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 Distances 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 those Curves; now the Satellites of Jupiter defcribe round that Planet circular Orbits, fenfibly regular and concentric to Jupiter, the Distances of these 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 stronger 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 Mafs 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 thoufandth 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 Reafoning may be applied to Saturn and its Satellites, whose Orbits are fenfibly concentric to Saturn.

Experience and Obfervation therefore leads us to conclude, that the Attraction of the Celeftial Bodics is proportional to the Mafios, 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.

XXXII.

Attraction

formly &

There is another Property of Attraction, by which it acts equally on Bodies whether at Rest or in Motion, and produces equal Accelerations in act 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 fhewn before, are only greater Projectiles regulated by the fame Laws. rest or in

XXXIII.

motion.

At

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 for of it is evident that the Sun having a much greater Mafs than the Planets, the planets their Action on him fhould 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 Mass of the Sun being to that of Jupiter as I to and the diftance 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 reafoning 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 fcarce be one of his Diameters diftant from his Center. For tho' we cannot determine the Masses 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

the common

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 late round fpeaking we fhould not regard the central Body as fixed. The two Bodies, 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 inverfe ratio of their Maffes, the Curve defcribed y fyftem by the Body which has the leaft Mafs is almost infenfible: For this Reason the Curve defcribed by the Body whofe revolution is fenfible is only confidered, and the small Motion of the central Body, which is regarded as fixed, is neglected.

This com

mon center

of gravity is at reft.

The Earth and the Moon therefore revolve round their common Center 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 should 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 conftantly correfponds to the fame fixed Stars; now, if this Center was not at reft but moves uniformly in a straight Line, during fo many thousand Years that the Heavens have been obferved, 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 plaHence 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 Syftem 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 Positions 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 Mafs 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 attraЯ 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 Anfwer 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 Eodies 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 Atratc tions are abforbed and rendered infenfible by that of the Earth.

not being

fenfible.

It is fenfi

XXXIX.

The Academicians who meafured 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 tion 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 should result from the Bulk of the Mountain for befides that these Observati- raco. ons do not determine the precife Quantity of the Devitation,on account of the errors infeperable from practice, Theory does not furnish any Method of eftimating exactly the quantity of this Devitation, as the entire Magnitude, Denfity &c. of the Mountain are unknown.

XL.

The fame reafon that hinders us from perceiving the mutual Attraction of Bodies on the surface of the Earth, renders also the mutual Attraction of the heavenly Bodies very seldom sensible. For the more powerful Action that the Sun exerts on them, prevents this mutual Attraction from appearing. However in fome cafes 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 abforbed by that of the Sun.

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

city have different Newton demonftrates (Prop, 66.) that the mutual Attractions of two caufes from Bodies revolving round a Third, difturb lefs the Regularity of their motions the univer when the Body round which they revolve is agitated by their Attractions, 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.

fal attraction of bodies

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 Distance of each of the irregula the other Planets, is more or less 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 defcribe their Orbs are differently fituated with arifing from respect 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 second 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

traction of

the planets

compounded Force and the fimple central Force which has no other Source but the Sun, is called the perturbating Force. The third Force is the deturbating Force, compounded of all the fame central Forces of the Planets reduced to one in a Direction perpendicular to the Planes of their Orbits; this Force is very fmall in comparison of the two others, un account of the fmall Inclination of thofe Planes to one another, and because the Sun placed in the Interfection of all thofe Planes does no way contribute to the Abstracting from the Production of this deturbating Force. If the Planets were only actuated by mutual at the two firft Forces their Combination would ferve to determine their Trajectories which would be each in a conftant Plane, and if the perturtheir aphelia bating Force vanished then they would be regular Ellipfes, and confequentare at left. ly the Aphelia and Nodes of the Planets would be fixed (Prop. 14. B. 3. & Prop. 1. & 11. B. 1.) if not; thefe Trajectories might be confidered as moveable Ellipfes on account of the prodigious excefs of the central Force of the Sun over the perturbating Force, it is thus Newton investigated the quantity and direction of the Motion of the Line of the Apfides of the Planets occafioned by the Action of Jupiter and Saturn, which according to his Determination follows the Sefquiplicate Proportion of the distances of the Planets from the Sun, from whence he concludes (Prop. 14. B. 3.) that fuppofing the Motion of the line of the Apfides of Mars in which this Motion is the most fenfible to advance in a 100 Years 33m 20 in confequentia, The flow the Aphelia of the Earth, Venus and Mercury would advance 17" 40° motion of 10 53 & 4m 16' refpectively in the fame Time.

the aphelia This flow Motion of the Aphelia confirms the Law of univerfal Graof the planets is a new vitation, for Newton has demonftrated (Cor. 1. Prop. 45.) that if the proof that Proportion of the centripetal Force would recede from the Duplicate to apattraction proach to the Triplicate only the 60th Part, the Apfides would advance 3 inverfe ratio Degrees in a Revolution, therefore fince the Motion of the Apfides is alof the fquare most infenfible, Gravity follows the inverfe duplicate Proportion of the of the dif- diftances.

acts in the

tances

But the deturbating Force which acts at the fame Time causes the Planes of those moveable Ellipfes to Change continually their Pofition; let there be fuppofed in the Heavens an immoveable Plane, in a mean Pofition between all thofe the Trajectory of the Earth would take in confequence of the deturbating Force, which may be called the true Plane of the Ecliptic, it is manifeft that this Plane being very little enclined to the Plane of the Orbit of Each Planet, it is almoft parallel to it, and confequently the Direction of the deturbating Force is always fenfibly perpendicular to the true Plane of the Ecliptic, and it is eafy to conceive that the effect of this Force produced in the Direction in which it acts, is either to remove the Planets from or to make it approach the true Plane of the Ecliptick, confequently to cause a Variation in the Inclination of the fmall Arc which the Planet def