before it takes place. As a necessary consequence of the resistence of the ethereal fluid, they will perform their revolutions nearer and nearer to the sun, till at last they will be precipitated upon his surface. How many years must elapse before these extraordinary events take place, it is impossible to say, from our ignorance of the density of the sun's atmosphere, and of the comet.

Comets shine with a very pale and scattered light, which Schröter had an opportunity of comparing, on various occasions, with that of the planet Mars, and found it to be not more than one-third or one-half as bright. It has long been matter of doubt whether comets shine by their own or by reflected light. Unless they possess a solid nucleus capable of reflecting the sun's rays at its surface it could not be expected that they should exhibit phases like the moon or Venus, for if they be mere masses of vapour, the sun's light will penetrate into their interior, and being scattered, must give them that dull diffuse appearance which they generally have. We have stated that it has been doubted whether comets have any solidity at all; nevertheless, Cassini thought he could perceive phases in the comet of 1744; and certainly, that comet was in a favourable position for seeing them, being within the orbit of Mercury, and nearly between the sun and the earth. Phases, from the crescent to the full, are recorded to have been observed in the comet of 1769, and something of the same kind is mentioned of the comet of 1682. The comet of 1819 is said not only to have presented this phenomenon, but to have passed over the disc of the sun like a misty spot. These would be quite sufficient to establish the point, could they be relied on, but unfortunately the observations require confirmation. Some comets are recorded to have been as bright as any star in the heavens, and to have been visible during day-light. That which appeared in 1744 had the brilliancy of Sirius in one part of its course and that of Venus in another; and it was visible on the first of March at mid-day, even with the naked eye. From all recorded circumstances M. Arago has concluded that there is a gradation in comets from those that consist merely of vapour, and are altogether transparent, to such as probably have solid and opaque nuclei, and that comets, like planets, owe their lustre to the sun's rays. Light, emanating from all self-luminous bodies, is seen at distances when the bodies themselves are too small to be visible: while, on the contrary, such as shine by reflection, often become invisible from mere want of light, though still near enough to have sensible dimensions. We only know of the existence of the fixed stars by the light they send to us-themselves we never see—for viewed with the best telescopes they are only brilliant points, without sensible dimensions; so also the light of a candle is visible when

the

the candle itself is too distant to be seen. Comets, on the contrary, gradually grow more faint as they retire from the sun, and at last become too dim to be visible, while yet near enough to be of sensible magnitude. It frequently happens, that the night before a comet has vanished, it has appeared like a dull silver coin, ill defined, or a round film of vapour with a sensible diameter. Were these bodies self-luminous, they would be visible, like the stars, long after they had lost all sensible magnitude. Hitherto the most brilliant comets have become invisible when about five times as far from the sun as the earth is; nor is there one comet on record which has not approached nearer to the sun than Jupiter does; and the comet of 1756, after its last appearance, remained five years within the circuit in which Saturn revolves, without being seen. Thus vast numbers of comets must come to our system unperceived; and even if they come near enough to be within sight, one out of two must be concealed from view by daylight, fogs, and great southern declination. M. Arago estimates, that more than seven millions of comets frequent the planetary orbits. Hardly a year passes without the appearance of two or three, though the greater number are too distant, or too small, to be seen without a telescope.

Among such multitudes it is impossible to recognize the same comet on its return to our system from its aspect alone, since their external character changes at each revolution—not to mention the alterations they undergo during the short time they are in sight. It seemed at one time equally impossible to know them again by the path they move in, and it really was so as long as astronomers considered their motions with reference to the earth only; but as soon as they took into consideration the appearance they would present to a person in the centre of the sun, perfect regularity was found to obtain-the nature of their paths was discovered, and a method of ascertaining the identity of a comet on its return was established. To determine the real motion of a comet round the sun, from its path in the heavens, as seen from the earth, was perhaps the most difficult problem in astronomy, and a task worthy of Newton.

About the middle of the sixteenth century, Apian's observations on the direction of the tails led astronomers to suspect that there might be some connexion between comets and the sun, to which their motions and their tails might be owing. At that time an opinion prevailed, that comets were merely vapours moving in our atmosphere; but Tycho Brahe found, by the ordinary means for ascertaining the distances of the celestial bodies, that a comet which appeared in the year 1577 was nearly three times as distant as the moon; from which he was induced to believe that

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comets

comets were exhalations from the planets, and that they revolved about the sun, beyond the orbits of Mercury and Venus, in paths resembling the outline of an egg. Hevelius, by tracing the orbits of several comets upon a planisphere, showed that one part of the orbit was much curved, and the rest was very nearly a straight line; from which he inferred that the paths of comets must be elongated curves of a lenticular shape. He also thought comets were formed by exhalations from the planets, and that their course might be similar to that of bodies projected into our atmosphere--such as a cannon ball, which moves by the force with which it is thrown combined with the attraction of the earth. He therefore assumed, that comets move in consequence of two forces, one directed to the sun, and the other arising from the velocity with which they had left the planet they were exhaled from; and upon this supposition he found the path they describe to be a parabola. This curve has one end oval, but the two sides, instead of coming together, diverge so as never to meet.

