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they once, though by ever so little, increased their distance from the centre, would for ever have receded from it. The laws therefore of attraction, by which a system of revolving bodies could be upholden in their motions, lie within narrow limits, compared with the possible laws. I much under-rate the restriction, when I say that, in a scale of a mile, they are confined to an inch. All direct ratios of the distance are excluded, on account of danger from perturbing forces: all reciprocal ratios, except what lie beneath the cube of the distance, by the demonstrable consequence, that every the least change of distance would, under the operation of such laws, have been fatal to the repose
and order of the system. We do not know, that is, we seldom reflect, how interested we are in this matter. Small irregularities may be endured; but, changes within these limits being allowed for, the
permanency of our ellipse is a question of life and death to our whole sen. sitive world.
(*) III. That the subsisting law of attraction falls within the limits which utility requires, when these limits bear so small a proportion to the range of possi. bilities upon which chance might equally have cast it, is not, with any appearance of reason, to be accounted for, by any other cause than a regulation proceeding from a designing mind. But our next proposition carries the matter somewhat farther. We say, in the third place, that, out of the different laws which lie within the limits of admissible laws, the best is made choice of; that there are advantages in this particular law which cannot be demonstrated to belong to any other law; and, concerning some of which, it can be demonstrated that they do not belong to any
other. (*) 1. Whilst this law prevails between each particle of matter, the united attraction of a sphere, composed
of that matter, observes the same law. This property of the law is necessary, to render it applicable to a sys, tem composed of spheres, but it is a property which belongs to no other law of attraction that is admissible. The law of variation of the united attraction is in no other case the same as the law of attraction of each par. ticle, one case excepted, and that is of the attraction varying directly as the distance; the inconveniency of which law in other respects, we have already noticed.
We may follow this regulation somewhat farther, and still more strikingly perceive that it proceeded from a designing mind. A law both admissible and convenient was requisite. In what way is the law of the attracting globes obtained ? Astronomical observations and terrestrial experiments show that the attraction of the globes of the system is made up of the attraction of their parts; the attraction of each globe being compounded of the attractions of its parts. Now the admissible and convenient law which exists, could not be obtained in a system of bodies gravitating by the united gravitation of their parts, unless each particle of matter were attracted by a force varying by one particular law, viz. varying inversely as the square of the distance: for, if the action of the particles be according to any other law whatever, the admissible and convenient law, which is adopted, could not be obtained. Here then are clearly shown regulation and design. A law both admissible and convenient was to be obtained; the mode chosen for obtaining that law was by making each particle of matter act. After this choice was made, then farther attention was to be given to each particle of matter, and one, and one only parti. cular law of action to be assigned to it. No other law would have answered the purpose intended.
(*) 2. 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 strongest evidence of care and foresight that can be given. Now, we are able to demonstrate of our law of attraction, what can be demon. strated of no other, and what qualifies the dangers which arise from cross but unavoidable influences ; that the action of the parts of our system upon one another will not cause permanently increasing irregularities, but merely periodical or vibratory ones; that is, they will come to a limit, and then go back again. This we can demonstrate only of a system, in which the following properties concur, viz. that the force shall be inversely as the square of the distance; the masses of the revolving bodies small, compared with that of the body at the centre; the orbits not much inclined to one another; and their eccentricity little. In such a system, the grand points are secure. The mean distances and periodic times, upon which depend our temperature, and the regularity of our year, are constant, The ecoentricities, it is true, will still vary; but so, slowly, and to so small an extent, as to produce no inconveniency from fluctuation of temperature and
The same as to the obliquity of the planes of the orbits. For instance, the inclination of the ecliptic, to the equator will never change above two degrees (out of ninety), and that will require many thousand 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 so great distances from the rest, they act almost equally on the Sun and
on the inferior planets; which has nearly the same consequence as not acting at all upon
either. If it be said, that the planets might have been sent round the Sun in exact circles, in which case, no change of distance from the centre taking place, the law of variation of the attracting power would have never come in question, one law would have served as well as another; an answer to the scheme may be drawn from the consideration of these same perturbing forces: The system retaining in other respects its present constitution, though the planets had been at first sent 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 transgressed the limits above assigned, every evagation would have been fatal: the planet once drawn, as drawn it necessarily must have been, out of its course, would have wandered in endless error.
(*) V. What we have seen in the law of the cene tripetal 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 wisest choice; for, even under that law, it was still competent to the planets to have moved in paths possessing so great a degree of eccentricity, as, in the course of every revolution, to be brought very near to the Sun, and carried away to immense distances from him. - The comets actually move in orbits of this sort: and, had the planets done so, instead of going round in orbits nearly circular, the change from one extremity of temperature to another must, in ours at least, have destroyed every' animal and plant upon its surface. Now, the
distance from the centre at which a planet sets off, and the absolute force of attraction at that distance, being fixed, the figure of its orbit, its being a circle, or nearer to, or farther 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 result, 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 also near to this direction, to produce orbits, such as the planetary orbits are, nearly circular ; that is, ellipses with small eccentricities. The velocity and the direction must both be right. If the velocity be wrong, no direction will cure the error; if the direction be in any considerable degree oblique, no velocity will produce the orbit required. Take for example the attraction of gravity at the surface of the earth. The force of that attraction being what it is, out of all the degrees of velocity, swift and slow, with which a ball might be shot off, none would answer the purpose of which we are speaking, but what was nearly that of five miles in a second. If it were less than that, the body would not get round at all, but would come to the ground; if it were in any considerable degree more than that, the body would take one of those eccentric courses, those long ellipses, of which we have noticed the inconveni.
ency. If the velocity reached the rate of seven miles , in a second, ôr 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 serve but what was nearly a right one: