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Again, it is proved by Mathematicians, that all Bodies moving in any Curve Line defcribed in a Plane, and which by Radii drawn to any certain Point, defcribe Areas about the loint proportionable to the Times; arc impell'd, or a3ed on by (ome Power tending to that Point : Now it is ftiewn by the Aflronomers that the Primary Planets, round the Sun 5 and the Secundarv Planets, round the Primary ones, do defcribe Areas proportionable to the Times. Contequent- Jy, the Power whereby they are retain'd in their Orbits, is direiled towards the Bodies placed in the Centres thereof.
Laftly, it is demonflrated, that if feveral Bodies revolve with an equable Motion in Concentrical Circles, and the Squares of their Periodical Times be as the Cubes of the Diflances from the Common Centre; the Centripetal Forces of the revolving Bodies, will be reciprocally as the Squares of the Diflances. Or, if Bodies revolve in Orbits approach- ing to Circles, and the Apfides of thofe Orbits be at reft; the Centripetal Forces of the revolving Bodies, will be re- ciprocally as the Squares of rhe Diflances.
Now, the Aflronomers all agree, that both thefe Cafes obtain in all the Planets : Whence it follows, that the Cen- tripetal Powers of all the Planets are reciprocally as the Squares of the Dittanies from the Centres of the Orbits.
Upon the whole, it appears, that the Planets are retain'd in their Orbits by Tome Power which is continually afting on them : That this Power is directed toward the Centre of their Orbils: That the Intention, or Efficacy of this Power in- creafes upon an Approach toward the Centre, and diminifties at its Recefs from the fame; and that it increafes in the fame Proportion as the Diftance diminifhes ; and diminifties in the fame as the Diflance increafes — Now, by comparing this Centripetal Force of the Planets, with the Force of Gra- vity on Earth, they will be found perfeflly alike.
This we fhall illuftrate in the Cafe of the Moon, the nearcft to us of all the Planets — The Reailinear Spaces de- fcrib'd in any given Time by a falling Body urged by any Powers, reckoning from the Beginning of its Defcent, are proportionable to thofe Powers. Confequently, the Centri- petal Force of the Moon revolving in its Orbit, will be to the Force of Gravity on the Surface of the Earth ; as the Space which the Moon would defcribe in falling, any little Time, by her Centripetal Force towards the Earth, had ftie no circular Motion at all, to the Space, a Body near the Earth would defcribe in falling by its Gravity towards the fame.
Now, by an sftual Calculus of thofe two Spaces, it appears, that the firfl of them is to the fecond, i. e. the Centripe- tal Force of the Moon revolving in her Orbit, is to the Force of Gravity on the Surface of rhe Earth, as the Square of the Earth's Semidiameter, to the Square of the Semidiameter of her Orbit: Which is the fame Ratio, as that of the Moon's Centripetal Force in her Orbit, to the fame Force near the Surface of the Earth.
The Moon's Centripetal Force, therefore, is equal to the Force of Gravity, Thefe Forces, confequently, are not dif- ferent, but one and the fame: For, were they different, Bo- dies acted on by the two Powers conjointly, would fall to- wards the Earth, with a Velocity double to that ariling from the fole Power of Gravity,
It is evident, therefore, that the Moon's Centripetal Force, whereby ftie is retajn'd in her Orbit, and prevented from running off in Tangents ; is the very Power blGravity of the Earth, extended thither.
The Moon, therefore, gravitates towards the Earth ; and the Earth reciprocally towards the Moon : which is further confirm'd by the Phenomena of the Tides. See Tides.
The like Reafoning might be applied to the other Pla- nets — For, as the Revolutions of the Primary Planets round the Sun, and thofe of the Satellites of Jupiter and Saturn round their Primaries, are Phenomena of the fame Kind as the Revolution af the Moon round the Earth ; as the Cen- tripetal Powers of the Primary are directed towards the Centre of the Sun ; and thofe of the Satellites, towards the Centre of their Primaries ; and laftly, as all thefe Powers are reciprocally as the Squares of the Diflances from the Centres : it may fafely be concluded that the Power and Ca.ufe is the fame in all.
Therefore, as the Moon gravitates towards the Earth, and the Earth towards the Moon ; fo do all the Sccundaries to their Primary ones ; the Primary to their Secundary ones ; fo, alio, the Primary ones to the Sun, and the Sun to the Primary ones. See Planet, Comet, System, &c.
Phenomena, or 'Properties ofUniverfal Gravity.
i . All the feveral Particles of all Bodies in Nature gra- vitate to all the Particles of all other Bodies.
