# Original letter from Richard Bentley to Newton

Feb. 18. 1693.

Hon^{d} Sir,

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

Proved, in y^{e} 6 S^{on} That y^{e} present System of y^{e} world cannot have been eternal. So y^{t} Matter being eternal (according to y^{e} Atheists) All was once a Chaos, y^{t} is, all matter was evenly or near upon evenly diffused in the mundane spaces.

I proceed therefore in this 7^{th} to shew, y^{t} 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 y^{e} present World. And

(1) All bodies around our Earth gravitate, even y^{e} lightest comparatively, & in their Natural Elements.

(2) Gravity \or y^{e} weight of bodies/ is proportional to y^{e} Quantity of Matter, at equal distances from y^{e} Center.

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

(4) Now if Gravity be proportional to y^{e} Q^{ty} of Matter, there is a necessity of admitting a Vacuū

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

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

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

[Sir, to my conceptions, Universal Gravitation according to your Doctrine is so impossible to be solved mechanically, y^{t} I was much surprized to see you warn me what I ascribed to You, for you pretended not to know y^{e} cause of it. As to innate Gravity, you perceive y^{t} it is wholy against my purpose and argumentation. If I used y^{t} word, it was only for Brevity's sake. But I must needs desire your judgmēt of w^{t} is here {illeg} deliverd {illeg} to y^{t} 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 y^{t} it cannot explain universal Gravity, is confuted by y^{e} most vulgar phænomena. He makes long Filets of Materia subtilis reach from y^{e} top of y^{e} Earth's vortex to y^{e} Earth: all bodies descend y^{t} are in y^{e} lower half, because y^{e} superior part of y^{e} filets are y^{e} longer: all ascend in y^{e} higher half for y^{e} contrary reason. But in y^{e} middle of them there is a considerable space of equilibriū, indifferent both to ascent & descent, w^{ch} he calls *espace de repose*: and in y^{t} y^{e} moon moves in a Circle without ascending or descending. Very well. Therefore in y^{e} filets of y^{e} Suns Vortex, all y^{e} space between Mercury & Saturn is an Espace de repose, a small distance for y^{e} æquilibrium; so much longer than y^{e} {other} whole Half of y^{e} Filets from Mercury to y^{e} body of y^{e} 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, y^{e} summe of y^{e} 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, y^{t} all bodies have infinite puncta, so y^{t} there are infinite summs. indeed at y^{t} rate all numbers are infinite, as containing infinite fractions: even fractions themselves are infinite. But such puncta are not Quanta, so y^{t} 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 y^{e} 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 y^{e} middle of y^{e} space. and if never so unevenly diffused, all would convene still into one mass; though not in y^{e} middle of y^{e} mundane space, but in y^{e} center of y^{e} common gravity. (2) Nay though we suppose it once constituted; even then, even now all would convene together, in a finite system. I grant y^{t} if y^{e} whole World was but one Sun and all y^{e} rest planets moving about him, they would not convene. But in several fixt starrs, y^{t} have no motion about each other; they with their systems of planets would all convene in y^{e} common center of mundane gravity; if y^{e} 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 y^{e} supposition of an infinite space, let me ask your opinion. I acquiesce in your authority, y^{t} 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, y^{t} infinite such Masses in an infinite space should maintain an equilibrium, and not convene togetther {sic}? so y^{t} though our System was infinite, it could not be preserved but by y^{e} power of God.]

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

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

Hon^{d}. Sir. This is y^{e} contents of y^{e} former Sermon: y^{e} latter is an Argument of a divine Goodnes from y^{e} 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 y^{t}: But Sir, while I am writing this, I have received a letter from my Bookseller calling away for y^{e} 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. S^{r}, 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. S^{r} I am your most obliged & Hm S^{er}

R Bentley.

<envelope>For

The Hon^{d} M^{r} Isaac Newton

Math. Prof. and Fellow

of Trinity College, in

Post-paid 5. Cambridg.