tance being unity. With both these perihelion distances, the comet must have been invisible during its whole revolution. The perihelion distance in 1770 was 0.67.

'This comet was also remarkable by having approached nearer the earth than any other comet that has been observed: and by that approach having enabled us to ascertain a limit of its mass or quantity of matter. Laplace has computed, that if it had been equal to the earth, it would have shortened the length of our year by of a day. Now it has been perfectly ascertained, by the computations of Delambre on the Greenwich observations of the sun, that the length of the year has not been changed, in consequence of the approach of that comet by any perceptible quantity, and thence Laplace has concluded that the mass of that comet is less than 3600 of the mass of the earth. The smallness of its mass is also shown by its having traversed the orbits of the satellites of Jupiter without having occasioned an alteration in their motions. From those and other circumstances, it seems probable that the masses of the comets are in general very inconsiderable; and therefore, as Dr. Brinkley remarks, that astronomers need not be under apprehensions of having their tables deranged in consequence of the near approach of a comet to the earth or moon, or to any bodies of the solar system.

5. The motion of a comet, like that of a planet, is accelerated, when moving from its aphelion to its perihelion, and retarded from its perihelion to its aphelion. On account of the great eccentricity of a comet's orbit, its motion in the perihelion is prodigiously swift, and in the aphelion proportionably slow.

According to Newton, the velocity of the comet of 1680, which came nearest to the sun of any upon record, was eight hundred and eighty thousand miles an hour. On taking the perihelion distance of this comet, equal to .00603, as given by Pingré, (proportioned according to the present mean parallax of the sun deduced from the transit of Venus of 1769,) I find, says Squire in his Astronomy, by two different calculations, that the velocity of this comet in its perihelion was no less than 1,240,108 miles per hour; at which time it was only 572,850 miles from the centre of the sun, or about 130,000 miles from his surface.

The velocity of this comet in its perihelion was so great, that, if continued, would have carried it through 124 degrees in an hour. But its actual hourly motion during that interval, before and after it passed its perihelion, was 81° 46′52′′.

From Dr. Halley's determination of the orbit of this comet, it cannot be less than 13,000 millions of miles from the sun when in its aphelion.

According to Pingré, the elements of the orbit of the comet of 1680, were as follows: this comet passed through its perihelion December 18th, at 1 minute, 2 seconds after 12 o'clock at noon mean time at Greenwich; place of the perihelion 8s 22° 40′ 10′′, or 22° 40′ 10′′ of Sagittarius; and its distance from the sun when in the perihelion, .00603, the mean distance of the earth from the sun being considered as unity or 1; the longitude or place of the ascending node 9 signs, 1° 57′ 13′′, or 1° 57′ 18" of Capricornus; and the inclination of the orbit to the plane of the ecliptic 61° 22′ 55".

It appears from the great diurnal motion of some comets, that they must have come very near the earth. For, aсcording to Regiomontanus, the comet of 1472 moved over an arc of 1200 in one day. And the comet of 1759 described the apparent arc of 41 in the same interval of time.

The comet of 1811 was first seen at Viviers, by Flaugergues, on the 25th of March, and was visible till the end of May; it must have been very faint and near the horizon all the time, it having during that interval great southern latitude. The Earth was in about 5 degrees of Libra, on the 25th of March, and therefore the comet must be nearly in opposition to the Sun, which certainly was the most favourable position for seeing it. It was then moving towards its perihelion, but its motion being slow, and the Earth retreating from it, it was lost sight of when the Earth arrived at the beginning of Sagittarius. The comet passed the ascending node on July 11th, when the Earth was between Capricornus and Aquarius; it was then approaching its conjunction with the Sun, and was invisible from the end of May till the 31st of August, when, between 3 and 4 o'clock that morning, it was observed by Bouvard, at the imperial observatory; its right ascension was 1470 18', and declination 32° 53' north. The comet was first observed at Greenwich, on the 5th of September; its geocentric longitude at that time was 145° 3′ 10′′, and its geocentric latitude 280 36′39′′. The comet was at its perihelion, at a distance of 97,128,950 miles from the Sun on the 12th September.

was

On October 2d, the comet was 26° 33′ from the perihelion; its heliocentric longitude was 41° 53′ and latitude 720 1'; having two days before passed the higher part of its orbit, or 90 degrees from the node. The Earth at the same time was in about 90 of Aries; and the geocentric longitude of the comet was 174° 37', and its geocentric latitude 54°5′. The comet's distance from the Sun was 102,532,550, and from the Earth 120,413,930 miles. The comet was nearest the Earth on the 11th of October, when its distance was 113,630,450 miles, its apparent motion in longitude at this time was nearly four degrees in twenty-four hours. On the 12th, the comet 37° 33' from the perihelion, having a rapid geocentric motion in longitude, the direction of the Earth and comet conspiring to produce that effect. Its geocentric longitude was 2030 46', and latitude 610 39'; the Earth at the same time was 180 40 in the sign Aries. The comet's distance from the Sun was 108,342,464, and from the Earth 113,948,225 miles. On January 1st, 1812, the comet was $90 11' from the perihelion; its heliocentric longitude was 328° 15′, and latitude 230 33. The Earth was about 10° 21' in Cancer; the greatest geocentric longitude of the comet was 3120 2', and latitude 170 18. Its distance from the Sun was 190,520,000, and from the Earth 259,614,500 miles. See, for a delineation of a portion of this comet's orbit, Squire's Astronomy.

