*

and of Human Knowledge, which are never past the Evasions of refolved Scepticks. But I need not here enlarge, because I am well affur'd that all Aftronomers, who are compleat Masters of that Science, as foon as other Prejudices and Fears are over, will agree with me, that the Arguments under this Head, when allow'd their free and full Weight, do certainly prove that this Annual Revolution belongs to the Earth, and not to the Sun. I do not here mention that Annual Parallax of the Fixed Stars, which Dr. Hook and Mr. Flamfteed think they have discovered, which would certainly demonftrate the Earth's Annual Motion, and which I have elsewhere vindicated from the Objections of Dr. Gregory, and of the French; because it is See Aftron. not yet generally allow'd for true by the Learn- Lect. IV. ed. Nor need I have recourse to that Attempt: Philofophy. fince the most evident Annual Parallax of the Lect. XXI. Planets and Comets, already insisted on, does plainly prove this Annual Motion of the Earth.

N. B. The Reader will eafily perceive, that I propose the former Five Arguments as highly probable, but this laft as a certain Demonstration of the Annual Motion of the Earth.

And Math.

N. B. I do not here meddle with the feveral Objections made formerly against either the Diurnal or Annual Revolutions of the Earth, either from Scripture or from Nature; fince there are See Galifew of the truly Learned and Judicious which leo's Syft. do now infist upon them; and fince they have Cofmic. been fully confider'd and confuted by others, ham's 4in treating on this Argument; to whom I fhall ftrol. Theol refer Pref.

D 4

Mr. Der

refer the Reader, if he ftill want Satisfaction therein.

PRO P. III.

(1.) There is an universal Power of Gravity acting in the whole Syftem; whereby every Body, and part of a Body, Attracts and is Attracted by every other Body and part of a Body, through the whole Syftem. (2.) This Power of Gravity is greater in greater Bodies, and leffer in leffer; and that in the proportion of fuch their Magnitude. (3.) It is alfo greater when the Bodies are nearer, and leffer when they are farther off, and that in the exact duplicate proportion of fuch their nearness. (4.) This Power is the fame in all Places, and at all Times, and with regard to all Bodies whatsoever. (5.) This Power is entirely immechanical, and beyond the Abilities of all material Agents whatsoever.

Demonftration of the first Part; That there is fuch a Power of Gravity in the Universe.

(1.) Because all the Planets, Primary and Secondary, with the Comets, are perpetually drawn from their natural Rectilinear Courfes along ftrait Lines, the Tangents of their prefent Orbits, and made to revolve in Curves; there is therefore a continual Power or Force acting upon them; and because the Power or Force acts fo upon them, as to caufe the Bodies to move juft fo much quicker, as they are nearer their Central Bodies; and juft fo much flower, as they are farther off them; and thereby to oblige them by a Line drawn from the Cen

tral

tral Bodies ever to defcribe equal Area's in equal Times; it therefore follows, by Geometrick Demonstration, that this Power or Force See Math. always tends directly to the Centers of those Philof. Bodies about which they revolve; or is still a 16. Prop. Centripetal Power or Force, with regard to the fame Bodies.

(2.) This Power or Force is properly the Power or Force of Gravity, or the very fame which causes Stones and all heavy Bodies with us to gravitate, and thereby to defcend downward towards the Earth's Center; because upon exact Geometrick Deduction, and Arithmetick Calculation it appears, that the Force which retains the Moon in its Orbit, tends to the fame Center, and is exactly of the fame Quantity with that, which accelerates heavy Bodies with us on the Earth's Surface; due Allowance being made for the Difference of their Distan

ces from the Earth which Force caufes all Bo- See Math. dies whatfoever on the Earth's Surface to de- Philof. fcend a little more than 16 English Feet, in one Prop. 79% ̈

Second of Time.

Demonftration of the Second Part, that this Gravity is exactly proportional to the Magnitude of the Central Body.

(1.) Becaufe the Heavenly Bodies are all Sphærical, and the Force of Gravity tends ftill directly to their feveral Centers, that Force, by See Math. Geometrical Demonftration, is the very fame as Philof. if it tended to every Particle of thofe Central Prop. 45. Bodies, and as if the Gravity of each whole Central Body were compos'd of the Gravity to

each

each Part of the fame; which indeed is the only rational Conception of this Matter; becaufe otherwise this Force must respect not a Body, which is fomewhat real, but a Mathematical Point, which, phyfically speaking, is nothing at all.

(2.) In Fact, the greatest Bodies have the greatest Gravity towards them through the whole Universe. Thus by Calculation from the See Math. Heavenly Motions it appears, that the vastly greatest Force of Gravity is that tending to Prop. 84. the Sun, the next that to Jupiter, the next that

Philof.

to Saturn, the next that to the Earth, and the next that to the Moon; according to the known Order of the Magnitude of their feveral Bodies refpectively. Nor do I omit the other Planets and the Comets here, as if the Cafe. were not the fame in them alfo; but because they have no Planets, that we know of, moving about them; and because they occafion no fenfible Tides in our Ocean; which are the only Phænomena, whence we can draw any certain Indications of the Quantity of that Power of Gravity which tends to them.

Demonftration of the Third Part; that this Gravity is exactly in the Duplicate Proportion of the Nearness of Bodies, i. e. when twice as near, four Times; when thrice as near, nine Times; when four times as near, fixteen Times as ftrong; and fo for ever.

(1.) Because the Cubes of the Distances of the feveral primary Planets about tbe Sun, and

of

of the feveral Secondary Ones about their Primaries, are still found to bear accurately the fame Proportion to each other, which the Squares of their refpective Periodical Times of Revolving alfo bear; it follows, by ftrict Geo- See Math. metrick Reasoning, that the Centripetal Force, Philof. which keeps them in their feveral Curves, is Prop. 13. accurately in the duplicate Proportion of their Nearness to their Central Bodies.

(2.) Because all the primary Planets and Comets revolve about the Sun, and all the fecondary Ones, that are Eccentrical, about their Primaries in Ellipfes, or Conick Sections, and that about the Sun, or their Primaries, fituate in their Foci; it follows, by strict Geometrick Reafoning, that the Centripetal Force, which re- See Math. tains them in fuch Conick Sections, is exactly Philof. in the duplicate Proportion of their nearness to Prop. 21. their Central Bodies.

(3.) Because the Aphelia, or longer Axes of thefe Ellipfes do reft, as to the fixed Stars, in the primary Planets and Comets; and in the fecondary Ones, do move only in proportion to the disturbance they neceffarily meet with from the Inequality of their Distances from the Sun,

it follows from Mathematick Reafoning, that See Math. the Centripetal Force, which acts upon thofe Philof. Planets and Comets, is most accurately in the Prop. 33. duplicate Proportion of their Nearness to their Central Bodies.

N. B. That there appears no manner of Neceffity for this Proportion of Increase and Diminution of the Power of Gravity, as the Squares of the Nearnefs of Bodies, more than for any other Proportion; as fuppofe that of