Robert S. Ball

Discovery of Neptune—A Mathematical Achievement—The Sun's Attraction—All Bodies attract—Jupiter and Saturn—The Planetary Perturbations—Three Bodies—Nature has simplified the Problem—Approximate Solution—The Sources of Success—The Problem Stated for the Earth—The Discoveries of Lagrange—The Eccentricity—Necessity that all the Planets revolve in the same Direction—Lagrange's Discoveries have not the Dramatic Interest of the more Recent Achievements—The Irregularities of Uranus—The Unknown Planet must revolve outside the Path of Uranus—The Data for the Problem—Le Verrier and Adams both investigate the Question—Adams indicates the Place of the Planet—How the Search was to be conducted—Le Verrier also solves the Problem—The Telescopic Discovery of the Planet—The Rival Claims—Early Observation of Neptune—Difficulty of the Telescopic Study of Neptune—Numerical Details of the Orbit—Is there any Outer Planet?—Contrast between Mercury and Neptune.

We describe in this chapter a discovery so extraordinary that the whole annals of science may be searched in vain for a parallel. We are not here concerned with technicalities of practical astronomy. Neptune was first revealed by profound mathematical research rather than by minute telescopic investigation. We must develop the account of this striking epoch in the history of science with the fulness of detail which is commensurate with its importance; and it will accordingly be necessary, at the outset of our narrative, to make an excursion into a difficult but attractive department of astronomy, to which we have as yet made little reference.

The supreme controlling power in the solar system is the attraction of the sun. Each planet of the system experiences that attraction, and, in virtue thereof, is constrained to revolve around the sun in an elliptic path. The efficiency of a body as an attractive agent is directly proportional to its mass, and as the mass of the sun is more than a thousand times as great as that of Jupiter, which, itself, exceeds that of all the other planets collectively, the attraction of the sun is necessarily the chief determining force of the movements in our system. The law of gravitation, however, does not merely say that the sun attracts each planet. Gravitation is a doctrine much more general, for it asserts that every body in the universe attracts every other body. In obedience to this law, each planet must be attracted, not only by the sun, but by innumerable bodies, and the movement of the planet must be the joint effect of all such attractions. As for the influence of the stars on our solar system, it may be at once set aside as inappreciable. The stars are no doubt enormous bodies, in many cases possibly transcending the sun in magnitude, but the law of gravitation tells us that the intensity of the attraction decreases as the square of the distance increases. Most of the stars are a million times as remote as the sun, and consequently their attraction is so slight as to be absolutely inappreciable in the discussion of this question. The only attractions we need consider are those which arise from the action of one body of the system upon another. Let us take, for instance, the two largest planets of our system, Jupiter and Saturn. Each of these globes revolves mainly in consequence of the sun's attraction, but every planet also attracts every other, and the consequence is that each one is slightly drawn away from the position it would have otherwise occupied. In the language of astronomy, we would say that the path of Jupiter is perturbed by the attraction of Saturn; and, conversely, that the path of Saturn is perturbed by the attraction of Jupiter.

For many years these irregularities of the planetary motions presented problems with which astronomers were not able to cope. Gradually, however, one difficulty after another has been vanquished, and though there are no doubt some small irregularities still outstanding which have not been completely explained, yet all the larger and more important phenomena of the kind are well understood. The subject is one of the most difficult which the astronomer has to encounter in the whole range of his science. He has here to calculate what effect one planet is capable of producing on another planet. Such calculations bristle with formidable difficulties, and can only be overcome by consummate skill in the loftiest branches of mathematics. Let us state what the problem really is.

When two bodies move in virtue of their mutual attraction, both of them will revolve in a curve which admits of being exactly ascertained. Each path is, in fact, an ellipse, and they must have a common focus at the centre of gravity of the two bodies, considered as a single system. In the case of a sun and a planet, in which the mass of the sun preponderates enormously over the mass of the planet, the centre of gravity of the two lies very near the centre of the sun; the path of the great body is in such a case very small in comparison with the path of the planet. All these matters admit of perfectly accurate calculation of a somewhat elementary character. But now let us add a third body to the system which attracts each of the others and is attracted by them. In consequence of this attraction, the third body is displaced, and accordingly its influence on the others is modified; they in turn act upon it, and these actions and reactions introduce endless complexity into the system. Such is the famous "problem of three bodies," which has engaged the attention of almost every great mathematician since the time of Newton. Stated in its mathematical aspect, and without having its intricacy abated by any modifying circumstances, the problem is one that defies solution. Mathematicians have not yet been able to deal with the mutual attractions of three bodies moving freely in space. If the number of bodies be greater than three, as is actually the case in the solar system, the problem becomes still more hopeless.

