Cometary observations cannot usually be as accurate as those of the planets, because there always is a difficulty in fixing upon the centre, or rather the centre of gravity of the nucleus; and when the comet is faint the difficulty is increased. The errors thus committed render the period of revolution, when calculated directly from the observed places, to some extent uncertain. When there is a long series of observations the probable error of the calculated period is very much diminished.

On the 29th of August, 1844, De Vico, the Director of the Observatory at Rome, discovered a comet whose period was found to be about five and a half years. MM. Langier and Mauvais thought it identical with a comet observed by Tycho Brahe and Rothman in 1585. Their conclusions were drawn from a resemblance between the elements. Nothing but a thorough investigation of the question, in which the perturbations of the comet's motion were allowed for, could settle the question. Again we find De Verrier to come to the rescue. He traced the motion of De Vico's comet back to the year 1585, and he arrived at the conclusion that the comets are two totally distinct bodies. He also ascertained at the same time that the comet of 1844 is not identical with Lexell's. He thinks, however, that De Vico's comet is the same as the comet of 1678 observed by La Hire. We thus see how precarious it is to rely upon any conclusion drawn from appearances that have not been thoroughly investigated.

The periods of revolution of comets are as various as is their physical appearances. Encke's comet has the remarkably short period of three and a third years. Winnecke's, five years; De Vico's, five and a half; Brorsen's, five and twothirds; D'Arrest's, six and a half; Biela's, six and twothirds; Faye's, seven and a half; Tuttle's, thirteen and a half; Peter's, sixteen; Halley's seventy-five; great comet of 1848, probably one hundred and seventy-five; great comet of 1858, twenty-four hundred; great comet of 1811, thirty-three hundred; great comet of 1680 (according to Encke), eighty eight hundred years.

As soon as a sufficient number of observations have been made on the apparent place of a comet, parabolic elements

are computed for it, and in order to determine whether it has ever been observed before, a table of the elements of all the computed orbits is examined, and if a set is found to agree with that of the new comet within moderate limits, they are considered as applying to the same body. The comet, however, may have made several revolutions within the period of the two ascertained apparitions. When this is the case an eccentricity, less than the one applying to the whole period, is assumed, and if that does not correctly represent the observations, a new one is assumed, and so on till the correct period is ascertained. Instead of this method, the astronomer can compute the orbit directly from the observations, if he chooses.

The physical constitution of comets is not less extraordinary than their general appearance and motions. A comet may be divided into three parts and each treated separately : the tail, the envelope, and the nucleus. The tail is not an invariable accompaniment of other parts of a comet, since many telescopic comets have no vestige of a tail. A bright comet was seen in 1585 without any sign of a tail. The brightest and largest comets, when first discovered by means of the telescope, are usually without a tail.

Appian was the first European astronomer who discovered that the tails of comets point in a direction opposite to that of the sun. He was led to it by observations upon Halley's Comet in 1731, and upon four other comets which appeared between the years 1531 and 1539. Though Appian was the first European astronomer that recognized this phenomenon of comets, yet the fact was known in China at a much earlier date. According to the researches of M. Edward Biot, in the Chinese annals of the Dynasty of Thong, who reigned between the years 618 and 907 of the Christian era, there is an account of a comet which appeared on the 22d of March, 837. The account concludes with this remark: "In general, when a comet (literally a broom) appears in the morning, the tail extends towards the west; when it appears in the evening it extends towards the east. This is a constant rule."*

* Comptes Rendus des Sciences, tom. xvi., p. 751.

the double ap

Near the axis

Sir William Herschel was led to the conclusion, from observations on the great comet of 1811, that the tail of a comet is a hollow cone. This accounts for pearance which the tails of comets present. of the tail we see through a less amount of the cometic matter than we do nearer the edges, and this gives rise to the ap pearance of a darker space along the axis of the tail.

Some comets, however, have been characterized by remarkable peculiarities. We are informed by Chésaux that the comet of 1741 had six tails spread out like a fan. According to Bessel, the comet of 1807 had two tails, one making an angle of 8° with the prolongation of the radiusvector, and the other, which was fainter, making an angle of 29° with it. A comet which appeared towards the close of 1823 had two tails, one opposite to the sun, the other pointing almost directly towards it. The great comet of 1843 was observed in Chili to have a lateral tail issuing from the original one 10° from the head, and extending to a much greater distance than the other.

