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Bodies gravitate towards the Earth, and the Earth again towards Bodies, with equal Moments; the Weight of the Earth towards every Body, or the Force with which the Body attracts the Earth, will be equal to the Weight of the fame Body towards the Earth. But this Weight was fewn to be, as the Quantity of Matter in the Body; and therefore the Force with which every Body attracts the Earth, or the abfolute Force of the Body, will be as the fame Quantity of Matter.

THEREFORE the attractive Force of the entire Bodies, arifes from, and is compounded of the attractive Forces of the Parts; becaufe as was just fhewn: If the Bulk of the Matter be augmented, or diminished, its Virtue is proportionably augmented, or diminished. We muft therefore conclude, that the Action of the Earth is compounded of the united Actions of its Parts; and therefore, that all terreftrial Bodies must attract each other mutually, with abfolute Forces that are as the Marter attracting. This is the Nature of Gravity upon Earth; let us now fee what it is in the Heavens.

THAT every Body perfeveres in its State, either of Rest, or of moving uniformly in a right Line, (unless fo far as it is compell'd to change that State by Forces imprefs'd) is a Law of Nature univerfally received by all Philofo phers. But from thence it follows that Bodies which move in Curve Lines, and are therefore continually going off from the right Lines that are Tangents to their Orbits, are by fome continued Force retained in thofe curvilinear Paths. Since then the Planets move in curvilinear Orbits, there must be fome Force operating, by whofe repeated Actions they are perpetually made to deflect from the Tangents.

Now it is collected by mathematical Reasoning, and evidently demonftrated, that all Bodies that move in any Curve Line defcribed in a Plane; and which, by a Radius drawn to any Point, whether quiefcent, or any how mov'd, defcribe Areas about that Point, proportional to the Times, are urged by Forces directed towards that Point. This must therefore be granted. Since then all Aftronomers agree that the Primary Planets defcribe about the Sun, and the Secondary about the Primary, Areas proportional to the Times; it follows that the Forces

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by which they are perpetually turned afide from the rectilinear Tangents, and made to revolve in curvilinear Orbits, are directed towards the Bodies that are fituated in the Centre of the Orbits. This Force may therefore not improperly be called Centripetal in refpect of the revolving Body, and in Refpect of the Central Body attractive; whatever Cause it may be imagined to arife from.

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BUT befides, thefe Things must be alfo granted, as being Mathematically demonftrated: If feveral Bodies revolve with an equable Motion in concentric Circles, and the Squares of the Periodic Times are as the Cubes of the Distances from the common Centre; the Centripetal Forces will be reciprocally as the Squares of the Distances or, if Bodies revolve in Orbits that are very near to Circles, and the Apfides of the Orbits reft ; the Centripetal Forces of the revolving Bodies will be recipro cally as the Squares of the Distances. That both these Cafes hold in all the Planets, all Aftronomers confént. Therefore the Centripetal Forces of all the Planets are reciprocally as the Squares of the Distances from the Centres of their Orbits. If any fhould object, that the Apfides of the Planets, and efpecially of the Moon, are not perfectly at reft, but are carried with a flow-kind of Motion in Confequentia: One may give this Anfwer, That though we fhould grant this very flow Motion to arife from hence, that the Proportion of the Centripetal Force is a little different from the Duplicate; yet, that we are able to compute Mathematically the Quantity of that Aberration, and find it perfectly infenfible. For the Ratio of the Lunar Centripetal Force itself, which must be the moft irregular of them all, will be indeed a little greater than the Duplicate, but will be fixty Times nearer to that, than it is to the Triplicate. But we may give a truer Anfwer, by faying that this Progreffion of the Apfidès arifes not from an Aberration from the Duplicate proportion, but from a quite different Caufe, as is moft admirably fhewn in Sir Ifaac Newton's Principia. It is certain then, that the Centripetal Forces with which the Primary Planets tend to the Sun, and the Secondary to their Primary, are accurately, as the Squares of the Distances reciprocally.

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FROM what has been already faid, it is plain that the Planets are retained in their Orbits, by fome Force perpetually acting upon them; it is plain, that that Force is vsalways directed towards the Centres of their Orbits; it is plain that its efficacy is augmented with the nearness to the Centre, and diminished with the fame; and that it Das augmented in the very Proportion with which the Square of the Distance is diminished; and diminished an in the fame Proportion with which the Square of the Distance is augmented. Let us now fee whether, by making a Comparison between the Centripetal Forces of the Planets, and the Force of Gravity, we may not by Chance find them to be of the fame Kind. Now they will be of the fame Kind, if we find on both Sides the fame Laws, and the fame Affections. Let us then firft confider the Centripetal Force of the Moon, which is nearest to us.

