Robert S. Ball

Comets contrasted with Planets in Nature as well as in their Movements—Coggia's Comet—Periodic Returns—The Law of Gravitation—Parabolic and Elliptic Orbits—Theory in Advance of Observations—Most Cometary Orbits are sensibly Parabolic—The Labours of Halley—The Comet of 1682—Halley's Memorable Prediction—The Retardation produced by Disturbance—Successive Returns of Halley's Comet—Encke's Comet—Effect of Perturbations—Orbit of Encke's Comet—Attraction of Mercury and of Jupiter—How the Identity of the Comet is secured—How to weigh Mercury—Distance from the Earth to the Sun found by Encke's Comet—The Disturbing Medium—Remarkable Comets—Spectrum of a Comet—Passage of a Comet between the Earth and the Stars—Can the Comet be weighed?—Evidence of the Small Mass of the Comet derived from the Theory of Perturbation—The Tail of the Comet—Its Changes—Views as to its Nature—Carbon present in Comets—Origin of Periodic Comets.

In our previous chapters, which treated of the sun and the moon, the planets and their satellites, we found in all cases that the celestial bodies with which we were concerned were nearly globular in form, and many are undoubtedly of solid substance. All these objects possess a density which, even if in some cases it be much less than that of the earth, is still hundreds of times greater than the density of merely gaseous materials. We now, however, approach the consideration of a class of objects of a widely different character. We have no longer to deal with globular objects possessing considerable mass. Comets are of altogether irregular shape; they are in large part, at all events, formed of materials in the utmost state of tenuity, and their masses are so small that no means we possess have enabled them to be measured. Not only are comets different in constitution from planets or from the other more solid bodies of our system, but the movements of such bodies are quite distinct from the orderly return of the planets at their appointed seasons. The comets appear sometimes with almost startling unexpectedness; they rapidly swell in size to an extent that in superstitious ages called forth the utmost terror; presently they disappear, in many cases never again to return. Modern science has, no doubt, removed a great deal of the mystery which once invested the whole subject of comets. Their movements are now to a large extent explained, and some additions have been made to our knowledge of their nature, though we must still confess that what we do know bears but a very small proportion to what remains unknown.

Let me first describe in general terms the nature of a comet, in so far as its structure is disclosed by the aid of a powerful refracting telescope. We represent in Plate XII. two interesting sketches made at Harvard College Observatory of the great comet of 1874, distinguished by the name of its discoverer Coggia.

We see here the head of the comet, containing as its brightest spot what is called the nucleus, and in which the material of the comet seems to be much denser than elsewhere. Surrounding the nucleus we find certain definite layers of luminous material, the coma, or head, from 20,000 to 1,000,000 miles in diameter, from which the tail seems to stream away. This view may be regarded as that of a typical object of this class, but the varieties of structure presented by different comets are almost innumerable. In some cases we find the nucleus absent; in other cases we find the tail to be wanting. The tail is, no doubt, a conspicuous feature in those great comets which receive universal attention; but in the small telescopic objects, of which a few are generally found every year, this feature is usually absent. Not only do comets present great varieties in appearance, but even the aspect of a single object undergoes great change. The comet will sometimes increase enormously in bulk; sometimes it will diminish; sometimes it will have a large tail, or sometimes no tail at all. Measurements of a comet's size are almost futile; they may cease to be true even during the few hours in which a comet is observed in the course of a night. It is, in fact, impossible to identify a comet by any description of its personal appearance. Yet the question as to identity of a comet is often of very great consequence. We must provide means by which it can be established, entirely apart from what the comet may look like.

It is now well known that several of these bodies make periodic returns. After having been invisible for a certain number of years, a comet comes into view, and again retreats into space to perform another revolution. The question then arises as to how we are to recognise the body when it does come back? The personal features of its size or brightness, the presence or absence of a tail, large or small, are fleeting characters of no value for such a purpose. Fortunately, however, the law of elliptic motion established by Kepler has suggested the means of defining the identity of a comet with absolute precision.

After Newton had made his discovery of the law of gravitation, and succeeded in demonstrating that the elliptic paths of the planets around the sun were necessary consequences of that law, he was naturally tempted to apply the same reasoning to explain the movements of comets. Here, again, he met with marvellous success, and illustrated his theory by completely explaining the movements of the remarkable body which was visible from December, 1680, to March, 1681.

There is a certain beautiful curve known to geometricians by the name of the parabola. Its form is shown in the adjoining figure; it is a curved line which bends in towards and around a certain point known as the focus. This would not be the occasion for any allusion to the geometrical properties of this curve; they should be sought in works on mathematics. It will here be only necessary to point to the connection which exists between the parabola and the ellipse. In a former chapter we have explained the construction of the latter curve, and we have shown how it possesses two foci. Let us suppose that a series of ellipses are drawn, each of which has a greater distance between its foci than the preceding one. Imagine the process carried on until at length the distance between the foci became enormously great in comparison with the distance from each focus to the curve, then each end of this long ellipse will practically have the same form as a parabola. We may thus look on the latter curve represented in Fig. 69 as being one end of an ellipse of which the other end is at an indefinitely great distance. In 1681 Doerfel, a clergyman of Saxony, proved that the great comet then recently observed moved in a parabola, in the focus of which the sun was situated. Newton showed that the law of gravitation would permit a body to move in an ellipse of this very extreme type no less than in one of the more ordinary proportions. An object revolving in a parabolic orbit about the sun at the focus moves in gradually towards the sun, sweeps around the great luminary, and then begins to retreat. There is a necessary distinction between parabolic and elliptic motion. In the latter case the body, after its retreat to a certain distance, will turn round and again draw in towards the sun; in fact, it must make periodic circuits of its orbit, as the planets are found to do. But in the case of the true parabola the body can never return; to do so it would have to double the distant focus, and as that is infinitely remote, it could not be reached except in the lapse of infinite time.

