The compaperiodic

times and

Ratio of the Square of the Distances. If the Planets which perform their Revolutions round the Sun be furrounded by others which revolve round them, and obferving the fame Proportions in their Revolutions, we may conclude that these Satellites are urged by a centripetal Force directed to their Primaries, and that this Force decreases as that of the Sun in the duplicate Ratio of the Distance.

We can discover only three Planets attended with Satellites, Jupiter, the Earth, and Saturn; we know that the Satellites of those three Planets describe around them Areas proportional to the Times, and confequently are urged by a Force tending to those Planets.

XIV.

Jupiter and Saturn having each feveral Satellites whofe periodic Times and Distances are known, it is easy to discover whether the Times of their dittances of Revolution about their Planet, are to their Distance in the Proportion difcothe fatellites vered by Kepler; and Observations evince that the Satellites of Jupiter and of Saturn Saturn obferve alfo this fecond Law of Kepler in revolving round their Priand Juptier, proves that maries, and of confequence the centripetal Force of Jupiter and of Saturn the centri- decrease in the Ratio of the Square of the Distances of Bodies from the petal force Centre of those Planets.

of thofe pla

nets is alfo in the in

XV.

As the Earth is attended only by one Satellite, namely the Moon, it apverfe ratio of pears at firft View difficult to determine the Proportion in which the Force the fquare acts that makes the Moon revolve in her Orbit round the Earth, as in this of the dif- Cafe we have no Term of Comparison.

tances.

How New

attractive

lows the

tion.

Newton has found the Means of fupplying this Defect; his Method is as ton difcove- follows: All Bodies which fall on the Surface of the Earth, describe accordred that the ing to the Progreffion discovered by Gallileo, Spaces which are as the Squares of the Times of their Defcent. We know the mean Distance of the Moon force of the Earth fol- from the Earth which in round Numbers is about 60 Semidiameters of the Earth; and all Bodies near the Surface of the Earth are confidered as equifame propor- diftant from the Centre; therefore if the fame Force produces the Defcent of heavy Bodies, and the Revolution of the Moon in her Orbit; and if this Force decreases in the Ratio of the Square of the Distance, its Action on Bodies near the Surface of the Earth fhould be 3600 Times greater than what it exerts on the Moon, fince the Moon is 60 Times remoter from the Centre of the Earth; we know the Moon's Orbit, because we know at present the Measure of the Earth, we know that the Moon describes this Orbit in 27 Days, 7 Hours, 43 Minutes, hence we know the Arc fhe defcribes in one Minute; now by (Cor. 9 Prop. 4.) the Arc defcribed in a given Time by a Body revolving uniformly in a Circle with a given centripetal Force, is a mean Proportional between the Diameter of this Circle and the right Line defcribed in the Body's defcent during that Time.

It is true that the Moon does not revolve round the Earth in an exact Circle, but we may fuppofe it such in the present Cafe without any fenfible Error, and in this Hypothefis, the Line expreffing the Quantity of the Moon's descent in one Minute, produced by the centripetal Force, is found to be nearly 15 Feet.

But the Moon according to the Progreffion discovered by Gallileo, at her present Distance would defcribe a Space 3600 Times leís in a Second than in a Minute, and Bodies near the Surface of the Earth defcribe, according to the Experiments of Pendulums, for which we are indebted to Hu hens, about 15 feet in a Second, that is, 3600 Times more Space than the Moon describes in the fame Time; therefore the Force caufing their Descent acts 3600 Times more powerfully on them than it does on the Moon; but this is exactly the inverse Proportion of the Squares of their Distances.

The mea

By this Example we fee the Advantage of knowing the Measure of the Earth; for in order to compare the Verfe Sine which expreffes the Quantity of the Moon's defcent towards the Earth, with the cotemporary Space de-fure of the fcribed by Bodies falling by the Force of Gravity near the Earth, we muft Earth was know the abfolute Distance of the Moon from the Earth, reduced into Feet, neceffary for as also the Length of the Pendulum vibrating Seconds; for in this Cafe it is making this dilcovery. not fufficient to know the Ratio of Quantities, but their absolute Magnitudes.

Induction

tion follows

Jupiter, Saturn, and our Earth therefore attract Bodies, in the fame authorifes us Proportion that the Sun attracts those Planets, and Induction authorifes us to conclude, to conclude that Gravity follows the fame Proportion in Mars, Venus, and that attracMercury; for by all that we can discover of these three Planets, they appear thefame proto be Bodies of the fame Nature with the Earth, Jupiter, and Saturn; from portion in whence we may conclude, with the highest Probability, that they are en- the planets dued with the attractive Force, and that this Force decreases as the Square of the Distances.

