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We may therefore look on a comet as a swarm of tiny solid particles, each surrounded by gas.

When we watch a great comet approaching the sun the nucleus is first seen to become brighter and more clearly defined; at a later stage luminous matter appears to be projected from it towards the sun, often in the shape of a fan or a jet, which sometimes oscillates to and fro like a pendulum. In the head of Halley's comet, for instance, Bessel observed in October, 1835, that the jet in the course of eight hours swung through an angle of 36 deg.. On other occasions concentric arcs of light are formed round the nucleus, one after another, getting fainter as they travel further from the nucleus. Evidently the material of the fan or the arcs is repelled by the nucleus of the comet; but it is also repelled by the sun, and this latter repulsive force compels the luminous matter to overcome the attraction of gravitation, and to turn back all round the nucleus in the direction away from the sun. In this manner the tail is formed. (_See_ Plate XII.) The mathematical theory of the formation of comets' tails has been developed on the assumption that the matter which forms the tail is repelled both by the nucleus and by the sun. This investigation was first undertaken by the great astronomer Bessel, in his memoir on the appearance of Halley's comet in 1835, and it has since been considerably developed by Roche and the Russian astronomer Bredichin. Though we are, perhaps, hardly in a position to accept this theory as absolutely true, we can assert that it accounts well for the principal phenomena observed in the formation of comets' tails.

Professor Bredichin has conducted his labours in the philosophical manner which has led to many other great discoveries in science. He has carefully collated the measurements and drawings of the tails of various comets. One result has been obtained from this preliminary part of his enquiry, which possesses a value that cannot be affected even if the ulterior portion of his labours should be found to require qualification. In the examination of the various tails, he observed that the curvilinear shapes of the outlines fall into one or other of three special types. In the first we have the straightest tails, which point almost directly away from the sun. In the second are classed tails which, after starting away from the sun, are curved backwards from the direction towards which the comet is moving. In the third we find the appendage still more curved in towards the comet's path. It can be shown that the tails of comets can almost invariably be identified with one or other of these three types; and in cases where the comet exhibits two tails, as has sometimes happened, then they will be found to belong to two of the types.

The adjoining diagram (Fig. 72) gives a sketch of an imaginary comet furnished with tails of the three different types. The direction in which the comet is moving is shown by the arrow-head on the line passing through the nucleus. Bredichin concludes that the straightest of the three tails, marked as Type I., is most probably due to the element hydrogen; the tails of the second form are due to the presence of some of the hydrocarbons in the body of the comet; while the small tails of the third type may be due to iron or to some other element with a high atomic weight. It will, of course, be understood that this diagram does not represent any actual comet.

An interesting illustration of this theory is afforded in the case of the celebrated comet of 1858 already referred to, of which a drawing is shown in Fig. 73. We find here, besides the great tail, which is the characteristic feature of the body, two other faint streaks of light. These are the edges of the hollow cone which forms a tail of Type I. When we look through the central regions it will be easily understood that the light is not sufficiently intense to be visible; at the edges, however, a sufficient thickness of the cometary matter is presented, and thus we have the appearance shown in this figure. It would seem that Donati's comet possessed one tail due to hydrogen, and another due to some of the compounds of carbon. The carbon compounds involved appear to be of considerable variety, and there is, in consequence, a disposition in the tails of the second type to a more indefinite outline than in the hydrogen tails. Cases have been recorded in which several tails have been seen simultaneously on the same comet. The most celebrated of these is that which appeared in the year 1744. Professor Bredichin has devoted special attention to the theory of this marvellous object, and he has shown with a high degree of probability how the multiform tail could be accounted for. The adjoining figure (Fig. 74) is from a sketch of this object made on the morning of the 7th March by Mademoiselle Kirch at the Berlin Observatory. The figure shows eleven streaks, of which the first ten (counting from the left) represent the bright edges of five of the tails, while the sixth and shortest tail is at the extreme right. Sketches of this rare phenomenon were also made by Cheseaux at Lausanne and De L'Isle at St. Petersburg. Before the perihelion passage the comet had only had one tail, but a very splendid one.

