If not a star, what, then, could it be? The first step to enable this question to be answered was to observe the body for some time. This Herschel did. He looked at it one night after another, and soon he discovered another fundamental difference between this object and an ordinary star. The stars are, of course, characterised by their fixity, but this object was not fixed; night after night the place it occupied changed with respect to the stars. No longer could there be any doubt that this body was a member of the solar system, and that an interesting discovery had been made; many months, however, elapsed before Herschel knew the real merit of his achievement. He did not realise that he had made the superb discovery of another mighty planet revolving outside Saturn; he thought that it could only be a comet. No doubt this object looked very different from a great comet, decorated with a tail. It was not, however, so entirely different from some forms of telescopic comets as to make the suggestion of its being a body of this kind unlikely; and the discovery was at first announced in accordance with this view. Time was necessary before the true character of the object could be ascertained. It must be followed for a considerable distance along its path, and measures of its position at different epochs must be effected, before it is practicable for the mathematician to calculate the path which the body pursues; once, however, attention was devoted to the subject, many astronomers aided in making the necessary observations.

These were placed in the hands of mathematicians, and the result was proclaimed that this body was not a comet, but that, like all the planets, it revolved in nearly a circular path around the sun, and that the path lay millions of miles outside the path of Saturn, which had so long been regarded as the boundary of the solar system.

It is hardly possible to over-estimate the significance of this splendid discovery. The five planets had been known from all antiquity; they were all, at suitable seasons, brilliantly conspicuous to the unaided eye.

But it was now found that, far outside the outermost of these planets revolved another splendid planet, larger than Mercury or Mars, larger--far larger--than Venus and the earth, and only surpa.s.sed in bulk by Jupiter and by Saturn. This superb new planet was plunged into s.p.a.ce to such a depth that, notwithstanding its n.o.ble proportions, it seemed merely a tiny star, being only on rare occasions within reach of the unaided eye. This great globe required a period of eighty-four years to complete its majestic path, and the diameter of that path was 3,600,000,000 miles.

Although the history of astronomy is the record of brilliant discoveries--of the labours of Copernicus, and of Kepler--of the telescopic achievements of Galileo, and the splendid theory of Newton--of the refined discovery of the aberration of light--of many other imperishable triumphs of intellect--yet this achievement of the organist at the Octagon Chapel occupies a totally different position from any other. There never before had been any historic record of the discovery of one of the bodies of the particular system to which the earth belongs. The older planets were no doubt discovered by someone, but we can say little more about these discoveries than we can about the discovery of the sun or of the moon; all are alike prehistoric. Here was the first recorded instance of the discovery of a planet which, like the earth, revolves around the sun, and, like our earth, may conceivably be an inhabited globe. So unique an achievement instantly arrested the attention of the whole scientific world. The music-master at Bath, hitherto unheard of as an astronomer, was speedily placed in the very foremost rank of those ent.i.tled to the name. On all sides the greatest interest was manifested about the unknown philosopher. The name of Herschel, then unfamiliar to English ears, appeared in every journal, and a curious list has been preserved of the number of blunders which were made in spelling the name. The different scientific societies hastened to convey their congratulations on an occasion so memorable.

Tidings of the discovery made by the Hanoverian musician reached the ears of George III., and he sent for Herschel to come to the Court, that the King might learn what his achievement actually was from the discoverer's own lips. Herschel brought with him one of his telescopes, and he provided himself with a chart of the solar system, with which to explain precisely wherein the significance of the discovery lay. The King was greatly interested in Herschel's narrative, and not less in Herschel himself. The telescope was erected at Windsor, and, under the astronomer's guidance, the King was shown Saturn and other celebrated objects. It is also told how the ladies of the Court the next day asked Herschel to show them the wonders which had so pleased the King. The telescope was duly erected in a window of one of the Queen's apartments, but when evening arrived the sky was found to be overcast with clouds, and no stars could be seen. This was an experience with which Herschel, like every other astronomer, was unhappily only too familiar. But it is not every astronomer who would have shown the readiness of Herschel in escaping gracefully from the position. He showed to his lady pupils the construction of the telescope; he explained the mirror, and how he had fashioned it and given the polish; and then, seeing the clouds were inexorable, he proposed that, as he could not show them the real Saturn, he should exhibit an artificial one as the best subst.i.tute. The permission granted, Herschel turned the telescope away from the sky, and pointed it towards the wall of a distant garden. On looking into the telescope there was Saturn, his globe and his system of rings, so faithfully shown that, says Herschel, even a skilful astronomer might have been deceived. The fact was that during the course of the day Herschel saw that the sky would probably be overcast in the evening, and he had provided for the emergency by cutting a hole in a piece of cardboard, the shape of Saturn, which was then placed against the distant garden wall, and illuminated by a lamp at the back.