XVII.

which have

no fatellites.

Newton con

all the celef

It being proved by Obfervation and Induction that all the Planets are en- From dued with the attractive Power decreafing as the Square of the Distances; whence and by the second Law of Motion, Action is always equal to Re-action, cluded the we should conclude with Newton, (Prop. 5. B. 3.) that all the Planets gra- mutual at vitate to one another, and that as the Sun attracts the Planets, he is reci-traction of procally attracted by them; for as the Earth, Jupiter, and Saturn act on their Satellites in the inverse Ratio of the Square of the Distances, there is no Reason why this Action is not exerted at all Distances in the fame Proportion; thus the Planets fhould attract each other mutually, and the Effects of this mutual Attraction are fenfibly perceived in the Conjunction of Jupiter and Saturn.

tial bodies.

makes one

XVIII.

As Analogy enduces us to believe that the fecondary Planets are in all Refpects Bodies of the fame Nature with the primary Planets, it is highly probable that they are alfo endued with the attractive Power, and confequently attract their Primaries in the fame Manner they are attracted by them, and that they mutually attract each other. This is further confirmed by the Attraction of the Moon exerted on the Earth, the Effects of which are vifible in the Tides and the Preceffion of the Equinoxes, as will appear in the Sequel: We may therefore conclude that the attractive Power belongs to all the Heavenly Bodies, and that it acts in all our planetary Syftem in the inverse Ratio of the Square of the Diftances.

XIX.

But what is the Cause which makes one Body revolve round another? for What caufe inftance, the Earth and the Moon attracting each other with Forces decreabody revolve fing in the duplicate Ratio of their Distances, why fhould not the Earth ano-revolve round the Moon, inftead of caufing the Moon to revolve round the Earth; the Law which regulates Attraction does not therefore depend on the Distance alone, it must depend alfo on fome other Element, in order to account for this Determination, for the Distance alone is infufficient, fince it is the fame for one and the other Globe.

round ther.

This caufe From examining the Bodies that compofe our planetary System, it is natural appears to be to conclude that this Law is that of their Mafles; the Sun, round whom all the mais of the Heavenly Bodies turn, appears much bigger than any of them; Sathe central turn and Jupiter are much bigger than their Satellites, and our Earth is much bigger than the Moon which revolves round it.

body.

But as the Bulk and Mafs are two different things, to be certain that the The know- Gravity of the Celeftial Bodies follows the Law of their Maffes, it is necefledge of the malles of the fary to determine those Mafles.

planets ne- But how can the Maffes of the different Planets be determined? this ceffary to Newton has fhewn.

determine this point.

XX.

To trace the Road that conducted him to this Difcovery.

Since the Attraction of all the Celeftial Bodies on the Bodies which furRoad that round them follows the inverfe Ratio of the Square of the Distances, it is conducted highly probable that the Parts of which they are compofed attract each Newton to other in the fame Proportion.

this difcove

ry.

The total attractive Force of a Planet is compofed of the attractive Forces of its Parts; for fuppofing feveral fmall Planets to unite and compofe a big one, the Force of this big Planet will be compofed of the Sum of the Forces of all thofe small planets; and Newton has proved in (Prop. 74, 75 and 76,) that if the Parts of which a Sphere is compofed, attract each other mutually in the inverfe Ratio of the Square of the Distances, thele

entire Spheres will attract Bodies which are exterior to them, at whatever Distance they are placed in this fame inverse Ratio of the Square of Diftances; and of all the Laws of Attraction examined by Newton, he has found only two, namely, that in the inverse Ratio of the Square of the Distances, and that in the Ratio of the fimple Distances, according to which Spheres attract external Bodies in the fame Ratio in which their Parts mutually attract each other; from whence we fee the Force of the Reatoning which made Newton conclude that fince it is proved on one Hand from Theory, (Cor. 3. Prop. 74.) that when the Parts of a Sphere attract each other with Forces decreating in the duplicate Ratio of the Distances, the entire Sphere attracts external Bodies in the fame Ratio, and on the other, Obfervations evince that the Celestial Bodies attract external Bodies in this Ratio, it is obvious that the Parts of which the Heavenly Bodies are coinpofed, attract each other in this fame Ratio.