The characteristic feature of the movement in a parabola may be thus described. The body draws in gradually towards the focus from an indefinitely remote distance on one side, and after passing round the focus gradually recedes to an indefinitely remote distance on the other side, never again to return. When Newton had perceived that parabolic motion of this type could arise from the law of gravitation, it at once occurred to him (independently of Doerfel's discovery, of which he was not aware) that by its means the movements of a comet might be explained. He knew that comets must be attracted by the sun; he saw that the usual course of a comet was to appear suddenly, to sweep around the sun and then retreat, never again to return. Was this really a case of parabolic motion? Fortunately, the materials for the trial of this important suggestion were ready to his hand. He was able to avail himself of the known movements of the comet of 1680, and of observations of several other bodies of the same nature which had been collected by the diligence of astronomers. With his usual sagacity, Newton devised a method by which, from the known facts, the path which the comet pursues could be determined. He found that it was a parabola, and that the velocity of the comet was governed by the law that the straight line from the sun to the comet swept over equal areas in equal times. Here was another confirmation of the law of universal gravitation. In this case, indeed, the theory may be said to have been actually in advance of calculation. Kepler had determined from observation that the paths of the planets were ellipses, and Newton had shown how this fact was a consequence of the law of gravitation. But in the case of the comets their highly erratic orbits had never been reduced to geometrical form until the theory of Newton showed him that they were parabolic, and then he invoked observation to verify the anticipations of his theory.

The great majority of comets move in orbits which cannot be sensibly discriminated from parabolÆ, and any body whose orbit is of this character can only be seen at a single apparition. The theory of gravitation, though it admits the parabola as a possible orbit for a comet, does not assert that the path must necessarily be of this type. We have pointed out that this curve is only a very extreme type of ellipse, and it would still be in perfect accordance with the law of gravitation for a comet to pursue a path of any elliptical form, provided that the sun was placed at the focus, and that the comet obeyed the rule of describing equal areas in equal times. If a body move in an elliptic path, then it will return to the sun again, and consequently we shall have periodical visits from the same object.

An interesting field of enquiry was here presented to the astronomer. Nor was it long before the discovery of a periodic comet was made which illustrated, in a striking manner, the soundness of the anticipation just expressed. The name of the celebrated astronomer Halley is, perhaps, best known from its association with the great comet whose periodicity was discovered by his calculations. When Halley learned from the Newtonian theory the possibility that a comet might move in an elliptic orbit, he undertook a most laborious investigation; he collected from various records of observed comets all the reliable particulars that could be obtained, and thus he was enabled to ascertain, with tolerable accuracy, the nature of the paths pursued by about twenty-four large comets. One of these was the great body of 1682, which Halley himself observed, and whose path he computed in accordance with the principles of Newton. Halley then proceeded to investigate whether this comet of 1682 could have visited our system at any previous epoch. To answer this question he turned to the list of recorded comets which he had so carefully compiled, and he found that his comet very closely resembled, both in appearance and in orbit, a comet observed in 1607, and also another observed in 1531. Could these three bodies be identical? It was only necessary to suppose that a comet, instead of revolving in a parabolic orbit, really revolved in an extremely elongated ellipse, and that it completed each revolution in a period of about seventy-five or seventy-six years. He submitted this hypothesis to every test that he could devise; he found that the orbits, determined on each of the three occasions, were so nearly identical that it would be contrary to all probability that the coincidence should be accidental. Accordingly, he decided to submit his theory to the most supreme test known to astronomy. He ventured to make a prediction which posterity would have the opportunity of verifying. If the period of the comet were seventy-five or seventy-six years, as the former observations seemed to show, then Halley estimated that, if unmolested, it ought to return in 1757 or 1758. There were, however, certain sources of disturbance which he pointed out, and which would be quite powerful enough to affect materially the time of return. The comet in its journey passes near the path of Jupiter, and experiences great perturbations from that mighty planet. Halley concluded that the expected return might be accordingly delayed till the end of 1758 or the beginning of 1759.

This prediction was a memorable event in the history of astronomy, inasmuch as it was the first attempt to foretell the apparition of one of those mysterious bodies whose visits seemed guided by no fixed law, and which were usually regarded as omens of awful import. Halley felt the importance of his announcement. He knew that his earthly course would have run long before the comet had completed its revolution; and, in language almost touching, the great astronomer writes: "Wherefore if it should return according to our prediction about the year 1758, impartial posterity will not refuse to acknowledge that this was first discovered by an Englishman."

As the time drew near when this great event was expected, it awakened the liveliest interest among astronomers. The distinguished mathematician Clairaut undertook to compute anew, by the aid of improved methods, the effect which would be wrought on the comet by the attraction of the planets. His analysis of the perturbations was sufficient to show that the object would be kept back for 100 days by Saturn, and for 518 days by Jupiter. He therefore gave some additional exactness to the prediction of Halley, and finally concluded that this comet would reach the perihelion, or the point of its path nearest to the sun, about the middle of April, 1759. The sagacious astronomer (who, we must remember, lived long before the discovery of Uranus and of Neptune) further adds that as this body retreats so far, it may possibly be subject to influences of which we do not know, or to the disturbance even of some planet too remote to be ever perceived. He, accordingly, qualified his prediction with the statement that, owing to these unknown possibilities, his calculations might be a month wrong one way or the other. Clairaut made this memorable communication to the Academy of Sciences on the 14th of November, 1758. The attention of astronomers was immediately quickened to see whether the visitor, who last appeared seventy-six years previously, was about to return. Night after night the heavens were scanned. On Christmas Day in 1758 the comet was first detected, and it passed closest to the sun about midnight on the 12th of March, just a month earlier than the time announced by Clairaut, but still within the limits of error which he had assigned as being possible.

