and 1456, is longer than any other period of the comet that has been hitherto determined by observation *.

Besides the comets to which allusion has already been made in connexion with the theory of gravitation, there are several other bodies of the same class which have also been found to revolve in elliptic orbits. It may be remarked that the question whether a comet returns periodically to perihelion, or whether, after having once visited the solar system, it then passes off definitively into the boundless regions of space, may admit of being resolved in two different ways. The elements of two or more comets may be compared together, and if they should present a close resemblance, it may be inferred that each set of elements refers merely to a different return of the same body. This circumstance will, therefore, serve to establish the periodicity of the comet, and the interval included between two consecutive apparitions will indicate the time of revolution. It was by means of such a comparison that Halley succeeded in establishing the periodicity of the famous comet which bears his name, and in predicting the time of its next return to perihelion. This was the only mode of determining the time of a comet's revolution which Newton considered to be practicable, for he was of opinion that all comets, without exception, revolve in very elongated ellipses, although for the sake of simplicity it might be assumed that towards the perihelion the path of each comet did not deviate sensibly from a parabola. The great improvements which have been effected in the methods of calculation since Newton's time have emboldened astronomers in many instances to announce the periodicity of a comet, and to assign the time of its revolution by means of observations made on the occasion of only one apparition. This method is undoubtedly more direct and more generally applicable than that founded on the comparison of different apparitions; but the results obtained by the employment of it have seldom turned out to be satisfactory. The errors of observation bear so large a proportion to the deviations from parabolic motion, which, in this case, form the real data of the problem, and the arc described by the comet, during the period of its being visible, is usually so small, that the values assigned to the periodic time by different computers, have frequently exhibited a great discordance. With respect to many of those comets to which elliptic orbits have been assigned, their movements admit of being equally well represented by parabolas. It is only in those cases in which it is found to be impossible to reconcile the actual motion of the comet with any parabola whatever, that the application of the elliptic method may be expected to lead to trustworthy results.

The great comet of 1680 has been supposed to revolve in an elliptic orbit. Halley, by comparing it with several ancient comets, was induced to conclude that it accomplished a complete revolution in 575 years. Euler and Pingré, severally, calculated its period from the observations of 1680; but the results at which they arrived differed materially ⚫ The following are the periods which have been derived from the recorded observations of the comet.

From 1378 to 1456

77.58 years.

1456,, 1531

1531,, 1607

1607,, 1682

1682,, 1759

75.21

76.15

74.91

76.49

76.68

1759,, 1835

The mean of these periods is 76.1 years. Comptes Rendus, tome xvi.

p. 1006.

U

from each other, as well as from the period which Halley had deduced by the light of historical records.

In the year 1264, A. D., there appeared a splendid comet, which was visible both in Europe and China. From the resemblance of its apparent path to that of a comet observed in 1556, it has been concluded that the two bodies are identical. Such is the view of the subject which has been taken by Pingré, Lalande, and various astronomers of the present day. Mr. Hind, by a skilful discussion of the recorded observations, has arrived at results which render still more probable the identity of the two comets. If this be true, the comet ought to return again to perihelion about the year 1848, the period being somewhere about 292 years. Such would be the case if the motion of the comet was effected solely by the central action of the sun. It is necessary, however, to take into account the effects of planetary perturbation in determining the precise time of return to perihelion. This arduous task has been recently executed by M. Bomme, a geometer of the Netherlands, who has found that the action of the planets will retard the comet's arrival in perihelion until the year 1858 or 1860*. It is to be hoped that the expected stranger will, in due time, respond to the elaborate calculations of which it has formed the subject.

The great comet of 1811 was found by Bessel to have a period of 3383 years. Several other astronomers who have calculated the elliptic elements of this comet have obtained results agreeing very nearly with each other and also with that deduced by Bessel. Comets which take such an immense length of time to accomplish a single revolution, lose much of the interest which the periodic character of their movements is otherwise calculated to excite. The case is quite different with respect to such comets as those of Encke, Biela, Faye, and De Vico, which may be expected frequently to return to perihelion during the average period of human life. Two other comets have recently been found to revolve in elliptic orbits of comparatively small dimensions. One of these was discovered by M. Brorsen, on the 26th of February, 1816. Its period has been determined to be about five years and a half. The last passage of the perihelion took place on the 25th of January, 1846. The other comet of short period was discovered by M. Peters, on the 26th of June, 1846. It has been found by M. D'Arrest that the observations of this comet are capable of being represented by an elliptic orbit, with a period of 5804 days, or about sixteen years.

