We cannot here attempt to describe the reasoning which these great mathematicians employed. It can only be expressed by the formulae of the mathematician, and would then be hardly intelligible without previous years of mathematical study. It fortunately happens, however, that the results to which Lagrange and Laplace were conducted, and which have been abundantly confirmed by the labours of other mathematicians, admit of being described in simple language.

Let us suppose the case of the sun, and of two planets circulating around him. These two planets are mutually disturbing each other, but the amount of the disturbance is small in comparison with the effect of the sun on each of them. Lagrange demonstrated that, though the ellipse in which each planet moved was gradually altered in some respects by the attraction of the other planet, yet there is one feature of the curve which the perturbation is powerless to alter permanently: the longest axis of the ellipse, and, therefore, the mean distance of the planet from the sun, which is equal to one-half of it, must remain unchanged. This is really a discovery as important as it was unexpected. It at once removes all fear as to the effect which perturbations can produce on the stability of the system. It shows that, notwithstanding the attractions of Mars and of Venus, of Jupiter and of Saturn, our earth will for ever continue to revolve at the same mean distance from the sun, and thus the succession of the seasons and the length of the year, so far as this element at least is concerned, will remain for ever unchanged.

But Lagrange went further into the enquiry. He saw that the mean distance did not alter, but it remained to be seen whether the eccentricity of the ellipse described by the earth might not be affected by the perturbations. This is a matter of hardly less consequence than that just referred to. Even though the earth preserved the same average distance from the sun, yet the greatest and least distance might be widely unequal: the earth might pass very close to the sun at one part of its orbit, and then recede to a very great distance at the opposite part. So far as the welfare of our globe and its inhabitants is concerned, this is quite as important as the question of the mean distance; too much heat in one half of the year would afford but indifferent compensation for too little during the other half. Lagrange submitted this question also to his analysis. Again he vanquished the mathematical difficulties, and again he was able to give assurance of the permanence of our system. It is true that he was not this time able to say that the eccentricity of each path will remain constant; this is not the case. What he does assert, and what he has abundantly proved, is that the eccentricity of each orbit will always remain small. We learn that the shape of the earth's orbit gradually swells and gradually contracts; the greatest length of the ellipse is invariable, but sometimes it approaches more to a circle, and sometimes becomes more elliptical. These changes are comprised within narrow limits; so that, though they may probably correspond with measurable climatic changes, yet the safety of the system is not imperilled, as it would be if the eccentricity could increase indefinitely. Once again Lagrange applied the resources of his calculus to study the effect which perturbations can have on the inclination of the path in which the planet moves. The result in this case was similar to that obtained with respect to the eccentricities. If we commence with the assumption that the mutual inclinations of the planets are small, then mathematics assure us that they must always remain small. We are thus led to the conclusion that the planetary perturbations are unable to affect the stability of the solar system.

We shall perhaps more fully appreciate the importance of these memorable researches if we consider how easily matters might have been otherwise. Let us suppose a system resembling ours in every respect save one. Let that system have a sun, as ours has; a system of planets and of satellites like ours. Let the masses of all the bodies in this hypothetical system be identical with the masses in our system, and let the distances and the periodic times be the same in the two cases. Let all the planes of the orbits be similarly placed; and yet this hypothetical system might contain seeds of decay from which ours is free. There is one point in the imaginary scheme which we have not yet specified. In our system all the planets revolve in the same direction around the sun. Let us suppose this law violated in the hypothetical system by reversing one planet on its path. That slight change alone would expose the system to the risk of destruction by the planetary perturbations. Here, then, we find the necessity of that remarkable uniformity of the directions in which the planets revolve around the sun. Had these directions not been uniform, our system must, in all probability, have perished ages ago, and we should not be here to discuss perturbations or any other subject.

Great as was the success of the eminent French mathematician who made these beautiful discoveries, it was left for this century to witness the crowning triumph of mathematical analysis applied to the law of gravitation. The work of Lagrange lacks the dramatic interest of the discovery made by Le Verrier and Adams, which gave still wider extent to the solar system by the discovery of the planet Neptune revolving far outside Uranus.

We have already alluded to the difficulties which were experienced when it was sought to reconcile the early observations of Uranus with those made since its discovery. We have shown that the path in which this planet revolved experienced change, and that consequently Uranus must be exposed to the action of some other force besides the sun's attraction.

