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Feb. 18. 1693.

Honoured Sir,

Understanding that the publication of my Sermons might be delayed a while without any damage to the Bookseller, I have kept them in my hands, & shall keep them a little longer. And, though there were yet several matters in them, about which I would have purchased your Opinion at no small rate, nevertheless I had not presumed any further to interrupt your worthy design with Questions from a Stranger. But your unexpected and voluntary favour by the last Post doth encourage me to request you, that you would run over this Abstract and thread of my first unpublisht sermon; & to acquaint me with what you find in it that is not conformable to Truth & your Hypothesis. My mind would be very much at ease, if I have that satisfaction, before the discourses are out of my power.

Proved, in the 6 sermon That the present System of the world cannot have been eternal. So that Matter being eternal (according to the Atheists) All was once a Chaos, that is, all matter was evenly or near upon evenly diffused in the mundane spaces.

I proceed therefore in this 7th to shew, that Matter in such a Chaos could never naturally convene into this or a like System. To which end we must consider some systematical phænomena of the present World. And

(1) All bodies around our Earth gravitate, even the lightest comparatively, & in their Natural Elements.

(2) Gravity or the weight of bodies is proportional to the Quantity of Matter, at equal distances from the Center.

(3) Gravity is not peculiar to Terrestrial Bodies, but common to all the planets and the Sun. Nay the whole Bodies of Sun and planets mutually gravitate toward one another; and in a word 'All Bodies gravitate toward All. This Universal Gravitation or Attraction is the τὸ φαινόμενον or Matter of Fact, for the demonstration of which I must referr you to . . . . . Indeed as to the Cause and origin of this Gravity he was pleased to determin nothing. But you will perceive in the sequel of this Discourse, that it is above all Mechanism or power of inanimate Matter, & must proceed from a higher principle and a divine energy & impression.' [I have written these      words at large, that you may see if I am tender enough, how I engage your name in this Matter)

(4) Now if Gravity be proportional to the Quantity of Matter, there is a necessity of admitting a Vacuum

(5) And to æstimate what proportion the Void space in our system may bear to the solid Mass. Refined Gold (though even that be porous, because dissoluble in and Aqua Regia, and the tantum non impossibility that the figures of its Corpuscles should be adapted for total Contact) is to common water as 19 to 1 and water to common air as 850 to 1 so that Gold is to Air as 16150 to 1 so that the void space in the textur of Common Air is 16150 times as big, as the solid Mass. And because Air hath an Elastick endeavour to expand it self, and the space it occupies, being reciprocally as its compression, the higher it is, tis the less compressed and more rarefied, and at the hight of a few miles it has some Million parts of Void space to one of real Bodie and at the height of 1 terrestrial semidiameter (as . . . . hath calculated) tis so very tenuious, that a sphære of our common Air (already 16150 parts Nothing) expanded to the Thinness of that Region would more than take up the whole Orb of Saturn, which is many Million Millions of times bigger than all the Globe of the Earth: and yet higher above that, the Rarefaction gradually increases in immensum. So that the whole concave of the Firmament, except Sun, Planets, and Atmosphæres, may be considerd as a mere Void.

(6) Esto Hypothesis; That every fixt starr is as a Sun; so that the proportion of Void space to matter that is found in our Suns Vortex will near upon hold in the rest of the Mundane Space. [I know what Kepler says Epitome Astron. p. 36. therefore Quæro, if this Hypothesis may pass] Allow then that the Globe of the Earth is intirely solid and dense, and that all the Matter of our Sun, Planets, Atmosphæres and Æther is about 50000 times as much as the Bulk of the Earth. Astronomers will bear us witness that we are liberal enough. Now the Orbis Magnus (7000 Terrestrial Diameters wide) is 343,000,000,000 times as big as the whole Earth and therefore is 6860000 times as big as all the matter of our System. But by the doctrine of the parallaxis, we cannot well allow less (in the Copernican Hypothesis) than 100000 Diameters of the Orbis Magnus for the Diameter of the Firmament. So that the whole concave of the Firmament is (in the 3 parallactic Proposition) 1000,000,000,000,000 times as big as the sphære of the Orbis Magnus, and therefore (multiplying this by 6860000) it is 6860,000,000,000,000,000,000 times as big as all the matter of our System. So that if all that matter was eavenly disperst in the concave of the Firmament, every Corpuscle would have a sphære of void space around it 68600 …. times bigger than its own Dimensions: and the Diameter of the Sphære would be above 19,000,000 times longer than the Diameter of the Corpuscle (supposing the Corpuscle to be sphærical). and further, because of the equal sphæres of other Corpuscles about that Corpuscle, the void space about every corpuscle becomes twice as wide as it was, having a Diameter compounded of the Diameter of its own sphære and the 2 semidiameters of the sphæres of the 2 next corpuscles opposit. so that every Atom has a void space about it 8 + 68600 . . . . times as big as the Atom, <3v> and would be distant 19000,000 times its own length (if sphærical) from any other Corpuscle. And by the same supposition of equal diffusion, in the whole surface of the void sphære about every Atom (whose diameter is 38,000,000 times as long as the Diameter of the Atoms, there can be no more than 12 Atoms placed at equal distances from the central one & from each other (like the center & angles of an Icosaedron). So that lastly every atom is not only so many million millions of times distant from any other Atom, but if it should be moved & impelled (without Attraction or gravitation) to the length of that distance, it is many more million millions odds to an Unit, that it doth not hit & strike upon one of those 12 atoms. But the proportion of this Void to Matter within our firmament, may hold in all the other mundane spaces beyond it. [the measure of the Orbis Magnus 7000 terrestrial Diameters and of the Firmament 100000 Diameters of the Orbis Magnus I take from And: Tacquet, being round Numbers. If you substitute better instead of them, the calculation may be soon altered]

