Feb. 18. 1693.

Hond Sir,

Understanding yt the publication of my Sermons might be delayed a while without any damage to ye 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 yr unexpected and voluntary favour by the last Post doth encourage me to request you, yt you would run over this Abstract and thread of my first unpublisht sermon; & to acquaint me with what you find in it yt is not conformable to Truth & your Hypothesis. My mind would be very much at ease, if I have that satisfaction, before ye discourses are out of my power.

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

I proceed therefore in this 7th to shew, yt 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 ye present World. And

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

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

(3) Gravity is not peculiar to Terrestrial Bodies, but common to all ye planets and ye 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 ye τὸ φαινόμενον or Matter of Fact, for ye 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, yt 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, yt you may see if I am tender enough, how I engage your name in this Matter)

(4) Now if Gravity be proportional to ye Qty of Matter, there is a necessity of admitting a Vacuū

(5) And to æstimate wt proportion ye Void space in our system may bear to ye solid Mass. Refined Gold (though even yt be porous, because dissoluble in and Aqua Regia, and ye tantū non impossibility yt 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 yt Gold is to Air as 16150 to 1 so yt ye void space in the textur of Con Air is 16150 times as big, as ye solid Mass. And because Air hath an Elastick endeavour to expand it self, and ye space it occupies, being reciprocally as its compression, the higher it is, tis ye less compressed and more rarefied, and at ye hight of a few miles it has some Million parts of Void space to one of real Bodie and at ye height of 1 terr. semid: (as . . . . hath calculated) tis so very tenuious, yt a sphære of our common Air (already 16150 parts Nothing) expanded to ye Thinness of yt Region would more than take up ye whole Orb of Saturn, which is many Million Millions of times bigger than all ye Globe of ye Earth: and yet higher above yt, ye Rarefaction gradually increases in immensum. So yt the whole concave of ye 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 yt the proportion of Void space to matter yt is found in our Suns Vortex will near upon hold in ye rest of ye Mundane Space. [I know what Kepler says Epitome Astron. p. 36. therefore Quæro, if this Hypothesis may pass] Allow then yt the Globe of ye Earth is intirely solid and dense, and yt all ye Matter of our Sun, Planets, Atmosphæres and Æther is about 50000 times as much as ye Bulk of ye Earth. Astronomers will bear us witness yt we are liberal enough. Now the Orbis Magnus (7000 Terr. Diam. wide) is 343,000,000,000 times as big as the whole Earth and therefore is 6860000 times as big as all ye matter of our System. But by the doctrine of ye parallaxis, we cannot well {illeg}allow less (in ye Copernican Hypothesis) than 100000 Diam. of ye Orb Mag: for the Diameter of ye Firmament. So yt the whole concave of ye Firmament is (in ye 3 plic. Prop) 1000,000,000,000,000 times as big as ye sphære of ye Orbis Magnus, and therefore (multiplying this by 6860000) it is 6860,000,000,000,000,000,000 times as big as all ye matter of our System. So yt if all yt matter was eavenly disperst in ye concave of ye Firmament, every Corpuscle would have \a sphære/ of void space around it 68600 …. times bigger than its own Dimensions: and ye Diameter of ye Sphære would be above 19,000,000 times longer than ye Diameter of ye Corpuscle (supposing ye Corpuscle to be sphærical). and {therefor} \further/, because of ye equal sphæres of other Corpuscles about yt Corpuscle, ye void space about every corpuscle becomes twice as wide as it was, having a Diam. compounded of ye Diameter of its own sphære and ye 2 semidiameters of ye sphæres of ye 2 next corpuscles opposit. so yt every Atom has a void space about it 8 + 68600 . . . . times as big as ye Atom, <3v> and would be distant 19000,000 times its own length (if sphærical) from any other Corpuscle. And by ye same supposition of equal diffusion, in ye whole surface of ye void sphære about every Atom (whose diam. is 38,000,000 times as long as ye Diam. of ye Atoms, there can be no more than 12 Atoms placed at equal distances from ye central one & from each other (like ye center & angles of an Icosaedron). So yt 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 ye length of yt distance, it is many more million millions of times odds to an Unit, yt it doth not hit & strike upon one of those 12 atoms. But ye proportion of this Void to Matter within our firmament, may hold in all ye other mundane spaces beyond it. [the measure of ye Orbis M. 7000 terrest. Diam. and of ye Firmament 100000 Diam. of ye Orbis Magnus I take from And: Tacquet, being round Numbers. If you substitute better instead of them, ye calculation may be soon altered]