The question arises as to the nature of these disturbing forces. From what we have already learned of the mutual deranging influence between any two planets, it seems natural to inquire whether the irregularities of Uranus could not be accounted for by the attraction of the other planets. Uranus revolves just outside Saturn. The mass of Saturn is much larger than the mass of Uranus. Could it not be that Saturn draws Uranus aside, and thus causes the changes? This is a question to be decided by the mathematician. He can compute what Saturn is able to do, and he finds, no doubt, that Saturn is capable of producing some displacement of Uranus. In a similar manner Jupiter, with his mighty mass, acts on Uranus, and produces a disturbance which the mathematician calculates. When the figures had been worked out for all the known planets they were applied to Uranus, and we might expect to find that they would fully account for the observed irregularities of his path. This was, however, not the case. After every known source of disturbance had been carefully allowed for, Uranus was still shown to be influenced by some further agent; and hence the conclusion was established that Uranus must be affected by some unknown body. What could this unknown body be, and where must it be situated? Analogy was here the guide of those who speculated on this matter. We know no cause of disturbance of a planet's motion except it be the attraction of another planet. Could it be that Uranus was really attracted by some other planet at that time utterly unknown? This suggestion was made by many astronomers, and it was possible to determine some conditions which the unknown body should fulfil. In the first place its orbit must lie outside the orbit of Uranus. This was necessary, because the unknown planet must be a large and massive one to produce the observed irregularities. If, therefore, it were nearer than Uranus, it would be a conspicuous object, and must have been discovered long ago. Other reasonings were also available to show that if the disturbances of Uranus were caused by the attraction of a planet, that body must revolve outside the globe discovered by Herschel. The general analogies of the planetary system might also be invoked in support of the hypothesis that the path of the unknown planet, though necessarily elliptic, did not differ widely from a circle, and that the plane in which it moved must also be nearly coincident with the plane of the earth's orbit.

The measured deviations of Uranus at the different points of its orbit were the sole data available for the discovery of the new planet. We have to fit the orbit of the unknown globe, as well as the mass of the planet itself, in such a way as to account for the various perturbations. Let us, for instance, assume a certain distance for the hypothetical body, and try if we can assign both an orbit and a mass for the planet, at that distance, which shall account for the perturbations. Our first assumption is perhaps too great. We try again with a lesser distance. We can now represent the observations with greater accuracy. A third attempt will give the result still more closely, until at length the distance of the unknown planet is determined. In a similar way the mass of the body can be also determined. We assume a certain value, and calculate the perturbations. If the results seem greater than those obtained by observations, then the assumed mass is too great. We amend the assumption, and recompute with a lesser amount, and so on until at length we determine a mass for the planet which harmonises with the results of actual measurement. The other elements of the unknown orbit—its eccentricity and the position of its axis—are all to be ascertained in a similar manner. At length it appeared that the perturbations of Uranus could be completely explained if the unknown planet had a certain mass, and moved in an orbit which had a certain position, while it was also manifest that no very different orbit or greatly altered mass would explain the observed facts.

These remarkable computations were undertaken quite independently by two astronomers—one in England and one in France. Each of them attacked, and each of them succeeded in solving, the great problem. The scientific men of England and the scientific men of France joined issue on the question as to the claims of their respective champions to the great discovery; but in the forty years which have elapsed since these memorable researches the question has gradually become settled. It is the impartial verdict of the scientific world outside England and France, that the merits of this splendid triumph of science must be divided equally between the late distinguished Professor J.C. Adams, of Cambridge, and the late U.J.J. Le Verrier, the director of the Paris Observatory.

Shortly after Mr. Adams had taken his degree at Cambridge, in 1843, when he obtained the distinction of Senior Wrangler, he turned his attention to the perturbations of Uranus, and, guided by these perturbations alone, commenced his search for the unknown planet. Long and arduous was the enquiry—demanding an enormous amount of numerical calculation, as well as consummate mathematical resource; but gradually Mr. Adams overcame the difficulties. As the subject unfolded itself, he saw how the perturbations of Uranus could be fully explained by the existence of an exterior planet, and at length he had ascertained, not alone the orbit of this outer body, but he was even able to indicate the part of the heavens in which the unknown globe must be sought. With his researches in this advanced condition, Mr. Adams called on the Astronomer-Royal, Sir George Airy, at Greenwich, in October, 1845, and placed in his hands the computations which indicated with marvellous accuracy the place of the yet unobserved planet. It thus appears that seven months before anyone else had solved this problem Mr. Adams had conquered its difficulties, and had actually located the planet in a position but little more than a degree distant from the spot which it is now known to have occupied. All that was wanted to complete the discovery, and to gain for Professor Adams and for English science the undivided glory of this achievement, was a strict telescopic search through the heavens in the neighbourhood indicated.

