thus, one of each Luminary at a Fortnight's Distance, and another Pair, in the fame manner, about half a Year after.

The Shadows which both the Earth and the Moon caft behind them, which cause the Eclipfes, are of a conical Figure, terminating in a Point at a Distance from their Bodies; which is proved thus:

If the Shadow of the Earth were a Cylinder, or every where of the fame width, (which must be the Cafe, if the Sun, and the Earth were of the fame Bigness,) or if it grew wider and wider the further it extended, (which would be the Cafe, if the Earth were bigger than the Sun,) it would run out into infinite Space; and fometimes it would involve in it, and eclipfe the Planets Mars, Jupiter and Saturn. But, as that never happens, we may reasonably conclude, that the Shadow of the Earth is a Cone, whose Point, or Vertex, falls fhort of any of thofe Planets. Befides, it is found that the Moon is longer. in paffing thro' the Earth's Shadow, when the is in her Perigee, or nearer the Earth, than when he is in her Apogee, or further off from it; which affords another Proof that the Shadow of the Earth is a Cone, which grows lefs the further it is extended; and confequently this proves too that the Sun is bigger than the Earth.

If the Diameter of the Earth's Shadow, where it reaches the Moon, were not fo long.

as

as the Diameter of the Moon, (as would be the Cafe if the Moon were bigger, or as big as the Earth,) the Moon could never be totally eclipsed by it. But fince the Moon is often totally eclipfed by the Shadow of the Earth, the must be less than the Earth, therefore much less than the Sun, and confequently her Shadow must be also conical.

The Shadow of the Moon, where it reaches the Earth, is fo fmall, that but a little Part of the Earth can be covered by it at a Time; therefore a total Eclipfe of the Sun cán last no longer, in one Place, than about four Minutes. But the Diameter of the Earth's Shadow, where the Moon paffes thro' it, is three or four Times longer than the Diameter of the Moon's Body; therefore the Moon is fometimes totally eclipfed for about three Hours together.

Since when the Moon is eclipsed, she is really darkned, and lofes the Light of the Sun, from fo much of her Disk as is involved in the Shadow of the Earth, a lunar Eclipse must appear just the same in all Parts of the World, where it is feen. But when the Sun appears eclipfed, he, in Reality, lofes none of his Light, only the Moon stands in the Way of our feeing him, either wholly or in part. And fince the Moon can hide. the Sun but from a little Part of the Earth. at one Time, a folar Eclipse will appear differently in different Places. In one Place it

may

may be central and total, the Moon being just between that Place and the Sun, or that Place being juft in the Center of the Moon's Shadow; while the Moon hides but Part of the Sun from other Places; and from others, no part of him at all.

Thus in Fig. V. at all Places of the Earth between y and y the Sun is feen eclipsed, either totally or partially; between o and othe Eclipfe is total; between e and e it is annúlar; at u the Sun appears half darkened; but in Parts more remote from the Center of the Shadow thany, there is no Eclipse at all. A lunar Eclipfe feen from the Moon, is an Eclipfe of the Sun.

If a folar Eclipfe (which is more properly an Eclipse of the Earth can be seen from the Moon, it appears only as a dark Spot paffing over the Disk of the Earth.

It is obferved that the Moon, even when fhe is totally eclipsed, or wholly involved in the Shadow of the Earth, does not lose all her Light, but still appears of a faint dusky red Colour; which is owing to the Sun's Rays being refracted, or bent inwards, in paffing thro' the Earth's Atmosphere, (just as they are in paffing through a Burning-glafs,) by which Means they enter, and, in fome Meafure, enlighten the conical Shadow of the Earth, where it involves the Moon; and it is by that faint Light that the Moon is ftill visible, even in the midft of a central Eclipfe. Aftro

Aftronomers divide the Diameters both of the Sun and Moon into twelve equal Parts, which they call Digits, and each Digit into Minutes, &c. by which they measure the Quantity of Obfcuration, or the Bigness of an Eclipse.

COROLLARIE S.

1. The Shadow of the Earth, which is visible upon the Moon in a lunar Eclipse, appearing always circular, is a fenfible Demonftration of the globular Form of the Earth.

2. Since the Bignefs of an Eclipfe depends on the Bigness of the Shadow that falls on the eclipfed Body, and That on the Bigness, and Distance of the Body which cafts the Shadow; and as the Time of an Eclipfe depends on the Motions of those Bodies, it is evident that an Eclipse could not be computed before it happened, unless all these were known. But certain it is, that Aftronomers are able to compute* Eclipfes beforehand, to almoft a Minute of Time; therefore we must conclude, that their Knowledge of these Matters is very confiderable and certain.

The Computation of Eclipfes requires a great deal more previous mathematical Knowledge than the Perfons, for whofe Service this Treatife is defigned, are fuppofed to be furnished with; therefore I wholly omit it. Thofe that would acquaint themfelves with the Method of computing Eclipfes, both folar and lunar, may fee it in Dr. Gregory's or Dr. Keill's Aftronomy. And they may find good Tables for calculating Eclipfes in Dunthorne's Practi'cal Aftronomy of the Moon. СНАР.

CHAP. VI.

The Doctrine of the Tides.

TH

HE Surface of the whole Globe (as alfo its internal Parts) is every where preffed by Gravitation towards its Center.

If the Globe were all fluid, and fome Parts of the Surface were more preffed than others, the Parts that were moft preffed would be lowest, or neareft the Center; and the Parts leaft preffed would be the highest, or furtheft from the Center.

Both Sun and Moon attract the Earth with Forces which pervade the whole Globe; but which are greater or lefs in the different Parts of it, as thofe Parts are nearer to or further from thofe Luminaries, and the Moon by Reason of her being fo much nearer to the Earth than the Sun, has the greateft Influence and caufes the greatest Alteration in the Figure of the Earth or raising the Tides *.

:

The Effects of the Moon's Attraction upon the Fluids of the Globe, to alter their natural fpherical Figure, must be as follows:

The Reader, may fee this Matter fully explained in Maclaurin's Account of Sir Ifaac Newton's Philosph. Discoveries, B.4. Ch.7.

3

First,