XXVI.

tions which

If Attraction be proportional to the Maffes, the Alteration caused by the The altera Action of Jupiter on the Orbit of Saturn in their Conjunction, ought the planets much to exceed that produced in the Orbit of Jupiter by the Action of Sa- mutually turn, fince the Mafs of Jupiter is much greater than that of Saturn, and produce in this Obfervation evinces; the Alteration in the Orbit of Jupiter in its Con- follow the junction with Saturn, though fenfible is confiderably lefs than what is ob- ratio of their ferved in the Orbit of Saturn.

XXVII.

But if the Effect of Attraction, or the Space described by the attracted Body, depends on the Mafs of the attracting Body, why should it not allo depend on the Mass of the attracted Body? This Point furely deferves to

be examined.

Experiment proves that all Bodies near the Surface of the Earth, when the Refiftance of the Air is removed, defcend with equal Velocities; for in the Air-pump, after exhaufting the Air, Gold and Feathers fall to the Bottom in the fame Time.

Newton has confirmed this Experiment by another, in which the smallest Difference becomes obvious to our Senfes. He relates (Prop. 24. B. 2. and Prop. 6. B. 3.) that he composed several Pendulums of Materials entirely different; for inftance of Water, Wood, Gold, Glafs, &c. and having fufpended them by Threads of equal Length, for a confiderable Time their Ofcillations were Synchronal.

XXVIII.

their courfes

maffes,

Attraction

out

It admits therefore of no Doubt, that the attractive Force of our Earth is proportioned to the Maffes of the Bodies it attracts, and at equal Distan- is proportioces it depends folely on their Maffes, that is on their Quantities of Matter; nal to the hence if the terreftrial Bodies were transferred to the Orbit of the Moon, males withit having been proved Iready that the fame Force acts on the Moon and fpect being on thofe Bodies, and that it decrcafes as the Square of the Distances. The had to the Distances being fuppofed equal, it follows, that fuppofing the Moon de-form or fpeprived of her projectile Force, thofe Bodies and the Moon would fall in attracting the fame Time to the Surface of the Earth, and would describe equal Spa-bodies. ces in equal Times, the Refiftance of the Air being taken away.

XXIX.

The fame Thing is proved of all the Planets having Satellites, for inftance, of Jupiter and Saturn; if the Satellites of Jupiter, for example, were all placed at the fame Distance from the Centre of this Planet, and deprived of their projectile Force, they would defcend towards it and reach its Surface in the fame Time; this follows from the Proportion between the Distances of the Satellites and their periodic Times.

cies of the

XXX.

From the Proportion between the periodic Times and Distances of the primary Planets from the Sun, it may be proved in like Manner, that the Sun acts on each of them proportionally to its Mafs, for at equal Diftances their periodic Times would be equal, in which Cafe, fuppofing their projectile Force deftroyed, they would all reach the Sun at the fame Time; therefore the Sun attracts each Planet in the direct Ratio of its Mass.

XXXI.

This Truth is further confirmed by the Regularity of the Orbits which the Satellites of Jupiter defcribe round this Planet, for Newton has proved (Cor. 3. Prop. 65.) that when a Syftem of Bodies move in Circles or regular Ellipfes, thefe Bodies cannot be acted upon by any fenfible Force but the attractive Force which makes them defcribe thofe Curves; now the Satellites of Jupiter defcribe round that Planet circular Orbits, fenfibly regular and concentric to Jupiter, the Distances of thefe Moons and of Jupiter from the Sun fhould be confidered as equal, the Difference of their Distances bearing no Proportion to the entire Distance; therefore if any of the Satellites of Jupiter, or Jupiter himself, were more attracted by the Sun in Proportion to its Mafs than any other Satellite, then this ftronger Attraction of the Sun would disturb the Orbit of this Satellite; and Newton fays, (Prop. 6. B. 3.) that if this Action of the Sun on one of the Satellites of Jupiter was greater or less in Proportion to its Mass than that which it exerts on Jupiter in Proportion to his, only one thoufandth part of its total Gravity, the Distance of the Centre of the Orbit of this Satellite from the Sun would be greater or less than the Distance of the Centre of Jupiter from the Sun, by the two thousandth part of its whole Diftance, that is by a fifth Part of the Diftance of the outermoft Satellite of Jupiter from Jupiter, which would render its Orbit fenfibly excentric; fince then thofe Orbits are fenfibly concentric to Jupiter, the accelerating Gravities of the Sun on Jupiter and on its Satellites, are proportional to their Quantities of Matter.