Nature, however, has in this matter dealt kindly with us. She has, it is true, proposed a problem which cannot be accurately solved; but she has introduced into the problem, as proposed in the solar system, certain special features which materially reduce the difficulty. We are still unable to make what a mathematician would describe as a rigorous solution of the question; we cannot solve it with the completeness of a sum in arithmetic; but we can do what is nearly if not quite as useful. We can solve the problem approximately; we can find out what the effect of one planet on the other is very nearly, and by additional labour we can reduce the limits of uncertainty to as low a point as may be desired. We thus obtain a practical solution of the problem adequate for all the purposes of science. It avails us little to know the place of a planet with absolute mathematical accuracy. If we can determine what we want with so close an approximation to the true position that no telescope could possibly disclose the difference, then every practical end will have been attained. The reason why in this case we are enabled to get round the difficulties which we cannot surmount lies in the exceptional character of the problem of three bodies as exhibited in the solar system. In the first place, the sun is of such pre-eminent mass that many matters may be overlooked which would be of moment were he rivalled in mass by any of the planets. Another source of our success arises from the small inclinations of the planetary orbits to each other; while the fact that the orbits are nearly circular also greatly facilitates the work. The mathematicians who may reside in some of the other parts of the universe are not equally favoured. Among the sidereal systems we find not a few cases where the problem of three bodies, or even of more than three, would have to be faced without any of the alleviating circumstances which our system presents. In such groups as the marvellous star T Orionis, we have three or four bodies comparable in size, which must produce movements of the utmost complexity. Even if terrestrial mathematicians shall ever have the hardihood to face such problems, there is no likelihood of their being able to do so for ages to come; such researches must repose on accurate observations as their foundation; and the observations of these distant systems are at present utterly inadequate for the purpose.

The undisturbed revolution of a planet around the sun, in conformity with Kepler's law, would assure for that planet permanent conditions of climate. The earth, for instance, if guided solely by Kepler's laws, would return each day of the year exactly to the same position which it had on the same day of last year. From age to age the quantity of heat received by the earth would remain constant if the sun continued unaltered, and the present climate might thus be preserved indefinitely. But since the existence of planetary perturbation has become recognised, questions arise of the gravest importance with reference to the possible effects which such perturbations may have. We now see that the path of the earth is not absolutely fixed. That path is deranged by Venus and by Mars; it is deranged, it must be deranged, by every planet in our system. It is true that in a year, or even in a century, the amount of alteration produced is not very great; the ellipse which represents the path of our earth this year does not differ considerably from the ellipse which represented the movement of the earth one hundred years ago. But the important question arises as to whether the slight difference which does exist may not be constantly increasing, and may not ultimately assume such proportions as to modify our climates, or even to render life utterly impossible. Indeed, if we look at the subject without attentive calculation, nothing would seem more probable than that such should be the fate of our system. This globe revolves in a path inside that of the mighty Jupiter. It is, therefore, constantly attracted by Jupiter, and when it overtakes the vast planet, and comes between him and the sun, then the two bodies are comparatively close together, and the earth is pulled outwards by Jupiter. It might be supposed that the tendency of such disturbances would be to draw the earth gradually away from the sun, and thus to cause our globe to describe a path ever growing wider and wider. It is not, however, possible to decide a dynamical question by merely superficial reasoning of this character. The question has to be brought before the tribunal of mathematical analysis, where every element in the case is duly taken into account. Such an enquiry is by no means a simple one. It worthily occupied the splendid talents of Lagrange and Laplace, whose discoveries in the theory of planetary perturbation are some of the most remarkable achievements in astronomy.

We cannot here attempt to describe the reasoning which these great mathematicians employed. It can only be expressed by the formulÆ 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 AstrÆa—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 pÆans of triumph with which the enthusiastic French nation hailed the discovery of Le Verrier, there appeared a letter from Sir John Herschel in the AthenÆum 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 CÉleste" 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° 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.