Ethereal Medium—Comets—Do not disturb the Solar System—Their Orbits and Disturbances—M. Faye’s Comet probably the same with Lexel’s—Periods of other three known—Acceleration in the mean Motions of Encke’s and Biela’s Comets—The Shock of a Comet—Disturbing Action of the Earth and Planets on Encke’s and Biela’s Comets—Velocity of Comets—The Comet of 1264—The great Comet of 1343—Physical Constitution—Shine by borrowed Light—Estimation of their Number.
In considering the constitution of the earth, and the fluids which surround it, various subjects have presented themselves to our notice, of which some, for aught we know, are confined to the planet we inhabit; some are common to it and to the other bodies of our system. But an all-pervading ether must fill the whole visible creation, since it conveys, in the form of light, tremors which may have been excited in the deepest recesses of the universe thousands of years before we were called into being. The existence of such a medium, though at first hypothetical, is proved by the undulatory theory of light, and rendered certain by the motion of comets, and by its action upon the vapours of which they are chiefly composed. It has often been imagined that the tails of comets have infused new substances into our atmosphere. Possibly the earth may attract some of that nebulous matter, since the vapours raised by the sun’s heat, when the comets are in perihelio, and which form their tails, are scattered through space in their passage to their aphelion; but it has hitherto produced no effect, nor have the seasons ever been influenced by these bodies. The light of the comet of the year 1811, which was so brilliant, did not impart any heat even when condensed on the bulb of a thermometer of a structure so delicate that it would have made the hundredth part of a degree evident. In all probability, the tails of comets may have passed over the earth without its inhabitants being conscious of their presence; and there is reason to believe that the tail of the great comet of 1843 did so. M. Valz observed that the light of a brilliant comet was eclipsed as it passed over a star of the 7th magnitude, whence M. Babinet computed that the light of the comet must have been sixty times less than that of the star, and that matter so attenuated could not penetrate the earth’s atmosphere, but the constitution of these bodies is still a matter of conjecture.
The passage of comets has never sensibly disturbed the stability of the solar system; their nucleus, being in general only a mass of vapour, is so rare, and their transit so rapid, even when they had a solid part, that the time has not been long enough to admit of a sufficient accumulation of impetus to produce a perceptible action. Indeed, M. Dusejour has shown that, under the most favourable circumstances, a comet cannot remain longer than two hours and a half at a less distance from the earth than 10,500 leagues. The comet of 1770 passed within about six times the distance of the moon from the earth, without even affecting our tides. According to La Place, the action of the earth on the comet of 1770 augmented the period of its revolution by more than two days; and, if comets had any perceptible disturbing energy, the reaction of the comet ought to have increased the length of our year. Had the mass of that comet been equal to the mass of the earth, its disturbing action would have increased the length of the sidereal year by 2h 53m; but, as Delambre’s computations from the Greenwich observations of the sun show that the length of the year has not been increased by the fraction of a second, its mass could not have been equal to the 1/5000th part of that of the earth. This accounts for the same comet having twice swept through the system of Jupiter’s satellites without deranging the motion of these moons. M. Dusejour has computed that a comet, equal in mass to the earth, passing at the distance of 12,150 leagues from our planet, would increase the length of the year to 367d 16h 5m, and the obliquity of the ecliptic as much as 2°. So the principal action of comets would be to alter the calendar, even if they were dense enough to affect the earth.
Comets traverse all parts of the heavens; their paths have every possible inclination to the plane of the ecliptic, and, unlike the planets, the motion of more than half of those that have appeared has been retrograde, that is, from east to west. They are only visible when near their perihelia; then their velocity is such, that its square is twice as great as that of a body moving in a circle at the same distance: they consequently remain but a very short time within the planetary orbits. And, as all the conic sections of the same focal distance sensibly coincide, through a small arc, on each side of the extremity of their axis, it is difficult to ascertain in which of these curves the comets move, from observations made, as they necessarily must be, near their perihelia (N.227). Probably they all move in extremely excentric ellipses; although, in most cases, the parabolic curve coincides most nearly with their observed motions. Some few seem to describe hyperbolas; such, being once visible to us, would vanish for ever, to wander through boundless space, to the remote systems of the universe. If a planet be supposed to revolve in a circular orbit, whose radius is equal to the perihelion distance of a comet moving in a parabola, the areas described by these two bodies in the same time will be as unity to the square root of two, which forms such a connexion between the motion of comets and planets, that, by Kepler’s law, the ratio of the areas described during the same time by the comet and the earth may be found; so that the place of a comet may be computed at any time in its parabolic orbit, estimated from the instant of its passage at the perihelion. It is a problem of very great difficulty to determine all the other elements of parabolic motion—namely, the comet’s perihelion distance, or shortest distance from the sun, estimated in parts of the mean distance of the earth from the sun; the longitude of the perihelion; the inclination of the orbit on the plane of the ecliptic; and the longitude of the ascending node. Three observed longitudes and latitudes of a comet are sufficient for computing the approximate values of these quantities; but an accurate estimation of them can only be obtained by successive corrections, from a number of observations, distant from one another. When the motion of a comet is retrograde, the place of the ascending node is exactly opposite to what it is when the motion is direct. Hence the place of the ascending node, together with the direction of the comet’s motion, show whether the inclination of the orbit is on the north or south side of the plane of the ecliptic. If the motion be direct, the inclination is on the north side; if retrograde, it is on the south side.
The identity of the elements is the only proof of the return of a comet to our system. Should the elements of a new comet be the same, or nearly the same, with those of any one previously known, the probability of the identity of the two bodies is very great, since the similarity extends to no less than four elements, every one of which is capable of an infinity of variations. But, even if the orbit be determined with all the accuracy the case admits of, it may be difficult, or even impossible, to recognize a comet on its return, because its orbit would be very much changed if it passed near any of the large planets of this or of any other system, in consequence of their disturbing energy, which would be very great on bodies of so rare a nature.