different

Newton examines (in Prop. 8. B. 3.) what the fame Body would weigh at the Surfaces of the different Planets, and he found by means of (Cor. He finds the 2. Prop. 4.) in which he had demonftrated, that the Weights of equal Bo-weight of dies revolving in Circles, are as the Diameters of thofe Circles, divided the fame boby the Squares of their periodic Times, therefore the periodic Times of dy upon the Venus round the Sun, of the Satellites of Jupiter round this Planet, of the planets at Satellites of Saturn round Saturn, and of the Moon round the Earth, and the fame difthe Distances of thofe Bodies from the Centres about which they revolve tance being known, fuppofing alfo that they defcribe Circles, which may be fuppofed in the prefent Caie, he difcovers how much the fame Body would weigh transferred fucceffively on the Surfaces of Jupiter, Saturn and of the Earth.

from

their centres

that their

Having thus found the Weights of the fame Body on the Surface of the different Planets at the fame Distance from their Centres, Newton dedu- And proves ces the Quantities of Matter they contain, for Attraction depending on the quantities of Mafs and the Distance, at equal Diftances the attractive Forces are as the matter are Quantities of Matter in the attracting Bodies; therefore the Mafies of the proportional different Planets are as the Weights of the fame Body at equal Distances weights.

from their Centres.

XXI.

to those

whence he. deduces

We may discover after the fame Manner the Density of the Sun and of thofe Planets which have Satellites, that is, the Proportion of their Bulks From and Maffes, for Newton, (Prop. 72.) has proved, that the Weights of equal Bodies, at the Surfaces of unequal homogeneous Sphere, are as their denfi. the Diameters of thofe Spheres; therefore if thole Spheres were heteroge-ties. neous and equal, the Weights of Bodies at their Surfaces would be as their Denfity, fuppofing the Law of Attraction to depend only of the Distance,

The smallest

and the Mass of the attracting Body; therefore the Weights of Bodies at the Surfaces of unequal and heterogeneous Spheres, are in the compound Ratio of their Denfities and Diameters; confequently the Denfities are as the Weights of the Bodies divided by their Diameters.

XXII.

From hence we find, that the finaller Planets are denfer and placed nearand denfefter the Sun, for where all the Proportions of our System were laid down, planets are, we faw that the Earth, which is lefs and nearer the Sun than Jupiter and fun. Saturn, is more dense than those Planets.

nearest the

Newton.

XXIII.

Newton deduces from thence, the Reason of the Arrangement of the Celestial Bodies of our planetary Syftem, which is adapted to the Denfity of their Matter, in order that each might receive a Degree of Heat more or lefs according to its Denfity and Distance; for Experience fhews us that The reafon the denfer any Body is, the more difficultly does it receive Heat; from affigned by whence Newton concludes that the Matter of which Mercury is compofed fhould be feven Times denfer than the Earth, in order that Vegetation might take place; for Illumination, to which, ceteris paribus, Heat is proportional, is inversely as the Square of the Distance; but we know the Proportion of the Distances of the Earth and Mercury from the Sun, and from this Proportion we discover that Mercury is feven Times more illuminated, and confequently feven Times more heated than the Earth; and Newton difcovered, from his Experiments on the Thermometer, that the Heat of our Summer Sun, feven Times augmented, would make Water boil; therefore if the Earth was placed at the Distance of Mercury from the Sun, our Ocean would be diffipated into Vapour; removed to the Distance of Saturn from the Sun, the Ocean would be perpetually frozen, and in both Cafes all Vegetation would ceafe, and Plants and Animals would perish.

The denfi

planets

XXIV.

It eafily appears, that the Maffes and Denfities of fuch Planets only as ties of the are attended by Satellites can be difcovered, fince to arrive at this Difcovewhich have ry we must compare the periodic Times of the Bodies revolving round thofe fatellites on Planets, the Moon alone is to be excepted, of which mention will be made ly can be dif hereafter.

covered, the

moon ex

is the centre

XXV.

cepted. Having determined the Maffes of the Planets, we find that thofe Bodies Why the fun which have lefs Mafs, revolve round those which have a greater, and the of the centre greater Mafs a Body has the greater is, ceteris paribus, its attractive Force; tial revolu- thus all the Planets revolve round the Sun, because the Sun has a much greater Mafs than any of the Planets, for the Maffes of the Sun, Jupiter, and Saturn are respectively as 1, 1100 and 3000; fince therefore the Malfes of thefe Planets exceed thofe of any other in our Syftem, it follows that the Sun fhould be the Centre of the Motions of our planetary Syftem.

tions.