and the

XVIII.

What has hitherto been fet forth was known before the Time of Newton, but no one thought before him, that it was poffible to discover the Quantities of Matter in the Planets, their Denfities, and the different Weights of one and the fame Body fucceffively transferred to the Surfaces of the difmasses of the ferent Planets. How Newton attained to thofe aftonishing Discoveries will Sun, Iupi- be explained in the Sequel; at prefent it fuffices to fay, that he found out ter, Saturn, that the Maffes of the Sun, Jupiter, Saturn, and the Earth, that is the Earth. Quantities of Matter thofe Bodies contain, are to one another, as I 1587 3013 & 189252, fuppofing (r) the Parallax of the Sun to be 10" 3'; that their Their denfi Denfities are as 100, 94, 67, and 400; & that the Weights of the fame Body, Weights placed fucceffively on the Surfaces of the Sun, Jupiter, Saturn, and the Earth, of the fame would be as 10000, 943, 529, and 435; in determining those Proportions, body at their Newton has fuppofed the Semidiameters of the Sun, Jupiter, Saturn, and the why thofe Earth, to be as 10000, 997, 791, and 109. it will be fhewn hereafter why neiproportions ther the Denfity, nor the Quantity of Matter of Mercury, Venus, and are not difco Mars, or the Weights of Bodies at their respective Surfaces, are known.

ties

furface.

vered in the

⚫therplanets

XIX.

It follows from all thofe Propertions that Saturn is nearly 500 Times lefs proportions than the Sun, and contains 3000 Times lefs Matter, that Jupiter is 1000 of the bulks Times less than the Sun, and contains 1033 Times lefs Matter. Comandmaffes of pared with the Sun the Earth is only as a Point, being 100,0000 Times lefs; the planets and of the and in fine, that the Sun is 116 Times greater, than all the Planets togeher.

Sun.

on of the

XX.

Comparing the Flanets with one another, we find that Mercury and Mars are the only Planets lefs than the Earth; that Jupiter is not only the biggest of all the Planets, but is bigger than all the Planets together, and that this Planet is two thousand Times bigger than the Earth.

XXI

The Earth befides her annual and diurnal Motion, has also a third MoThe preceffition, by which her Axis recedes from its Parallelifm, (f) & after a certain Time equinoxes. is directed to different Points of the Heavens, from this Motion arifes what is called the Preceffion of the Equinoxes that is, the Regreffion of the equiIn what di noctial Points, or thofe Points in which the tereftrial Equator cuts the performed Feliptic. The equinoctial Points move contrary to the Order of the Signs, and in what and their Motion is fo very flow, that they do not compleat a Revolution in lefs than 25920 Years, they recede a Degree in 72 Years, and the ancomplished. its annual nual Quantity is about, 50''.

rection it is

time it is ac;,

quantity

(r) The parallax of the Sun, is the Angle, under which the Semidiameter of the Earth is feen from the Sun, and in general the parallax of any celeftial Body, with respect to the Earth, is the Angle under which the Semidiameter of the Earth wonld be feen from that Body.

(1) A line is faid to be parallel when it always preferves the fame pofition with respect to a Point fuppofed fixed.

Newton found, as will appear in the Sequel, the Cause of this Motion in the Attraction of the Sun and Moon on the Elevation of the equatorial Parts of the Earth.

year.

The Preceffion of the Equinoxes has caufed a Diftination of the Year Tropical into the tropical and fydereal. The tropical Year is the Interval of Time year. Sydereal elapfed between two fucceffive vernal or autumnal Equinoxes, in two annual Revolutions of the Earth. This Year is fomewhat fhorter than the fydereal Year, or the Time intervening the Earth's Departure from any Point of her Orbit, and her Return to the fame.

XXII.

It remains to defcribe the fecondary Planets, which exclufive of the Ring The feconda of Saturn, are 10 in Number; namely, the 5 Satellites of Saturn, the 4 ry planets. of Jupiter, and the Moon, the only Satellite attending the Earth.

Obfervation proves that these Satellites in revolving round their Primaries, They obobferve the Laws of Kepler.

serve the laws of

The Satellites of Jupiter have been but lately discovered: The Discovery Kepler. before the Invention of Telescopes was impoffible. Gallileo difcovered the Difcovery of four Satellites of Jupiter, which in Honour of his Patron, he termed the of Jupiter. Medicean Stars. Thefe are of the greatest Utility in Geography and Aftro

nomy.

the fatellites

Hugbens was the first who discovered one of Saturn's Satellites; it ftill re- And of those tains his Name, and is the fourth. Afterwards Caffini discovered the four of faturn.

others.

XXIII.

Taking the Semidiameter of Jupiter as a common Measure, his 4 Satel- Distances of lites revolve at the following Distances; the first at the Distance of 5 Semi- the moons diameters, the fecond of 9, the third of 14, and the fourth of 25, neglect- from this of Jupiter ing Fractions. These Determinations have been deduced by Caffini from his planet. Obfervations of their Eclipfes.

