3
Feb. 18. 1693.
HondHonoured Sir,
Understanding ytthat the publication of my Sermons might be delayed a while without any damage to yethe
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, never
theless I had not presumed any further to interrupt your worthy design with Questions from a Stran
ger. But yryour unexpected and voluntary favour by the last Post doth encourage me to request you,
ytthat you would run over this Abstract and thread of my first unpublisht sermon; & to acquaint me
with what you find in it ytthat is not conformable to Truth & your Hypothesis. My mind would be very much
at ease, if I have that satisfaction, before yethe discourses are out of my power.
Proved, in yethe 6 Sonsermon That yethe present System of yethe world cannot have been eternal. So ytthat Matter
being eternal (according to yethe Atheists) All was once a Chaos, ytthat is, all matter was evenly or
near upon evenly diffused in the mundane spaces.
I proceed therefore in this 7th to shew, ytthat Matter in such a Chaos could never naturally
convene into this or a like System. To which end we must consider some systematical phæno
mena of yethe present World. And
(1) All bodies around our Earth gravitate, even yethe lightest comparatively, & in their Natural Elements.
(2) Gravity or yethe weight of bodies is proportional to yethe Quantity of Matter, at equal distances from yethe Center.
(3) Gravity is not peculiar to Terrestrial Bodies, but common to all yethe planets and yethe 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 yethe τὸ φαινόμενον
or Matter of Fact, for yethe 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, ytthat 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, ytthat you may see if I am tender enough, how I engage your name in this Matter)
(4) Now if Gravity be proportional to yethe QtyQuantity of Matter, there is a necessity of admitting a Vacuūum
(5) And to æstimate wtwhat proportion yethe Void space in our system may bear to yethe solid Mass. Refined Gold
(though even ytthat be porous, because dissoluble in ☿ and Aqua Regia, and yethe tantūum non impossibility ytthat 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 ytthat Gold is to Air as 16150 to 1 so ytthat yethe void space in the textur of ConCommon
Air is 16150 times as big, as yethe solid Mass. And because Air hath an Elastick endeavour to expand it
self, and yethe space it occupies, being reciprocally as its compression, the higher it is, tis yethe less compressed
and more rarefied, and at yethe hight of a few miles it has some Million parts of Void space to one
of real Bodie and at yethe height of 1 terr.terrestrial semid:semidiameter (as . . . . hath calculated) tis so very tenuious, ytthat
a sphære of our common Air (already 16150 parts Nothing) expanded to yethe Thinness of ytthat Region
would more than take up yethe whole Orb of Saturn, which is many Million Millions of times bigger
than all yethe Globe of yethe Earth: and yet higher above ytthat, yethe Rarefaction gradually increases in immensum.
So ytthat the whole concave of yethe 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 ytthat the proportion of Void space to matter
ytthat is found in our Suns Vortex will near upon hold in yethe rest of yethe Mundane Space. [I know what
Kepler says Epitome Astron. p. 36. therefore Quæro, if this Hypothesis may pass] Allow then ytthat the Globe
of yethe Earth is intirely solid and dense, and ytthat all yethe Matter of our Sun, Planets, Atmosphæres and Æther is
about 50000 times as much as yethe Bulk of yethe Earth. Astronomers will bear us witness ytthat we are liberal enough.