It is possible to submit some of the questions involved to the test of calculation, and it can be shown that the repulsive force adequate to produce the straight tail of Type I. need only be about twelve times as large as the attraction of gravitation. Tails of the second type could be produced by a repulsive force which was about equal to gravitation, while tails of the third type would only require a repulsive force about one-quarter the power of gravitation.[33] The chief repulsive force known in nature is derived from electricity, and it has naturally been surmised that the phenomena of comets' tails are due to the electric condition of the sun and of the comet. It would be premature to assert that the electric character of the comet's tail has been absolutely demonstrated; all that can be said is that, as it seems to account for the observed facts, it would be undesirable to introduce some mere hypothetical repulsive force. It must be remembered that on quite other grounds it is known that the sun is the seat of electric phenomena.

As the comet gradually recedes from the sun the repulsive force becomes weaker, and accordingly we find that the tail of the comet declines. If the comet be a periodic one, the same series of changes may take place at its next return to perihelion. A new tail is formed, which also gradually disappears as the comet regains the depths of space. If we may employ the analogy of terrestrial vapours to guide us in our reasoning, then it would seem that, as the comet retreats, its tail would condense into myriads of small particles. Over these small particles the law of gravitation would resume its undivided sway, no longer obscured by the superior efficiency of the repulsion. The mass of the comet is, however, so extremely small that it would not be able to recall these particles by the mere force of attraction. It follows that, as the comet at each perihelion passage makes a tail, it must on each occasion expend a corresponding quantity of tail-making material. Let us suppose that the comet was endowed in the beginning with a certain capital of those particular materials which are adapted for the production of tails. Each perihelion passage witnesses the formation of a tail, and the expenditure of a corresponding amount of the capital. It is obvious that this operation cannot go on indefinitely. In the case of the great majority of comets the visits to perihelion are so extremely rare that the consequences of the extravagance are not very apparent; but to those periodic comets which have short periods and make frequent returns, the consequences are precisely what might have been anticipated: the tail-making capital has been gradually squandered, and thus at length we have the spectacle of a comet without any tail at all. We can even conceive that a comet may in this manner be completely dissipated, and we shall see in the next chapter how this fate seems to have overtaken Biela's periodic comet.

But as it sweeps through the solar system the comet may chance to pass very near one of the larger planets, and, in passing, its motion may be seriously disturbed by the attraction of the planet. If the velocity of the comet is accelerated by this disturbing influence, the orbit will be changed from a parabola into another curve known as a hyperbola, and the comet will swing round the sun and pass away never to return. But if the planet is so situated as to retard the velocity of the comet, the parabolic orbit will be changed into an ellipse, and the comet will become a periodic one. We can hardly doubt that some periodic comets have been "captured" in this manner and thereby made permanent members of our solar system, if we remark that the comets of short periods (from three to eight years) come very near the orbit of Jupiter at some point or other of their paths. Each of them must, therefore, have been near the giant planet at some moment during their past history. Similarly the other periodic comets of longer period approach near to the orbits of either Saturn, Uranus, or Neptune, the last-mentioned planet being probably responsible for the periodicity of Halley's comet. We have, indeed, on more than one occasion, actually witnessed the violent disturbance of a cometary orbit. The most interesting case is that of Lexell's comet. In 1770 the French astronomer Messier (who devoted himself with great success to the discovery of comets) detected a comet for which Lexell computed the orbit, and found an ellipse with a period of five years and some months. Yet the comet had never been seen before, nor did it ever come back again. Long afterwards it was found, from most laborious investigations by Burckhardt and Le Verrier, that the comet had moved in a totally different orbit previous to 1767. But at the beginning of the year 1767 it happened to come so close to Jupiter that the powerful attraction of this planet forced it into a new orbit, with a period of five and a half years. It passed the perihelion on the 13th August, 1770, and again in 1776, but in the latter year it was not conveniently situated for being seen from the earth. In the summer of 1779 the comet was again in the neighbourhood of Jupiter, and was thrown out of its elliptic orbit, so that we have never seen it since, or, perhaps, it would be safer to say that we have not with certainty identified Lexell's comet with any comet observed since then. We are also, in the case of several other periodic comets, able to fix in a similar way the date when they started on their journeys in their present elliptic orbits.

Such is a brief outline of the principal facts known with regard to these interesting but perplexing bodies. We must be content with the recital of what we know, rather than hazard guesses about matters beyond our reach. We see that they are obedient to the great laws of gravitation, and afford a striking illustration of their truth. We have seen how modern science has dissipated the superstition with which, in earlier ages, the advent of a comet was regarded. We no
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