Their periodic Times round Jupiter are fo much the longer as they are remoter from this Planet. The first revolves in 42 Hours, the second in 85, the third in 171, and the fourth in 400, neglecting the Minutes.

The diurnal Rotations, Diameters, Bulks, Maffes, Denfities, and attractive Forces of these Satellites, have not as yet been discovered; and the best Telescopes represent them fo vastly small, that there is no Hopes of ever attaining Certainty in these points; the fame is the Cafe with regard to the Satellites of Saturn: These are placed still further beyond the reach of our Researches.

XXIV.

Taking the Diameter of Saturn's Ring for a common Measure, Distances of the Satellites of Saturn commencing with the innermoft, in the following Proportions.

the

Their perios

dic times about Jupiter

Distances of are of faturn

the moons

from faturn.

& their peri

The firft is expreffed by 1, the fecond by 2, the third by 3, the fourth by odic times 8, and the fifth by 24, neglecting Fractions; and their periodic Times, ac cording to Caffini, are 45h, 65h, 109h, 382h, and 1903 respectively.

round this

planet.

The Moons of Saturn, all revolve in the Plane of the Equator of that Planet, except the fifth, which recedes from it about 15 or 16 Degrees.

Several Philofophers, and among them Hugbens, have fufpected, that if Conjectures Telescopes were once brought to perfection, a fixth Satellite of Saturn beof Hughens concerning a tween the fourth and fifth would be difcovered, the Distance between those fixth fatel- two Satellites being two great in Proportion to that which separates the lite of Sa others; but there would then occur this other Difficulty, that this Satellite, turn. which would be the fifth, notwithstanding must be less than any of the four interior Moons, fince with our most perfect Telescopes it cannot be perceived.

The Orbits of the Satellites of Jupiter, and of Saturn, are nearly con

centric to those Planets.

Obfervation Maraldi has obferved Spots on the Moons of Jupiter, but no Confequenof Maraldi ces could as yet be derived from this Observation, which if properly pursued concerning thefatellites and accurately repeated, might conduct us to the Knowledge of feveral inof Jupiter. terefting Particulars refpecting the Motions of the Satellites.

adhere to

Its diftance

XXV.

Of the ring Saturn, exclufive of his five Moons, is also furrounded by a Ring, no of Saturn. where adhering to his Body; for through the Interval which separates his It does not Body from the Ring, we can view the fixed Stars: The Diameter of this the body of Ring is to the Diameter of Saturn as 9 to 4, according to Hugbens, that is this planet. more than the Double of the Diameter of Saturn; the Distance of the Body from the bo- of Saturn from his Ring, is nearly equal to his Semidiameter; fo that the dy of the Breadth of the Ring is nearly equal to the Distance between its interior planet. Limb and the Globe of Saturn. Its Thickness is very inconfiderable, for Its breadth when it turns its Edge to the Eye, it is no longer visible, but only appears as Its thick- a black Line extended across the Globe of Saturn. Thus this Ring undergoes Phafes according to the Pofition of Saturn in his Orbit, which proves It is an o- it to be an opaque Body; and which like the other Bodies that compose our paque body fubject to planetary Syftem, fhines only by reflecting the Light it receives from the phates.

Its diameter

nefs.

Of the dif

Sun.

We cannot discover whether the Ring of Saturn has any Motion of Rotation, as no Changes in its Afpe&t are obferved to authorile us to conclude this Rotation.

The Plane of this Ring always forms with the Plane of the Ecliptic an Angle of 23°, hence its Axis remains always parallel to itfelf in its Revolution round the Sun.

The Discovery of the Ring of Saturn, the only Phenomenon of the Kind covery of obferved in the Heavens is due to Hugbens. Before his Time, Aftronomers this ring. obferved Phafes in Saturn, for they confounded Saturn with his Ring; but thofe Opinion con angit be Phafes were fo different from thole of the other Planets as to be utterly inex

plicable. In Hevelius may be feen the Names he gives to thofe Appearances fore Huof Saturn, and how far (t) he was from affigning the true Cause.

gheas.

cerning this

Hugbens comparing the different Appearances of Saturn, found they were produced by a Ring furrounding his Body; and this Suppofition is fo conformable with all Telescopic Discoveries, as to be now generally received. Gregory defcribing the Notion of Halley, that the terreftrial Globe is Notion of Gregory con only an Affemblage of Shells concentric to an internal Nucleus, propofes a Conjecture concerning this Ring, that it is formed of feveral concentric ring. Shells detached from the Body of that Planet, whofe Diameter was formerly equal to the Sum of its actual Diameter, and the Breadth of the Ring. Another Conje&ture has alfo been propofed, that the Ring of Saturn is on- The fatelly an Affemblage of Moons, which from the immense Distance appear to lites of Jupi be contiguous; but thofe Conjectures are not grounded on any Obfervation. ter and SaBy the Shadows of the Satellites of Jupiter and Saturn projected on spherical bo their Primaries, it has been difcovered, that they are spherical Bodies, dies.

