the train of the comet is hid behind its body; except the extremities of the train, which being broader than the body of the comet, appear, as it were, round the edges of it like a border of hair, from which it is called a hairy comet.

The comets make a part of the solar system, and move in elliptical orbits, having the Sun in one of their foci, and describe areas proportional to the times of their motions, like the planets. The reafon why they fometimes appear vifible, and fometimes not, is the great eccentricity of their orbits, which is very confiderable, for when they are in that part of the orbit most remote from the Sun, they are much beyond the orbit of Jupiter; and in their perihelion they frequently defcend within the orbit of Mars, and fometimes within those of the inferior planets.

SECT. IV.

OF ECLIPSES.

AN eclipfe is the privation of the light of one of the luminaries by the interpofition of fome opake body, either between the luminary and the eye, or between it and the Sun.

The duration of an eclipse is the time of its continuance.

The immenfion, or incidence of an eclipfe, is the moment when the eclipse begins; or when part of the luminary first begins to be obfcured.

The emerfion, or expurgation of an eclipfe, is the time

when the ecipfed luminary begins to reappear, or emerge out of the fhadow.

The quantity of an eclipfe, is the part of the luminary eclipfed. To determine this quantity, the diameter of the eclipfed body is divided into 12 equal parts, called digits; and the eclipfe is faid to be of fo many digits as are contained in that part of the diameter which is eclipfed.

Eclipfes are either those of the Sun, the Moon, or of fome of the fatellites, and are either total, partial, annular, central, &c.

A total eclipfe, is when the whole body of the luminary is darkened.

A partial eclipfe, is when only a part of the luminary is eclipfed.

A central eclipfe, is when the centres of the two luminaries and the Earth come in a ftraight line, and is always total.

An annular eclipse, is when the whole body is eclipsed, except a ring or annulus, which appears round the border or edge.

An eclipfe of the Moon, is a privation of the light of the Moon, and occafioned by the body of the Earth being directly between the Sun and the Moon, and fo intercepting the Sun's rays, that they cannot arrive at the Moon; confequently the Moon paffes through a part of the conical shadow of the Earth, as seen in fig. 12, plate 17, where D E C reprefents the Earth, and D G F C the conical fhadow thereof, in which is the Moon in an eclipfe. The dotted fpaces DG s, and FC r, fhow thofe parts of the fhadow called the penumbra, in which the Moon is deprived only of part of the Sun's light.

An eclipfe of the Sun, is an obscuration of the Sun's body, occafioned by the Moon's coming between the Earth and the Sun, and thus intercepting the light of the Sun from us, on which account fome have confidered it an eclipfe of the Earth.

The

The folar eclipfe is reprefented fig. 11, where m reprefents the Moon, C D the Earth, and rm so the Moon's conical fhadow, travelling over that part of the Earth Co D, and caufing a complete eclipfe of the Sun to all the inhabitants. who refide in the tract C D. The spaces Cro and D se include the penumbra, and all the inhabitants within those fpaces will perceive a faint fhadow of the eclipse.

Hence, an eclipfe of the Moon can happen only at the time of the full Moon, or when he is oppofite to the Sun; and an eclipfe of the Sun will take place only at the time of a new Moon, or when the Moon is between the Sun and Earth.

From hence fome may imagine that there may be two eclipses, viz. one of the Sun and another of the Moon, in every lunation, which would really be the cafe, if the Moon moved in the fame plane with the ecliptic; but the orbit of the Moon not being in the plane of the ecliptic, but inclined thereto in an angle of 5 degrees 35 minutes, and paffing through the plane of the ecliptic, it must neceffarily follow, that an eclipfe can only take place when the Moon is near that part of its orbit which pasles through the plane of the ecliptic. Thefe two oppofite points where the Moon's orbit intercepts the ecliptic, are called its Nodes.

That point where the Moon afcends from the south to the north fide of the ecliptic, is called the afcending node, or dragon's head, and marked ; and the oppofite point, where the Moon defcends from the north to the south fide of the ecliptic, is called the defcending node, or dragon's tail, and marked 8; and a line drawn from one node to the other, is called the line of the nodes. Thus, if (fig. 13) abcd be the orbit of the Moon, and eg the ecliptic, the points a c, where the orbit cuts the ecliptic, are the two nodes, and the dotted line a c the line of the nodes. From a view of the figure, it is plain, when the full or new Moon happens when the Moon is at the points bor d, there

can

can be no eclipfe, the fhadow of the Moon or Earth falling either above or below the other luminary; but when the full or new Moon is at the points a or c, or within 17 degrees of these points, there will be an eclipse of one of the luminaries.

In order to calculate an eclipfe, it is neceffary to know how to take the parallax of the Sun, or any heavenly body; as alfo to take the parallactic angle.

The parallactic angle, called alfo the parallax, is the angle EST (fig. 1, plate 18), made at the centre of a star, or other bodies, by two lines, one drawn from the centre of the Earth T, and the other from its furface E; or, which is the fame thing, it is the difference of the two angles CE A and BT A.

Parallax is an arch of the heavens intercepted between the true and apparent place of any ftar, or heavenly body,

The true place of a ftar, S, is that point of the heavens, B, where it would be feen by an obferver placed in the centre of the Earth T: and the apparent place of the fame ftar is the point C in the heavens, where it would appear to an observer on the furface of the Earth, at E. This difference of the two places of the same star is the parallax, fometimes called, for diftinction fake, the parallax of altitude; and is an angle formed by two vifual rays, the one drawn from the centre, and the other from the circumference, of the Earth, and traverfing the body of the ftar; the measure of it being an arch of a great circle, intercepted between the points of the true and apparent places, B and C.

The parallax B C is alfo the difference between the true distance of the ftar from the zenith A, and the apparent distance A C. Hence the parallax diminishes the altitude of a ftar, or increases its diftance from the zenith.

The parallax is greatest in the horizon, which is therefore called the horizontal parallax, as E F T. From the horizon the parallax decreases all the way to the zenith A, where the true and apparent places of the ftar coincide.

The parallax of the annual orbit of the Earth, is the angle under which the femidiameter of the Earth's orbit is feen.

To find the parallax of a celestial body, observe when the body is in the fame vertical line with a fixed star which is near it; and while it is in that position, measure its apparent distance from the star; then observe when the ftar and body are at equal altitudes from the horizon, and there measure their distances again, and the difference of these distances will be the parallax.

The Aftronomy of Eclipfes.

To calculate a lunar eclipse it is necessary, first, to find the length of the Earth's conical fhadow, which may be found by finding the distance between the Earth and Sun, and the proportion of their diameters. Thus, fuppofe the feui axis of the Earth's orbit to be 95,000,000 miles, and the eccentricity of the orbit 1,377,000, which, added together, make 96,377,000 miles, or 24,194 femidiameters of the Earth; and the Sun's femidiameter being to that of the Earth as 112 to 1; then, as A D is to BE, fo is DB to EC (fig. 2), that is, as 111 is to 1, fo is 24,194 to 218 femidiameters of the Earth, equal to E C, the length of the Earth's shadow.

To find the apparent femidiameter of the Earth's fhadow, in the place where the Moon paffes through it, add together the parallaxes of the Sun and Moon, and from the fam fubtract the apparent femidiameter of the Sun, and the remainder will be the apparent femidiameter of the fhadow at the place where the Moon paffes through it.

Note. The Sun's parallax may very well be omitted in this calculation; and the apparent femidiameter of the fhadow increased by adding one whole minute.

It is also neceffary to have the true diftances of the Moon from the node at the mean oppofition; alfo the true time of the oppofition, with the true place of the Sun and Moon

reduced