I am aware, that Half of the diameter of the Firmament should be allowed for the Radij of the several Vortices of the next Fixt stars: so that the space of our Suns Vortex should be diminished, as 8 to 1. But because the Semidiameter of the Firmament may be immensly greater than we supposed it, we think that abatement not worth considering.

(1) Now the design of all this is to shew, which (if the premises be granted) is evident at first sight, that in the supposition of such a Chaos, no Quantity of common Motion (without attraction) could ever cause those stragling Atoms to convene into great Masses & move, as they do in our System, a Circular motion being impossible to be produced Naturally, unless there be either a Gravitation or want of Room.

(2) And as for Gravitation, tis impossible that That should either be coæternal & essential to Matter, or ever acquired by it. Not essential & coæternal to Matter; for then even our System would have been eternal (if gravity could form it) against our Atheists supposition & what we have proved in our Last. For let them assign any given time, that Matter convened from a Chaos into our System, they must affirm that before that given time matter gravitated eternally without convening, which is absurd. [Sir, I make account, that your courteous suggestion by your Last, that a Chaos is inconsistent with the Hypothesis of innate Gravity, is included in this paragraph of Mine.] and again, tis unconceivable, that inanimate brute matter should (without a divine impression) operate upon & affect other matter without mutual contact: as it must, if gravitation be essential and inherent in it.

(3) But then if Gravitation cannot be essential to matter, neither could it ever be acquired by matter. This is self evident if Gravitation be true Attraction. And if it be not true Attraction, Matter could never convene from a Chaos into a System like ours (paragraph. 1) Nay even now, since the forming of our System, Gravitation is inexplicable otherwise than by attraction. Tis not Magnetism, as You have shewn. Tis not the effect of Vortical motion; because it is proportional to the Quantity of Matter, for if the Earth was hollow, there would be no less weight of Bodies in the Air (according to Vortices) than if it was solid to the Centre; there would be no less pressure toward the Sun, if the whole space of the Sun were a mere Void, than if a dense bodie. Again a Vortical motion, without gravitation antecedent to it, supposeth and requires either an Absolute Full, or at least a dense texture of the Æthereal matter; contrary to what is proved before, & what appears from the motions of Comets: and besides, as You have shewn it contradicts the Phænomena of the slower Motion of Planets in Apheliis quam Periheliis, and the sesquialteral proportion of the periodical motions to their Orbs. In a word; if Gravity be not Attraction, it must be caused by impulse and contact; but that can never solve Universal gravitation, in all scituations, lateral as well as descending &c according to the phænomena of your Hypothesis.

[Sir, to my conceptions, Universal Gravitation according to your Doctrine is so impossible to be solved mechanically, that I was much surprized to see you warn me what I ascribed to You, for you pretended not to know the cause of it. As to innate Gravity, you perceive that it is wholy against my purpose and argumentation. If I used that word, it was only for Brevity's sake. But I must needs desire your judgment of what is here deliverd to that purpose. I look't a little into Hugenius de la Pesanteur, when it newly came out; and I well remember, that it cannot be reconciled to your Doctrine, and Varignon's book I read, which, besides that it cannot explain universal Gravity, is confuted by the most vulgar phænomena. He makes long Filets of Materia subtilis reach from the top of the Earth's vortex to the Earth: all bodies descend that are in the lower half, because the superior part of the filets are the longer: all ascend in the higher half for the contrary reason. But in the middle of them there is a considerable space of equilibrium, indifferent both to ascent & descent, which he calls espace de repose: and in that the moon moves in a Circle without ascending or descending. Very well. Therefore in the filets of the Suns Vortex, all the space between Mercury & Saturn is an Espace de repose, a small distance for the æquilibrium; so much longer than the whole Half of the Filets from Mercury to the body of the Sun.]