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

(1) Now the design of all this is to shew, which (if ye premises be granted) is evident at first sight, yt in ye 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 Systē, 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 yt 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, yt Matter convened from a Chaos into our System, they must affirm yt before yt given time matter gravitated eternally without convening, which is absurd. [Sir, I make account, yt your courteous suggestion by your Last, yt a Chaos is inconsistent with ye Hypothesis of innate Gravity, is included in this paragraph of Mine.] and again, tis unconceivable, yt 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 Gravitation \Attraction/, Matter could never convene from a Chaos into a System like ours (paragraph. 1) Nay even now, since ye forming of our System, Gravitation is inexplicable otherwise than by attraction. Tis not Magnetism, as You have shewn. Tis not ye effect of Vortical motion; because it is proportional to ye Q. of Matter, for if the Earth was hollow, there would be no less weight of Bodies in ye Air (according to Vortices) than if it was solid to ye Centre; there would be no less pressure toward ye Sun, if ye whole space of ye Sun were a mere Void, than if a dense bodie. Again a Vortical motion, without gravitation antecedent to it, suppposeth {sic} and requires either an Absolute Full, or at least a dense texture of ye Æthereal matter; contrary to what is proved before, & what appears from ye motions of Comets: and besides, as You have shewn it contradicts ye Phænomena of ye slower Motion of Planets in Apheliis quā Periheliis, and ye sesquialteral proportion of ye periodical motions to their Orbs. In a word; if Gravity be not Attraction, it must be caused by impulse and contact; but yt can never solve Universal Att|gr|avitation, in all scituations, lateral as well as descending &c according to ye phænomena of your Hypothesis.

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


(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, ye summe of ye 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, yt all bodies have infinite puncta, so yt there are infinite summs. indeed at yt rate all numbers are infinite, as containing infinite fractions: even fractions themselves are infinite. But such puncta are not Quanta, so yt 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 ye 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 ye middle of ye space. and if never so unevenly diffused, all would convene still into one mass; though not in ye middle of ye mundane space, but in ye center of ye common gravity. (2) Nay though we suppose it once constituted; even then, even now all would convene together, in a finite system. I grant yt if ye whole World was but one Sun and all ye rest planets moving about him, they would not convene. But in several fixt starrs, yt have no motion about each other; they with their systems of planets would all convene in ye common center of mundane gravity; if ye present world was not susteind by a divine power.

[Sir, In a finite world where ar|th|ere are outward fixt starrs, this seems plainly necessary. But in ye supposition of an infinite space, let me ask your opinion. I acquiesce in your authority, yt 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, yt infinite such Masses in an infinite space should maintain an equilibrium, and not convene togetther {sic}? so yt though our System was infinite, it could not be preserved but by ye power of God.]

(3) Moreover if|n| such a chaos though Gravity should supervene to Matter, ye planets could never acquire their transverse motions about ye Sun &c. If they were formed in ye same Orbs they now move in; they could never begin to move circularly; ye æthereal matter could not impress it, for yt 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 ye 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 ye Sun, unless a Divine power gave them yt transve motion, against yt vast impetus yt such great bodies must fall with. So yt on all accounts theres a necessity of introducing a God.

[As to what you cite from Blondel, I have read ye same in Hon: Fabri's Astronomia physica, and Galilæo's System p. 10 and 17: who adds yt by the velocity of Saturn one may compute at what distance from ye Sun it was formed, according to ye degrees of acceleration, found out by himself, {illeg}|of| ye progression of odd numbers. (But he must surely have erred, not knowing wt you have since shewn, yt ye velocity of descent as well as weight of Bodies decreases as ye square of ye distance increases) and yt there is yt proportion{at} of ye distances and velocities of all ye planets quam proxime, as if they all dropt from ye same hight (But you seem to reject this, saying, yt the gravit{illeg}|a|t\ion/ of ye sun must be doubled, at ye very moment they reach their Orbs) I confess I could make no use of ye passage of Galilæo & Fabri; because I could not calculate: so yt I said no more, but in general, as above; & ye 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, yt if I could understand yt thing; it would not be only ornamental to ye discourse; but a great improvement of ye Argument for a divine powe {sic}. For if|I| think it more impossible yt they should be all formed \naturally/ at ye same, yn at various distances: and tis ye 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 ye very same Moment. Which is necessary, if I rightly conceive your meaning about doubling ye Suns attraction. For if Mercury fell first, and when he reached his own orb, ye Suns attraction was doubled. That y|c|ontinuing doubled, ye descents of ye succeeding planets would be proportionably accelerated. Which would disturb ye supposed proportion betwixt Mercul|r|ies velocity and theirs.

Hond. Sir. This is ye contents of ye former Sermon: ye latter is an Argument of a divine Goodnes from ye 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 yt: But Sir, while I am writing this, I have received a letter from my Bookseller calling away for ye 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. Sr, 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. Sr I am your most obliged & Hm Ser

R Bentley.


The Hond Mr Isaac Newton
Math. Prof. and Fellow
of Trinity College, in

Post-paid 5.          Cambridg.

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