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there be any sufficient reason to believe, that attraction is produced by an emanation. For my part, I am totally at a loss to comprehend, how particles streamings/row a centre, should draw a body towards it. The impulse, if impulse it be, is all the other way. Nor shall we find less difficulty in conceiving, a conflux of particles, incessantly flowing to a centre, and carrying down all bodies along with it, that centre also itself being in a state of rapid motion through absolute space; for, by what source is the stream fed, or what becomes of the accumulation? Add to which, that it seems to imply a contrariety of properties, to suppose an ethereal fluid to act but not to resist; powerful enough to carry down bodies with great force towards a centre, yet, inconsistently with the nature of inert matter, powerless and perfectly yielding with respect to the motions which result from the projectile impulse. By calculations drawn from ancient notices of eclipses of the moon, we can prove, that, if such a fluid exist at all, its resistance has had no sensible effect upon the moon's motion for two thoufand five hundred years. The truth is, except this one circumstance of the variation of the attracting force at different distances
agreeing agreeing with the variation of the spiffitude, there is no reason whatever to support the hypothesis of an emanation; and, as it seems to me, almost insuperable reasons against it.
II. (*) Our second proposition is, that, whilst the possible laws of variation were infinite, the admissible laws, or the laws compatible with the preservation of the system, lay within narrow limits. If the attracting force had varied according to any direct law of the distance, let it have been what it would, great destruction and confusion would have taken place. The direct simple proportion of the distance would, it is true, have produced an ellipse; but the perturbing forces would have acted with so much advantage, as to be continually changing the dimensions of the ellipse, in a manner inconsistent with our terrestrial creation. For instance; if the planet Saturn, so large and so remote, had attracted the earth, both in proportion to the quantity of matter contained in it, which it does; and also in any proportion to its distance, i. e. if it had pulled the harder for being the further off, (instead of the reverse of it,) it would have dragged the globe which we inhabit out of its • course, \
course, and have perplexed its motions, to a degree incompatible with' our security, our enjoyments, and probably our existence. Of the inverse laws, if the centripetal force had changed as the cube of the distance, or in any higher proportion, that is, (for I speak to the unlearned,) if, at double the distance, the attractive force had been diminished to an eighth part, or to less than that, the consequence would Have been, that the planets, if they once began to approach the fun would have fallen into his body; if 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 upheld in their motions, lie within narrow limits, compared with the possible laws. I much underrate the restriction, when I fay, 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 sensitive world.
III. C) 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 possibilities, 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 further. We fay, 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.
(*) I. Whilst this law prevails between each
particle particle of matter, the united attraction of a sphere, composed of that matter, observes the fame law. This property of the law is necessary, to render it applicable to a system 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 fame as the law of attraction of each particle, one cafe excepted, and that is of the attraction varying directly as the distance; the inconveniency of which law in other respects we have already noticed.
(*) 2. Under the subsisting law, the apsides, the returning points, or points of greatest and least distance from the centre, are quiescent, and, therefore, the body moves every revolution in exactly the fame path relative to the attracting centre: which it would not do, under any other law whatever except that of the direct ratio of the distance, which we have seen to be objectionable. The planetary system required that the law of attraction should be a law which gave an orbit returning into itself. Now, out of an infinite number of laws, admissible and inadmissible, out of a vast