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there be any fufficient reason to believe, that attraction is produced by an emanation. For my part, I am totally at a lofs to comprehend, how particles streaming from a centre, should draw a body towards it. The impulse, if impulfe it be, is all the other way. Nor fhall we find less difficulty in conceiving, a conflux of particles, inceffantly flowing to a centre, and carrying down all bodies along with it, that centre also itself being in a state of rapid motion through abfolute space; for, by what fource is the ftream fed, or what becomes of the accumulation? Add to which, that it seems to imply a contrariety of properties, to fuppose an æthereal fluid to act but not to resist; powerful enough to carry down bodies with great force towards a centre, yet, inconfiftently with the nature of inert matter, powerless and perfectly yielding with respect to the motions which refult from the projectile impulfe. By calculations drawn from ancient notices of eclipfes of the moon, we can prove, that, if fuch a fluid exist at all, its refiftance has had no fenfible effect upon the moon's motion for two thousand five hundred years. The truth is, except this one circumftance of the variation of the attracting force at different diftances

agreeing

agreeing with the variation of the fpiffitude, there is no reason whatever to support the hypothesis of an emanation; and, as it seems to me, almost infuperable reafons against it.

II. (*) Our fecond propofition is, that, whilst the poffible laws of variation were infinite, the admiffible laws, or the laws compatible with the preservation of the fyftem, 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 deftruction and confufion would have taken place. The direct fimple proportion of the distance would, it is true, have produced an ellipfe; but the perturbing forces would have acted with so much advantage, as to be continually changing the dimenfions of the ellipfe, in a manner inconfiftent with our terreftrial creation. For instance; if the planet Saturn, fo large and fo remote, had attracted the earth, both in proportion to the quantity of matter contained in it, which it does; and alfo in any proportion to its diftance, i. e. if it had pulled the harder for being the further off, (inftead of the reverse of it,) it would have dragged the globe which we inhabit out of its

course,

courfe, and have perplexed its motions, to a degree incompatible with our fecurity, our enjoyments, and probably our existence. Of the inverse laws, if the centripetal force had changed as the cube of the diftance, 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 fo little, increased their diftance from the centre, would for ever have receded from it. The laws therefore of attraction, by which a sys tem of revolving bodies could be upheld in their motions, lie within narrow limits, compared with the poffible laws. I much underrate the reftriction, when I fay, that in a scale of a mile they are confined to an inch. All direct ratios of the diftance are excluded, on account of danger from perturbing forces: all reciprocal ratios, except what lie beneath the cube of the diftance, by the demonftrable confequence, that every the least change of distance, would, under the operation of fuch

laws,

laws, have been fatal to the repofe and order of the fyftem. We do not know, that is, we feldom reflect, how interefted we are in this matter. Small irregularities may be endured; but, changes within these limits being allowed for, the permanency of our ellipfe is a queftion of life and death to our whole fenfitive world.

III. (*) That the fubfifting law of attraction falls within the limits which utility requires, when these limits bear fo fmall a proportion to the range of poffibilities, upon which chance might equally have caft it, is not, with any appearance of reason, to be accounted for, by any other cause than a regulation proceeding from a defigning mind. But our next propofition carries the matter fomewhat further. We fay, in the third place, that, out of the different laws which lie within the limits of admiffible laws, the beft is made choice of; that there are advantages in this particular law which cannot be demonftrated to belong to any other law; and, concerning fome of which, it can be demonftrated that they do not belong to any other.

(*) 1. Whilst this law prevails between each

particle

particle of matter, the united attraction of a fphere, compofed of that matter, obferves the fame law. This property of the law is neceffary, to render it applicable to a fyftem compofed of spheres, but it is a property which belongs to no other law of attraction that is admiffible. The law of variation of the united attraction is in no other cafe the fame as the law of attraction of each particle, one cafe excepted, and that is of the attraction varying directly as the diftance; the inconveniency of which law in other refpects we have already noticed.

(*) 2. Under the fubfifting law, the apfides, the returning points, or points of greatest and least distance from the centre, are quiefcent, 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 feen to be objectionable. The planetary sys tem 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, admiffible and inadmissible, out of a vast

variety

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