Why, it may be said, was not such an enquiry instituted at once? No doubt this would have been done, if the observatories had been generally furnished forty years ago with those elaborate star-charts which they now possess. In the absence of a chart (and none had yet been published of the part of the sky where the unknown planet was) the search for the planet was a most tedious undertaking. It had been suggested that the new globe could be detected by its visible disc; but it must be remembered that even Uranus, so much closer to us, had a disc so small that it was observed nearly a score of times without particular notice, though it did not escape the eagle glance of Herschel. There remained then only one available method of finding Neptune. It was to construct a chart of the heavens in the neighbourhood indicated, and then to compare this chart night after night with the stars in the heavens. Before recommending the commencement of a labour so onerous, the Astronomer-Royal thought it right to submit Mr. Adams's researches to a crucial preliminary test. Mr. Adams had shown how his theory rendered an exact account of the perturbations of Uranus in longitude. The Astronomer-Royal asked Mr. Adams whether he was able to give an equally clear explanation of the notable variations in the distance of Uranus. There can be no doubt that his theory would have rendered a satisfactory account of these variations also; but, unfortunately, Mr. Adams seems not to have thought the matter of sufficient importance to give the Astronomer-Royal any speedy reply, and hence it happened that no less than nine months elapsed between the time when Mr. Adams first communicated his results to the Astronomer-Royal and the time when the telescopic search for the planet was systematically commenced. Up to this time no account of Mr. Adams's researches had been published. His labours were known to but few besides the Astronomer-Royal and Professor Challis of Cambridge, to whom the duty of making the search was afterwards entrusted.

In the meantime the attention of Le Verrier, the great French mathematician and astronomer, had been specially directed by Arago to the problem of the perturbations of Uranus. With exhaustive analysis Le Verrier investigated every possible known source of disturbance. The influences of the older planets were estimated once more with every precision, but only to confirm the conclusion already arrived at as to their inadequacy to account for the perturbations. Le Verrier then commenced the search for the unknown planet by the aid of mathematical investigation, in complete ignorance of the labours of Adams. In November, 1845, and again on the 1st of June, 1846, portions of the French astronomer's results were announced. The Astronomer-Royal then perceived that his calculations coincided practically with those of Adams, insomuch that the places assigned to the unknown planet by the two astronomers were not more than a degree apart! This was, indeed, a remarkable result. Here was a planet unknown to human sight, yet felt, as it were, by mathematical analysis with a certainty so great that two astronomers, each in total ignorance of the other's labours, concurred in locating the planet in almost the same spot of the heavens. The existence of the new globe was thus raised nearly to a certainty, and it became incumbent on practical astronomers to commence the search forthwith. In June, 1846, the Astronomer-Royal announced to the visitors of the Greenwich Observatory the close coincidence between the calculations of Le Verrier and of Adams, and urged that a strict scrutiny of the region indicated should be at once instituted. Professor Challis, having the command of the great Northumberland equatorial telescope at Cambridge, was induced to undertake the work, and on the 29th July, 1846, he began his labours.

The plan of search adopted by Professor Challis was an onerous one. He first took the theoretical place of the planet, as given by Mr. Adams, and after allowing a very large margin for the uncertainties of a calculation so recondite, he marked out a certain region of the heavens, near the ecliptic, in which it might be anticipated that the unknown planet must be found. He then determined to observe all the stars in this region and measure their relative positions. When this work was once done it was to be repeated a second time. His scheme even contemplated a third complete set of observations of the stars contained within this selected region. There could be no doubt that this process would determine the planet if it were bright enough to come within the limits of stellar magnitude which Professor Challis adopted. The globe would be detected by its motion relatively to the stars, when the three series of measures came to be compared. The scheme was organised so thoroughly that it must have led to the expected discovery—in fact, it afterwards appeared that Professor Challis did actually observe the planet more than once, and a subsequent comparison of its positions must infallibly have led to the detection of the new globe.