Comets frequently exhibit a most imposing aspect in consequence of the great length of their tails. The ancients have recorded the appearance of numerous comets whose tails were from 50° to 90° in apparent length. Halley's comet in 1456 had a tail 60° long; the great comet of 1680 had a train 90° in length, as observed at Constantinople; the comet of 1769 had a tail 97° in length; the comet of 1618 exhibited one 104° long; the great comet of 1861 had a tail 106° in length; and the first comet of 1865 (seen in the southern hemisphere) for several days after the perihelion passage, had “a tail almost perfectly straight 150° long.”*

The apparent length which the tails of comets present is influenced very much by moonlight and the state of the atmosphere. The same comet not unfrequently exhibits a tail of very different lengths as viewed from different places. Thus, the tail of the great comet of 1769, as seen at London on the 9th of September, was 43° in length; on the same day at Paris it measured 55°; and at the Isle of Bourbon

* R. J. Ellery, Month. Notices, vol. xxv. p. 220.

it was 60°. The tails of comets appear longer in tropical climates than in more temperate latitudes.

The apparent length of the tail of a comet does not usually give us much idea of its real length in miles. This depends upon its apparent length, its distance from us, and its direction with respect to our position in space. The tail of the great comet of 1680 was 96 million miles in length; that of 1769, 38 millions; and the tail of the great comet of 1811 was more than 120 millions of miles in length, and 15 million broad at its extremity.

The tails of comets are developed as they approach the sun, whilst the volume of the head diminishes. This seems to show very clearly that the matter of the envelop is driven off by solar influence, and goes to form the tail. We quote the conclusions at which Sir John Herschel arrived from his observations on Halley's comet at its last appearance in 1835-6. He says: 1st. "That the matter of the nucleus of a comet is powerfully excited and dilated into a vaporous state by the action of the sun's says, escaping in streams and jets at those points of its surface which oppose the least resistance, and in all probability throwing that surface, or the nucleus itself, into irregular motions by its reaction in the act of so escaping and thus altering its direction. 2d. That this process chiefly takes place in that portion of the nucleus which is turned towards the sun-the vapor escaping chiefly in that direction. 3d. That when so emitted, it is prevented from proceeding in the direction originally impressed upon it, by some force directed from the sun drifting it back, and carrying it out to vast distances behind the nucleus, forming the tail, or so much of the tail as can be considered as consisting of material substance. 4th. That this force, whatever its nature, acts unequally on the materials of the comet, the greater portion remaining unvaporized, &c. considerable part of the vapor actually produced remaining in its neighborhood, forming the head and coma. the force thus acting on the materials of the tail cannot possibly be identical with the ordinary gravitation of matter, being centrifugal or repulsive as respects the sun, and of an energy very far exceeding the gravitating force towards that

5th. That

luminary. This will be evident if we consider the enormous velocity with which the matter of the tail is carried backward, in opposition both to the motion which it had as part of the nucleus, and to that which it acquired in the act of its emission, both which motions have to be destroyed in the first instance, before any movement in the contrary direction can be impulsed." It would seem to be impossible for matter driven to such enormous distances from the nucleus ever to be recalled by the attractive force of the comet. It is thus quite probable that some portion of the tails of comets is left behind at every return to the perihelion. This cometic matter thus left may be attracted to the earth and the planets, and be one source whence sporadic meteors are derived.

The tails of comets do not usually attain their greatest length till a short time after their perihelion passage. This is what we should expect if the sun is the principal producing cause. The tail usually inclines a little towards the region last quitted. The tails of some comets are considerably curved, others are nearly straight. The convex side, or that which is in the direction of the comet's motion, is much brighter than the other. Any theory of comets' tails must, it is evident, explain all these observed facts.

Various theories of comets' tails have been proposed to account for the phenomena which they present. Some have maintained that the conditions of equilibrium of a comet when acted on by its own feeble internal attraction and the powerful influence of the sun, are sufficient to account for all the phenomena presented by, their tails. Kepler and others have attributed to the light of the sun a repulsive action sufficient to drive off the lighter portions of the comet in the form of the tail.

Others proposed a theory which, as subsequently modified by Bessel, is as follows: They suppose a repulsive force to reside in the sun, of a polar nature like magnetism and electricity. Olbers supposed the force to be electrical producing the repulsive force in the sun and a similar one in the comet, and a specific action in the sun which we may suppose exhibited in the case of many tails. Bessel subjected Olbers' hypothesis to a rigorous mathematical cal