This visit to Windsor was productive of consequences momentous to Herschel, momentous to science. He had made so favourable an impression, that the King proposed to create for him the special appointment of King's Astronomer at Windsor. The King was to provide the means for erecting the great telescopes, and he allocated to Herschel a salary of 200 a year, the figures being based, it must be admitted, on a somewhat moderate estimate of the requirements of an astronomer's household.

Herschel mentioned these particulars to no one save to his constant and generous friend, Sir W. Watson, who exclaimed, "Never bought monarch honour so cheap." To other enquirers, Herschel merely said that the King had provided for him. In accepting this post, the great astronomer took no doubt a serious step. He at once sacrificed entirely his musical career, now, from many sources, a lucrative one; but his determination was speedily taken. The splendid earnest that he had already given of his devotion to astronomy was, he knew, only the commencement of a series of memorable labours. He had indeed long been feeling that it was his bounden duty to follow that path in life which his genius indicated.

He was no longer a young man. He had attained middle age, and the years had become especially precious to one who knew that he had still a life-work to accomplish. He at one stroke freed himself from all distractions; his pupils and concerts, his whole connection at Bath, were immediately renounced; he accepted the King's offer with alacrity, and after one or two changes settled permanently at Slough, near Windsor.

It has, indeed, been well remarked that the most important event in connection with the discovery of Ura.n.u.s was the discovery of Herschel's unrivalled powers of observation. Ura.n.u.s must, sooner or later, have been found. Had Herschel not lived, we would still, no doubt, have known Ura.n.u.s long ere this. The really important point for science was that Herschel's genius should be given full scope, by setting him free from the engrossing details of an ordinary professional calling. The discovery of Ura.n.u.s secured all this, and accordingly obtained for astronomy all Herschel's future labours.[30]

Ura.n.u.s is so remote that even the best of our modern telescopes cannot make of it a striking picture. We can see, as Herschel did, that it has a measurable disc, and from measurements of that disc we conclude that the diameter of the planet is about 31,700 miles. This is about four times as great as the diameter of the earth, and we accordingly see that the volume of Ura.n.u.s must be about sixty-four times as great as that of the earth. We also find that, like the other giant planets, Ura.n.u.s seems to be composed of materials much lighter, on the whole, than those we find here; so that, though sixty-four times as large as the earth, Ura.n.u.s is only fifteen times as heavy. If we may trust to the a.n.a.logies of what we see everywhere else in our system, we can feel but little doubt that Ura.n.u.s must rotate about an axis. The ordinary means of demonstrating this rotation can be hardly available in a body whose surface appears so small and so faint. The period of rotation is accordingly unknown. The spectroscope tells us that a remarkable atmosphere, containing apparently some gases foreign to our own, deeply envelops Ura.n.u.s.

There is, however, one feature about Ura.n.u.s which presents many points of interest to those astronomers who are possessed of telescopes of unusual size and perfection. Ura.n.u.s is accompanied by a system of satellites, some of which are so faint as to require the closest scrutiny for their detection. The discovery of these satellites was one of the subsequent achievements of Herschel. It is, however, remarkable that even his penetration and care did not preserve him from errors with regard to these very delicate objects. Some of the points which he thought to be satellites must, it would now seem, have been merely stars enormously more distant, which happened to lie in the field of view. It has been since ascertained that the known satellites of Ura.n.u.s are four in number, and their movements have been made the subject of prolonged and interesting telescopic research. The four satellites bear the names of Ariel, Umbriel, t.i.tania, and Oberon. Arranged in order of their distance from the central body, Ariel, the nearest, accomplishes its journey in 2 days and 12 hours. Oberon, the most distant, completes its journey in 13 days and 11 hours.

The law of Kepler declares that the path of a satellite around its primary, no less than of the primary around the sun, must be an ellipse.

It leaves, however, boundless lat.i.tude in the actual eccentricity of the curve. The ellipse may be nearly a circle, it may be absolutely a circle, or it may be something quite different from a circle. The paths pursued by the planets are, generally speaking, nearly circles; but we meet with no exact circle among planetary orbits. So far as we at present know, the closest approach made to a perfectly circular movement is that by which the satellites of Ura.n.u.s revolve around their primary.

We are not prepared to say that these paths are absolutely circular. All that can be said is that our telescopes fail to show any measurable departure therefrom. It is also to be noted as an interesting circ.u.mstance that the orbits of the satellites of Ura.n.u.s all lie in the same plane. This is not true of the orbits of the planets around the sun, nor is it true of the orbits of any other system of satellites around their primary. The most singular circ.u.mstance attending the Uranian system is, however, found in the position which this plane occupies. This is indeed almost as great an anomaly in our system as are the rings of Saturn themselves. We have already had occasion to notice that the plane in which the earth revolves around the sun is very nearly coincident with the planes in which all the other great planets revolve.