By far the most curious and interesting instance of the disturbing action of the great bodies of our system is found in the comet of 1770. The elements of its orbit, determined by Messier, did not agree with those of any comet that had hitherto been computed, yet Lexel ascertained that it described an ellipse about the sun, whose major axis was only equal to three times the length of the diameter of the terrestrial orbit, and consequently that it must return to the sun at intervals of five years and a half. This result was confirmed by numerous observations, as the comet was visible through an arc of 170°; yet this comet had never been observed before the year 1770, nor has it ever again been seen till 1843, though very brilliant. The disturbing action of the larger planets affords a solution of this anomaly, as Lexel ascertained that in 1767 the comet must have passed Jupiter at a distance less than the fifty-eighth part of its distance from the sun, and that in 1779 it would be 500 times nearer Jupiter than the sun; consequently the action of the sun on the comet would not be the fiftieth part of what it would experience from Jupiter, so that Jupiter became the primum mobile. Assuming the orbit to be such as Lexel had determined in 1770, La Place found that the action of Jupiter, previous to the year 1770, had so completely changed the form of it, that the comet which had been invisible to us before 1770 was then brought into view, and that the action of the same planet, producing a contrary effect, has subsequently to that year removed it from our sight, since it was computed to be revolving in an orbit whose perihelion was beyond the orbit of Ceres. However, the action of Jupiter during the summer of 1840 must have been so great, from his proximity to that singular body, that he seems to have brought it back to its former path as he had done in 1767, for the elements of the orbit of a comet which was discovered in November 1843, by M. Faye, agree so nearly with those of the orbit of Lexel’s comet that the two bodies were supposed to be identical; by the subsequent computation of M. le Verrier, it appears, however, that they are not the same, that they were both brought to our system by Jupiter’s attraction, and that they have been in it more than a century, and have frequently come near the earth without having been seen. From the smallness of the excentricity of Lexel’s comet, the orbit resembles those of the planets, but this comet is liable to greater perturbations than any other body in the system, because it comes very near the orbit of Mars when in perihelion, and very near that of Jupiter when in aphelion; besides, it passes within a comparatively small distance of the orbits of the minor planets; and as it will continue to cross the orbit of Jupiter at each revolution till the two bodies meet, its periodic time, now about seven years, will again be changed, but in the mean time it ought to have returned to its perihelion in the year 1851. This comet might have been seen from the earth in 1776, had its light not been eclipsed by that of the sun. There is still so much doubt with regard to Lexel’s comet that during the present year, 1858, M. le Verrier has constructed a table of all the orbits in which the comet may have moved after leaving Jupiter in 1770, which will enable astronomers to recognise the comet even should the elements of its orbit be much altered. He thinks it possible that its path may have become hyperbolic, but that it is more likely an augmentation of its periodic time may have taken place. It is quite possible that comets frequenting our system may be turned away, or others brought to the sun, by the attraction of planets revolving beyond the orbit of Neptune, or by bodies still farther removed from the solar influence.
Other comets, liable to less disturbance, return to the sun at stated intervals. Halley computed the elements of the orbit of a comet that appeared in the year 1682, which agreed so nearly with those of the comets of 1607 and 1531, that he concluded it to be the same body returning to the sun at intervals of about seventy-five years. He consequently predicted its reappearance in the year 1758, or in the beginning of 1759. Science was not sufficiently advanced in the time of Halley to enable him to determine the perturbations this comet might experience; but Clairaut computed that, in consequence of the attraction of Jupiter and Saturn, its periodic time would be so much shorter than during its revolution between 1607 and 1682, that it would pass its perihelion on the 18th of April, 1759. The comet did arrive at that point of its orbit on the 12th of March, which was thirty-seven days before the time assigned. Clairaut subsequently reduced the error to twenty-three days; and La Place has since shown that it would only have been thirteen days if the mass of Saturn had been as well known as it is now. It appears, from this, that the path of the comet was not quite known at that period; and, although many observations were then made, they were far from attaining the accuracy of those of the present day. Besides, since the year 1759, the orbit of the comet has been altered by the attraction of Jupiter in one direction, and that of Saturn, Uranus, and Neptune in the other; yet, notwithstanding these sources of uncertainty, and our ignorance of all the possible causes of derangement from unknown bodies on the confines of our system, or in the regions beyond it, the comet appeared exactly at the time, and not far from the place assigned to it by astronomers; and its actual arrival at its perihelion a little before noon on the 16th of November, 1835, only differed from the computed time by a very few days, which was probably owing to the attraction of Neptune.
The fulfilment of this astronomical prediction is truly wonderful, if it be considered that the comet is seen only for a few weeks during its passage through our system, and that it wanders from the sun for seventy-five years to twice the distance of Uranus. This enormous orbit is four times longer than it is broad; its length is about 3420 millions of miles, or about thirty-six times the mean distance of the earth from the sun. At its perihelion the comet comes within nearly fifty-seven millions of miles of the sun, and at its aphelion it is sixty times more distant. On account of this extensive range it must experience 3600 times more light and heat when nearest to the sun than in the most remote point of its orbit. In the one position the sun will seem to be four times larger than he appears to us, and at the other he will not be apparently larger than a star (N.228.)
On the first appearance of Halley’s comet, early in August 1835, it seemed to be merely a globular mass of dim vapour, without a tail. A concentration of light, a little on one side of the centre, increased as the comet approached the sun and earth, and latterly looked so like the disc of a small planet, that it might have been mistaken for a solid nucleus. M. Struve, however, saw a central occultation of a star of the ninth magnitude by the comet, at Dorpat, on the 29th of September. The star remained constantly visible, without any considerable diminution of light; and, instead of being eclipsed, the nucleus of the comet disappeared at the moment of conjunction from the brilliancy of the star. The tail increased as the comet approached its perihelion, and shortly before it was lost in the sun’s rays it was between thirty and forty degrees in length.