The most splendid comet of the present century was that which appeared in the early part of the year 1843. The following elements of its motion, calculated by Sig. Capocci, will serve to give an idea of the orbit in which it moves. They have been selected for this purpose on account of the perihelion distance coinciding almost exactly with the mean of the perihelion distances arrived at by various other astronomers who have computed the elements of the comet:

Passage of the perihelion, February 27.5643

Mr. Hind's elements of the comet of 1556, when employed as the basis of calculation, fix the passage of the perihelion in the year 1858. Halley's elements make the passage two years later.

It appears from the above value of the perihelion distance that the comet approached nearer the sun than any other comet recorded in history. The great comet of 1680 had been hitherto the most remarkable in this respect of all those comets whose elements had been determined, having approached the sun's surface within one-third of his diameter. The least distance of the comet of 1843 from the sun's surface did not amount to more than one-seventh of the solar diameter. The comet, therefore, approached twice as near the sun as the comet of 1680.

The immense velocity of the comet of 1843, when revolving in the neighbourhood of the sun, arising from the smallness of its perihelion distance, occasioned some extraordinary peculiarities in its motion. Thus between the 27th and 28th of February it described upon its orbit an arc of 292°. Supposing it to revolve in an elliptic orbit, this would leave only 68° to be described during the time which elapses until the next arrival in perihelion. On the evening of the 27th of February it described the whole of the northern part of its orbit, having occupied only 2h 11m in passing from the ascending to the descending node. It was twice in conjunction with the sun on the 27th of February. The first conjunction took place at 9h 24m P. M. The comet was then revolving beyond the sun. The second conjunction took place at 12h 15m P. M. The comet was then passing between the sun and the earth. The time at which this interesting event occurred, prevented astronomers from ascertaining whether the comet would have been visible when projected upon the solar disk *.

It has been suspected that the comet of 1843 is identical with another great comet which appeared in the same region of the heavens in the year 1668, and which was visible at San Salvador in Brazil, at Bologna, and Lisbon. On the evening of the 5th of March the comet was seen at San Salvador by Father Valentine Estancel. It then appeared a little above the western horizon. The tail measured 23° in length, and resembled a huge beam of light, extending nearly in a horizontal direction from west to south. Its light was so vivid that persons standing on the shore were enabled to discern its reflexion on the sea; but the head was so small as to be scarcely visible t. The comet was observed by the same individual on the 7th of March. Cassini observed it at Bologna on the 10th and 14th of the same month. Drawings of the direction of its tail, as determined by him on those days, were afterwards communicated by Maraldi to the Academy of Sciences. It is a remarkable fact that if this comet be supposed to have passed its perihelion on the 27th of February, 1668, the Brazilian observations, as well as those of Cassini, will be represented with sufficient accuracy by the orbit of the comet of 1843. This would assign to the comet a period of exactly 175 years.

The elements of the comet of 1843 presented also a strong resemblance to those of a comet observed in 1689. The most discordant element was the inclination, which, in the case of the latter comet, amounted to 69° 17′ according to the calculations of Pingré. The same astronomer found the passage of the perihelion to have taken place on December 1.6, 1689. Sig. Capocci, however, remarked, that if the comet be supposed to have passed its perihelion on December 3, all the recorded observations will be accurately satisfied by the elements of the comet of 1843.

Comptes Rendus, tome xvi., p. 642.

+ Cométographie, tome ii., p. 22. Mém. Acad. des Sciences, 1702, p. 107.'

Hence, in order to reconcile this conclusion with that arrived at relative to the comet of 1668, it would be necessary to diminish the period of the comet to 21 years. But there are other comets which astronomers have suspected to be identical with the comet of 1843, especially those of 1618 and 1702. Capocci, therefore, suggested the probability of the period of the comet being somewhere about seven years, remarking that this hypothesis would afford a satisfactory account of numerous apparitions of comets recorded in history. The opinions of this astronomer have received a remarkable confirmation from the subsequent researches of Prof. Pierce and M. Clausen. Prof. Pierce having recomputed the elements of the comet of 1689, obtained 30° 25′ for the inclination of the orbit. This result agreed almost exactly with that obtained for the inclination of the comet of 1843. He also found the passage of the perihelion to have taken place on December 2.1463, 1689. M. Clausen having discussed the totality of the observations of the comet of 1843, found that they would be best represented by supposing the comet to revolve in an elliptic orbit, the period of which he fixed at 6.8 years. It is not easy to reconcile this conclusion with the fact of the comet not having been more frequently recognised on former occasions of its return to perihelion. This circumstance may be accounted for in some instances by the peculiar position of the orbit of the comet, in others, perhaps, by changes in its physical constitution, which may exercise a material influence on its visibility.

The physical constitution of comets forms a subject of research at once so varied and extensive that it has been deemed expedient to devote a separate chapter to an account of the labours of astronomers in connexion with it.