The same is true, to a large extent, of the orbits of the minor planets; though here, no doubt, we meet with a few cases in which the plane of the orbit is inclined at no inconsiderable angle to the plane in which the earth moves. The plane in which the moon revolves also approximates to this system of planetary planes. So, too, do the orbits of the satellites of Saturn and of Jupiter, while even the more recently discovered satellites of Mars form no exception to the rule. The whole solar system--at least so far as the great planets are concerned--would require comparatively little alteration if the orbits were to be entirely flattened down into one plane. There are, however, some notable exceptions to this rule. The satellites of Ura.n.u.s revolve in a plane which is far from coinciding with the plane to which all other orbits approximate. In fact, the paths of the satellites of Ura.n.u.s lie in a plane nearly at right angles to the orbit of Ura.n.u.s. We are not in a position to give any satisfactory explanation of this circ.u.mstance. It is, however, evident that in the genesis of the Uranian system there must have been some influence of a quite exceptional and local character.

Soon after the discovery of the planet Ura.n.u.s, in 1781, sufficient observations were acc.u.mulated to enable the orbit it follows to be determined. When the path was known, it was then a mere matter of mathematical calculation to ascertain where the planet was situated at any past time, and where it would be situated at any future time. An interesting enquiry was thus originated as to how far it might be possible to find any observations of the planet made previously to its discovery by Herschel. Ura.n.u.s looks like a star of the sixth magnitude.

Not many astronomers were provided with telescopes of the perfection attained by Herschel, and the personal delicacy of perception characteristic of Herschel was a still more rare possession. It was, therefore, to be expected that, if such previous observations existed, they would merely record Ura.n.u.s as a star visible, and indeed bright, in a moderate telescope, but still not claiming any exceptional attention over thousands of apparently similar stars. Many of the early astronomers had devoted themselves to the useful and laborious work of forming catalogues of stars. In the preparation of a star catalogue, the telescope was directed to the heavens, the stars were observed, their places were carefully measured, the brightness of the star was also estimated, and thus the catalogue was gradually compiled in which each star had its place faithfully recorded, so that at any future time it could be identified. The stars were thus registered, by hundreds and by thousands, at various dates from the birth of accurate astronomy till the present time. The suggestion was then made that, as Ura.n.u.s looked so like a star, and as it was quite bright enough to have engaged the attention of astronomers possessed of even very moderate instrumental powers, there was a possibility that it had already been observed, and thus actually lay recorded as a star in some of the older catalogues.

This was indeed an idea worthy of every attention, and pregnant with the most important consequences in connection with the immortal discovery to be discussed in our next chapter. But how was such an examination of the catalogues to be conducted? Ura.n.u.s is constantly moving about; does it not seem that there is every element of uncertainty in such an investigation? Let us consider a notable example.

The great national observatory at Greenwich was founded in 1675, and the first Astronomer-Royal was the ill.u.s.trious Flamsteed, who in 1676 commenced that series of observations of the heavenly bodies which has been continued to the present day with such incalculable benefits to science. At first the instruments were of a rather primitive description, but in the course of some years Flamsteed succeeded in procuring instruments adequate to the production of a catalogue of stars, and he devoted himself with extraordinary zeal to the undertaking. It is in this memorable work, the "Historia Coelestis" of Flamsteed, that the earliest observation of Ura.n.u.s is recorded. In the first place it was known that the orbit of this body, like the orbit of every other great planet, was inclined at a very small angle to the ecliptic. It hence follows that Ura.n.u.s is at all times only to be met with along the ecliptic, and it is possible to calculate where the planet has been in each year. It was thus seen that in 1690 the planet was situated in that part of the ecliptic where Flamsteed was at the same date making his observations. It was natural to search the observations of Flamsteed, and see whether any of the so-called stars could have been Ura.n.u.s. An object was found in the "Historia Coelestis" which occupied a position identical with that which Ura.n.u.s must have filled on the same date. Could this be Ura.n.u.s? A decisive test was at once available. The telescope was directed to the spot in the heavens where Flamsteed saw a sixth-magnitude star. If that were really a star, then would it still be visible. The trial was made: no such star could be found, and hence the presumption that this was really Ura.n.u.s could hardly be for a moment doubted. Speedily other confirmation flowed in. It was shown that Ura.n.u.s had been observed by Bradley and by Tobias Mayer, and it also became apparent that Flamsteed had observed Ura.n.u.s not only once, but that he had actually measured its place four times in the years 1712 and 1715. Yet Flamsteed was never conscious of the discovery that lay so nearly in his grasp. He was, of course, under the impression that all these observations related to different stars. A still more remarkable case is that of Lemonnier, who had actually observed Ura.n.u.s twelve times, and even recorded it on four consecutive days in January, 1769. If Lemonnier had only carefully looked over his own work; if he had perceived, as he might have done, how the star he observed yesterday was gone to-day, while the star visible to-day had moved away by to-morrow, there is no doubt that Ura.n.u.s would have been discovered, and William Herschel would have been antic.i.p.ated. Would Lemonnier have made as good use of his fame as Herschel did? This seems a question which can never be decided, but those who estimate Herschel as the present writer thinks he ought to be estimated, will probably agree in thinking that it was most fortunate for science that Lemonnier did _not_ compare his observations.[31]