Le Verrier was steadily maturing his no less elaborate investigations in the same direction. He felt confident of the existence of the planet, and he went so far as to predict not only the situation of the globe but even its actual appearance. He thought the planet would be large enough (though still of course only a telescopic object) to be distinguished from the stars by the possession of a disc. These definite predictions strengthened the belief that we were on the verge of another great discovery in the solar system, so much so that when Sir John Herschel addressed the British Association on the 10th of September, 1846, he uttered the following words:—"The past year has given to us the new planet Astraea—it has done more, it has given us the probable prospect of another. We see it as Columbus saw America from the shores of Spain. Its movements have been felt trembling along the far-reaching line of our analysis, with a certainty hardly inferior to ocular demonstration."

The time of the discovery was now rapidly approaching. On the 18th of September, 1846, Le Verrier wrote to Dr. Galle of the Berlin Observatory, describing the place of the planet indicated by his calculations, and asking him to make its telescopic discovery. The request thus preferred was similar to that made on behalf of Adams to Professor Challis. Both at Berlin and at Cambridge the telescopic research was to be made in the same region of the heavens. The Berlin astronomers were, however, fortunate in possessing an invaluable aid to the research which was not at the time in the hands of Professor Challis. We have mentioned how the search for a telescopic planet can be facilitated by the use of a carefully-executed chart of the stars. In fact, a mere comparison of the chart with the sky is all that is necessary. It happened that the preparation of a series of star charts had been undertaken by the Berlin Academy of Sciences some years previously. On these charts the place of every star, down even to the tenth magnitude, had been faithfully engraved. This work was one of much utility, but its originators could hardly have anticipated the brilliant discovery which would arise from their years of tedious labour. It was found convenient to publish such an extensive piece of surveying work by instalments, and accordingly, as the chart was completed, it issued from the press sheet by sheet. It happened that just before the news of Le Verrier's labours reached Berlin the chart of that part of the heavens had been engraved and printed.

It was on the 23rd of September that Le Verrier's letter reached Dr. Galle at Berlin. The sky that night was clear, and we can imagine with what anxiety Dr. Galle directed his telescope to the heavens. The instrument was pointed in accordance with Le Verrier's instructions. The field of view showed a multitude of stars, as does every part of the heavens. One of these was really the planet. The new chart was unrolled, and, star by star, the heavens were compared with it. As the identification of the stars went on, one object after another was found to lie in the heavens as it was engraved on the chart, and was of course rejected. At length a star of the eighth magnitude—a brilliant object—was brought into review. The chart was examined, but there was no star there. This object could not have been in its present place when the chart was formed. The object was therefore a wanderer—a planet. Yet it was necessary to be cautious in such a matter. Many possibilities had to be guarded against. It was, for instance, at least conceivable that the object was really a star which, by some mischance, eluded the careful eye of the astronomer who had constructed the map. It was even possible that the star might be one of the large class of variables which alternate in brightness, and it might have been too faint to have been visible when the chart was made. Or it might be one of the minor planets moving between Mars and Jupiter. Even if none of these explanations would answer, it was still necessary to show that the object was moving with that particular velocity and in that particular direction which the theory of Le Verrier indicated. The lapse of a single day was sufficient to dissipate all doubts. The next night the object was again observed. It had moved, and when its motion was measured it was found to accord precisely with what Le Verrier had foretold. Indeed, as if no circumstance in the confirmation should be wanting, the diameter of the planet, as measured by the micrometers at Berlin, proved to be practically coincident with that anticipated by Le Verrier.

The world speedily rang with the news of this splendid achievement. Instantly the name of Le Verrier rose to a pinnacle hardly surpassed by that of any astronomer of any age or country. The circumstances of the discovery were highly dramatic. We picture the great astronomer buried in profound meditation for many months; his eyes are bent, not on the stars, but on his calculations. No telescope is in his hand; the human intellect is the instrument he alone uses. With patient labour, guided by consummate mathematical artifice, he manipulates his columns of figures. He attempts one solution after another. In each he learns something to avoid; by each he obtains some light to guide him in his future labours. At length he begins to see harmony in those results where before there was but discord. Gradually the clouds disperse, and he discerns with a certainty little short of actual vision the planet glittering in the far depths of space. He rises from his desk and invokes the aid of a practical astronomer; and lo! there is the planet in the indicated spot. The annals of science present no such spectacle as this. It was the most triumphant proof of the law of universal gravitation. The Newtonian theory had indeed long ere this attained an impregnable position; but, as if to place its truth in the most conspicuous light, this discovery of Neptune was accomplished.

