, that every body in the system would describe, or seem to describe, about every other, an exact elliptical orbit; and that the times of the revolution of every body in its orbit would be all equal. This is proved by Newton, in the sixty-fourth proposition of the Principia. There would be nothing to prevent all the planets, on this supposition, from moving round the sun in orbits exactly circular, or nearly circular, according to the mode in which they were set in motion. But though the perturbations of the system would not make this law inadmissible, there are other circumstances which would do so. Under this law, the gravity of bodies at the earth’s surface would cease to exist. Nothing would fall or weigh downwards. The greater action of the distant sun and planets would exactly neutralize the gravity of the earth: a ball thrown from the hand, however gently, would immediately become a satellite of the earth, and would for the future accompany it in its course, revolving about it in the space of one year. All terrestrial things would float about with no principle of coherence or stability: they would obey the general law of the system, but would acknowledge no particular relation to the earth. We can hardly pretend to judge of the abstract possibility of such a system of things; but it is clear that it could not exist without an utter subversion of all that we can conceive of the economy and structure of the world which we inhabit. With any other direct law of force, we should in like manner lose gravity, without gaining the theoretical regularity of the planetary motions which we have described in the case just considered.