Now the Orbis Magnus (7000 Terr.Terrestrial Diam.Diameters wide) is 343,000,000,000 times as big as the whole Earth
and therefore is 6860000 times as big as all yethe matter of our System. But by the doctrine of yethe parall
axis, we cannot well ethe Copernican Hypothesis) than 100000 Diam.Diameters of yethe OrbOrbis Mag:Magnus
for the Diameter of yethe Firmament. So ytthat the whole concave of yethe Firmament is (in yethe 3 plic.parallactic PropProposition)
1000,000,000,000,000 times as big as yethe sphære of yethe Orbis Magnus, and therefore (multiplying this
by 6860000) it is 6860,000,000,000,000,000,000 times as big as all yethe matter of our System. So ytthat if
all ytthat matter was eavenly disperst in yethe concave of yethe Firmament, every Corpuscle would
have a sphære of void space around it 68600 …. times bigger than its own Dimensions: and yethe Diameter
of yethe Sphære would be above 19,000,000 times longer than yethe Diameter of yethe Corpuscle (supposing
yethe Corpuscle to be sphærical). and therefor further, because of yethe equal sphæres of other Corpuscles about
ytthat Corpuscle, yethe void space about every corpuscle becomes twice as wide as it was, having a Diam.Diameter
compounded of yethe Diameter of its own sphære and yethe 2 semidiameters of yethe sphæres of yethe 2 next
corpuscles opposit. so ytthat every Atom has a void space about it 8 + 68600 . . . . times as big as yethe Atom,
and would be distant 19000,000 times its own length (if sphærical) from any other Corpuscle. And by yethe
same supposition of equal diffusion, in yethe whole surface of yethe void sphære about every Atom (whose diam.diameter
is 38,000,000 times as long as yethe Diam.Diameter of yethe Atoms, there can be no more than 12 Atoms placed at e
qual distances from yethe central one & from each other (like yethe center & angles of an Icosaedron). So ytthat 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 yethe length of ytthat distance, it is many
more million millions of times odds to an Unit, ytthat it doth not hit & strike upon one of those
12 atoms. But yethe proportion of this Void to Matter within our firmament, may hold in all yethe other
mundane spaces beyond it. [the measure of yethe Orbis M.Magnus 7000 terrest.terrestrial Diam.Diameters and of yethe Firmament
100000 Diam.Diameters of yethe Orbis Magnus I take from And: Tacquet, being round Numbers. If you sub
stitute better instead of them, yethe calculation may be soon altered]
I am aware, ytthat Half of yethe diameter of yethe Firm.Firmament should be allowed for yethe Radij of yethe several
Vortices of yethe next Fixt stars: so ytthat the space of our Suns Vortex should be diminished, as 8 to 1.
But because yethe Semid.Semidiameter of yethe Firm.Firmament may be immensly greater than we supposed it, we think ytthat abate
ment not worth considering.
(1) Now the design of all this is to shew, which (if yethe premises be granted) is evident at
first sight, ytthat in yethe 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 Systēem,
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 ytthat 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, ytthat Matter convened from a Chaos into our
System, they must affirm ytthat before ytthat given time matter gravitated eternally without convening,
which is absurd. [Sir, I make account, ytthat your courteous suggestion by your Last, ytthat a
Chaos is inconsistent with yethe Hypothesis of innate Gravity, is included in this paragraph of Mine.]
and again, tis unconceivable, ytthat 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 mat
ter. 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 yethe forming
of our System, Gravitation is inexplicable otherwise than by attraction. Tis not Magnetism, as You
have shewn. Tis not yethe effect of Vortical motion; because it is proportional to yethe Q.Quantity of Matter, for if
the Earth was hollow, there would be no less weight of Bodies in yethe Air (according to Vortices) than if
it was solid to yethe Centre; there would be no less pressure toward yethe Sun, if yethe whole space of yethe Sun were
a mere Void, than if a dense bodie. Again a Vortical motion, without gravitation antecedent to it, sup
pposethsupposeth and requires either an Absolute Full, or at least a dense texture of yethe Æthereal matter; contra
ry to what is proved before, & what appears from yethe motions of Comets: and besides, as You have shewn
it contradicts yethe Phænomena of yethe slower Motion of Planets in Apheliis quāam Periheliis, and yethe sesqui
alteral proportion of yethe periodical motions to their Orbs. In a word; if Gravity be not Attraction,
it must be caused by impulse and contact; but ytthat can never solve Universal Attgravitation, in all sci
tuations, lateral as well as descending &c according to yethe phænomena of your Hypothesis.