According to the observations of M. Valz, the nebulosity increased in magnitude as it approached the sun; but no other comet on record has exhibited such sudden and unaccountable changes of aspect. It was invisible for two months when near its perihelion passage, and when it reappeared on the 24th of January, 1836, its aspect was completely changed; it had no tail, and to the naked eye was like a hazy star; but with a powerful telescope it presented a small, round, planetary-looking nucleus 2 in diameter, surrounded by an extensive coma, and in the centre it had a small, bright, solid part. The nucleus, clear and well defined, like the disc of a planet, was observed on one occasion to become obscure and enlarged in the course of a few hours. But by far the most remarkable circumstance was the sudden appearance of certain luminous brushes or sectors, diverging from the centre of the nucleus through the nebulosity. M. Struve describes the nucleus of the comet, in the beginning of October, as elliptical, and like a burning coal, out of which there issued, in a direction nearly opposite to the tail, a divergent flame, varying in intensity, form, and direction, appearing occasionally even double, and suggesting the idea of luminous gas bursting from the nucleus. On one occasion M. Arago saw three of these divergent flames on the side opposite the tail, rising through the nebulosity, which they greatly exceeded in brilliancy: after the comet had passed its perihelion, it acquired another of these luminous fans, which was observed by Sir John Herschel at the Cape of Good Hope. Hevelius describes an appearance precisely similar, which he had witnessed in this comet at its approach to the sun in the year 1682, and something of the kind seems to have been noticed in the comet of 1744. Possibly the second tail of the comet of 1724, which was directed towards the sun, may have been of this nature.
The influence of the ethereal medium on the motions of Halley’s comet will be known after another revolution, and future astronomers will learn, by the accuracy of its returns, whether it has met with any unknown cause of disturbance in its distant journey. Undiscovered planets, beyond the visible boundary of our system, may change its path and the period of its revolution, and thus may indirectly reveal to us their existence, and even their physical nature and orbit. The secrets of the yet more distant heavens may be disclosed to future generations by comets which penetrate still farther into space, such as that of 1763, which, if any faith may be placed in the computation, goes nearly forty-three times farther from the sun than Halley’s does, and shows that the sun’s attraction is powerful enough, at the enormous distance of 15,500 millions of miles, to recall the comet to its perihelion. The periods of some comets are said to be of many thousand years, and even the average time of the revolution of comets generally is about a thousand years; which proves that the sun’s gravitating force extends very far. La Place estimates that the solar attraction is felt throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun.
Authentic records of Halley’s comet do not extend beyond the year 1456, yet it may be traced, with some degree of probability, even to a period preceding the Christian era. But as the evidence only rests upon coincidences of its periodic time, which may vary as much as eighteen months from the disturbing action of the planets, its identity with comets of such remote times must be regarded as extremely doubtful.
This is the first comet whose periodicity has been established. It is also the first whose elements have been determined from observations made in Europe; for, although the comets which appeared in the years 240, 539, 565, and 837, are the most ancient of those whose orbits have been traced, their elements were computed from Chinese observations.
Besides Halley’s and Lexel’s comets, ten or twelve others are now known to form part of the solar system; that is to say, they return to the sun at stated periods. Six of them have periods of less than eight years. That generally called Encke’s comet, or the comet of the short period, was first seen by MM. Messier and Mechain in 1786, again by Miss Herschel in 1805, and its returns, in the years 1805 and 1819, were observed by other astronomers, under the impression that all four were different bodies. However, Professor Encke not only proved their identity, but determined the circumstances of the comet’s motion. Its reappearance in the years 1825, 1828, and 1832, accorded with the orbit assigned by M. Encke, who thus established the length of its period to be 1204 days, nearly. This comet is very small, of feeble light, and invisible to the naked eye, except under very favourable circumstances, and in particular positions. It has no tail, it revolves in an ellipse of great excentricity inclined at an angle of 13° 22' to the plane of the ecliptic, and is subject to considerable perturbations from the attraction of the planets, which occasion variations in its periodic time. Among the many perturbations to which the planets are liable, their mean motions, and therefore the major axes of their orbits, experience no change; while, on the contrary, the mean motion of the moon is accelerated from age to age—a circumstance at first attributed to the resistance of an ethereal medium pervading space, but subsequently proved to arise from the secular diminution of the excentricity of the terrestrial orbit. Although the resistance of such a medium has not hitherto been perceived in the motions of such dense bodies as the planets and satellites, its effects on the revolutions of the comets leave no doubt of its existence. From the numerous observations that have been made on each return of the comet of the short period, the elements have been computed with great accuracy on the hypothesis of its moving in vacuo. Its perturbations occasioned by the disturbing action of the planets have been determined; and, after everything that could influence its motion had been duly considered, M. Encke found that an acceleration of about two days in each revolution has taken place in its mean motion, precisely similar to that which would be occasioned by the resistance of an ethereal medium. And, as it cannot be attributed to a cause like that which produces the acceleration of the moon, it must be concluded that the celestial bodies do not perform their revolutions in an absolute void, and that, although the medium be too rare to have a sensible effect on the masses of the planets and satellites, it nevertheless has a considerable influence on so rare a body as a comet. Contradictory as it may seem that the motion of a body should be accelerated by the resistance of an ethereal medium, the truth becomes evident if it be considered that both planets and comets are retained in their orbits by two forces which exactly balance one another; namely, the centrifugal force producing the velocity in the tangent, and the attraction of the gravitating force directed to the centre of the sun. If one of these forces be diminished by any cause, the other will be proportionally increased. Now, the necessary effect of a resisting medium is to diminish the tangential velocity, so that the balance is destroyed, gravity preponderates, the body descends towards the sun till equilibrium is again restored between the two forces; and, as it then describes a smaller orbit, it moves with increased velocity. Thus, the resistance of an ethereal medium actually accelerates the motion of a body; but, as the resisting force is confined to the plane of the orbit, it has no influence whatever on the inclination of the orbit, or on the place of the nodes. In computing its effect, M. Encke assumed the increase to be inversely as the square of the distance, and that its resistance acts as a tangential force proportional to the squares of the comet’s actual velocity in each point of its orbit. Another comet belonging to our system, which returns to its perihelion after a period of 63/4 years, has been accelerated in its motion by a whole day during one revolution, which puts the existence of ether beyond a doubt, and confirms the undulatory theory of light. Since this comet, which revolves nearly between the orbits of the earth and Jupiter, is only accelerated one day at each revolution, while Encke’s, revolving nearly between the orbits of Mercury and Pallas, is accelerated two, the ethereal medium must increase in density towards the sun. The comet in question was discovered by M. Biela at Josephstadt on the 27th of February, 1826, and ten days afterwards it was seen by M. Gambart at Marseilles, who computed its parabolic elements, and found that they agreed with those of the comets which had appeared in the years 1789 and 1795, whence he concluded them to be the same body moving in an ellipse, and accomplishing its revolution in 2460 days. The perturbations of this comet were computed by M. Damoiseau, who predicted that it would cross the plane of the ecliptic on the 29th of October, 1832, a little before midnight, at a point nearly 18,484 miles within the earth’s orbit; and as M. Olbers of Bremen, in 1805, had determined the radius of the comet’s head to be about 21,136 miles, it was evident that its nebulosity would envelop a portion of the earth’s orbit,—a circumstance which caused some alarm in France, from the notion that, if any disturbing cause had delayed the arrival of the comet for one month, the earth must have passed through its head. M. Arago dispelled these fears by his excellent treatise on comets, in the Annuaire of 1832, where he proves that, as the earth would never be nearer the comet than 18,000,000 British leagues, there could be no danger of collision. The earth is in more danger from these two small comets than from any other. Encke’s crosses the terrestrial orbit sixty times in a century, and may ultimately come into collision, but both are so extremely rare, that little injury is to be apprehended.