The verification of this prediction was a further confirmation of the theory of gravitation. Since then, Halley's comet has returned once again, in 1835, in circumstances somewhat similar to those just narrated. Further historical research has also succeeded in identifying Halley's comet with numerous memorable apparitions of comets in former times. It has even been shown that a splendid object, which appeared eleven years before the commencement of the Christian era, was merely Halley's comet in one of its former returns. Among the most celebrated visits of this body was that of 1066, when the apparition attracted universal attention. A picture of the comet on this occasion forms a quaint feature in the Bayeux Tapestry. The next return of Halley's comet is expected about the year 1910.

There are now several comets known which revolve in elliptic paths, and are, accordingly, entitled to be termed periodic. These objects are chiefly telescopic, and are thus in strong contrast to the splendid comet of Halley. Most of the other periodic comets have periods much shorter than that of Halley. Of these objects, by far the most celebrated is that known as Encke's comet, which merits our careful attention.

The object to which we refer has had a striking career during which it has provided many illustrations of the law of gravitation. We are not here concerned with the prosaic routine of a mere planetary orbit. A planet is mainly subordinated to the compelling sway of the sun's gravitation. It is also to some slight extent affected by the attractions which it experiences from the other planets. Mathematicians have long been accustomed to anticipate the movements of these globes by actual calculation. They know how the place of the planet is approximately decided by the sun's attraction, and they can discriminate the different adjustments which that place is to receive in consequence of the disturbances produced by the other planets. The capabilities of the planets for producing disturbance are greatly increased when the disturbed body follows the eccentric path of a comet. It is frequently found that the path of such a body comes very near the track of a planet, so that the comet may actually sweep by the planet itself, even if the two bodies do not actually run into collision. On such an occasion the disturbing effect is enormously augmented, and we therefore turn to the comets when we desire to illustrate the theory of planetary perturbations by some striking example.

Having decided to choose a comet, the next question is, What comet? There cannot here be much room for hesitation. Those splendid comets which appear so capriciously may be at once excluded. They are visitors apparently coming for the first time, and retreating without any distinct promise that mankind shall ever see them again. A comet of this kind moves in a parabolic path, sweeps once around the sun, and thence retreats into the space whence it came. We cannot study the effect of perturbations on a comet completely until it has been watched during successive returns to the sun. Our choice is thus limited to the comparatively small class of objects known as periodic comets; and, from a survey of the entire group, we select the most suitable to our purpose. It is the object generally known as Encke's comet, for, though Encke was not the discoverer, yet it is to his calculations that the comet owes its fame. This body is rendered more suitable for our purpose by the researches to which it has recently given rise.

In the year 1818 a comet was discovered by the painstaking astronomer Pons at Marseilles. We are not to imagine that this body produced a splendid spectacle. It was a small telescopic object, not unlike one of those dim nebulÆ which are scattered in thousands over the heavens. The comet is, however, readily distinguished from a nebula by its movement relatively to the stars, while the nebula remains at rest for centuries. The position of this comet was ascertained by its discoverer, as well as by other astronomers. Encke found from the observations that the comet returned to the sun once in every three years and a few months. This was a startling announcement. At that time no other comet of short period had been detected, so that this new addition to the solar system awakened the liveliest interest. The question was immediately raised as to whether this comet, which revolved so frequently, might not have been observed during previous returns. The historical records of the apparitions of comets are counted by hundreds, and how among this host are we to select those objects which were identical with the comet discovered by Pons?

We may at once relinquish any hope of identification from drawings of the object, but, fortunately, there is one feature of a comet on which we can seize, and which no fluctuations of the actual structure can modify or disguise. The path in which the body travels through space is independent of the bodily changes in its structure. The shape of that path and its position depend entirely upon those other bodies of the solar system which are specially involved in the theory of Encke's comet. In Fig. 70 we show the orbits of three of the planets. They have been chosen with such proportions as shall make the innermost represent the orbit of Mercury; the next is the orbit of the earth, while the outermost is the orbit of Jupiter. Besides these three we perceive in the figure a much more elliptical path, representing the orbit of Encke's comet, projected down on the plane of the earth's motion. The sun is situated at the focus of the ellipse. The comet is constrained to revolve in this curve by the attraction of the sun, and it requires a little more than three years to accomplish a complete revolution. It passes close to the sun at perihelion, at a point inside the path of Mercury, while at its greatest distance it approaches the path of Jupiter. This elliptic orbit is mainly determined by the attraction of the sun. Whether the comet weighed an ounce, a ton, a thousand tons, or a million tons, whether it was a few miles, or many thousands of miles in diameter, the orbit would still be the same. It is by the shape of this ellipse, by its actual size, and by the position in which it lies, that we identify the comet. It had been observed in 1786, 1795, and 1805, but on these occasions it had not been noticed that the comet's path deviated from the parabola.

Encke's comet is usually so faint that even the most powerful telescope in the world would not show a trace of it. After one of its periodical visits, the body withdraws until it recedes to the outermost part of its path, then it will turn, and again approach the sun. It would seem that it becomes invigorated by the sun's rays, and commences to dilate under their genial influence. While moving in this part of its path the comet lessens its distance from the earth. It daily increases in splendour, until at length, partly by the intrinsic increase in brightness and partly by the decrease in distance from the earth, it comes within the range of our telescopes. We can generally anticipate when this will occur, and we can tell to what point of the heavens the telescope is to be pointed so as to discern the comet at its next return to perihelion. The comet cannot elude the grasp of the mathematician. He can tell when and where the comet is to be found, but no one can say what it will be like.

