make it doubtful whether it be what is really meant); and that of Bofcovich is not fo much as mentioned.

Concerning the fyftem of Defcartes, it was not neceffary to enter into much detail; and Mr Vince has very properly abftained from doing fo. The vortices of that ingenious theorift have long ceafed to afford fatisfaction even to the most fuperficial reasoner. They are known now only in the hiftory of opinions, and, in that history, will ever furnish a moft inftructive chapter. The manner in which the system sprung up at the dawn of science, flourishedon the ruins of the fchool philofophy, and faded of itself in the brighter light of experiment and obfervation, is the beft proof of the fuperior value of the inductive philofophy which Descartes fo unwifely affected to defpife.

A very juft remark made by Mr Vince on the fyftem of Defcartes, and on all others that depend on the fame principle, is, that the planets being carried in vortices round the fun, the quantity of matter in the fun will not affect the velocity of the vortex, or the bodies immersed in it, inafmuch as that velocity might be the fame, though there were no central body whatfoever. The quantity of matter in the fun, therefore, cannot enter at all as an element into the expreffion of the force by which the planet is impelled toward the fun. Therefore, as the fact is, that the quantity of matter in the central body does enter as a moft material element into the expreflion of the gravitation of the planet, it is impoffible to afcribe that gravitation to the action of a vortex. This argument is perfectly conclufive. It was not to this, however, that the fyftem of vortices really owed its downfal, but chiefly to another, which Maupertuis has very well stated in his Differtation on the Figure of the Heavenly Bodies, viz. that whenever you fuppofe the vortex fo arranged, that it will explain one of those great facts in the planetary motions, known by the name of Kepler's Laws, it becomes quite inconfiftent with the reft.

The next fyftem that was imagined for explaining the law of gravitation, was that of an elaftic ether, mentioned by Sir Ifaac Newton in the Queries at the end of his Optics, and proposed with fuch modesty and diffidence, as entitles it to great indulgence. It is the conjecture of the philofopher, who had demonftrated the existence of the law of gravitation, concerning the mechanifm by which this univerfal tendency is produced; and feems to be thrown out with the view of preventing those who followed him from thinking that it was fufficient to fay that gravitation was an effential quality of matter, and that there was no occafion to trouble themselves about the cause of it. It was to ferve as a ftimulus to future inquiry, and as a caution against fuppofing that the fabric of phyfical aftronomy was complete. According

to

to it, the mutual tendency of bodies toward one another, arifes from the action of a fluid highly elastic, diffused through all space, but more rare within bodies than without, and more rare at a fmaller diftance from them than at a greater. Bodies are propelled through this fluid from the denfer to the rarer parts, that is, from the parts where the elafticity is greater, to those where it is lefs. Thus, with refpect to the earth, the elafticity of the circumfufed ether being greater at a distance from that body than near it, other bodies would, by that greater elafticity, be urged toward the quarter where the elafticity is lefs, that is, toward the earth. The fame would hold of the fun and moon, and all the great bodies of the universe. This hypothefis, to which it must be confeffed that many objections may be made, appears to have been fuggested to Newton by the phenomena of optics, which it is better calculated to folve than thofe of aftronomy. That a subtle fluid existed, and was diffused through those spaces from which air was exhaufted, appeared to him evident from many confiderations, and particularly from this, that a thermometer in vacue will grow warm almoft as foon as a thermometer not in vacuo. Is not the heat, therefore,' faid he, of a warm room conveyed through the vacuum by the vibrations of a much fubtler medium than air, which, after the air was drawn out, remained in the vacuum?' Again, he says, Doth not the refraction of light proceed from the different denfities of this ethereal medium in different places, the light receding always from the denfer parts of the medium towards the rarer? And is not the denfity thereof greater in free and open spaces void of air and other grofs bodies, than within the pores of water, glass, crystal, and other compact bodies? For when light paffes through glafs or cryftal, and, falling obliquely upon the further surface thereof, is totally reflected, the total reflection ought rather to proceed from the density and vigour of the medium without, than from its rarity and weakness. Now, in applying this fluid to account for the gravitation of diftant bodies toward one another, he fuppofes, as before stated, that its denfity, and, of course, its elafticity, increases as you recede from the fun and other great bodies; that it is lefs within than at the furface; lefs there than at a small distance from it, (as the phenomena of optics feemed to require); and that it goes on continually, though flowly, increafing. Though this increase of density,' he adds, may be exceeding flow at great distances, yet if the elastic force of the medium be exceeding great, it may fuffice to impel bodies from the denfer parts of the medium towards the rarer, with all that power which we call Gravity.' Optics, Query 21. &c.

1

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Various objections may be undoubtedly offered to this hypothefis; and Mr Vince dwells particularly on one deduced from the impoffibility

impoffibility of affigning to this medium any law of variation of denfity and of elasticity, by which its force on the bodies furrounded by it can be made to vary inversely as the fquares of the distances from a given point. But, notwithstanding that the reafoning he employs to prove this impoffibility, is mathematical, and proceeds on calculation, we must acknowledge that it does not appear to us to be at all fatisfactory. He fuppofes the density of the ethereal fluid to vary as any power whatever, m, of the distance from the centre of the fun, and its elafticity to vary as any power, n, of the distance of the particles of the fluid from one another; then taking a spherical body, and computing the force of this elaftic ether on the hemifphere furthest from the fun, and on that nearest it, the difference is the force impelling the body to the fun, and ought therefore to be inverfely as the fquare of the diftance from the fun. But the refult of our author's computation is, that whatever values are assigned to m and n, the force obtained as above will not follow the inverse ratio of the fquares of the diftances; and may even in fome cafes become negative, indicating a force directed from, and not toward the centre of the fun. This conclufion he next endeavours to extend to all the laws of variation of density and of elasticity that can poffibly exist, by fhowing that no one can be admitted that is not capable of being expreffed by a fingle term, and confequently by the mth or nth power of the distance. It is here, if we mistake not, that the error lies. For, though a variation of denfity or of elasticity, expreffed thus, Ax+Bx", cannot take place, because the force arifing from it would also involve two terms, yet if one of the terms be conftant, as if mo, and so the expreffion = A + B x1, then the force would be expreffed by one term only, viz. by the fluxion of Bx", that is, by a quantity proportional to x

