and the third, the Application of the two first to the Explication of the Phænomena of the Syftem of the World.

XIII.

The Principia commence with eight Definitions; Newton fhews in the Definitions. two firft how the Quantity of Matter and the Quantity of Motion fhould be measured; he defines in the third, the Vis intertia, or refifting Force,which all Matter is endued with; he explains in the fourth what is to be understood by active Force; he defines in the fifth the centripetal Force, and lays down in the fixth, seventh and eighth the Manner of measuring its abfolute Quantity, its motrix Quantity, and its accelarative Quantity; afterwards he establishes the three following Laws of Motion.

XIV.

Laws of mo 1 ft. That a Body always perfeveres of itfelf, in its State of Reft, or of uniform Motion in a straight Line.

tion.

First book,

the ift fecti

2d. That the change of Motion, is proportional to the Force impressed, and is produced in the ftraight Line in which that Force acts.

3d. That Action and Reaction are always equal with oppofite Directions.

XV.

Newton having explained thofe Laws, and deduced from them several on contains Corollaries, commences his firft Book with eleven Lemmas, which comthe princi- pofe the first Section, he unfolds in those eleven Lemmas his Method of ples of infiPrime and ultimate Ratios; this Method is the Foundation of infiniteffimal Geometry, and by its Affiftance, this Geometry is rendered as certain as that of the Ancients.

niteffimal

geometry

the other 13

The thirteen other Sections of the first Book of the Principia, are employgeneral pro-ed in demonftrating general Propofitions on the Motion of Bodies, Abitracpofitions on the motion ting from the Species of these Bodies and of the Medium in which they

of bodies.

Second book

move.

It is in this first Book that Newton unfolds all his Theory of the gravitation of the celeftial Bodies, but does not confine himself to examine the Questions relative to it; he has rendered his Solutions general, and has given a great Number of Applications of thofe Solutions.

XVI.

it treats of In the fecond Book, Newton treats of the Motion of Bodies in resisting the motionof Mediums. bodies in re

diums.

This fecond Book which contains a very profound Theory of Fluids, and fifting me- of the Motion of Bodies which are immerfed in them, feems to have been intended to destined to over throw the System of Vortices, though it is only in the Scholiverthrow um of the last Propofition,that Newton openly attacks Defcartes, and proves of Defcartes that the celestial Motions are not produced by Vortices.

the vortices

XVII.

it treats of

In fine, the third Book of the Principia treats of the Syftem of the World; Third book. in this Book, Newton applies the Propofitions of the two firft: in the fyftem this Application we fhall endeavour to follow Newton, and point out the of the world.. Connection of his Principles, and shew how naturally they unravel the Mechanifm of the Univerfe.

XVIII.

The Term, Attraction, I employ in the Senfe in which Newton has defined What is it, understanding by it nothing more than that Force, by which Bodies tend meant bythe towards a Center, without pretending to affign the Caufe of this Tendency. tion.

Principal Phenomena of the Syftem of the World.

I.

THE Knowledge of the Difpofition and Motions of the Celestial Bo

dies muft precede a juft Enquiry into their Caufes. It will not therefore appear unneceffary to prepare our Readers by a fuccinct description of our planetary Syftem for our Account of the manner Newton demonftrates the powers which govern the Celestial Motions and produce their mutual Influences. This Defcription muft neceffarily comprize fome Truths, difcovered by that illuftrious. Philofopher, the Manner he attained them will be described in the Sequel.

II.

word attrac

Firftdivifion

The celestial Bodies that compofe our planetary System, are divided into of the celefPrimary Planets, that is, thofe which revolve round the Sun, as their Center tial bodies and Secondary Planets, otherwife, called Satellites, which revolve round their of our plane tary fyftem refpective Primaries as Centers: There are fix Primary Planets whose into princiNames and Characters are as follows,

Mercury,
Venus,
The Earth,.
Mars,
Jupiter,,
Saturn..

pal and fecon dary planets.

Names and characters of the prin cipal planets.

Which are the planets that have

enumeration

In enumerating the Primary Planets, we follow the Order of their Diftances from the Sun, commencing with those which are nearest to him. The Earth, Jupiter, and Saturn, are the only Planets which have been fatellites, difcovered to be attended by Secondaries: The Earth has only one Satellite, of the cele namely, the Moon; Jupiter has four, and Saturn five, exclufive of his Ring, ftial bodies of fo that our Planetary Syftem is compofed of eighteen celestial Bodies, in- our planetacluding the Sun and the Ring of Saturn.