The earth would fall to the sun in 641/2 days, if it were struck by a comet with sufficient impetus to destroy its centrifugal force. What the earth’s primitive velocity may have been it is impossible to say. Therefore a comet may have given it a shock without changing the axis of rotation, but only destroying part of its tangential velocity, so as to diminish the size of the orbit—a thing by no means impossible, though highly improbable. At all events, there is no proof of this having occurred; and it is manifest that the axis of the earth’s rotation has not been changed, because, as the ether offers no sensible resistance to so dense a body as the earth, the libration would to this day be evident in the variation it must have occasioned in the terrestrial latitudes. Supposing the nucleus of a comet to have a diameter only equal to the fourth part of that of the earth, and that its perihelion is nearer to the sun than we are ourselves, its orbit being otherwise unknown, M. Arago has computed that the probability of the earth receiving a shock from it is only one in 281 millions, and that the chance of our coming in contact with its nebulosity is about ten or twelve times greater. Only comets with retrograde motions can come into direct collision with the earth, and if the momentum were great the event might be fatal; but in general the substance of comets is so rare, that it is likely they would not do much harm if they were to impinge; and even then the mischief would probably be local, and the equilibrium soon restored, provided the nucleus were gaseous, or very small. It is, however, more probable that the earth would only be deflected a little from its course by the approach of a comet, without being touched by it. The comets that have come nearest to the earth were that of the year 837, which remained four days within less than 1,240,000 leagues from our orbit: that of 1770, which approached within about six times the distance of the moon. The celebrated comet of 1680 also came very near to us; and the comet whose period is 63/4 years was ten times nearer the earth in 1805 than in 1832, when it caused so much alarm.
Encke’s and Biela’s comets are at present far removed from the influence of Jupiter, but they will not always remain so, because, the aphelia and nodes of the orbits of these two comets being the points which approach nearest to the orbit of Jupiter at each meeting of the planet and comets, the major axis of Encke’s comet will be increased and that of Biela’s diminished, till in the course of time, when the proximity has increased sufficiently, the orbits will be completely changed, as that of Lexel’s was in 1770. Every twenty-third year, or after seven revolutions of Encke’s comet, its greatest proximity to Jupiter takes place, and at that time his attraction increases the period of its revolution by nine days—a circumstance which took place in the end of the years 1820 and 1843. But from the position of the bodies there is a diminution of three days in the six following revolutions, which reduces the increase to six days in seven revolutions. Thus, before the year 1819, the periodic time of Encke’s comet was 1204 days, and it was 1219 days in accomplishing the revolution that ended in 1845. By this progressive increase the orbit of the comet will reach that of Jupiter in seven or eight centuries, and then by the very near approach of the two bodies it will be completely changed.
At present the Earth and Mercury have the most powerful influence on the motions of Encke’s and Biela’s comets; and have had for so long a time that, according to the computation of Mr. Airy, the present orbit of the latter was formed by the attraction of the Earth, and that of Encke’s by the action of Mercury. With regard to the latter comet, that event must have taken place in February 1776. In 1786 Encke’s comet had both a tail and a nucleus, now it has neither; a singular instance of the possibility of their disappearance. It was in perihelio in 1855.
In 1846 Biela’s comet was divided into two distinct bodies, by what strange accident is altogether a mystery. The nuclei of the two comets were separated by about 150,000 miles, and they travelled together with their tails parallel, and an arch of light over their heads. Till that time Biela’s comet never had been seen with a tail. The new head was dull at first, but increased in size and brightness till it surpassed its companion in both; besides, it had a bright flashing diamond-like point in its centre—gradually it resumed its dull appearance, and its period was computed to be eight days longer than that of the original head. They had separated to a greater distance from one another in 1853, but were still travelling together, one having become smaller than the other.
A comet discovered by M. Brorsen of Kiel, on the 26th of February, 1846, came, on the 20th of April following, nearly as close to Jupiter as his fourth satellite, when Jupiter’s attraction must have been ten times greater than that of the sun; so there is every reason to believe that the comet’s orbit will be as much altered as that of Lexel’s; and another discovered by Padre de Vico at Rome, on the 22nd of August, will, in all probability, be as much disturbed by the same cause. One of the comets found by that astronomer has a period which varies, according to different computations, from 55 to 99 years; it certainly has an elliptical orbit. That discovered at Naples by Mr. Peters revolves about the sun in 16 years; but Olbers’s comet of 1815 must go nearly the same distance into space with Halley’s, since its period is 74 years. Two discovered by M. Brorsen have periods, one of 500 and the other of 28 years; but of the latter there is some uncertainty.
The comet which appeared in 1596 and 1845 has a period of 249 years; and should M. Argelander’s computation be accurate, the orbit which has hitherto been assigned to the great comet of 1811 must be erroneous, since he has ascertained its period to be 3066 years.