Though the real or heliocentric motion of this comet was not within the sphere of the Earth's orbit, yet its geocentric track, when referred to the ecliptic, crossed the orbit of the Earth; hence, the apparent place of the comet, during the greater part of the time it was visible, was towards the opposite part of the heavens to its true place.

From the true and apparent places of the comet, given above, for particular days, its real and visible path may be traced upon the celestial globe. Dr. Herschel makes the planetary body of this comet not more than 428 miles in diameter; but the real diameter of the head he makes to be about 127,000 miles.

The apparent motion of this comet was direct, yet very unequal, for when it first became visible after passing the ascending node, it was nearly stationary, and the same about the time of its disappearance, but when nearest the Earth it equalled that of Mercury.

This comet was visible a longer time than almost any other upon record, and therefore none has ever afforded such certain means of information with respect to its orbit. Had its heliocentric motion been direct, it would have been visible much longer, and would have passed within 44,485,850 miles of the Earth, had it crossed the line of its nodes at the same time. The comet would then have appeared a large nebulous body, but without a tail, as that appendage would have been projected in a direct line from behind its body.

6. The most striking phenomena, that makes the comets objects of attention to all mankind, is the tail of light which they often exhibit. When approaching the Sun, a nebulous tail of light is seen to issue from them, in a direction opposite to the Sun. This, after having increased, again decreases till it disappears. The stars are visible through it.

The nebulosity with which those comets are almost always surrounded, seems to be formed by the vapours which the solar heat raises on their surface. It is imagined that the great heat which they experience towards their periheion, rarifies the particles which have been congealed by the xcessive cold of the aphelion.

It appears also that the trains of comets are only these va pours elevated to a considerable height by this rarefaction, combined either with the solar rays or with the dissolution of those vapours in the fluid, which reflects the zodaical light to us. This seems to result from the direction of their trains,, which are always beyond the comets, relatively to the Sun, and which only becoming visible near their perihelion, are not at a maximum till after their passage through this point, when the heat communicated to the comet by the Sun, is increased by its duration, and by the proximity to this luminary.

Dr. Hamilton supposes the tails of comets, the aurora borealis, and the electric fluid to be matter of the same kind. He supports this opinion by many strong arguments, which are found in his ingenious essay on the subject. According to this hypothesis, it would follow that the tails are hollow; and there is every reason to suppose this, from the scarcely perceptible diminution of the lustre of the stars seer through them. He supposes that the electric matter, which continually escapes from the planets, is brought back by the assistance of the comets.

But much is yet to be known on this subject. Objections

may be made to his hypothesis, although so ingeniously supported. According to the opinion of Kepler, the rays of the Sun carry away some gross parts of the comets, which reflect other rays of the Sun, and give the appearance of a tail.

CHAPTER XVIII.

Of the Firmament of Fixed Stars.

1. The number of stars visible to the naked eye, as has already been remarked, is not more than 2000. We observe, says Dr. Brinkley, about 3000 stars visible to the naked eye, very irregularly scattered over the concave surface of the heavens. There are seldom above 2000 visible at once, even on the most favourable star-light night.

This may at first appear incredible to some, because ai first sight they seem to be innumerable; but the deception arises from looking upon them hastily, without reducing them into any kind of order. For let a person look steadily for some time upon a large portion of the heavens, and count the number of stars in it, and he will be surprised to find the number so small. And if the moon be observed for a short interval of time, she will be found to pass very few in her way, although there are as many about her path as in any other part of the heavens. Flamstead's Catalogue contains only 3000 stars, and many of those are not visible without a telescope. But although the number of stars may be small when examined with the naked eye, yet when examined with powerful telescope, the number exceeds all computation. For a good telescope, directed to almost any part of the heavens, discovers multitudes that are lost to the naked eye. In some places, however, they are crowded together; and in others, there are considerable spaces where no stars can be seen. In the small group called the Pleiades, in which only 6 or 7 stars can be seen by the naked eye, Dr. Hook, with a telescope of 12 feet long, discovered 78 stars. And F. de Rheita affirms, that he has observed more than 2000 stars in the constellation Orion; and above 188 in the Pleiades.

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