III.

ry svstem. Second divifion of the

the planets into

The Primary Planets are divided into fuperior and inferior Planets, inferior Planets are those which are nearer the Sun than the Earth is; thefe fuperior and

inferior,

which are are Mercury and Venus; the Orbit (a) of Venus includes that of Mercury the inferior and alfo the Sun, and the Orbit of the Earth is exterior to those of Mercury what is their and of Ve nus, and inclofes them and the Sun alfo.

planets and

arrainge

ment.

This order is difcovered, by Venus and Mercury fometimes appearing to be interpofed between the Sun and us, which could never happen unless how this or- thefe Planets revolved nearer the Sun than the Earth, and it is very perceivder has been able that Venus recedes farther from the Sun than Mercury does, and condifcovered. fequently its Orbit includes that of Mercury.

which are

The fuperior Planets are those which are more diftant from the Sun than the fuperior the Earth is, thefe are three in Number, Mars, Jupiter and Saturn; we planets and know that the Orbits of these Planets inclofe the Orbit of the Earth, bewhat is their caufe the Earth is fometimes interpofed between them and the Sun.

arrainge

ment.

how it has

The Orbit of Mars inclofes that of the Earth, the Orbit of Jupiter that of Mars, and the Orbit of Saturn that of Jupiter; fo that of the three fuperior Planets Saturn is the remoteft from the Earth, and Mars is the

nearest.

This Arraingement is difcovered by thofe Planets which are nearer the been difco- Earth (b) fometimes coming between the Eye and the Remoter, and intercepting them from our View.

vered.

IV.

All the Planets are opaque Bodies; this appears of Venus and Mercury, The planets because when they pafs between us and the Sun, they refemble black Spots are opaque traverfing his Body, aud affume all those various Appearances which are called Phases, that is, the Quantity of their Illumination depends on their Pofition in respect to the Sun and us.

bodies.

For the fame Reason, fince Mars has Phafes we infer his Opacity, and the fame Conclufion is extended to Jupiter and Saturn, because their Satelites do not appear illuminated while their Primaries are between them, and the Sun which proves that that Hemisphere of those Planets which is turnThe planets ed from the Sun is opaque: Laftly, we know that the Planets are spheriare spherical cal Bodies, because, whatever be their Pofition, in refpe&t of us, their Surface always appears to be terminated by a Curve.

We conclude that the Earth is spherical, because in Eclipfes her Shadow, always appears to be bounded by a Curve, and when a Ship fails out of fight, it gradually disappears, firft the Hulk, next the Sails, and lastly the Mast, finking to the Eye and vanifhing, and moreover, it the Earth was an extended Plane, Navigation would have discovered its Limits and Boundaries the contrary of which is proved by many Voyagers, fuch as Drake, Forbish, and Lord Anson, who have failed round the World.

(a) Orbit is the Curve which a Planet defcribes in revolving round the Body which ferves it as a Center.

(b) Wolf's Elements of Aftronomy.

V.

All that we know therefore concerning the primary Planets, proves that The planete they are opaque, folid and fpherical Bodies.

appear to be

all of the

The Sun appears to be a Body of a Nature entirely different from the Pla- fame nature, nets; we know not whether the Parts of which it is compofed be folid or It is proba fluid; all that we can discover is, that those Parts emit light & heat, and burn ble that the when condensed and affembled in sufficient Quantity; hence we may probably the Sun is a conclude, that the Sun is a Globe of Fire refembling terreftrial Fire, fince the globe of fire, Effects produced by this and the folar Rays, are exactly the fame.

VI.

lettial bodies

apfides the

All the celestial Bodies compleat their Revolutions round the Sun in Ellip- In what fes (c), more or lefs excentic, the Sun refiding in the common Focus of all curve the ce their Orbits; hence the Planets in their Revolutions fometimes approach revolve anearer, and fometimes recede farther from the Sun; a right Line paffing bout the fun. through the Sun and terminating in the two Points of the Orbit of a Planet, what is the which are nearest and remotest from the Sun, is called the Line of the Apfides, line of the the Point of the Orbit which is nearest the Sun is called the Peribelium; and the Point of the Orbit which is remoteft from the Sun is called the phelium and periheli Aphelium. The primary Planets in their Revolutions round the Sun, carry alfo their In what diSatellites, which at the fame Time revolve round them as their Centers. rection the All these Revolutions are performed in a direction from West to Eaft (d), planets reThere appear from Time to Time Stars that move in all Directions, and with aftonishing Rapidity, when they are fufficiently near to be visible, these are called Comets.

umn.

volve.