To what has been urged in Proof hereof, from the Ana- logy between the Motions of the feveral Bodies in our Sy- ftem ; it may be added, that Saturn is actually obferved by Aflronomers to change its Courie when nearefl to Jupiter-, and Jupiter i alfo, is found to diflurb the Motion of the Si-
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£m££ ftT i nVr h " the &***** "f thoft Bodie, is Matter of actual Obfervation. See Jupiter Saturn and Satellites ; fee alfo Disturbing Force. ^ "*'"
2. The Quantity of this Gravity at equal ^Diflances. is always proportional to the gitantity of Matter in the gravitating Bodies.
For, the Powers of Gravity, are as the Quantities of Mo- tion they generate; which Quantities, in unequal Bodies, equally fwift, are t0 each othel . as the Qu ant i ties of Matter: Confequently, fince unequal Bodies, which are equally fwift, are to each other as the Quantities of Matter; therefore, in regard unequal Bodies at the fame Diftance from the attract- ing tiody are found to move equally fwift, by Gravity: It is evident, the Forces of Gravity are proportionable to the Quantities of Matter. .
3. The Proportion of the Increafe, or 'Dccreafe of Gra- vity m the Approach, or Removal of Bodies from each other, is this; that the Force is reciprocally in a Im- plicate Ratio ; i. e. As the Squares of the Diflances.
Thus fuppofe a Body of an hundred Pounds, at the Di- itance i at ten Diameters from the Earth ; the fame Body,
i I S?" C ? wer , e , but half fo 8 rcat > would have quadru- ple the Weight : If its Diftance were bur one third of the former, its Weight would be nine times as great, ®c.
Hence, we gather the following Corollaries. i° That at equal Diflances from the Centre of Homogeneal Bodies, the Gravity is direftly as the Quantity of Matter, and inverfely as the Square of the Diameter. z° That on the Surfaces of equal, fpherical, and homogeneous Bodies, the Gravities are as rhe Denfities. 3 ° That on the Surfaces of fpheri- cal, homogeneous, equally denfe, but unequal Bodies, the Gravities are inverfely as the Squares of rhe Diameters. 4° That if both the Denfities and Diameters differ, the Gravities on the Surfaces will be in a Ratio compounded of the Denfities, and the Diameters. Laftly, rhat a Body placed any where, within a hollow Sphere, which is homo- geneous, and every where of the fame Thickncfs, will have no Gravity, wherefoever it be placed ; the oppofite Gravities always precifely deftroying each other.
For the Particular Laws of the Defcem of Bodies, by the Force of Gravity, fee Descent of Bodies; and Cen- tripetal Force.
•Caufe of Gravity
We have various Theories advanced by the Philofophers of various Ages to account for this Grand Principle of Gra- vitation. The antients, who were only acquainted with particular Gravity, or the Tendency of fublunar Bodies to- wards the Earth, aim'dno further than at a Syflem which fnould amwer the more obvious Phenomena of the fame • But the Moderns, as their Principle is higher and more extenfive, fo fhould their Theory be.
Ariflotle, and the Peripateticks, content themfelves to re- fer Gravity or Weight to a native Inclination in heavy Bo- dies to be m their proper Place or Sphere, the Centre of the Earth. See Sphere and Element.
Copernicus afcribes it to an innate Principle in all Parrs of Matter, whereby when feparated from their Wholes they endeavour to return to them again, the neareft way.
But neither of thefe Syftems affigns any Phyfical Caufe of this great Effect : They only amount to this, that Bodies deicend, becauTe they defcend.—
Gaffendus, Kepler, Gilbert, and others afcribe Gravitv to a certain Magnetic Attraction of the Earth.
Thefe Authors conceive the Earth to be one great Maenet continually emitting Effluvia, which lay hold on all Bodies and draw them toward the Earth— But this, we have ob- ierv d, is inconfiftent with the Pha:nomena. See Magne- tism.
Ties Cartes, and his Followers, Rohault, &c. attribute Gravity to an external Impulfe, or Trufion of fome fubtle Matter. SeeCARTEsiANisM.
By the Rotation of the Earth, fay they, all the Parts and Appendages thereof neceffarily endeavour to recede from the Centre ot Rotation : But they cannot, all, aflually recede, as thete is no Vacuum or Space to receive them.
If now, wefuppofetheEarthABCD, Tab. Mechanicks t Fig. 8. and L a Terreflrial Body placed in the Pyrami- dal Space, A E B : It follows, that the Matter in this Py- ramid, will have fo much lets Endeavour to recede from the Centre, as the Body L has a lets Endeavour than the fluid Matter whole Place it poffeffes. Hence it will follow, that the Matter of the adjacent Pyramids receding with more Force; that in the Pyramid A E B, and particularly the Body L will be thereby driven toward the Centre • for the fame Reafons, as Cork, tho' a heavy Eody, alcends in Water.
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