For a moment it seemed as if the French were to enjoy the undivided honour of this splendid triumph; nor would it, indeed, have been unfitting that the nation which gave birth to Lagrange and to Laplace, and which developed the great Newtonian theory by their immortal labours, should have obtained this distinction. Up to the time of the telescopic discovery of the planet by Dr. Galle at Berlin, no public announcement had been made of the labours of Challis in searching for the planet, nor even of the theoretical researches of Adams on which those observations were based. But in the midst of the paeans of triumph with which the enthusiastic French nation hailed the discovery of Le Verrier, there appeared a letter from Sir John Herschel in the Athenaeum for 3rd October, 1846, in which he announced the researches made by Adams, and claimed for him a participation in the glory of the discovery. Subsequent enquiry has shown that this claim was a just one, and it is now universally admitted by all independent authorities. Yet it will easily be imagined that the French savants, jealous of the fame of their countryman, could not at first be brought to recognise a claim so put forward. They were asked to divide the unparalleled honour between their own illustrious countryman and a young foreigner of whom but few had ever heard, and who had not even published a line of his work, nor had any claim been made on his part until after the work had been completely finished by Le Verrier. The demand made on behalf of Adams was accordingly refused any acknowledgment in France; and an embittered controversy was the consequence. Point by point the English astronomers succeeded in establishing the claim of their countryman. It was true that Adams had not published his researches to the world, but he had communicated them to the Astronomer-Royal, the official head of the science in this country. They were also well known to Professor Challis, the Professor of Astronomy at Cambridge. Then, too, the work of Adams was published, and it was found to be quite as thorough and quite as successful as that of Le Verrier. It was also found that the method of search adopted by Professor Challis not only must have been eventually successful, but that it actually was in a sense already successful. When the telescopic discovery of the planet had been achieved, Challis turned naturally to see whether he had observed the new globe also. It was on the 1st October that he heard of the success of Dr. Galle, and by that time Challis had accumulated observations in connection with this research of no fewer than 3,150 stars. Among them he speedily found that an object observed on the 12th of August was not in the same place on the 30th of July. This was really the planet; and its discovery would thus have been assured had Challis had time to compare his measurements. In fact, if he had only discussed his observations at once, there cannot be much doubt that the entire glory of the discovery would have been awarded to Adams. He would then have been first, no less in the theoretical calculations than in the optical verification of the planet's existence. It may also be remarked that Challis narrowly missed making the discovery of Neptune in another way. Le Verrier had pointed out in his paper the possibility of detecting the sought-for globe by its disc. Challis made the attempt, and before the intelligence of the actual discovery at Berlin had reached him he had made an examination of the region indicated by Le Verrier. About 300 stars passed through the field of view, and among them he selected one on account of its disc; it afterwards appeared that this was indeed the planet.

If the researches of Le Verrier and of Adams had never been undertaken it is certain that the distant Neptune must have been some time discovered; yet that might have been made in a manner which every true lover of science would now deplore. We hear constantly that new minor planets are observed, yet no one attaches to such achievements a fraction of the consequence belonging to the discovery of Neptune. The danger was, that Neptune should have been merely dropped upon by simple survey work, just as Uranus was discovered, or just as the hosts of minor planets are now found. In this case Theoretical Astronomy, the great science founded by Newton, would have been deprived of its most brilliant illustration.

Neptune had, in fact, a very narrow escape on at least one previous occasion of being discovered in a very simple way. This was shown when sufficient observations had been collected to enable the path of the planet to be calculated. It was then possible to trace back the movements of the planet among the stars and thus to institute a search in the catalogues of earlier astronomers to see whether they contained any record of Neptune, erroneously noted as a star. Several such instances have been discovered. I shall, however, only refer to one, which possesses a singular interest. It was found that the place of the planet on May 10th, 1795, must have coincided with that of a so-called star recorded on that day in the "Histoire Celeste" of Lalande. By actual examination of the heavens it further appeared that there was no star in the place indicated by Lalande, so the fact that here was really an observation of Neptune was placed quite beyond doubt. When reference was made to the original manuscripts of Lalande, a matter of great interest was brought to light. It was there found that he had observed the same star (for so he regarded it) both on May 8th and on May 10th; on each day he had determined its position, and both observations are duly recorded. But when he came to prepare his catalogue and found that the places on the two occasions were different, he discarded the earlier result, and merely printed the latter.