Of the con

ets.

We have not yet collected Obfervations fufficient to determine their Number, all that we know concerning them, and 'tis but lately that the Dif covery has been made; is that they are Planets revolving round the Sun like The comets the other Bodies of our Syftem, and that they defcribe Ellipfes fo very excentric as to be visible only while they are moving over a very small Part of their Orbit.

VII.

are planets.

and comets obferve the

All the Planets in their Revolutions round the Sun, obferve the two Laws The planets of Kepler. Obfervations evince, that the Comets obferve the first of thefe Laws, laws of Kep `namely, that which makes the celestial Bodies (e) defcribe equal Areas in e- ler

(c) A Species of Curve, which is the fame with what is commonly called an OVAL, the foci are the points in which Gardeners fix their pegs in order to trace this curve of which they make a frequent ufe.

(c) The Spectator is fuppofed to be placed on the Earth.

(e) By the Word Area, in general is understood a Surface, here it fignifies the Space included between two Lines drawn from the Center to two Points where the Planet is found;

Proofs of the

the earth

qual Times; and in the fequel it will be fhewn, that all the Obfervations that have hitherto been made, concerning their Motions, render it highly probable that they are regulated by the fecond Law, that is, that their periodic (†) Times are in the fefquiplicate ratio of their mean Distances.

VIII.

Admitting thefe two Laws of Kepler, confirmed by all aftronomical Obmotion of fervations, from them we may derive feveral convincing Proofs of the Motion of the Earth, a Point which had been fo long contefted; for fuppofing the Earth to be the Center of the Celestial Motions, these two Laws are not obferved; the Planets do not defcribe Areas proportional to the Times around the Earth, and the periodic Times of the Sun and the Moon, for inftance, round this Planet, are not as the Square Roots of the Cubes of their mean Distances from the Earth; for the periodic Time of the Sun around the Earth, being nearly thirteen Times greater than that of the Moon, its Diftance from the Earth would be, according to Kepler's Rule, between five and fix Times greater than that of the Moon, but Obfervations demonstrate, that this Distance is about four-hundred Times greater, therefore, admitting the Laws of Kepler, the Earth is not the Center of the celestial Ro volutions.

The centripetal Force(g) which Newton has demonftrated to be the Caufe of the Revolutions of the Planets renders the Curve they defcribe around their Center concave (h) towards it, fince this Force is exerted in drawing them off from the tangent (i); now the Orbits of Mercury and Venus, in fome Parts, are convex to the Earth; of confequence, the inferior Planets do not revolve round the Earth.

The fame may easily be proved of the fuperior Planets; for these are thofe Areas are proportional to the Times, that is, they are greater or lefs, as the Times in which they are defcribed are longer or shorter.

(f) Periodical Time is the Time that a Planet employs in compleating its Revolution in its Orbit. An Example, of Sesquiplicate Ratio will render it more intelligible than a Definition; Suppose then the mean Distance of Mercury from the Sun, to be 4, that of Venus 9, the periodical Time of Mercury 40 Days, and let the periodical Time of Venus be required, cubing the two first Numbers 4 and 9, there will result 64 and 729; afterwards extracting the Square-Roots of thefe two Numbers, there will be found 8 for that of the first, and 27 for that of the second, and by the Rule of three you will have 8:27::40: 135, That is the Square-Root of the Cube of the mean Distance of Mercury from the Sun, is to the Square Root of the Cube of the mean Distance of Venus from the Sun, as the periodic Time of Mercury round the Sun is to the periodic Time fought of Venus round the Sun,which is found to be 135, according to the Suppofitions which have been made, and this is what is called Sefquiplicate Ratio..

(g) The Word CENTRIPETAL FORCE carries its Definition along with it, for it fignifies no more than that Force which makes a Body tend to a Center.

(h) The two Sides of the Crystal of a Watch may ferve to explain thofe Words CoNCAVE and CONVEX; the Side exterior to the Watch is CONVEX, and that which is on the Side of the Dial-plate is coN CAVE.

(i) A Tangent is a right Line which touches a Curve, without cutting it.