CHAPTER XV.

General Aspect of Comets.-Translucency of Cometic Matter.-Structure and Dimensions of the Envelope.-Description of the Tail.-Its Direction and Curvature. Peculiarities of Structure.-Dimensions.-Phenomena Observed during the Passage of Comets through their Perihelia.-Comet of Halley.-Comet of 1799.Variation of the Volume of Comets.-Hevelius.-Newton.-Struve.-Herschel.Dissolution of Comets.-Historical Statement of Ephorus.-Comet of Biela.- Developement of the Tail.—Comet of 1680.—Comet of 1769.—Anomalous Appearances in the Tail.-Instances of Remarkable Comets.-Hypotheses respecting their Physical Constitution. Theories of the Variation of a Comet's Volume.-Newton.-Valz.Herschel.-Theories of the Tails of Comets.-- Kepler.-Newton.-Electrical Theory.Light of Comets.-Appearance of Phases.-Cassini.-Cacciatore.-Polarization of the Light of Comets.-Researches of Arago.-Question respecting the Solidity of Comets. Newton.-Laplace. - Smallness of a Comet's Mass.-Ultimate condition of Cometary Bodies. Opinions of Newton, Laplace, and Herschel on this point.

THE question relative to the constitution of Comets is one of the most interesting in the whole range of celestial physics. There is something in the sudden apparition and strange aspect of these bodies which is calculated to arrest the attention of the most careless observer of nature. In former ages they were regarded with superstitious dread, as manifestations of divine displeasure, and the harbingers of impending calamities. Every feature in their appearance was gazed upon with intense anxiety, and was assimilated, by the influence of an excited imagination, to the awe-inspiring lineament of a supernatural phantom. In recent times, when a more ad

vanced state of civilization has led to juster views of celestial phenomena, it has become an interesting branch of study to enquire into the nature of comets, and the purposes which they fulfil in the economy of the material universe. And although it must be acknowledged that little progress has hitherto been made towards obtaining a satisfactory solution of these questions, still a multitude of facts have been disclosed by the observations of astronomers, which have formed the groundwork of much ingenious speculation, and have tended to throw some degree of light on the mysterious subject to which they relate.

Comets exhibit various peculiarities by means of which they are readily distinguishable from other bodies. The light by which they shine is generally pale, compared with that of the planets or stars. The principal part of their structure is the head, which presents the appearance of a nebulous body, more or less condensed towards the centre. Within the head a bright point is seen, approaching in lustre to a planet. This is called the nucleus of the comet. The nebulosity of the head is surrounded by a hazy contour, termed the coma. But the most remarkable part in the structure of a comet is the tail, which appears as a long train of light issuing from the head. Although these are the more prominent features by which comets are in many instances characterised, they are found actually to exhibit a great variety of aspect. Multitudes of comets, which are visible only in telescopes, present neither tail nor nucleus; but merely resemble a round mass of vapours slightly condensed towards the centre. Even of those comets which are visible to the naked eye there have been some which did not exhibit the usual features of these bodies. The comet of 1585, observed by Tycho Brahé, possessed neither tail nor coma, but appeared perfectly round like a planet *. Various examples of the same sort are to be found in the records of astronomical observation.

It

The substance of which comets are composed is characterised by an extreme degree of tenuity. This has been inferred from the fact that stars have been seen through them without exhibiting any sensible diminution of lustre. Even as early as the time of Seneca it was remarked that stars were occasionally visible through the substance of comets. might well be supposed that the rude observations of ancient times would be incapable of indicating delicate alterations of brightness, even although they should exist. Modern astronomers, however, universally agree in representing the translucency of cometic matter to be in most cases so perfect as to offer no obstacle to vision. Numerous observations might be cited in confirmation of this fact. Thus, on the 9th of November, 1795, Sir William Herschel observed the comet of that year pass centrally over a telescopic double star of the eleventh or twelfth magnitude; but, notwithstanding this circumstance, the smaller of the two component stars continued, during the whole time of the transit, to be distinctly visible t. Olbers perceived a star of the tenth magnitude through the comet of 1802; but he was unable to persuade himself that it exhibited any diminution of its usual brightness. On the 7th of November, 1828, M. Struve perceived a star of the tenth magnitude within a few seconds of the brightest part of Encke's comet; but the light of the star did not seem to be enfeebled in the slightest degree. Sir John Herschel, in a

• Planè rotunda extitit; nec ullam caudam aut barbam in unam magis quam in aliam partem portendebat. (Epist. ad Landgrav. p. 13.)

+ Phil. Trans. 1796, Pt. I., p. 133. This comet was discovered by Miss Caroline Herschel; it has since been ascertained to have been an apparition of Encke's comet.