The great comet of 1264, which had a tail that extended over 100° of the celestial vault, was observed and recorded by the Chinese, and was ascertained to be the same that had appeared in 1556, and of whose motions observations were taken at Vienna in the reign of the Emperor Charles V., but it was then less brilliant. In consequence of the discovery of the original observations of the comet of 1556, by Fabricius at Vienna, and by Heller at Nuremburg, Mr. Hind was induced to compute its orbit for that year; but after much labour, aided by all the improved methods of calculation, he found Heller’s observations so confused, and even erroneous, that he could not determine the curve described by the comet at that time with any precision, and therefore could only predict that the epoch of its return would be some time between 1848 and 1861. Before comets reach the sun they are rarely conspicuous; but if after passing their perihelion they come near the earth, then they have tails, and become brilliant in consequence of the sun’s action upon the matter of which they are formed. Now if the comet in question should pass its perihelion between the months of March and October, it possibly may be as remarkable as ever; but should it come nearest to the sun in winter, such is the position of its orbit with regard to the earth, that it may pass unnoticed—which is very unlikely, as search is being made for it at almost all the observatories in Europe and in the United States. Nearly the whole of its orbit lies below the plane of the ecliptic, and far from the paths of the larger planets, but it extends into space more than twice the distance of Neptune, or nearly six thousand millions of miles from the sun.
Comets in or near their perihelion move with prodigious velocity. That of 1680 appears to have gone half round the sun in ten hours and a half, moving at the rate of 880,000 miles an hour. If its enormous centrifugal force had ceased when passing its perihelion, it would have fallen to the sun in about three minutes, as it was then less than 147,000 miles from his surface. So near the sun, it would be exposed to a heat 27,500 times greater than that received by the earth; and as the sun’s heat is supposed to be in proportion to the intensity of his light, it is probable that a degree of heat so intense would be sufficient to convert into vapour every terrestrial substance with which we are acquainted. At the perihelion distance the sun’s diameter would be seen from the comet under an angle of 73°, so that the sun, viewed from the comet, would nearly cover the whole extent of the heavens from the horizon to the zenith. As this comet is presumed to have a period of 575 years, the major axis of its orbit must be so great, that at the aphelion the sun’s diameter would only subtend an angle of about fourteen seconds, which is not so great by half as the diameter of Mars appears to us when in opposition. The sun would consequently impart no heat, so that the comet would then be exposed to the temperature of the ethereal regions, which is 239° below the zero point of Fahrenheit. A body of such tenuity as the comet, moving with such velocity, must have met with great resistance from the dense atmosphere of the sun, while passing so near his surface at its perihelion. The centrifugal force must consequently have been diminished, and the sun’s attraction proportionally augmented, so that it must have come nearer to the sun in 1680 than in its preceding revolution, and would subsequently describe a smaller orbit. As this diminution of its orbit will be repeated at each revolution, the comet will infallibly end by falling on the surface of the sun, unless its course be changed by the disturbing influence of some large body in the unknown expanse of creation. Our ignorance of the actual density of the sun’s atmosphere, of the density of the comet, and of the period of its revolution, renders it impossible to form any idea of the number of centuries which must elapse before this event takes place.
The same cause may affect the motions of the planets, and ultimately be the means of destroying the solar system. But, as Sir John Herschel observes, they could hardly all revolve in the same direction round the sun for so many ages without impressing a corresponding motion on the ethereal medium, which may preserve them from the accumulated effects of its resistance. Should this material medium revolve about the sun like a vortex, it will accelerate the revolutions of such comets as have direct motions, and retard those that have retrograde motions.
The comet which appeared unexpectedly in the beginning of the year 1843 was one of the most splendid that ever visited the solar system. It was in the constellation of Antinous in the end of January, at a distance of 115 millions of miles from the earth, and it passed through its perihelion on the 27th of February, when it was lost in the sun’s rays; but it began to be visible about the 3rd of March, at which time it was near the star Iota CetÆ, and its tail extended towards the Hare. Before the passage at the perihelion it had no tail; but at that epoch the tail suddenly darted out, and extended to a distance of 1826 millions of miles in about an hour and a half—a most inexplicable speed of development, which indicates some powerful repulsive force at the moment of the greatest proximity to the sun, at which time the tails are formed. The brightness of the comet and the length of its tail continued to increase till the latter stretched far beyond the constellation of the Hare towards a point above Sirius. Stars were distinctly seen through it, and when near perihelion the comet was so bright that it was seen in clear sunshine, in the United States, like a white cloud. The motion was retrograde, and on leaving the solar system it retreated so rapidly at once from the sun and earth that it was soon lost sight of for want of light. On the 1st of April it was between the sun and the earth, and only 40 millions of miles from the latter; and as its tail was at least 60 millions of miles long, and 20 millions of miles broad, we probably passed through it without being aware of it. There is some discrepancy in the different computations of the elements of the orbit, but in the greater number of cases the perihelion distance was found to be less than the semidiameter of the sun, so that the comet must have grazed his surface, if it did not actually impinge obliquely on him.
The perihelion distance of this comet differs little from that of the great comet of 1668, which came so near the sun. The motion of both was retrograde, and a certain resemblance in the two orbits makes it probable that they are the same body performing a revolution in 175 years.
Though already so well acquainted with the motions of comets, we know nothing of their physical constitution. A vast number, especially of telescopic comets, are only like clouds or masses of vapour, often without tails. The head commonly consists of a concentrated mass of light, like a planet, surrounded by a very transparent atmosphere, and the whole, viewed with a telescope, is so diaphanous, that the smallest star may be seen even through the densest part of the nucleus; in general their solid parts, when they have any, are so minute, that they have no sensible diameter, like that of the comet of 1811, which appeared to Sir William Herschel like a luminous point in the middle of the nebulous matter. The nuclei, which seem to be formed of the denser strata of that nebulous matter in successive coatings, are sometimes of great magnitude. Those comets which came to the sun in the years 1799 and 1807 had nuclei whose diameters measured 180 and 275 leagues respectively, and the second comet of 1811 had a nucleus 1350 leagues in diameter.