The ovals in which comets are now known to move are so much elongated, that they may readily be mistaken for parabolas, since only a very small portion of the curved end is visible to us; so perfect indeed is the resemblance, that in the first instance, at least, the orbits of new comets are always computed as if they moved in a parabola, and the necessary alterations are made afterwards. Hevelius even remarked, that the velocity of comets must be greatest at the point where the orbit is most curved, which really is the case; from this he concluded, that the sun must be situate in the plane of the comet's orbit, and in the straight line passing through its centre, called the axis. A very great step was thus made by Hevelius; but, in the beginning of the seventeenth century, Henry Percy, Earl of Northumberland, hazarded the conjecture, that comets move in elliptical or oval paths. Newton, at length, arose to settle the question for ever, by the unerring truth of demonstration. Having already discovered that the bodies of the solar system are governed by the laws of gravitation alone, the comet of 1680-the most splendid, and in many other respects the most remarkable, upon record-induced him to investigate the motions of comets also: the result was, a clear proof that these bodies obey the very same laws that regulate the revolutions of the planets and satellites. It may be asked, why comets move in paths differing so much in form and position from those of the planets, if they be subject to the same laws of gravitation?the answer is, that the form of the path of a celestial body depends entirely upon the relation between the sun's attraction and the force with which the body was projected into space at its creation, while the position of the orbit depends upon the direction of that force. A comet

A comet or planet propelled into space perpendicularly to its distance from the sun, with a force exactly equal to the force of the sun's attraction, would move in a circle. Should the propelling force be less, or greater than the force of the sun's attraction, but not greater by so much as forty-one per cent., the body would move in an ellipse. Should the force of projection be exactly forty-one per cent. greater than the sun's attraction, the path of the body would be a parabola; and, if the propelling force be still greater, the orbit would be a hyperbola, which is also a curve closed at one end, and having two infinitely diverging branches at the other.

For instance, the earth, when nearest to the sun, moves with a velocity of 102,300 feet in a second; this velocity arises from the force with which it was first thrown into space, combined with the sun's attraction; and the path in which it travels is an ellipse, differing very little from a circle; but had it been thrown from the same point with a force so much greater as to produce a velocity of 144,700 feet in a second, it would have gone once round the sun, and then darted off in nearly a straight line, never to return: the curve would have been a parabola. Had the primitive impulse been still greater, the earth would have moved in a hyperbola. And, lastly, had the force of projection been such as to make the earth's velocity only 101,000 feet in a second, its orbit would have been a perfect circle. These four curves are the conic sections. The preceding velocities are suited to the shortest distance of the earth from the sun; but the great comet of 1680, which nearly swept over his surface with a velocity of 880,000 miles an hour, is consequently constrained to move in an extremely elongated ellipse. In fact, if its speed had not been so enormous, it would have fallen into the sun. It appears then from the investigation of this curious subject, that circumstances are most favourable to produce motion in the ellipse or hyperbola, since an infinity of relations between the two forces will cause a body to move in either of these, while circular and parabolic motion depend upon one relation only. The probability therefore is, that comets do really move in orbits of the elliptical form, more or less elongated, though instances are not wanting where the path seems to have two infinitely diverging branches. A comet moving in that curve would go once round the sun, and then vanish for ever into the deep recesses of the universe, possibly to wander from system to system, and from sun to sun. There is reason to believe that the comets of 1771 and 1824 moved in such paths. None of the celestial bodies move in a circle, nor is it possible that they should as the laws of nature are constituted, since, even if a body had begun

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begun to move in that curve, the smallest disturbance would have changed its path for ever. For the same reason, parabolic motion, if it does exist, is probably very rare. The circular motion of the two first of Jupiter's satellites is not a case in point, because there are other causes in operation.

Comets are visible only for a very short time during their passage round the sun, which includes a very small portion of their orbit, and that portion is such that it is difficult to distinguish to which of the three curves mentioned it belongs, in any of which the comet might move, for the circle is out of the question. But although these three curves are so much alike throughout a small extent, they differ widely from one another in the remainder. It has already been stated that one is an ellipse or very elongated oval, of which there may be an infinite variety, all passing through the point which is the shortest distance of the comet from the sun: the other two are precisely similar to the ovals at one end, but the sides, instead of meeting at the other extremity, diverge more and more, and never meet again. Now it is clear, that if a comet moves in the first, it will return to our system again and again; but if either of the other two be the form of its path, it will appear once, and then for ever retire. There are no observations sufficiently exact to enable astronomers to determine with, certainty in which of these curves a new comet moves; yet the form of the small portion of the orbit visible to us, and its position with regard to the ecliptic or path of the earth, may be made out sufficiently to trace with some probability that part of its course which extends beyond vision, and to enable us to determine its identity with the orbit of any comet that has already appeared, or may hereafter come into view; and it is indeed the only means we have of doing so. The exact path, and the length of the period of its revolution, can only be ascertained with certainty at its return.

The chances are many millions to one, that two comets do not move in orbits exactly alike. It is very improbable that the shortest distance of a comet from the sun should be the same in two instances, or that in any two cases the point of the orbit in which that happens should have exactly the same position in the heavens. Moreover, the orbits or paths of the earth and a comet do not lie in the same plane as they would do when drawn on a sheet of paper; they may have an infinity of inclinations with regard to one another, and the odds are as much against the probability of the orbits of two comets having the same position in space as they are against their agreeing in form.

Equality in the periods of their revolution also affords means

of