variety even of admiffible laws, there are few, except the actual law, which would do this. Here then is choice.

(*) 3. All systems must be liable to perturbations. And therefore to guard against these perturbations, or rather to guard against their running to destructive lengths, is perhaps the ftrongest evidence of care and forefight that can be given. Now we are able to demonftrate of our law of attraction, what can be demonftrated of no cther, and what qualifies the dangers which arife from cross but unavoidable influences, that the action of the parts of our fyftem upon one another will not cause permanently increasing irregularities, but merely periodical ones: that is, they will come to a limit, and then go back again. This we can demonftrate only of a fyftem, in which the following properties concur, viz. that the force shall be inversely as the square of the distance; the maffes of the revolving bodies fmall, compared with that of the body at the centre; the orbits not much inclined to one another; and their eccentricity little. In fuch a system the grand points are fecure. The mean distances. and periodic times, upon which depend our temperature, and the regularity of our year,

are conftant. The eccentricities, it is true, will still vary, but fo flowly, and to so small an extent, as to produce no inconveniency from fluctuation of temperature and season. The fame as to the obliquity of the planes of the orbits. For inftance, the inclination of the ecliptic to the equator will never change above two degrees, (out of ninety,) and that will require many thoufand years in performing.

It has been rightly also remarked, that, if the great planets Jupiter and Saturn had moved in lower spheres, their influences would have had much more effect as to disturbing the planetary motions than they now have. While they revolve at fo great distances from the rest, they act almoft equally on the Sun and on the inferior planets, which has nearly the fame confequence as not acting at all upon either.

If it be faid that the planets might have been fent round the Sun in exact circles, in which cafe, no change of diftance from the centre taking place, the law of variation of the attracting power would have never come in question; one law would have ferved as well as another; an answer to the scheme may be drawn from the confideration of these fame perturbing forces. The fyftem retaining in

other respects its present conftitution, though the planets had been at firft fent round in exact circular orbits, they could not have kept them: and if the law of attraction had not been what it is, (or, at least, if the prevailing law had tranfgreffed the limits above affigned,) every evagation would have been fatal: the planet once drawn, as drawn it neceffarily must have been, out of its courfe, would have wandered in endless error.

(*) V. What we have feen in the law of the centripetal force, viz. a choice guided by views of utility, and a choice of one law out of thousands which might equally have taken place, we see no less in the figures of the planetary orbits. It was not enough to fix the law of the centripetal force, though by the wifeft choice, for, even under that law, it was ftill competent to the planets to have moved in paths poffeffing so great a degree of eccentricity, as, in the courfe of every revolution, to be brought very near to the fun, and carried away to immense distances from him. The comets actually move in orbits of this fort: and, had the planets done fo, instead of going round in orbits nearly circular, the change from one extremity of temperature to

another

another muft, in ours at least, have destroyed every animal and plant upon its furface. Now, the distance from the centre at which a planet fets off, and the abfolute force of attraction at that distance, being fixed, the figure of his orbit, its being a circle, or nearer to, or further off from, a circle, viz. a rounder or a longer oval, depends upon two things, the velocity with which, and the direction in which, the planet is projected. And these, in order to produce a right refult, must be both brought within certain narrow limits. One, and only one, velocity, united with one, and only one, direction, will produce a perfect circle. And the velocity must be near to this velocity, and the direction alfo near to this direction, to produce orbits, fuch as the planetary orbits are, nearly circular; that is, ellipfes with small eccentricities. The velocity and the direction muft both be right. If the velocity be wrong, no direction will cure the error; if the direction be in any confiderable degree oblique, no velocity will produce the orbit required. Take for example the attraction of gravity at the furface of the earth. The force of that attraction being what it is, out of all the degrees of velocity, fwift and flow, with which a ball

might be shot off, none would anfwer the purpose of which we are speaking but what was nearly that of five miles in a second. If it were lefs than that, the body would not get round at all, but would come to the ground: if it were in any confiderable degree more than that, the body would take one of those eccentric courses, thofe long ellipfes, of which we have noticed the inconveniency. If the velocity reached the rate of feven miles in a fecond, or went beyond that, the ball would fly off from the earth, and never be heard of more. In like manner with respect to the direction; out of the innumerable angles in which the ball might be sent off, I mean angles formed with a line drawn to the centre, none would ferve but what was nearly a right one; out of the various directions in which the cannon might be pointed, upwards and downwards, every one would fail, but what was exactly or nearly horizontal. The fame thing holds true of the planets; of our own amongst the rest. We are entitled therefore to ask, and to urge the queftion, Why did the projectile velocity, and projectile direction of the earth happen to be nearly those which would retain it in a circular form? Why not one of the infinite 2 F number