Were all the other bodies of the system removed, then the path of Encke's comet must be for ever performed in the same ellipse and with absolute regularity. The chief interest for our present purpose lies not in the regularity of its path, but in the irregularities introduced into that path by the presence of the other bodies of the solar system. Let us, for instance, follow the progress of the comet through its perihelion passage, in which the track lies near that of the planet Mercury. It will usually happen that Mercury is situated in a distant part of its path at the moment the comet is passing, and the influence of the planet will then be comparatively small. It may, however, sometimes happen that the planet and the comet come close together. One of the most interesting instances of a close approach to Mercury took place on the 22nd November, 1848. On that day the comet and the planet were only separated by an interval of about one-thirtieth of the earth's distance from the sun, i.e. about 3,000,000 miles. On several other occasions the distance between Encke's comet and Mercury has been less than 10,000,000 miles—an amount of trifling import in comparison with the dimensions of our system. Approaches so close as this are fraught with serious consequences to the movements of the comet. Mercury, though a small body, is still sufficiently massive. It always attracts the comet, but the efficacy of that attraction is enormously enhanced when the comet in its wanderings comes near the planet. The effect of this attraction is to force the comet to swerve from its path, and to impress certain changes upon its velocity. As the comet recedes, the disturbing influence of Mercury rapidly abates, and ere long becomes insensible. But time cannot efface from the orbit of the comet the effect which the disturbance of Mercury has actually accomplished. The disturbed orbit is different from the undisturbed ellipse which the comet would have occupied had the influence of the sun alone determined its shape. We are able to calculate the movements of the comet as determined by the sun. We can also calculate the effects arising from the disturbance produced by Mercury, provided we know the mass of the latter.

Though Mercury is one of the smallest of the planets, it is perhaps the most troublesome to the astronomer. It lies so close to the sun that it is seen but seldom in comparison with the other great planets. Its orbit is very eccentric, and it experiences disturbances by the attraction of other bodies in a way not yet fully understood. A special difficulty has also been found in the attempt to place Mercury in the weighing scales. We can weigh the whole earth, we can weigh the sun, the moon, and even Jupiter and other planets, but Mercury presents difficulties of a peculiar character. Le Verrier, however, succeeded in devising a method of weighing it. He demonstrated that our earth is attracted by this planet, and he showed how the amount of attraction may be disclosed by observations of the sun, so that, from an examination of the observations, he made an approximate determination of the mass of Mercury. Le Verrier's result indicated that the weight of the planet was about the fourteenth part of the weight of the earth. In other words, if our earth was placed in a balance, and fourteen globes, each equal to Mercury, were laid in the other, the scales would hang evenly. It was necessary that this result should be received with great caution. It depended upon a delicate interpretation of somewhat precarious measurements. It could only be regarded as of provisional value, to be discarded when a better one should be obtained.

The approach of Encke's comet to Mercury, and the elaborate investigations of Von Asten and Backlund, in which the observations of the body were discussed, have thrown much light on the subject; but, owing to a peculiarity in the motion of this comet, which we shall presently mention, the difficulties of this investigation are enormous. Backlund's latest result is, that the sun is 9,700,000 times as heavy as Mercury, and he considers that this is worthy of great confidence. There is a considerable difference between this result (which makes the earth about thirty times as heavy as Mercury) and that of Le Verrier; and, on the other hand, Haerdtl has, from the motion of Winnecke's periodic comet, found a value of the mass of Mercury which is not very different from Le Verrier's. Mercury is, however, the only planet about the mass of which there is any serious uncertainty, and this must not make us doubt the accuracy of this delicate weighing-machine. Look at the orbit of Jupiter, to which Encke's comet approaches so nearly when it retreats from the sun. It will sometimes happen that Jupiter and the comet are in close proximity, and then the mighty planet seriously disturbs the pliable orbit of the comet. The path of the latter bears unmistakable traces of the Jupiter perturbations, as well as of the Mercury perturbations. It might seem a hopeless task to discriminate between the influences of the two planets, overshadowed as they both are by the supreme control of the sun, but contrivances of mathematical analysis are adequate to deal with the problem. They point out how much is due to Mercury, how much is due to Jupiter; and the wanderings of Encke's comet can thus be made to disclose the mass of Jupiter as well as that of Mercury. Here we have a means of testing the precision of our weighing appliances. The mass of Jupiter can be measured by his moons, in the way mentioned in a previous chapter. As the satellites revolve round and round the planet, they furnish a method of measuring his weight by the rapidity of their motion. They tell us that if the sun were placed in one scale of the celestial balance, it would take 1,047 bodies equal to Jupiter in the other to weigh him down. Hardly a trace of uncertainty clings to this determination, and it is therefore of great interest to test the theory of Encke's comet by seeing whether it gives an accordant result. The comparison has been made by Von Asten. Encke's comet tells us that the sun is 1,050 times as heavy as Jupiter; so the results are practically identical, and the accuracy of the indications of the comet are confirmed. But the calculation of the perturbations of Encke's comet is so extremely intricate that Asten's result is not of great value. From the motion of Winnecke's periodic comet, Haerdtl has found that the sun is 1,047·17 times as heavy as Jupiter, in perfect accordance with the best results derived from the attraction of Jupiter on his satellites and the other planets.

