Part 40

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 20-1/2 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 λ 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 3ʺ; 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 20ʹ 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).