impoffibility of affigning to this medium any law of variation of denfity and of elafticity, by which its force on the bodies furrounded by it can be made to vary inverfely as the squares of the diftances 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 denfity 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 elastic 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 affigned to m and n, the force obtained as above will not follow the inverse ratio of the fquares of the distances; 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 elafticity, expreffed thus, Ax+Bx", cannot take place, because the force arifing from it would alfo involve two terms, yet if one of the terms be constant, as if mo, and so the expression = A + B x", then the force would be expreffed by one term only, viz. by the fluxion of B x”, that is, by a quantity proportional to xa-i.

Thus, for example, if x be any diftance from the fun's centre, D the denfity of the ether at that distance, and E its elasticity. Let D increase in the direct ratio of x or D = A. x; and suppose

E = b − = b − 1, where b is a conftant quantity, that

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. it is equal to nothing at the diftances from the

If, for example, fun's centre, or

ferential of this being taken, gives È =

A.x2

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

1

the fun; and it varies as or in the inverfe ratio of the fquares of the distances from the fun. It is therefore POSSIBLE that an elaftic fluid may be fo conflituted as to produce a tendency of one body to another, varying inverfely as the fquares of the diftances of thefe 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., and Eb This is directly contrary to Mr

D

1

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 clasticity 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

stion

stion which Bernoulli proposed to resolve, evidently presupposed the existence of vortices; and he, accordingly, proceeding on that hypothesis, imagines that there are vortices of a very subtle matter, which belong to the sun and to each of the planets. The pure and unmixed matter of the vortex, he supposes to be a fluid so perfect, as to give no resistance to the bodies that move in it; so that its parts are, in effect, as Mr Vince states it, without inertia, though we do not observe that Bernoulli himself has ever made use of this expression. Toward the centre of the solar vortex, where the matter composing it is the purest, it is the same with the substance of the sun, and constitutes the particles of light and heat. In the remoter parts, the matter of the vortex is less pure, and is mixed with corpuscles of a grosser substance. It is to the action of this vortex that the angular motion of the planets is to be ascribed. Their tendency to the sun, by which they are prevented from obeying the centrifugal force, is next accounted for. The sun, consisting, as was said, of the purest matter of the vortex, and that matter being in a state of great agitation and effervescence, a vast multitude of particles are perpetually thrown off from it, which form both light and heat. These fly off in right lines in all directions, in a vast number, and with inconceivable velocity. When they reach the extremity of the vortex, where it is pressed on by other vortices, they meet with particles of the same sort, that have in like manner made their way through these last mentioned vortices, and, uniting with those particles, form little balls, which, though very small, are far larger than the original molecules which compose them. The balls thus formed must in general have motion, as their constituent parts had; so that some of them are carried into other vortices ; while others fall back on the same vortex from which they came, and have their motion directed to its centre. Hence, there is in each vortex a perpetual shower of such balls moving from the circumference to the centre; and as the balls are less subtle than the particles that compose them, they do not so easily pass through the pores of the gross bodies, such as the earth, against which they strike. The blows given in this manner to the hemisphere turned from the sun, is the cause of the earth's tendency or gravitation toward that body.

This, as far as we are able to comprehend it, and can afford room for explaining it, is the hypothefis of Bernoulli. We have drawn up our abftract rather from the author himself than from Mr Vince, who has omitted a very important circumftance, the formation of the balls that are the cause of the gravitation to the fun.

The whole, however, is such an affemblage of gratuitous and improbable, not to fay impoffible affumptions, that it does not deferve

refutation.

refutation. The ideas of mankind concerning what are the true objects of philofophy, are certainly greatly improved fince the time when this paper was crowned by the Academy of Sciences. There is not at this moment in Europe, we are perfuaded, any learned fociety from which even the name of Bernoulli could obtain for it a patient hearing. The author is fo well fatisfied, however, with this modification of the theory of vortices, that he goes on to deduce from it the inclination of the planetary orbits to the plane of the fun's rotation, or that in which the vortex revolves. If the planets were spherical, they would revolve exactly in that plane; but, being fpheroidal, they make, as he expreffes it, a kind of leeway in their motion round the fun, and deviate by that means from the plane in which it revolves. In the cafe of the earth, he goes on to demonftrate, that this deviation agrees exactly with what might be expected, fuppofing the earth to be an oblong fpheroid (lengthened at the poles) as determined by Caffini. Unfortunately for this coincidence, of which Bernoulli makes great account, the figure of the earth is known to be oblate, directly contrary to what he fuppofed.

One circumftance in the favour of a hypothefis which has fo little, in other refpects, to recommend it, we must not omit to mention. It is, that the formation of the particles iffuing from the fun into little balls which return to the fun again, prefents us with fomething like a circulation, by which light is made to return to the luminary from which it was originally emitted. That light does fo return in reality, by fome means or other, is extremely probable, and conformable to the maxim, that nature nowhere admits of unlimited and' progreffive change. Such change, however flow, muft deftroy the order of which it makes a part; and is therefore very unlike the economy obferved in the other phenomena of the heavens. Bernoulli's theory, therefore, includes at least one particular, in which the wisdom and fimplicity of nature appears to have been confulted.

Such are the three fyftems for explaining the phenomena of gravitation, of which Profeffor Vince has given an account; and having found them all to be very imperfect, he concludes, that no mechanical explanation of gravity can be given; that it cannot be referred to a fecond cause; and must needs be confidered as the immediate agency of the Supreme Being. Before coming to this conclufion, however, and planting the facred barriers which phyfical inquiry was never to tranfgrefs, it was incumbent on him to be well affured that his enumeration was complete. But it is, fo far from being complete, that a fyftem, which appears to us by far more ingenious and fatisfactory than any of the three juft mentioned, if not entirely omitted, is fo incorrectly stated

by