We have hitherto discussed the adventures of Encke's comet in cases where they throw light on questions otherwise more or less known to us. We now approach a celebrated problem, on which Encke's comet is our only authority. Every 1,210 days that comet revolves completely around its orbit, and returns again to the neighbourhood of the sun. The movements of the comet are, however, somewhat irregular. We have already explained how perturbations arise from Mercury and from Jupiter. Further disturbances arise from the attraction of the earth and of the other remaining planets; but all these can be allowed for, and then we are entitled to expect, if the law of gravitation be universally true, that the comet shall obey the calculations of mathematics. Encke's comet has not justified this anticipation; at each revolution the period is getting steadily shorter! Each time the comet comes back to perihelion in two and a half hours less than on the former occasion. Two and a half hours is, no doubt, a small period in comparison with that of an entire revolution; but in the region of its path visible to us the comet is moving so quickly that its motion in two and a half hours is considerable. This irregularity cannot be overlooked, inasmuch as it has been confirmed by the returns during about twenty revolutions. It has sometimes been thought that the discrepancies might be attributed to some planetary perturbations omitted or not fully accounted for. The masterly analysis of Von Asten and Backlund has, however, disposed of this explanation. They have minutely studied the observations down to 1891, but only to confirm the reality of this diminution in the periodic time of Encke's comet.

An explanation of these irregularities was suggested by Encke long ago. Let us briefly attempt to describe this memorable hypothesis. When we say that a body will move in an elliptic path around the sun in virtue of gravitation, it is always assumed that the body has a free course through space. It is assumed that there is no friction, no air, or other source of disturbance. But suppose that this assumption should be incorrect; suppose that there really is some medium pervading space which offers resistance to the comet in the same way as the air impedes the flight of a rifle bullet, what effect ought such a medium to produce? This is the idea which Encke put forward. Even if the greater part of space be utterly void, so that the path of the filmy and almost spiritual comet is incapable of feeling resistance, yet in the neighbourhood of the sun it was supposed that there might be some medium of excessive tenuity capable of affecting so light a body. It can be demonstrated that a resisting medium such as we have supposed would lessen the size of the comet's path, and diminish the periodic time. This hypothesis has, however, now been abandoned. It has always appeared strange that no other comet showed the least sign of being retarded by the assumed resisting medium. But the labours of Backlund have now proved beyond a doubt that the acceleration of the motion of Encke's comet is not a constant one, and cannot be accounted for by assuming a resisting medium distributed round the sun, no matter how we imagine this medium to be constituted with regard to density at different distances from the sun. Backlund found that the acceleration was fairly constant from 1819 to 1858; it commenced to decrease between 1858 and 1862, and continued to diminish till some time between 1868 and 1871, since which time it has remained fairly constant. He considers that the acceleration can only be produced by the comet encountering periodically a swarm of meteors, and if we could only observe the comet during its motion through the greater part of its orbit we should be able to point out the locality where this encounter takes place.

We have selected the comets of Halley and of Encke as illustrations of the class of periodic comets, of which, indeed, they are the most remarkable members. Another very remarkable periodic comet is that of Biela, of which we shall have more to say in the next chapter. Of the much more numerous class of non-periodic comets, examples in abundance may be cited. We shall mention a few which have appeared during the present century. There is first the splendid comet of 1843, which appeared suddenly in February of that year, and was so brilliant that it could be seen during full daylight. This comet followed a path which could not be certainly distinguished from a parabola, though there is no doubt that it might have been a very elongated ellipse. It is frequently impossible to decide a question of this kind, during the brief opportunities available for finding the place of the comet. We can only see the object during a very small arc of its orbit, and even then it is not a very well-defined point which admits of being measured with the precision attainable in observations of a star or a planet. This comet of 1843 is, however, especially remarkable for the rapidity with which it moved, and for the close approach which it made to the sun. The heat to which it was exposed during its passage around the sun must have been enormously greater than the heat which can be raised in our mightiest furnaces. If the materials had been agate or cornelian, or the most infusible substances known on the earth, they would have been fused and driven into vapour by the intensity of the sun's rays.

The great comet of 1858 was one of the celestial spectacles of modern times. It was first observed on June 2nd of that year by Donati, whose name the comet has subsequently borne; it was then merely a faint nebulous spot, and for about three months it pursued its way across the heavens without giving any indications of the splendour which it was so soon to attain. The comet had hardly become visible to the unaided eye at the end of August, and was then furnished with only a very small tail, but as it gradually drew nearer and nearer to the sun in September, it soon became invested with splendour. A tail of majestic proportions was quickly developed, and by the middle of October, when the maximum brightness was attained, its length extended over an arc of forty degrees. The beauty and interest of this comet were greatly enhanced by its favourable position in the sky at a season when the nights were sufficiently dark.

On the 22nd May, 1881, Mr. Tebbutt, of Windsor, in New South Wales, discovered a comet which speedily developed into one of the most interesting celestial objects seen by this generation. About the 22nd of June it became visible from these latitudes in the northern sky at midnight. Gradually it ascended higher and higher until it passed around the pole. The nucleus of the comet was as bright as a star of the first magnitude, and its tail was about 20° long. On the 2nd of September it ceased to be visible to the unaided eye, but remained visible in telescopes until the following February. This was the first comet which was successfully photographed, and it may be remarked that comets possess very little actinic power. It has been estimated that moonlight possesses an intensity 300,000 times greater than that of a comet where the purposes of photography are concerned.

