:

The Moon<

is diftant

from the

Earth's Cen

ter about

240.000

{

Miles

These Distances, as to their Proportion, are well known from plain Trigonometry; I mean, by the utmost Elongation of the Inferiors; where in a Rectanglar Triangle, joining the Eye, the Center of the Sun, and the Center of the Planet, two of the Sides bear this Proportion to each other: And by the Angle of Retrogradation thereto equivalent, in the Superiors; for 'tis but imagining your Eye, transferr'd to the Superior Planet, and the Earth is an Inferior one with refpect to the Eye, and the Proportion as before is given; as alfo by the Pofition of Jupiter's Shadow in the Eclipfes of its Satellits, where the Middle of the Eclipfe gives the Pofition of the Central Shadow of Jupiter from the Sun; and our Inftruments give the Pofition hence So that we have all the Angles in a plain Triangle made by the Center of the Sun, the Center of Jupiter's Shadow, and the Eye, which gives the Proportion of the Sides, or of the Distances; and by the Proportion of the Periodick Times, compar'd with the mean Distances in the Comets, all which Methods agree together in the prefent Cafe. And as to the Diftances in Miles themselves, they are derived from the best Obfervations of the Parallax of Mars and Venus, by Mr. Flamsteed, Caffini, and others, which give us that of the Sun about 10", and which is followed by Sir Ifaac Newtou in the fecond Edition of his Principia. Only we may Note, that this Parallax cannot be

much

much larger, because that would easily be difcover'd by our Inftruments, but may be a little lefs, because that is more difficult to be found out. So that it is more probable that thefe Diftances are somewhat too little, than that they' are at all too great. But as to fuch farther Exactness, it must be left to the nicest Obfervations of Pofterity. Nor will it be at all difficult in that Cafe to fettle more exact Numbers for thefe Distances before us; viz. thofe in the reciprocal Proportion to that Parallax.

Corollary. From these two Tables compar'd together, we learn the Mean Annual Horary Velocities of the Primary Planets, and of the four Comets about the Sun, and of the Secondaries about their Primaries; as follows:

N. B. Light moves about 650,000.000 Miles in an Hour; 10,800.000 in a Minute; and about 180.000 in a fecond of Time.

(4.) The real Diameters of the Heavenly Bodies have been by me thus determined, in English Statute Miles, according to Mr. Flamfeed's Obfervations.

Thefe Numbers, which are difcover'd by the apparent Diameters, compared with their real Diftances, are as to the Earth and Moon, within a small Latitude, certainly true in the Miles themselves; and as to the reft, are within no great Latitude, certainly true, in the Proportion of one to another; but not fo certain as to the Miles themselves. The Reafon is plain, that the real Bignefs of the Earth, and of our Neighbour the Moon, are easily discover'd, and meafur'd by the Rules of Aftronomers; but that the reft are fo vaftly remote from us, that our nicest Instruments cannot yet perfectly define the Distances of any of them; and fo by Confequence cannot perfectly determine their real Diameters, which depend thereon. Only fo far I may, as before, venture to conjecture, that the real Diftances and Diameters are rather larger than fmaller than thofe here fet down; becaufe if the Distances, and fo the Diameters, were much lefs, they would be certainly discover'd by our Inftruments; whereas if they be suppos'd confiderably greater, it must be ftill harder to difcover those Distances and Diameters by the fame Inftruments.

N. B. The Diameters of the Circumjovials and Circumfaturnals, have not yet been exactly obferv'd by Aftronomers; fo they can have no Place in this and fome other Calculations. Only fo far we perceive by Mr. Huygens's Infor- Cofmoth. mation, that they are full as large as our Moon; P. 101, nay rather, as the leffer of the primary Planets themselves.

N. B. Hence we learn the Contents of all thefe Surfaces in Square Miles, by the help of the Elements of Geometry.

E 4

The

N. B. Hence alfo, by the fame Help of the Elements, we learn the folid Contents of all thefe Bodies in Cubical Miles, as follows.

N. B. Mr. Huygens's Numbers of the apparent Diameters, are confiderably different from thofe of Mr. Flamsteed. And I do fuppofe ftill, what I once propos'd to the Reverend Mr. DerP. 11, 12. ham, and which he approves of in his Astrotheology, that the middle Number between Mr. Flamsteed's and Mr. Huygens may be the trueft: Yet do I, in all my Calculations here, follow thofe of Mr. Flamsteed; because Sir Ifaac Newton has done fo, even in the laft

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