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THE rectilinear Spaces, which Bodies let fall from Reft, defcribe in a given Time at the very beginning of the Motion, when the Bodies are urged by any Forces whatfoever, are proportional to the Forces: This appears from Mathematical reafoning. Therefore the Centripetal Force of the Moon revolving in its Orbit, is to the Force of Gravity sat the Surface of the Earth, as the Space (which in a very fmall Particle of Time, the Moon deprived of all its circular Force, and defcending by its Centripetal Force towards the Earth) would defcribe, is to the Space which a heavy Body would defcribe, when falling by the Force of its Gravity near to the Earth, in the fame given Particle of Time. The first of these Spaces is equal to the verfed Sign of the Arc, defcribed Lby the Moon in the fame Time, because that verfed Sign measures the Tranflation of the Moon from the Tangent, produced by the Centripetal Force; and therefore may be computed, if the Periodic Time of the Moon, and its Distance from the Centre of the Earth are given The laft Space is found by Experiments of Pendulums,ras Mr. Huygens has fhewn. Therefore by making a Calculation, we shall find, that the firft Spaces to the latter, or the Centripetal Force of the Moon revolving in its Orbit, will be to the Force of Gravity at the Superficies of the Earth as the Square of the Semi

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diameter of the Earth, to the Square of the Semidiameter of the Orbit.

BUT, by what was fhewn before, the very fame Ratio holds between the Centripetal Force of the Moon revolving in its Orbit, and the Centripetal Force of the Moon near the Surface of the Earth: Therefore the Centripetal Force near the Surface of the Earth, is equal to the Force of Gravity. Therefore thefe are not two different Forces, but one and the fame; for if they were dif ferent, thefe Forces united would caufe Bodies to defcend to the Earth with twice the Velocity they would: fall with by the Force of Gravity alone. Therefore it is plain, that the Centripetal Force, by which the Moon is perpetually, either impelled or attracted out of the Tangent, and retained in its Orbit, is the very Force of terre Atrial Gravity reaching up to the Moon: And it is very: reasonable to believe, that Virtue fhould extend itself to vaft Distances, fince upon the Tops of the highest Moun-. tains we find no fenfible Diminution of it.

THEREFORE the Moon gravitates towards the Earth ; but, on the other hand, the Earth, by a mutual Action, gravitates towards the Moon: Which is alfo abundantly confirmed by the Newtonian Philofophy, where the Tides in the Sea, and the Præceffion of the Equinoxes are treated of; which arife from the Action both of the Moon and, of the Sun upon the Earth. Hence, laftly, we discover. by what Law the Force of Gravity decreafes at great Distances from the Earth. For fince Gravity is no ways, different from the Moon's Centripetal Force, and this is reciprocally proportional to the Square of the Distance i it follows, that it is in that very Ratio that the Force of Gravity decreases.

LET us now go on to the reft of the Planets. Be cause the Revolutions of the primary Planets, about the SUN, and of the Secondary about Jupiter and Saturn, are Phenomena of the fame Kind with the Revolution of the MOON about the Earth; and because it has been moreover demonftrated, that the Centripetal Forces of the primary Planets are directed towards the Centre of the SUN, and thofe of the Secondary towards the Centres of Jupiter and Saturn, in the fame Manner as the Centripetal Force of the Moon is directed towards the

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Centre of the Earth; and fince befides, all thefe Forces are reciprocally as the Squares of the Distances from the Centres, in the fame Manner as the Centripetal Force of the Moon is as the Square of the Distance from the Centre of the Earth; we must of Courfe conclude, that the Nature of all is the fame. Therefore as the Moon gra-7 vitates towards the Earth, and the Earth again towards the Moon; fo alfo the Secondary Planets will gravitate towards their Primary, and the Primary Planets again towards their Secondary ; and fo all the Primary towards the SUN; and the Sun again towards them.

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THEREFORE the Sun gravitates towards all the Planets, and all the Planets towards the Sun. For the Secondary Planets, while they accompany the Primary, revolve the mean while with the Primary about the Sun. Therefore, by the fame Argument, the Planets of both Kinds gravitate towards the Sun, and the Sun towards them. That the Secondary Planets gravitate towards the Sun, is moreover abundantly clear from the Inequalities of the Moon; a moft accurate Theory of which, laid open with a moft admirable Sagacity, we find explained in the Third Book of Sir ISAAC NEWTON's Principia.

THAT the attractive Virtue of the SUN is propagated on all Sides to prodigious Distances, and is diffufed to every Part of the wide Space that furrounds it, is moft evidently fhewn by the Motion of the Comets; which, coming from Places immenfly diftant from the Sun, approach very near to it; and fometimes fo near, that in their Perihelia they almoft touch its Body. The Theory of thefe Bodies was altogether unknown to Aftronomers, tiil in our own Times the excellent NEWTON moft happily discovered it, and demonftrated the Truth of it by most certain Obfervations. So that it is now apparent, that the Comets move in Conic-Sections, having their Foci in the Sun's Centre; and, by Radii drawn to the Sun, defcribe Areas proportionable to the Times. But from thefe Phenomena it is manifeft, and mathematically demonftrated, that thefe Forces, by which the Comets are retained in their Orbits, refpect the Sun, and are reciprocally proportional to the Squares of the Distances from its Centre. Therefore the Comets gravitate towards the

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