Another of the bodies of this class which have received great and deserved attention was that discovered in the southern hemisphere early in September, 1882. It increased so much in brilliancy that it was seen in daylight by Mr. Common on the 17th of that month, while on the same day the astronomers at the Cape of Good Hope were fortunate enough to have observed the body actually approach the sun's limb, where it ceased to be visible. We know that the comet must have passed between the earth and the sun, and it is very interesting to learn from the Cape observers that it was totally invisible when it was actually projected on the sun's disc. The following day it was again visible to the naked eye in full daylight, not far from the sun, and valuable spectroscopic observations were secured at Dunecht and Palermo. At that time the comet was rushing through the part of its orbit closest to the sun, and about a week later it began to be visible in the morning before sunrise, near the eastern horizon, exhibiting a fine long tail. (See Plate XVII.) The nucleus gradually lengthened until it broke into four separate pieces, lying in a straight line, while the comet's head became enveloped in a sort of faint, nebulous tube, pointing towards the sun. Several small detached nebulous masses became also visible, which travelled along with the comet, though not with the same velocity. The comet became invisible to the naked eye in February, and was last observed telescopically in South America on the 1st June, 1883.

There is a remarkable resemblance between the orbit of this comet and the orbits in which the comet of 1668, the great comet of 1843, and a great comet seen in 1880 in the southern hemisphere, travelled round the sun. In fact, these four comets moved along very nearly the same track and rushed round the sun within a couple of hundred thousand miles of the surface of the photosphere. It is also possible that the comet which, according to Aristotle, appeared in the year 372 B.C. followed the same orbit. And yet we cannot suppose that all these were apparitions of one and the same comet, as the observations of the comet of 1882 give the period of revolution of that body equal to about 772 years. It is not impossible that the comets of 1843 and 1880 are one and the same, but in both years the observations extend over too short a time to enable us to decide whether the orbit was a parabola or an ellipse. But as the comet of 1882 was in any case a distinct body, it seems more likely that we have here a family of comets approaching the sun from the same region of space and pursuing almost the same course. We know a few other instances of such resemblances between the orbits of distinct comets.

Of other interesting comets seen within the last few years we may mention one discovered by Mr. Holmes in London on the 6th November, 1892. It was then situated not far from the bright nebula in the constellation Andromeda, and like it was just visible to the naked eye. The comet became gradually fainter and more diffused, but on the 16th January following it appeared suddenly with a central condensation, like a star of the eighth magnitude, surrounded by a small coma. Gradually it expanded again, and grew fainter, until it was last observed on the 6th April.[32] The orbit was found to be an ellipse more nearly circular than the orbit of any other known comet, the period being nearly seven years. Another comet of 1892 is remarkable as having been discovered by Professor Barnard, of the Lick Observatory, on a photograph of a region in Aquila; he was at once able to distinguish the comet from a nebula by its motion.

Since 1864 the light of every comet which has made its appearance has been analysed by the spectroscope. The slight surface-brightness of these bodies renders it necessary to open the slit of the spectroscope rather wide, and the dispersion employed cannot be very great, which again makes accurate measurements difficult. The spectrum of a comet is chiefly characterised by three bright bands shading gradually off towards the violet, and sharply defined on the side towards the red. This appearance is caused by a large number of fine and close lines, whose intensity and distance apart decrease towards the violet. These three bands reveal the existence of hydrocarbon in comets.

The important rÔle which we thus find carbon playing in the constitution of comets is especially striking when we reflect on the significance of the same element on the earth. We see it as the chief constituent of all vegetable life, we find it to be invariably present in animal life. It is an interesting fact that this element, of such transcendent importance on the earth, should now have been proved to be present in these wandering bodies. The hydrocarbon bands are, however, not always the only features visible in cometary spectra. In a comet seen in the spring months of 1882, Professor Copeland discovered that a new bright yellow line, coinciding in position with the D-line of sodium, had suddenly appeared, and it was subsequently, both by him and by other observers, seen beautifully double. In fact, sodium was so strongly represented in this comet, that both the head and the tail could be perfectly well seen in sodium light by merely opening the slit of the spectroscope very wide, just as a solar prominence may be seen in hydrogen light. The sodium line attained its greatest brilliance at the time when the comet was nearest to the sun, while the hydrocarbon bands were either invisible or very faint. The same connection between the intensity of the sodium line and the distance from the sun was noticed in the great September comet of 1882.

The spectrum of the great comet of 1882 was observed by Copeland and Lohse on the 18th September in daylight, and, in addition to the sodium line, they saw a number of other bright lines, which seemed to be due to iron vapour, while the only line of manganese visible at the temperature of a Bunsen burner was also seen. This very remarkable observation was made less than a day after the perihelion passage, and illustrates the wonderful activity in the interior of a comet when very close to the sun.

In addition to the bright lines comets generally show a faint continuous spectrum, in which dark Fraunhofer lines can occasionally be distinguished. Of course, this shows that the continuous spectrum is to a great extent due to reflected sunlight, but there is no doubt that part of it is often due to light actually developed in the comets. This was certainly the case in the first comet of 1884, as a sudden outburst of light in this body was accompanied by a considerable increase of brightness of the continuous spectrum. A change in the relative brightness of the three hydrocarbon bands indicated a considerable rise of temperature, during the continuance of which the comet emitted white light.