The fame Reasoning may be applied to Saturn and its Satellites, whose Orbits are sensibly concentric to Saturn.

Experience and Obfervation therefore leads us to conclude, that the Attraction of the Celestial Bodies is proportional to the Maffes, as well in the Attraction attracting Body, as in the Body attracted; that it is the Mafs which deteris always re- mines a Body to revolve round another, that every Body may be confiderciprocal. ed indifferently, either as attracting or attracted; in fine, that Attraction is always mutual and reciprocal between two Bodies, and that it is the Proportion between their Maffes which decides when this double Attraction fhall or fhall not be fenfible.

formly &

There is another Property of Attraction, by which it as equally on Attraction Bodies whether at Reft or in Motion, and produces equal Accelerations in acts uniequal Times, from whence it follows that its Action is continued and uni- continually form. Which fufficiently appears from the Manner gravity accelerates whether the falling Bodies, and from the Motion of the Planets, which as we have Bodies be at shewn before, are only greater Projectiles regulated by the fame Laws.

reft or in

motion.

Since the Proportion fubfifting between the Maffes of Bodies which at- Effects of tract each other determines how much one approaches towards the other, the Atit is evident that the Sun having a much greater Mafs than the Planets, the planets their Action on him should be infenfible. However the Action of the on the fun Planets upon the Sun, tho' too inconfiderable to be fenfible, produces its Effect; and on Examination we find that the center round which each Planet revolves is not the center of the Sun, but the Point which is the common center of Gravity of the Sun and Planet whofe revolution is confidered. Thus the Mafs of the Sun being to that of Jupiter as i toy and the distance of Jupiter from the Sun being to the Sun's femi diameter in a Ratio fomewhat greater, it follows that the common Center of Gravity of Jupiter and the Sun is not far diftant from the Surface of the Sun.

By the fame way of reasoning we find that the common Center of Gravity of Saturn and the Sun falls within the Surface of the Sun, and making the fame Calculation for all the Planets, Newton fays (Prop. 12, B, 3.) that if the Earth and all the Planets were placed on the fame Side of the Sun, the common Center of Gravity of the Sun and all the Planets would scarce be one of his Diameters distant from his Center. For tho' we cannot determine the Maffes of Mercury, Venus and Mars, yet as these Planets are ftill less than Saturn and Jupiter, which have infinitly lefs Mafs than the Sun, we may conclude that their Maffes do not alter this Proportion.

XXXIV.

making the

center of

It is about this common Center of Gravity that the Planets revolve, and This effect the Sun himself ofcillates round this Center of Gravity in Proportion to the confifts in Actions of the Planets exerted on him. When therefore we confider the fun ofcilMotion of two Bodies whereof one revolves round the other, rigorously liate round fpeaking we should not regard the central Body as fixed. The two Bodies, the common viz the central Body and that which revolves round it, both revolve round gravity of their common center of Gravity, but the spaces they defcribe round this com- our planetamon Center being in the inverse ratio of their Maffes, the Curve defcribed ry fyftem by the Body which has the leaft Mafs is almoft infenfible: For this Reason the Curve defcribed by the Body whofe revolution is fenfible is only confidered, and the fmall Motion of the central Body, which is regarded as fixed, is neglected.

This com mon center

of gravity is at reft.

XXXV.

The Earth and the Moon therefore revolve round their common Centor of Gravity, and this Center revolves round the Center of Gravity of the Earth and the Sun. The Cafe is the fame with Jupiter and his Moons, Saturn and his Satellites, and with the Sun and all the Planets. Hence the Sun according to the different Pofitions of the Planets fhould move fucceffively on every Side around the common Center of Gravity of our planetary System.

XXXVI.

This common Center of Gravity is at reft, for the different Parts of this System constantly corresponds to the fame fixed Stars; now, if this Center was not at rest but moves uniformly in a straight Line, during fo many thousand Years that the Heavens have been observed, there must have been remarked fome Alteration in the Relation that the different Parts of our planetary System bear to the fixed Stars; but as no Alteration has been obferved; it is natural to conclude that the common center of Gravity of our System is at reft. This Center is the Point where all the Bodies of our pla Hence this netary Syftem would meet if their projectile Forces were destroy'd.

center can

not be the

As the Center of Gravity of our planetary System is at reft, the Center of center of the the Sun cannot be this Center of Gravity fince it moves according to the fun, which different Pofitions of the Planets, though on Account of the small Distance moves per between the Center of the Sun and the common Center of gravity of our petually. planetary World it never fenfibly recedes from its Place.