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(4) But though we could suppose Gravitation essential to matter, or rather supervene into Matter while it was diffused in a Chaos; yet it could never naturally constitute a System like ours.

(1) for if Matter be finite; and seeing Extension is not Matter, the summe of the mundane matter must consist of separate parts divided and disterminated by Vacuum; but such parts cannot be positively infinite, any more than there can be an actually and positively infinite arithmetical Summe, which is a contradiction in terms. It may be said, that all bodies have infinite puncta, so that there are infinite summs. indeed at that rate all numbers are infinite, as containing infinite fractions: even fractions themselves are infinite. But such puncta are not Quanta, so that the case is different toto genere. Can a positive summe contain infinite ones, two's, or infinite given fractions? Can it have infinite quota and quanta (as the atoms we speak of are{)}? I say then if Matter be finite it must be in a finite space: But then, by universal Gravity, in an even diffusion all Matter would convene in one mass in the middle of the space. and if never so unevenly diffused, all would convene still into one mass; though not in the middle of the mundane space, but in the center of the common gravity. (2) Nay though we suppose it once constituted; even then, even now all would convene together, in a finite system. I grant that if the whole World was but one Sun and all the rest planets moving about him, they would not convene. But in several fixt starrs, that have no motion about each other; they with their systems of planets would all convene in the common center of mundane gravity; if the present world was not susteind by a divine power.

[Sir, In a finite world where there are outward fixt starrs, this seems plainly necessary. But in the supposition of an infinite space, let me ask your opinion. I acquiesce in your authority, that in matter diffused in an infinite space, tis as hard to keep those infinite particles fixt at an equilibrium, as poise infinite needles on their points upon an infinite speculum. Instead of particles, let me assume Fixt starrs or great Fixt Masses of opake matter; is it not as hard, that infinite such Masses in an infinite space should maintain an equilibrium, and not convene together? so that though our System was infinite, it could not be preserved but by the power of God.]

(3) Moreover in such a chaos though Gravity should supervene to Matter, the planets could never acquire their transverse motions about the Sun &c. If they were formed in the same Orbs they now move in; they could never begin to move circularly; the æthereal matter could not impress it, for that is too thin, & is indifferent to east or west, as appears from Comets. Nor could G{ravity} act in an horizontal line, as they move in, where there is no inclination nor descent. We therefore suppose the planets to be formed in some higher regions, & first descend towards the Sun, wherby they would acquire their velocities? But then they would have continued their descent to the Sun, unless a Divine power gave them that transverse motion, against that vast impetus that such great bodies must fall with. So that on all accounts theres a necessity of introducing a God.

[As to what you cite from Blondel, I have read the same in Hon: Fabri's Astronomia physica, and Galilæo's System p. 10 and 17: who adds that by the velocity of Saturn one may compute at what distance from the Sun it was formed, according to the degrees of acceleration, found out by himself, of the progression of odd numbers. (But he must surely have erred, not knowing what you have since shewn, that the velocity of descent as well as weight of Bodies decreases as the square of the distance increases) and that there is that proportion of the distances and velocities of all the planets quam proxime, as if they all dropt from the same hight (But you seem to reject this, saying, that the gravitation of the sun must be doubled, at the very moment they reach their Orbs) I confess I could make no use of the passage of Galilæo & Fabri; because I could not calculate: so that I said no more, but in general, as above; & the rather; because I knew that there must be some given hights, from whence each of them descending might acquire their present velocities. But I own, that if I could understand that thing; it would not be only ornamental to the discourse; but a great improvement of the Argument for a divine power. For I think it more impossible that they should be all formed naturally at the same, than at various distances: and tis the miracle of all miracles, if they were naturally formed at such intervals of time, as all of them to arrive at their respective Orbs at the very same Moment. Which is necessary, if I rightly conceive your meaning about doubling the Suns attraction. For if Mercury fell first, and when he reached his own orb, the Suns attraction was doubled. That continuing doubled, the descents of the succeeding planets would be proportionably accelerated. Which would disturb the supposed proportion betwixt Mercuries velocity and theirs.

Honoured Sir. This is the contents of the former Sermon: the latter is an Argument of a divine Goodnes from the Meliority in our system, above what was necessary to be in Natural Causality. I hope I shall have no need to give you more trouble in that: But Sir, while I am writing this, I have received a letter from my Bookseller calling away for the Press. Let me but begg of you by the next post some brief hints, what you approve of and what not. For I have resolved to expect your answer let him be never so clamorous. Sir, I heartily ask your pardon for giving you the trouble of this; which I must increase likewise by another piece of Boldnes in desiring your good leave to present you with my 8 poor discourses; when these 2 last are made publick. Sir I am your most obliged & Humble Servant

R Bentley.

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