XXVI.

turn are

Of

The Earth has only one Satellite, namely the Moon; but her Proximity of the moon has enabled us to push our Enquiries concerning this Satellite much further than about the others.

round the

The Moon performs its Revolution round the Earth in an Ellipfe, the What curve Earth being placed in one of the Foci: The Form and Pofition of this El- it describes lipfe is continually changing; thefe Variations are caused by the Action of the earth. Sun, as will appear in the Sequel.

The Moon in her Revolution round the Earth obferves the first of the two Laws of Kepler, and recedes from it only by the Action of the Sun upon her; The compleats her Revolution round the Earth from West to East in 27 d. Its periodic 7 h. 43 m. which is called its periodical Month.

month.

Her fynodic

The Dife of the Moon is fometimes totally, and at other times partially, illuminated by the Sun. The illuminated Part is greater, or lefs, according to its Pofition with respect to the Sun and the Earth; these are called her Her phases. Pbafes. She affumes all those various Phases during the Time of her fynodic month. Revolution, or the Interval between two fucceffive Conjunctions with the Sun. This fynodic Month of the Moon confifts of 29 Days nearly. The Phafes of the Moon prove that she is an opaque Body, fhining only by reflecting the Light of the Sun.

We know that the Moon is a spherical Body, because fhe always appears to be bounded by a Curve.

The Earth enlightens the Moon during her Nights, as the Moon does the Earth during ours; and it is by the reflected Light of the Earth that we see the Moon, when she is not illuftrated by the Sun.

(t) Hevelids in opufculo de Saturni Nativa facie distinguishes the different Aspects of Saturn by the Names of Monafphericum, Trifphericum, Spherico-anfatum, ellipti-coanfatum, spheri cocufpidatum, and subdivides them again into other Phases.

The moon is an opaque and spheri cal body.

The earth enlightens the moon during her nights.

Proportion of this illumination.

Inclination

As the Surface of the Earth is about 14 times greater than that of the Moon, the Earth seen from the Moon would appear 14 times brighter, and reflect 14 times more rays to the Moon, than the Moon does to us, fuppofing both equally capable of reflecting Light.

The Plane of the lunar Orbit forms with the Plane of the Ecliptic, an of the orbit Angle of about 5d.

of the moon

Time of the

revolution of the line

of the ap

fides. Revolution

The great Axis of the Ellipfe which the Moon defcribes round the Earth, is called the Line of the Apfides (u) of the Moon.

The Moon accompanies the Earth in her annual Revolution round the Sun.

If the Orbit of the Moon had no other Motion but that by which it is carried round the Sun along with the Earth, the Axis of this Orbit would always remain parallel to itself; and Moon being in her Apogee, and in her Perigee, would be always at the fame Distances from the Earth, and would always correfpond to the fame Points of the Heavens; but the Line of the Apfides of the Moon revolves with an angular Motion round the Earth, according to the Order of the Signs; and the Apogee and Perigee of the Moon do not return to the fame Points in less than 9 Years, which is the Time of the Revolution of the Line of the Apfides of the Moon.

The Orbit of the Moon interfeas the Orbit of the Earth in two Points, of the nodes which are called her Nodes; these Points are not always the fame, but change of the moon perpetually by a retrogreffive Motion that is contrary to the Order of the Time of its Signs, and this Motion is fuch, that in the fpace of 19 Years the Nodes revolution. perform a whole Revolution, after which they return to the fame Points of the Orbit of the Earth, or of the Ecliptic.

Excentricity of the

moon.

Its motion round its axis.

In what time it is

The Excentricity of the Orbit of the Moon changes also continually; this Excentricity fometimes increases, sometimes diminishes, fo that the Difference of the greatest and leaft Excentricity exceeds half the least.

It will be explained in the Sequel how Newton discovered the Cause of all thofe Inequalities of the Moon.

The only uniform Motion that the Moon has, is its Motion of Rotation about her Axis; this Motion is performed exactly in the fame Time as its Revolution about the Earth, hence its Days confift of 27 of our Days, 7h 43.

This equality of the lunar Day and the periodic Month makes the Moon performed. always prefent to us nearly the fame Difc.

The uniform Motion of the Moon about its Axis, combined with the Inequality of its Motion round the Earth, produces the apparent Ofcillation Libration of of the Moon about her Axis, fometimes Eaftward, and at other times Weftthe moon. ward, and this is what is called ber Libration; by this Motion the prefents

(u) The Line of the Apfides of the Moon is the Line which passes through the Apogee and Perigee; apogee is the Point of the Orbit the Remoteft from the Earth, and the Perigee is the Point of the Orbit the nearest to the Earth; and in general, the Apfides of any Orbit are the Points the Remoteft from, and nearest to, the central Point.