Answer to

on founded

on the attrac

XXXVII.

Since Attraction is proportional to the Mass of the attracting Body, and that of the Body attracted, we fhould conclude that it belongs to every Particle of Matter, and that all the Particles of which a Body is composed attra& each other; for if Attraction was not inherent in every Particle of Matter it would not be proportional to the Mass.

XXXVIII.

This Property of Attraction, of being proportional to the Maffes, fupplys the objecti- us with an Answer to an Objection which has been alledged against the mutual Attraction of Bodies. If all Bodies it is faid are endued with this tion of teref: Property of mutually attracting each other, why is not the Attraction which trial bodies tereftrial Bodies exert on each other fenfible? but it is eafly perceived that Attraction being proportional to the Maffes of the Attracting Bodies,the Attraction exerted by the Earth on tereftrial Bodies is far more intense than what they exert on each other, and of Confequence these partial Atrate tions are abforbed and rendered infenfible by that of the Earth.

fenfible.

It is fenfi

XXXIX.

The Academicians who measured a Degree of the Meridian in Peru, imble in fome agined they perceived a fenfible Deviation in the plumb Line occafioned by cafes, as in the Attraction of the Mountain Chimboraco the highest of the Cordiliers it is sion of the certain from Theory that the Attraction of this Mountain should affect the

the devia

of chimbo

Plumb Line and all Bodies in its Neighberhood: but it remains to know plumb line whether the quantity of the obferved Deviation correfponds with that which at the foot fhould refult from the Bulk of the Mountain for befides that these Obfervati- raco. ons do not determine the precife Quantity of the Devitation,on account of the errors infeperable from practice, Theory does not furnifh ahy Method of eftimating exactly the quantity of this Devitation, as the entire Magnitude, Denfity &c. of the Mountain are unknown.

XL.

The fame reason that hinders us from perceiving the mutual Attraction of Bodies on the furface of the Earth, renders alfo the mutual Attraction of the heavenly Bodies very feldom fenfible. For the more powerful Action that the Sun exerts on them, prevents this mutual Attraction from appearing. However in some cases it is perceivable, for inftance in the conjunction of Saturn and Jupiter their Orbits are fenfibly disturbed, the Attraction of those two Planets being too strong to be absorbed by that of the Sun.

As to the fenfible Attractions of certain terestrial Bodies, such as Magne- Magnetifm tifm and Electricity, they follow other Laws and probably arife from Caufes and electri different from the univerfal Attraction of Matter.

city have different

fal attracti

Newton demonstrates (Prop. 66.) that the mutual Attractions of two caufes from Bodies revolving round a Third, difturb less the Regularity of their motions the univer when the Body round which they revolve is agitated by their Attractions, on of bodies than if it was at reft; hence the inconfiderable Irregularities obferved in the planetary Motions, is a further Proof of the mutual attraction of the celeftial Bodies.

XLI.

rities in the

al attractions

The Irregularities in the Motion of any Planet arifing from the Actions Manner of of the reft, are more or less confiderable, in Proportion as the Sum of the determining Fractions compofed each of the Mafs and Square of the Diftance of each of the irregula the other Planets, is more or lefs confiderable with respect to the Mass of motion of the Sun divided by the Square of its diftance from the Planet, but as the the planets Planes in which the Planets describe their Orbs are differently fituated with arifing from refpe&t to each other, the Directions of the Central Forces of which the their mutuPlanets are the Origin, are each in different Planes, and they cannot be all reduced to fewer than Three, by the Rules of the Compofition of Forces; each Planet therefore fhould be confidered as actuated every inftant by three Forces at the fame Time, the first is a tangential Force, or a Force acting in the Direction of the Tangent of the Planets Orb, which is the Refult of the Compofition of all the Motions which the Planet was affected with the precedent Inftant. The fecond is an accelerating Force, compounded of all the central Forces of the Planets, reduced to one in a right Line in a Plane whofe Pofition is determined by the Center of the Sun, and by the Direction of the tangential Force; the Difference between this