Thus, for example, if x be any distance from the fun's centre, D the density of the ether at that distance, and E its elafticity. Let D increase in the direct ratio of x or D= A. x; and suppose where b is a conftant quantity, that

E = b - D

=b

I
A.x

would be determined, if we knew at what distance from the fun's centre, the elafticity of the ether is equal to o. If, for example, it is equal to nothing at the distance

from the fun's centre, or

difference of elafticity for the change of diftance x; and therefore is the force with which a small spherical body, or a fingle particle

of

of matter, impervious to the ether, would be impelled toward

of the distances from the fun. It is therefore POSSIBLE that an elaftic fluid may be fo confituted as to produce a tendency of one body to another, varying inverfely as the fquares of the distances of these bodies.

For this purpose, there is only required an elastic fluid, of which the density is as the distance from the sun, and the elasticity as a certain given magnitude diminished by the reciprocal of that distance. There are many other hypotheses concerning the density and elasticity of the fluid which will give the same result with this; all, indeed, in which we have these equations, D=A.x", and E = b This is directly contrary to Mr

1

D
$

m

Vince's conclusion drawn in 20.

That it is not possible for any law of variation of the density of the fluid in terms of the distance from the sun, combined with any law of variation of the repulsive force of the particles of the fluid in terms of their distance, to satisfy the law of gravitation. And if we were to suppose the law of density to vary in terms of any other quantities besides the distance from the sun, such quantities must enter into the law of force, and thereby make a still further deviation from the law of the inverse square of the distance. Considering the matter therefore only in a mathematical point of view, we are justified in rejecting this hypothesis as the cause of gravitation. But it may be proper further to consider, whether such a fluid could exist under all the circumstances which were supposed to be necessary for solving the phænomena. p. 22, 23.

'

If from mathematical we pass to physical objections, it must be confessed, that the doctrine of an elastic ether is not equally invulnerable, and that Mr Vince's objections in this quarter are well founded. An elastic fluid which did not gravitate to any body (and we cannot suppose a fluid to gravitate which is itself the cause of gravitation), would diffuse itself uniformly over space, without more density or more elasticity in one place than in another. This follows from the nature of fluidity alone, to which, if elasticity be joined, the fluid ought to be dissipated in the immensity of space. If, therefore, a fluid which is elastic, and does not gravitate, remains of a greater density in one place than another, this must arise from some unknown cause,-some power that retains the fluid in a state not natural for it to assume. As we cannot imagine to ourselves what this power is, unless it be gravitation, the very thing for which we would account, it appears that we have gone round in a sort of circle, and have advanced nothing by all the suppositions and reasonings we have accumulated. Hence the hypothesis of an elastic ether for explaining

the

the phenomena of gravitation, unless these physical difficulties can be resolved, must necessarily be abandoned. Yet it must be carefully observed, that it is not in consequence of the mathematical difficulties, or the contradiction supposed by Mr Vince between the hypothesis and the facts to be accounted for, that we have come to this conclusion; but in consequence of physical difficulties, arising from a want of analogy between this and other elastic fluids; difficulties which, though certainly great, are not so insurmountable, nor of the same order with the former.

We confess, that we have some satisfaction in having vindicated Newton from the imputation of having invented a theory that is mathematically false; and in having shown, that the constitution which he supposed in the elastic ether would fit it for producing the effects which he ascribed to it. We are at the same time sure, that the satisfaction we have in this vindication, has had no share in leading us to it; for, on the first perusal of Mr Vince's paper, we were convinced that he was right in his mathematical reasoning. We began this review under that impression; and it was only in the course of that accurate examination, which is necessary when the meaning of one man is to be conveyed in the language of another, that we discovered the fallacy which we have just pointed out.

The other system which the learned Professor considers, is that of John Bernoulli, proposed long after that of Newton, and intended by the author to unite the advantages of the Cartesian and Newtonian systems, without being subject to the difficulties of either, but which, in our opinion, does exactly the reverse, uniting the difficulties of both without the advantages of either. The truth is, that John Bernoulli, though one of the first mathematicians of his age, was far from maintaining the same rank among philosophers. His theory of gravitation is accordingly almost forgotten, and is at present so little known, even to scientific men, that Mr Vince may be accused of some neglect in not naming the work in which that theory is laid down, nor pointing out where it is to be found. The title of the tract is, Essai d'une Nouvelle Physique Céleste,' and it is inserted in the third volume of the Geneva edition of Bernoulli's works, p. 263. It was written on occasion of a question proposed by the Academy of Sciences of Paris in 1734, What is the physical cause of the inclination of the orbits of the planets to the plane of the sun's revolution on its axis; and whence is it that the inclinations of these orbits are different from one another?' By their answers to this question, John Bernoulli and his son Daniel had the singular happiness of sharing the prize between them; an event which, if it was ever to happen, was likely to fall out in the illustrious family of Bernoulli. The que