Had Lalande possessed a proper confidence in his own observations, an immortal discovery lay in his grasp; had he manfully said, "I was right on the 10th of May and I was right on the 8th of May; I made no mistake on either occasion, and the object I saw on the 8th must have moved between that and the 10th," then he must without fail have found Neptune. But had he done so, how lamentable would have been the loss to science! The discovery of Neptune would then merely have been an accidental reward to a laborious worker, instead of being one of the most glorious achievements in the loftiest department of human reason.

Besides this brief sketch of the discovery of Neptune, we have but little to tell with regard to this distant planet. If we fail to see in Uranus any of those features which make Mars or Venus, Jupiter or Saturn, such attractive telescopic objects, what can we expect to find in Neptune, which is half as far again as Uranus? With a good telescope and a suitable magnifying power we can indeed see that Neptune has a disc, but no features on that disc can be identified. We are consequently not in a position to ascertain the period in which Neptune rotates around its axis, though from the general analogy of the system we must feel assured that it really does rotate. More successful have been the attempts to measure the diameter of Neptune, which is found to be about 35,000 miles, or more than four times the diameter of the earth. It would also seem that, like Jupiter and like Saturn, the planet must be enveloped with a vast cloud-laden atmosphere, for the mean density of the globe is only about one-fifth that of the earth. This great globe revolves around the sun at a mean distance of no less than 2,800 millions of miles, which is about thirty times as great as the mean distance from the earth to the sun. The journey, though accomplished at the rate of more than three miles a second, is yet so long that Neptune requires almost 165 years to complete one revolution. Since its discovery, some fifty years ago, Neptune has moved through about one-third of its path, and even since the date when it was first casually seen by Lalande, in 1795, it has only had time to traverse three-fifths of its mighty circuit.

Neptune, like our earth, is attended by a single satellite; this delicate object was discovered by Mr. Lassell with his two-foot reflecting telescope shortly after the planet itself became known. The motion of the satellite of Neptune is nearly circular. Its orbit is inclined at an angle of about 35 deg. to the Ecliptic, and it is specially noteworthy that, like the satellites of Uranus, the direction of the motion runs counter to the planetary movements generally. The satellite performs its journey around Neptune in a period of a little less than six days. By observing the motions of this moon we are enabled to determine the mass of the planet, and thus it appears that the weight of Neptune is about one nineteen-thousandth part of that of the sun.

No planets beyond Neptune have been seen, nor is there at present any good ground for believing in their existence as visual objects. In the chapter on the minor planets I have entered into a discussion of the way in which these objects are discovered. It is by minute and diligent comparison of the heavens with elaborate star charts that these bodies are brought to light. Such enquiries would be equally efficacious in searching for an ultra-Neptunian planet; in fact, we could design no better method to seek for such a body, if it existed, than that which is at this moment in constant practice at many observatories. The labours of those who search for small planets have been abundantly rewarded with discoveries now counted by hundreds. Yet it is a noteworthy fact that all these planets are limited to one region of the solar system. It has sometimes been conjectured that time may disclose perturbations in the orbit of Neptune, and that these perturbations may lead to the discovery of a planet still more remote, even though that planet be so distant and so faint that it eludes all telescopic research. At present, however, such an enquiry can hardly come within the range of practical astronomy. Its movements have no doubt been studied minutely, but it must describe a larger part of its orbit before it would be feasible to conclude, from the perturbations of its path, the existence of an unknown and still more remote planet.

We have thus seen that the planetary system is bounded on one side by Mercury and on the other by Neptune. The discovery of Mercury was an achievement of prehistoric times. The early astronomer who accomplished that feat, when devoid of instrumental assistance and unsupported by accurate theoretical knowledge, merits our hearty admiration for his untutored acuteness and penetration. On the other hand, the discovery of the exterior boundary of the planetary system is worthy of special attention from the fact that it was founded solely on profound theoretical learning.

Though we here close our account of the planets and their satellites, we have still two chapters to add before we shall have completed what is to be said with regard to the solar system. A further and notable class of bodies, neither planets nor satellites, own allegiance to the sun, and revolve round him in conformity with the laws of universal gravitation. These bodies are the comets, and their somewhat more humble associates, the shooting stars. We find in the study of these objects many matters of interest, which we shall discuss in the ensuing chapters.



CHAPTER XVI.

COMETS.

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 parabolae, 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 nebulae 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 deg. 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 role 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.