It must, however, be stated that, as comets are generally at prodigious distances from the earth, the solid parts of the nuclei appear like mere points of light, so minute that it is impossible to measure them with any kind of accuracy, so that the best astronomers often differ in the estimation of their size by one-half of the whole diameter. The transit of a comet across the sun would afford the best information with regard to the nature of the nuclei. It was computed that such an event was to take place in the year 1827; unfortunately the sun was hid by clouds from the British astronomers, but it was examined at Viviers and at Marseilles at the time the comet must have been projected on its disc, but no spot or cloud was to be seen, so that it must have had no solid part whatever. The nuclei of many comets which seemed solid and brilliant to the naked eye have been resolved into mere vapour by telescopes of high powers; in Halley’s comet there was no solid part at all.
The nebulosity immediately round the nucleus is so diaphanous, that it gives little light; but at a small distance the nebulous matter becomes suddenly brilliant, so as to look like a bright ring round the body. Sometimes there are two or three of these luminous concentric rings separated by dark intervals, but they are generally incomplete on the part next the tail.
These annular appearances are an optical effect, arising from a succession of envelopes of the nebulous matter with intervals between them, of which the first is sometimes in contact with the nucleus and sometimes not. The thickness of these bright diaphanous coatings in the comets of 1799 and 1807 was about 7000 and 10,000 leagues respectively; and in the first comet of 1811 the luminous ring was 8000 leagues thick, and the distance between its interior surface and the centre of the head was 10,000 leagues. The latter comet was by much the most brilliant that has been seen in modern times; it was first discovered in this country by Mr. James Vietch of Inchbonny, and was observed in all its changes by Sir William Herschel and M. Olbers. To the naked eye, the head had the appearance of an ill-defined round mass of light, which was resolved into several distinct parts when viewed with a telescope. A very brilliant interior circular mass of nebulous matter was surrounded by a black space having a parabolic form, very distinct from the dark blue of the sky. This dark space was of a very appreciable breadth. Exterior to the black interval there was a luminous parabolic contour of considerable thickness, which was prolonged on each side in two diverging branches, which formed the bifid tail of the comet. Sir William Herschel found that the brilliant interior circular mass lost the distinctness of its outline as he increased the magnifying power of the telescope, and presented the appearance of a more and more diffuse mass of greenish or blueish green light, whose intensity decreased gradually, not from the centre, but from an eccentric brilliant speck, supposed to be the truly solid part of the comet. The luminous envelope was of a decided yellow, which contrasted strongly with the greenish tint of the interior nebulous mass. Stars were nearly veiled by the luminous envelope, whilst, on the contrary, Sir William Herschel saw three extremely small stars shining clearly in the black space, which was singularly transparent. As the envelopes were formed in succession as the comet approached the sun, Sir William Herschel conceived them to be vapours raised by his heat at the surface of the nucleus, and suspended round it like a vault or dome by the elastic force of an extensive and highly transparent atmosphere. In coming to the sun, the coatings began to form when the comet was as distant as the orbit of Jupiter, and in its return they very soon entirely vanished; but a new one was formed after it had retreated as far as the orbit of Mars, which lasted for a few days. Indeed, comets in general are subject to sudden and violent convulsions in their interior, even when far from the sun, which produce changes that are visible at enormous distances, and baffle all attempts at explanation—probably arising from electricity, or even causes with which we are unacquainted. The envelopes surrounding the nucleus of the comet on the side next to the sun diverge on the opposite side, where they are prolonged into the form of a hollow cone, which is the tail. Two repulsive forces seem to be concerned in producing this effect; one from the comet and another from the sun, the latter being the most powerful. The envelopes are nearer the centre of the comet on the side next to the sun, where these forces are opposed to one another; but on the other side the forces conspire to form the tail, conveying the nebulous particles to enormous distances.
The lateral edges of the tail reflect more light than the central part, because the line of vision passes through a greater depth of nebulous matter, which produces the effect of two streams somewhat like the aurora. Stars shine with undiminished lustre through the central part of the tail, because their rays traverse it perpendicularly to its thickness; but, though distinctly seen through its edges, their light is weakened by its oblique transmission. The tail of the great comet of 1811 was of wonderful tenuity; stars which would have been entirely concealed by the slightest fog were seen through 64,000 leagues of nebulous matter without the smallest refraction. Possibly some part of the changes in the appearance of the tails arises from rotation. Several comets have been observed to rotate about an axis passing through the centre of the tail. That of 1825 performed its rotation in 201/2 hours, and the rapid changes in the luminous sectors which issued from the nucleus of Halley’s comet in all probability were owing to rotatory motion.
The two streams of light which form the edges of the tail in most cases unite at a greater or less distance from the nucleus, and are generally situate in the plane of the orbit. The tails follow comets in their descent towards the sun, but precede them in their return, with a small degree of curvature; their apparent extent and form vary according to the positions of the orbits with regard to the ecliptic. In some cases the tail has been at right angles to the line joining the sun and comet. The curvature is in part owing to the resistance of the ether, and partly to the velocity of the comet being greater than that of the particles at the extremity of its tail, which lag behind. The tails are generally of enormous lengths; the comet of 1811 had one no less than a hundred millions of miles in length, and those which appeared in the years 1618, 1680, and 1769, had tails which extended respectively over 104, 90, and 97 degrees of space. Consequently, when the heads of these comets were set, a portion of the extremity of their tails was still in the zenith. Sometimes the tail is divided into several branches, like the comet of 1744, which had six, separated by dark intervals, each of them about 4° broad, and from 30° to 44° long. They were probably formed by three hollow cones of the nebulous matter proceeding from the different envelopes, and enclosing one another, with intervals between; the lateral edges of these cones would give the appearance of six streams of light. The tails do not attain their full magnitude till the comet has left the sun. When comets first appear, they resemble round films of vapour, with little or no tail. As they approach the sun, they increase in brilliancy, and their tail in length, till they are lost in his rays; and it is not till they emerge from the sun’s more vivid light that they assume their full splendour. They then gradually decrease, their tails diminish, and they disappear, nearly or altogether, before they are beyond the sphere of telescopic vision. Many comets have no tails, as, for example, Encke’s comet. Those which appeared in the years 1585, 1763, and 1682, were also without tails, though the latter is recorded to have been as bright as Jupiter. The matter of the tail must be extremely buoyant to precede a body moving with such velocity: indeed, the rapidity of its ascent cannot be accounted for. It has been attributed to that power in the sun which produces those vibrations of ether which constitute light; but as this theory will not account for the comet of 1824, which is said to have had two tails, one directed towards the sun, and a very short one diametrically opposite to it, our ignorance on this subject must be confessed. In this case the repelling power of the comet seems to have been greater than that of the sun. Whatever that unknown power may be, there are instances in which its effects are enormous; for, immediately after the great comet of 1680 had passed its perihelion, its tail was 100,000,000 miles in length, and was projected from the comet’s head in the short space of two days. A body of such extreme tenuity as a comet is most likely incapable of an attraction powerful enough to recall matter sent to such an enormous distance; it is therefore, in all probability, scattered in space or absorbed by the zodiacal light or nebula that surrounds the sun, which may account for the rapid decrease observed in the tails of comets every time they return to their perihelia. Should the great comet of 1843 prove to be the same with that of 1668, its tail must have diminished considerably.