As comets are much nearer to the earth than the stars, it will occasionally happen that the comet must arrive at a position directly between the earth and a star. There is quite a similar phenomenon in the movement of the moon. A star is frequently occulted in this way, and the observations of such phenomena are familiar to astronomers; but when a comet passes in front of a star the circumstances are widely different. The star is indeed seen nearly as well through the comet as it would be if the comet were entirely out of the way. This has often been noticed. One of the most celebrated observations of this kind was made by the late Sir John Herschel on Biela's comet, which is one of the periodic class, and will be alluded to in the next chapter. The illustrious astronomer saw on one occasion this object pass over a star cluster. It consisted of excessively minute stars, which could only be seen by a powerful telescope, such as the one Sir John was using. The faintest haze or the merest trace of a cloud would have sufficed to hide all the stars. It was therefore with no little interest that the astronomer watched the progress of Biela's comet. Gradually the wanderer encroached on the group of stars, so that if it had any appreciable solidity the numerous twinkling points would have been completely screened. But what were the facts? Down to the most minute star in that cluster, down to the smallest point of light which the great telescope could show, every object in the group was distinctly seen to twinkle right through the mass of Biela's comet.

This was an important observation. We must recollect that the veil drawn between the cluster and the telescope was not a thin curtain; it was a volume of cometary substance many thousands of miles in thickness. Contrast, then, the almost inconceivable tenuity of a comet with the clouds to which we are accustomed. A cloud a few hundred feet thick will hide not only the stars, but even the great sun himself. The lightest haze that ever floated in a summer sky would do more to screen the stars from our view than would one hundred thousand miles of such cometary material as was here interposed.

The great comet of Donati passed over many stars which were visible distinctly through its tail. Among these stars was a very bright one—the well-known Arcturus. The comet, fortunately, happened to pass over Arcturus, and though nearly the densest part of the comet was interposed between the earth and the star, yet Arcturus twinkled on with undiminished lustre through the thickness of this stupendous curtain. Recent observations have, however, shown that stars in some cases experience change in lustre when the denser part of the comet passes over them. It is, indeed, difficult to imagine that a star would remain visible if the nucleus of a really large comet passed over it; but it does not seem that an opportunity of testing this supposition has yet arisen.

As a comet contains transparent gaseous material we might expect that the place of a star would be deranged when the comet approached it. The refractive power of air is very considerable. When we look at the sunset, we see the sun appearing to pass below the horizon; yet the sun has actually sunk beneath the horizon before any part of its disk appears to have commenced its descent. The refractive power of the air bends the luminous rays round and shows the sun, though it is directly screened by the intervening obstacles. The refractive power of the material of comets has been carefully tested. A comet has been observed to approach two stars; one of which was seen through the comet, while the other could be observed directly. If the body had any appreciable quantity of gas in its composition the relative places of the two stars would be altered. This question has been more than once submitted to the test of actual measurement. It has sometimes been found that no appreciable change of position could be detected, and that accordingly in such cases the comet has no perceptible density. Careful measurements of the great comet in 1881 showed, however, that in the neighbourhood of the nucleus there was some refractive power, though quite insignificant in comparison with the refraction of our atmosphere.

From these considerations it will probably be at once admitted that the mass of a comet must be indeed a very small quantity in comparison with its bulk. When we attempt actually to weigh the comet, our efforts have proved abortive. We have been able to weigh the mighty planets Jupiter and Saturn; we have been even able to weigh the vast sun himself; the law of gravitation has provided us with a stupendous weighing apparatus, which has been applied in all these cases with success, but the same methods applied to comets are speedily seen to be illusory. No weighing machinery known to the astronomer is delicate enough to determine the weight of a comet. All that we can accomplish in any circumstances is to weigh one heavenly body in comparison with another. Comets seem to be almost imponderable when estimated by such robust masses as those of the earth, or any of the other great planets. Of course, it will be understood that when we say the weight of a comet is inappreciable, we mean with regard to the other bodies of our system. Perhaps no one now doubts that a great comet must really weigh tons; though whether those tons are to be reckoned in tens, in hundreds, in thousands, or in millions, the total seems quite insignificant when compared with the weight of a body like the earth.

The small mass of comets is also brought before us in a very striking way when we recall what has been said in the last chapter on the important subject of the planetary perturbations. We have there treated of the permanence of our system, and we have shown that this permanence depends upon certain laws which the planetary motions must invariably fulfil. The planets move nearly in circles, their orbits are all nearly in the same plane, and they all move in the same direction. The permanence of the system would be imperilled if any one of these conditions was not fulfilled. In that discussion we made no allusion to the comets. Yet they are members of our system, and they far outnumber the planets. The comets repudiate these rules of the road which the planets so rigorously obey. Their orbits are never like circles; they are, indeed, more usually parabolic, and thus differ as widely as possible from the circular path. Nor do the planes of the orbits of comets affect any particular aspect; they are inclined at all sorts of angles, and the directions in which they move seem to be mere matters of caprice. All these articles of the planetary convention are violated by comets, but yet our system lasts; it has lasted for countless ages, and seems destined to last for ages to come. The comets are attracted by the planets, and conversely, the comets must attract the planets, and must perturb their orbits to some extent; but to what extent? If comets moved in orbits subject to the same general laws which characterise planetary motion, then our argument would break down. The planets might experience considerable derangements from cometary attraction, and yet in the lapse of time those disturbances would neutralise each other, and the permanence of the system would be unaffected. But the case is very different when we deal with the actual cometary orbits. If comets could appreciably disturb planets, those disturbances would not neutralise each other, and in the lapse of time the system would be wrecked by a continuous accumulation of irregularities. The facts, however, show that the system has lived, and is living, notwithstanding comets; and hence we are forced to the conclusion that their masses must be insignificant in comparison with those of the great planetary bodies.

