one of the foci. As the ellipses are in general extremely elongated, and the comets are only visible while they describe a small portion of their orbits on either side of their perihelia, their paths during the time of their appear ance differ very little from parabolas ; whence it is usual, on account of the facility of computation, to assume that they really move in parabolic curves. Newton employed the hypothesis of an elliptic motion to compute the orbit of the famous comet of 1680. They have received the name of comets (coma, hair) from the bearded appearance
which they frequently exhibit.
One of the most remarkable periodic comets with which we are acquainted is that known to astronomers as Halley's. Having perceived that the elements of the comet of 1682 were nearly the same as those of two comets which had respectively appeared in 1531 and 1607, he concluded that all the three orbits belonged to the same comet, of which the periodic time was about 76 years. After a rough estimate of the perturbations it must sustain from the attraction of the planets, Halley pre dicted its return for 1757, a bold prediction at that time, but justified by the event, for the comet again made its appearance as was expected, though it did not pass through its perihelion till the month of March 1759, the attraction of Jupiter and Saturn having caused, as was computed by Clairaut previously to its return, a retardation of 618 days. This comet had been observed in 1066, and the accounts which have been preserved represent it as having then appeared to be four times the size of Venus, and to have shone with a light equal to a fourth of that of the moon. History is silent respecting it from that time till the year 1456, when it passed very near to the earth : its tail then extended over 60 of the heavens, and had the form of a sabre. It returned to its perihelion in 1835, and the splendour of its appearance rendered it once more an object of universal interest ; it was well observed in almost every observatory.
The orbit of the comet of 1770 was calculated by Lexell, and subsequently by Burckhardt, and both these astronomers found that the observations could only be represented by an ellipse in which the time of revolution was five years and a half ; yet the comet has never been seen since, or at least has not been seen moving in the same orbit. Hence it is concluded with certainty that the attrac tion of Jupiter, near which planet it had passed, was so great as to compel it to move in a totally different ellipse.
Another famous comet, whose periodic returns have been verified by observation, received the name of Encke the astronomer, who first recognised it as having been observed in previous revolutions. It returns to its perihelion in 1208 days. Encke s comet, although its identity was not discovered till 1818, had been frequently observed, as in 1789, 1795, and 1805 ; and on these occasions it ex hibited very different appearances, having been seen. with and without a nucleus, and with and without a tail, circumstances which account for its having so long escaped being recognised as a regular attendant on the sun. In its returns to its perihelion in 1808, 1812, and 1815, it escaped detection; but it reappeared in 1818, and it was from the observations of that year that Encke computed the elliptic elements of its orbit. On its next return, in 1822, it was invisible in Europe ; but it was observed at Paramatta, in New South Wales, during the whole month of June, and the time of its perihelion passage was found to differ only by about three hours from that previously computed by Encke. During most of its returns since then it has been well observed.
Other periodical comets will be mentioned further on.
The appearances exhibited by comets are diversified, and sometimes remarkable. That which appeared in the year 134 B.C., at the birth of Mithridates, is said to have had a disk equal in magnitude to that of the sun. Ten years before this, one was seen which, according to Justin, occupied a fourth part of the sky (that is, extended over 45), and surpassed the sun in splendour. Another, equally remarkable, appeared in the year 117 of our era; and in 479 there was one, of which the disk, according to Freret, was of such magnitude, that it might have occasioned the extraordinary eclipse of the sun which took place about that time. In 400 one was observed, which is said to have resembled a sword, and to have extended from the zenith to the horizon. That of 531 was of greater magnitude still, and its appearance more terrific. Those which appeared in 1066 and 1505 exhibited disks larger than that of the moon. It is, however, probable that these accounts were exaggerated ; for since comets have be^n observed by astronomers, no instances have occurred in which their magnitudes and appearances have been so extraordinary. The most remarkable among those of which we possess accurate accounts appeared in the years 1456, 1618, 1680, 1744, 1759, 1769, 1807, 1811, 1841, 1858, 1861, and 1874.
The nucleus, which is the densest and most luminous part, may be said to form the true body of the comet. It is far, however, from having the dense and solid appearance of the planets, and astronomers consider it to be diaphanous, and believe that they have observed stars through it. But it is extremely difficult to distinguish the nucleus from the surrounding nebulosity. If the nucleus were an opaque globular body, it would exhibit phases like Venus or Mars, according to its different positions with relation to the sun and the earth ; and such were supposed to have been observed in the case of the comet of 1682, by Hevelius, Picard, and Lahire. But the nebulosity renders the phases obscure, and prevents the true body of the comet from being seen. The real nucleus has probably never been observed by any astronomer.
It is known certainly that comets are of small density, from the circumstance that they produce no appreciable effect on the motions of the planets. The comet of 1770 traversed the sjstem of Jupiter s satellites without causing any sensible perturbation of these small bodies. This comet also passed very near the earth ; and Laplace calculated that, if its mass had been equal in density to that of the earth, the effect of its attraction would have increased the length of the sidereal year by 2 hours 28 min. But since its influence was altogether insensible, it is certain that its mass was not equal to the five-thousandth part of that of the earth, and was probably much less than even this quantity.
If the real nuclei of comets were solid, the matter of which they are composed must be extremely fixed, in order to enable them to resist the intense heat they necessarily experience in their approaches to the sun. According to the computation of Newton, the great comet of 1680, at its perihelion, was only distant from the sun by the 163d part of the semidiameter of the earth s orbit, where it would be exposed to a heat above 2000 times greater than that of red-hot iron, a temperature of which we can form no conception, and which would instantly dissipate any substance with which we are acquainted.
The most interesting features of recent research into the subject of comets are (1) the spectroscopic examination of those comets which have appeared since the importance of spectroscopic analysis has been recognised, and (2) the association which has been recognised between meteor- systems and comets.
Before proceeding, however, to discuss these matters, we give the following tables indicating the progress which has been made in the determination of the orbits of periodic comets:—