It is remarkable that, although the tails of comets increase in length as they approach their perihelia, there is reason to believe that the real diameter of the head contracts on coming near the sun, and expands rapidly on leaving him. Hevelius first observed this phenomenon, which Encke’s comet has exhibited in a very extraordinary degree. On the 28th of October, 1828, this comet was about three times as far from the sun as it was on the 24th of December; yet at the first date its apparent diameter was twenty-five times greater than at the second, the decrease being progressive. M. Valz attributes the circumstance to a real condensation of volume from the pressure of the ethereal medium, which increases most rapidly in density towards the surface of the sun, and forms an extensive atmosphere around him. It did not occur to M. Valz, however, that the ethereal fluid would penetrate the nebulous matter instead of compressing it. Sir John Herschel, on the contrary, conjectures that it may be owing to the alternate conversion of evaporable materials in the upper regions of the transparent atmosphere of comets into the states of visible cloud and invisible gas by the effects of heat and cold; or that some of the external nebulous envelopes may come into view when the comet arrives at a darker part of the sky, which were overpowered by the superior light of the sun while in his vicinity. The first of these hypotheses he considers to be perfectly confirmed by his observations on Halley’s comet, made at the Cape of Good Hope, after its return from the sun. He thinks that, in all probability, the whole comet, except the densest part of its head, vanished, and was reduced to a transparent and invisible state during its passage at its perihelion: for when it first came into view, after leaving the sun, it had no tail, and its aspect was completely changed. A parabolic envelope soon began to appear, and increased so much and so rapidly that its augmentation was visible to the eye. This increase continued till it became so large and so faint, that at last it vanished entirely, leaving only the nucleus and a tail, which it had again acquired, but which also vanished; so that at last the nucleus alone remained. Not only the tails, but the nebulous part of comets, diminishes every time they return to their perihelia; after frequent returns they ought to lose it altogether, and present the appearance of a fixed nucleus: this ought to happen sooner to comets of short periods. M. de la Place supposes that the comet of 1682 must be approaching rapidly to that state. Should the substances be altogether, or even to a great degree, evaporated, the comet would disappear for ever. Possibly comets may have vanished from our view sooner than they would otherwise have done from this cause.
The comet discovered at Florence by Signore Donati, on the 2nd of June, 1858, was one of the most beautiful that has been seen from our planet for many years, whether for the brightness of the nucleus, or the length and graceful form of the coma; when first discovered it was near the star ? in the constellation of the Lion, being then at a distance of 288,000,000 miles from the earth; during the month of August its nucleus assumed an almost planetary aspect from the concentration of its light; on the 27th of September the head appeared almost as bright as Mercury, but smaller; when near its perihelion passage, on September 30th, its diameter, as ascertained by Signore Donati, was 3; during the early part of October it continued to increase in brilliancy, the tail becoming more elongated, and describing a beautiful arc in the heavens, occupying a space of nearly 40°, or a length of 40,000,000 miles in the solar system. On the evening of the 5th of October it was seen from most parts of Britain, within 20' of Arcturus, the brightest star in the northern heavens, across which the densest part nearly of the tail passed, and through which notwithstanding the star shone with undiminished brilliancy. On the 30th of October, when in perihelio, the comet was only 55,000,000 miles from the sun; on the 10th it approached nearest to the earth, from which it was then distant 51,000,000 miles; and on the 15th of the same month near to Venus, being at that time less than one-tenth the distance of the earth from the Sun; if the comet had reached its perihelion a few days earlier, Venus might have passed through its nucleus, the consequences of which to the planet it would be very difficult to imagine. The motion of Donati’s comet is what astronomer’s call retrograde, or from east to west. It ceased to be visible in our northern latitudes in the last week in October, having passed into the southern heavens, where it will traverse the constellations of Sagittarius, Telescopium, and Indus, approaching the large star of Toucan; after which it will disappear until it has nearly completed its revolution round the sun. The observed orbit of this remarkable comet coincides more nearly with an ellipse than a parabola; the longer diameter of the ellipse being 184 times that of the earth’s orbit, or the immense distance of 35,100,000,000 miles—a space which, however great, is less than the thousandth of the distance of the nearest fixed star. According to the calculations of M. Loewy, and adopting an elliptic orbit, Donati’s comet will not return to the same places in the heavens for 2495 years, being 500 less than the period of revolution of the great comet of 1811.
Signore Donati observed that between the 25th and 30th September two concentric, luminous, semicircular envelopes, with a dark space between them, were formed in the head. From the extremities of these the cone of the tail extended, and a non-luminous or dark space stretched for 20° from the nucleus into the tail. On the 1st October the two envelopes were combined into one. This comet, like Halley’s, has shown some singular irregularities, supposed to arise from the action of the sun when near its perihelion. At different periods of its apparition a violent agitation was observed in its nucleus, with luminous jets, spiral offshoots, &c., as in the great comets of 1680, 1744, 1811. A ray of light was thrown out from one side of the nucleus towards the sun, while a gas-like jet proceeded from the other side, which appeared to form the origin of a second tail within the great tail, and which was traced for half a degree by Mr. Hind on the 19th September. He observed decided spiral convolutions in the tail, which show that this comet has a rotatory motion about an axis passing through the tail.