These considerations exhibit the laws of universal gravitation and their relations to the permanence of our system in a very striking light. If we include the comets, we may say that the solar system includes many thousands of bodies, in orbits of all sizes, shapes, and positions, only agreeing in the fact that the sun occupies a focus common to all. The majority of these bodies are imponderable in comparison with planets, and their orbits are placed anyhow, so that, although they may suffer much from the perturbations of the other bodies, they can in no case inflict any appreciable disturbance. There are, however, a few great planets capable of producing vast disturbances; and if their orbits were not properly adjusted, chaos would sooner or later be the result. By the mutual adaptations of their orbits to a nearly circular form, to a nearly coincident plane, and to a uniformity of direction, a permanent truce has been effected among the great planets. They cannot now permanently disorganise each other, while the slight mass of the comets renders them incompetent to do so. The stability of the great planets is thus assured; but it is to be observed that there is no guarantee of stability for comets. Their eccentric and irregular paths may undergo the most enormous derangements; indeed, the history of astronomy contains many instances of the vicissitudes to which a cometary career is exposed.

Great comets appear in the heavens in the most diverse circumstances. There is no part of the sky, no constellation or region, which is not liable to occasional visits from these mysterious bodies. There is no season of the year, no hour of the day or of the night when comets may not be seen above the horizon. In like manner, the size and aspect of the comets are of every character, from the dim spot just visible to an eye fortified by a mighty telescope, up to a gigantic and brilliant object, with a tail stretching across the heavens for a distance which is as far as from the horizon to the zenith. So also the direction of the tail of the comet seems at first to admit of every possible position: it may stand straight up in the heavens, as if the comet were about to plunge below the horizon; it may stream down from the head of the comet, as if the body had been shot up from below; it may slope to the right or to the left. Amid all this variety and seeming caprice, can we discover any feature common to the different phenomena? We shall find that there is a very remarkable law which the tails of comets obey—a law so true and satisfactory, that if we are given the place of a comet in the heavens, it is possible at once to point out in what direction the tail will lie.

A beautiful comet appears in summer in the northern sky. It is near midnight; we are gazing on the faintly luminous tail, which stands up straight and points towards the zenith; perhaps it may be curved a little or possibly curved a good deal, but still, on the whole, it is directed from the horizon to the zenith. We are not here referring to any particular comet. Every comet, large or small, that appears in the north must at midnight have its tail pointed up in a nearly vertical direction. This fact, which has been verified on numerous occasions, is a striking illustration of the law of direction of comets' tails. Think for one moment of the facts of the case. It is summer; the twilight at the north shows the position of the sun, and the tail of the comet points directly away from the twilight and away from the sun. Take another case. It is evening; the sun has set, the stars have begun to shine, and a long-tailed comet is seen. Let that comet be high or low, north or south, east or west, its tail invariably points away from that point in the west where the departing sunlight still lingers. Again, a comet is watched in the early morning, and if the eye be moved from the place where the first streak of dawn is appearing to the head of the comet, then along that direction, streaming away from the sun, is found the tail of the comet. This law is of still more general application. At any season, at any hour of the night, the tail of a comet is directed away from the sun.

More than three hundred years ago this fact in the movement of comets arrested the attention of those who pondered on the movements of the heavenly bodies. It is a fact patent to ordinary observation, it gives some degree of consistency to the multitudinous phenomena of comets, and it must be made the basis of our enquiries into the structure of the tails.

In the adjoining figure, Fig. 71, we show a portion of the parabolic orbit of a comet, and we also represent the position of the tail of the comet at various points of its path. It would be, perhaps, going too far to assert that throughout the whole vast journey of the comet, its tail must always be directed from the sun. In the first place, it must be recollected that we can only see the comet during that small part of its journey when it is approaching to or receding from the sun. It is also to be remembered that, while actually passing round the sun, the brilliancy of the comet is so overpowered by the sun that the comet often becomes invisible, just as the stars are invisible in daylight. Indeed, in certain cases, jets of cometary material are actually projected towards the sun.

In a hasty consideration of the subject, it might be thought that as the comet was dashing along with enormous velocity the tail was merely streaming out behind, just as the shower of sparks from a rocket are strewn along the path which it follows. This would be an entirely erroneous analogy; the comet is moving not through an atmosphere, but through open space, where there is no medium sufficient to sweep the tail into the line of motion. Another very remarkable feature is the gradual growth of the tail as the comet approaches the sun. While the body is still at a great distance it has usually no perceptible tail, but as it draws in the tail gradually develops, and in some cases reaches stupendous dimensions. It is not to be supposed that this increase is a mere optical consequence of the diminution of distance. It can be shown that the growth of the tail takes place much more rapidly than it would be possible to explain in this way. We are thus led to connect the formation of the tail with the approach to the sun, and we are accordingly in the presence of an enigma without any analogy among the other bodies of our system.

That the comet as a whole is attracted by the sun there can be no doubt whatever. The fact that the comet moves in an ellipse or in a parabola proves that the two bodies act and react on each other in obedience to the law of universal gravitation. But while this is true of the comet as a whole, it is no less certain that the tail of the comet is repelled by the sun. It is impossible to speak with certainty as to how this comes about, but the facts of the case seem to point to an explanation of the following kind.

We have seen that the spectroscope has proved with certainty the presence of hydrocarbon and other gases in comets. But we are not to conclude from this that comets are merely masses of gas moving through space. Though the total quantity of matter in a comet, as we have seen, is exceedingly small, it is quite possible that the comet may consist of a number of widely scattered particles of appreciable density; indeed, we shall see in the next chapter, when describing the remarkable relationship between comets and meteors, that we have reason to believe this to be the case. 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°. 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 ChÉseaux 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 longer regard such a body as a sign of impending calamity; we may rather look upon it as an interesting and a beautiful visitor, which comes to please us and to instruct us, but never to threaten or to destroy.