[Sir, to my conceptions, Universal Gravitation according to your Doctrine is so impossible to be solved
mechanically, ytthat I was much surprized to see you warn me what I ascribed to You, for you pretended not
to know yethe cause of it. As to innate Gravity, you perceive ytthat it is wholy against my purpose and
argumentation. If I used ytthat word, it was only for Brevity's sake. But I must needs desire your judgmēent
of wtwhat is here tthat 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 ytthat it cannot explain universal Gravity, is confuted by yethe most vulgar phæno
mena. He makes long Filets of Materia subtilis reach from yethe top of yethe Earth's vortex to yethe Earth: all bodies
descend ytthat are in yethe lower half, because yethe superior part of yethe filets are yethe longer: all ascend in yethe higher
half for yethe contrary reason. But in yethe middle of them there is a considerable space of equilibriūum, in
different both to ascent & descent, wchwhich he calls espace de repose: and in ytthat yethe moon moves in a
Circle without ascending or descending. Very well. Therefore in yethe filets of yethe Suns Vortex, all yethe space
between Mercury & Saturn is an Espace de repose, a small distance for yethe æquilibrium; so much
longer than yethe other whole Half of yethe Filets from Mercury to yethe body of yethe 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, yethe summe of yethe mundane matter
must consist of separate parts divided and disterminated by Vacuum; but such parts cannot be posi
tively infinite, any more than there can be an actually and positively infinite arithmetical Summe,
which is a contradiction in terms. It may be said, ytthat all bodies have infinite puncta, so ytthat there are
infinite summs. indeed at ytthat rate all numbers are infinite, as containing infinite fractions:
even fractions themselves are infinite. But such puncta are not Quanta, so ytthat 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 yethe 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 yethe middle of yethe space. and if never so unevenly diffused, all would convene
still into one mass; though not in yethe middle of yethe mundane space, but in yethe center of yethe common
gravity. (2) Nay though we suppose it once constituted; even then, even now all would convene
together, in a finite system. I grant ytthat if yethe whole World was but one Sun and all yethe rest planets
moving about him, they would not convene. But in several fixt starrs, ytthat have no motion about
each other; they with their systems of planets would all convene in yethe common center of mundane
gravity; if yethe present world was not susteind by a divine power.
[Sir, In a finite world where arthere are outward fixt starrs, this seems plainly necessary.
But in yethe supposition of an infinite space, let me ask your opinion. I acquiesce in your authority,
ytthat 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 par
ticles, let me assume Fixt starrs or great Fixt Masses of opake matter; is it not as hard, ytthat in
finite such Masses in an infinite space should maintain an equilibrium, and not convene toget
thertogether? so ytthat though our System was infinite, it could not be preserved but by yethe power of God.]
(3) Moreover ifn such a chaos though Gravity should supervene to Matter, yethe planets could
never acquire their transverse motions about yethe Sun &c. If they were formed in yethe same Orbs
they now move in; they could never begin to move circularly; yethe æthereal matter could not impress
it, for ytthat is too thin, & is indifferent to east or west, as appears from Comets. Nor could Gravity
act in an horizontal line, as they move in, where there is no inclination nor descent. We
therefore suppose yethe 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 yethe Sun,
unless a Divine power gave them ytthat transvetransverse motion, against ytthat vast impetus ytthat such great bodies must
fall with. So ytthat on all accounts theres a necessity of introducing a God.
[As to what you cite from Blondel, I have read yethe same in Hon: Fabri's Astronomia physica, and
Galilæo's System p. 10 and 17: who adds ytthat by the velocity of Saturn one may compute at what di
stance from yethe Sun it was formed, according to yethe degrees of acceleration, found out by himself, ethe progression
of odd numbers. (But he must surely have erred, not knowing wtwhat you have since shewn, ytthat yethe velocity
of descent as well as weight of Bodies decreases as yethe square of yethe distance increases) and ytthat there
is ytthat proportionat of yethe distances and velocities of all yethe planets quam proxime, as if they all dropt
from yethe same hight (But you seem to reject this, saying, ytthat the gravitethe sun must be doubled, at yethe
very moment they reach their Orbs) I confess I could make no use of yethe passage of Galilæo & Fabri; be
cause I could not calculate: so ytthat I said no more, but in general, as above; & yethe 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, ytthat if I could understand ytthat thing; it would not be only ornamental to
yethe discourse; but a great improvement of yethe Argument for a divine powepower. For ifI think it more impossible
ytthat they should be all formed naturally at yethe same, ynthan at various distances: and tis yethe 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 yethe very same Moment. Which is necessary, if I rightly conceive your meaning about doubling yethe Suns
attraction. For if Mercury fell first, and when he reached his own orb, yethe Suns attraction was doubled.
That ycontinuing doubled, yethe descents of yethe succeeding planets would be proportionably accelerated. Which
would disturb yethe supposed proportion betwixt Merculries velocity and theirs.
Hond.Honoured Sir. This is yethe contents of yethe former Sermon: yethe latter is an Argument of a divine Goodnes
from yethe 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 ytthat: But Sir, while I am writing this, I have received
a letter from my Bookseller calling away for yethe 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. SrSir, 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. SrSir I am your most obliged & HmHumble SerServant
R Bentley.
For
The HondHonoured Mr Isaac Newton
Math. Prof. and Fellow
of Trinity College, in
Post-paid 5. Cambridg.