If comets shine by borrowed light, they ought, in certain positions, to exhibit phases like the moon; but no such appearance has been detected, except in one instance, when they are said to have been observed by Hevelius and La Hire, in the year 1682. In general, the light of comets is dull—that of the comet of 1811 was only equal to the tenth part of the light of the full moon—yet some have been brilliant enough to be visible in full daylight, especially the comet of 1744, which was seen without a telescope at one o’clock in the afternoon, while the sun was shining. Hence it may be inferred that, although some comets may be altogether diaphanous, others seem to possess a solid mass resembling a planet. But whether they shine by their own or by reflected light has never been satisfactorily made out till now. Even if the light of a comet were polarized, it would not afford a decisive test, since a body is capable of reflecting light, though it shines by its own. M. Arago, however, has, with great ingenuity, discovered a method of ascertaining this point, independent both of phases and polarization.
Since the rays of light diverge from a luminous point, they will be scattered over a greater space as the distance increases, so that the intensity of the light on a screen two feet from the object is four times less than at the distance of one foot; three feet from the object it is nine times less; and so on, decreasing in intensity as the square of the distance increases. As a self-luminous surface consists of an infinite number of luminous points, it is clear that, the greater the extent of surface, the more intense will be the light; whence it may be concluded that the illuminating power of such a surface is proportional to its extent, and decreases inversely as the square of the distance. Notwithstanding this, a self-luminous surface, plane or curved, viewed through a hole in a plate of metal, is of the same brilliancy at all possible distances as long as it subtends a sensible angle, because, as the distance increases, a greater portion comes into view; and, as the augmentation of surface is as the square of the diameter of the part seen through the whole, it increases as the square of the distance. Hence, though the number of rays from any one point of the surface which pass through the hole decreases inversely as the square of the distance, yet, as the extent of surface which comes into view increases also in that ratio, the brightness of the object is the same to the eye as long as it has a sensible diameter. For example—Uranus is about nineteen times farther from the sun than we are, so that the sun, seen from that planet, must appear like a star with a diameter of a hundred seconds, and must have the same brilliancy to the inhabitants that he would have to us if viewed through a small circular hole having a diameter of a hundred seconds. For it is obvious that light comes from every point of the sun’s surface to Uranus, whereas a very small portion of his disc is visible through the hole; so that extent of surface exactly compensates distance. Since, then, the visibility of a self-luminous object does not depend upon the angle it subtends as long as it is of sensible magnitude, if a comet shines by its own light, it should retain its brilliancy as long as its diameter is of a sensible magnitude; and, even after it has lost an apparent diameter, it ought to be visible, like the fixed stars, and should only vanish in consequence of extreme remoteness. That, however, is far from being the case—comets gradually become dim as their distance increases, and vanish merely from loss of light, while they still retain a sensible diameter, which is proved by observations made the evening before they disappear. It may therefore be concluded that comets shine by reflecting the sun’s light. The most brilliant comets have hitherto ceased to be visible when about five times as far from the sun as we are. Most of the comets that have been visible from the earth have their perihelia within the orbit of Mars, because they are invisible when as distant as the orbit of Saturn: on that account there is not one on record whose perihelion is situate beyond the orbit of Jupiter. Indeed, the comet of 1756, after its last appearance, remained five whole years within the ellipse described by Saturn without being once seen. More than a hundred and forty comets have appeared within the earth’s orbit during the last century that have not again been seen. If a thousand years be allowed as the average period of each, it may be computed, by the theory of probabilities, that the whole number which range within the earth’s orbit must be 1400; but, Uranus being about nineteen times more distant, there may be no less than 11,200,000 comets that come within the orbit of Uranus. M. Arago makes a different estimate; he considers that, as thirty comets are known to have their perihelion distance within the orbit of Mercury, if it be assumed that comets are uniformly distributed in space, the number having their perihelion within the orbit of Uranus must be to thirty as the cube of the radius of the orbit of Uranus to the cube of the radius of the orbit of Mercury, which makes the number of comets amount to 3,529,470. But that number may be doubled, if it be considered that, in consequence of daylight, fogs, and great southern declination, one comet out of two must be hid from us. According to M. Arago, more than seven millions of comets come within the orbit of Uranus.
The different degrees of velocity with which the planets and comets were originally propelled in space is the sole cause of the diversity in the form of their orbits, which depends only upon the mutual relation between the projectile force and the sun’s attraction.
When the two forces are exactly equal to one another, circular motion is produced; when the ratio of the projectile to the central force is exactly that of 1 to the square root of 2, the motion is parabolic; any ratio between these two will cause a body to move in an ellipse, and any ratio greater than that of 1 to the square root of 2 will produce hyperbolic motion (N.229).
The celestial bodies might move in any one of these four curves by the law of gravitation: but, as one particular velocity is necessary to produce either circular or parabolic motion, such motions can hardly be supposed to exist in the solar system, where the bodies are liable to such mutual disturbances as would infallibly change the ratio of the forces, and cause them to move in ellipses in the first case, and hyperbolas in the other. On the contrary, since every ratio between equality and that of 1 to the square root of 2 will produce elliptical motion, it is found in the solar system in all its varieties, from that which is nearly circular to such as borders on the parabolic from excessive ellipticity. On this depends the stability of the system; the mutual disturbances only cause the orbits to become more or less excentric without changing their nature.
For the same reason the bodies of the solar system might have moved in an infinite variety of hyperbolas, since any ratio of the forces, greater than that which causes parabolic motion, will make a body move in one of these curves. Hyperbolic motion is however very rare; only two comets appear to move in orbits of that nature, those of 1771 and 1824; probably all such comets have already come to their perihelia, and consequently will never return.
The ratio of the forces which fixed the nature of the celestial orbits is thus easily explained; but the circumstances which determined these ratios, which caused some bodies to move nearly in circles and others to wander towards the limits of the solar attraction, and which made all the heavenly bodies to rotate and revolve in the same direction, must have had their origin in the primeval state of things; but as it pleases the Supreme Intelligence to employ gravitation alone in the maintenance of this fair system, it may be presumed to have presided at its creation.
