absolute time at all places on the earth to which Jupiter is then visible, but at different hours of relative time, according to the distance between the meridians of the places at which observations are made; it follows that this difference of time converted into degrees, will be the difference of longitude between those places.

4. The instant of immersion or emersion, is more precisely defined than the beginning or end of a lunar eclipse; and, therefore, the longitude is more accurately found by the former.

5. For this purpose all the eclipses of the four satellites of Jupiter, that are visible in any part of the world, are given in the Nautical Almanac. The times of the immersions and emersions are calculated with great accuracy, for the meridian of Greenwich, from the very excellent tables of De Lambre.

6. The first satellite is the most proper for finding the longitude, its motions being best known, and its eclipses occuring most frequent.

7. When Jupiter is at such a distance from conjunction with the sun as to be more than eight degrees above the horizon, when the sun is 80 below, an eclipse of the satellites will be visible at any place; this may be determined near enough by the celestial globe.

8. The immersion or emersion of any satellite being carefully observed at any place according to mean time, the longitude from Greenwich is found immediately, by taking the difference of the observation from the corresponding time shown in the ephemeris, which must be converted into degrees, &c., by allowing 150 for every hour: and will be east or west of Greenwich, as the time observed is more or less than that of the ephemeris.

1. Comets are planetary bodies moving about the sun in elliptic orbits, and following the same laws as the planets; so that the areas described by their Hi vectores are equal in equal times.

When a comet appears, the observations to be made for ascertaining its orbit are of its declinations and right ascensions, from which the geocentric latitudes and longitudes are obtained. These observations of right ascension and declination must be made with an equatorial instrument, or by measuring with a micrometer, the differences of the declination and right ascension of the comet, and a neighbouring fixed star. The observations, according to Dr. Brinkley, ought to be made with the utmost care, as a small error may occasion a considerable one in the orbit.

From the beginning of the christian era to the present time, there has appeared not less than 500 comets; but the elements of not more than 99 have been computed, and of the latter number, 22 passed between the sun and Mercury in their perihelia; 40 between Mercury and Venus; 17 between Venus and the earth; 16 between the earth and Mars; and 4 between Mars and Jupiter.

The appearance of one comet has been several times recorded in history, viz. the comet of 1680. The period of this comet is 575 years. It exhibited at Paris a tail 620 long, and at Constantinople one of 900. When nearest the sun, it was only one-sixth part of the diameter of the sun distant from his surface; when farthest, its distance exceeded 138 times the distance of the sun from the earth.

2. As the orbits of the comets are very eccentric, the aphelion distance of a comet is so great, compared with its perihelion distance, that the small portion of the ellipse which it describes near its perihelion, or during its appearance, may, without any sensible error, be supposed to coincide with a parabola, and thus its motion during a short interval may be calculated as if that portion of the orbit was parabolical.

Dr. Halley makes the perihelion distance of the comet of 1680 to be to its aphelion distance, nearly as 1 to 22412; so that this comet was twenty-two thousand four hundred and twelve times farther from the sun in its aphelion than in its perihelion.

According to the laws of Kepler, the sectors described the same time by two planets, are to each other as the are of their ellipses divided by the square of the times of ti

wo'

1

GRAMMAR OF ASTRONOMY.

ution, and these squares are as the cubes of their semior axes. It is easy to conclude, that if we imagine a anet moving in a circular orbit, of which the radius is qual to the perihelion distance of a comet; the sector described by the radius vector of the comet, will be to the corresponding sector described by the radius vector of the planet, as the square root of the aphelion distance of the comet is to the square root of the semi-major axis of its orbit, a relation which, when the ellipse changes to a parabola, becomes that of the square root of 2 to unity.

The relation of the sector of the comet to that of the imaginary planet is thus obtained, and it is easy by what has been already said, to get the proportion of this last sector, to that which the radius vector of the earth describes in the same time. The area described by the radius vector of the comet may then be determined for any instant whatever, setting out from the moment of its passage through the perihelion, and its position may be fixed in the parabola, which it is supposed to describe. Nothing more is necessary, but to deduce from observation the elements of the parabolic motions.

3. The elements of a comet are, the perihelion distance of the comet, the position of the perihelion, the instant of its passage through the perihelion, the inclination of its orbit to the plane of the ecliptic, and the position of its nodes.

Elements of the Comet of 1811.

Time of Comet's passage through its

perihelion, Sep.

Place of the perihelion,
Distance of the perihelion

Place of the ascending node
Inclination of the orbit to the plane of the

ecliptic

Its heliocentric motion retrograde.

12d. 9h. 48m. 74° 12′ 00′′ 1 .02241

- 1400 13′ 00′′

72 12 00

The investigation of these five elements presents much greater difficulties than that of the elements of the planets, which being always visible, and having been observed during a long succession of years may be compared when in the most favourable position for determining these elements, instead

4. Comets do not alw ays move in the same direction like the planets. The real, or heliocentric motion of some is direc et, or according to the order of the signs; and of others, retrograde. But the geocentric motion of the same comet may be either retrograde or direc' according to the position of the earth with respect to the comet, and their relative velocities.

The heliocentri motion of half the comets, whose elements have been computed, is retrograde, and of the others, direct. The inclination of their orbits is not confined within a narrow zone like that of the planetary orbits; they present every variety of inclination from an orbit nearly coincident with the plane of the ecliptic, to that perpendicular to it.

A cornet is recognised when it re-appears by the identity of the elements of its orbit with those of the orbit of a comet already observed. If its perihelion distance, the position of its perihelion, its nodes, and the inclination of its orbit are very nearly the same, it is probable that the comet which appears is that which has been observed before, and which.. having receded to such a distance as to be invisible, retu to that part of its orbit nearest to the sun. The duratio the revolution of comets being very long, and having b observed with very little care, till within about two cen ries; the period of the revolution of one comet only, is kno

with certainty, that of 1682, which had been already observed in 1607 and 1531, and which has re-appeared in 1759. This comet takes about 76 years to return to its perihelion; therefore, taking the mean distance of the sun from the earth as unity, the greater axis of its orbit is 35.9, and as its perihelion distance is only 0.58, it recedes from the sun at least 5 times more than the earth, describing a very eccentric ellipse. Its return to the perihelon nas been longer by thirteen months from 1531 to 1607, than from 1607 to 1692; it has been 18 months shorter from 1607 to 1682, than from 168% to 1759.

The real or helioantric motion of this comet was retrograde, and the elements of the orbit deduced by Dr. Halley from the observations of Apian in 1531, of Kepler in 1607, and of himself in 1682, also the elements deduced from the observations in 1759, were as follows:

Per. dist.

Passage through Earth's per Place of Place of Inclination Perihelion. dist. unity. Perihelion Node. to ecliptic.

This comet was retarded by the acion of Jupiter, as Dr. Halley had foretold. This retardation was more exactly computed by Clairaut, who also calculated the retardation by Saturn. The result of his computation published before the return of the comet, fixed April 15, for the time of the passage throu through perihelion: it happened on March 12. Dr. Halley's computation appears also very exact, when it is considered that he did not allow for the retardation by Saturn. We may be nearly certain that this comet will reappear again in 1834.

The return of some other comets has been suspected: the most probable of these returns was that of the comet of 1532, which has been believed to be the same with that of 1661, and the revolution of which was fixed at 129 years; but this comet not having re-appeared in 1790, as was expected, there is great reason to believe that these two comets were not the same.

The preceding part of the present Chapter has been