These early accidental observations of Ura.n.u.s are not merely to be regarded as matters of historical interest or curiosity. That they are of the deepest importance with regard to the science itself a few words will enable us to show. It is to be remembered that Ura.n.u.s requires no less than eighty-four years to accomplish his mighty revolution around the sun. The planet has completed one entire revolution since its discovery, and up to the present time (1900) has accomplished more than one-third of another. For the careful study of the nature of the orbit, it was desirable to have as many measurements as possible, and extending over the widest possible interval. This was in a great measure secured by the identification of the early observations of Ura.n.u.s. An approximate knowledge of the orbit was quite capable of giving the places of the planet with sufficient accuracy to identify it when met with in the catalogues. But when by their aid the actual observations have been discovered, they tell us precisely the place of Ura.n.u.s; and hence, instead of our knowledge of the planet being limited to but little more than one revolution, we have at the present time information with regard to it extending over considerably more than two revolutions.

From the observations of the planet the ellipse in which it moves can be ascertained. We can compute this ellipse from the observations made during the time since the discovery. We can also compute the ellipse from the early observations made before the discovery. If Kepler's laws were rigorously verified, then, of course, the ellipse performed in the present revolution must differ in no respect from the ellipse performed in the preceding, or indeed in any other revolution. We can test this point in an interesting manner by comparing the ellipse derived from the ancient observations with that deduced from the modern ones. These ellipses closely resemble each other; they are nearly the same; but it is most important to observe that they are not _exactly_ the same, even when allowance has been made for every known source of disturbance in accordance with the principles explained in the next chapter. The law of Kepler seems thus not absolutely true in the case of Ura.n.u.s. Here is, indeed, a matter demanding our most earnest and careful attention. Have we not repeatedly laid down the universality of the laws of Kepler in controlling the planetary motions? How then can we reconcile this law with the irregularities proved beyond a doubt to exist in the motions of Ura.n.u.s?

Let us look a little more closely into the matter. We know that the laws of Kepler are a consequence of the laws of gravitation. We know that the planet moves in an elliptic path around the sun, in virtue of the sun's attraction, and we know that the ellipse will be preserved without the minutest alteration if the sun and the planet be left to their mutual attractions, and if no other force intervene. We can also calculate the influence of each of the known planets on the form and position of the orbit. But when allowance is made for all such perturbing influences it is found that the observed and computed orbits do not agree. The conclusion is irresistible. Ura.n.u.s does not move solely in consequence of the sun's attraction and that of the planets of our system interior to Ura.n.u.s; there must therefore be some further influence acting upon Ura.n.u.s besides those already known. To the development of this subject the next chapter will be devoted.

CHAPTER XV.

NEPTUNE.

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 Ura.n.u.s--The Unknown Planet must revolve outside the Path of Ura.n.u.s--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 ma.s.s, and as the ma.s.s 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 a.s.serts 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 ma.s.s of the sun preponderates enormously over the ma.s.s 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 circ.u.mstances, 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 s.p.a.ce. 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 ma.s.s that many matters may be overlooked which would be of moment were he rivalled in ma.s.s 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 circ.u.mstances which our system presents. In such groups as the marvellous star Th 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 a.s.sure 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 quant.i.ty 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 a.s.sume 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 a.n.a.lysis, 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 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 pa.s.s very close to the sun at one part of its...o...b..t, 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 a.n.a.lysis. Again he vanquished the mathematical difficulties, and again he was able to give a.s.surance 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 a.s.sert, 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...o...b..t 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 a.s.sumption that the mutual inclinations of the planets are small, then mathematics a.s.sure 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 ma.s.ses of all the bodies in this hypothetical system be identical with the ma.s.ses 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 a.n.a.lysis 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 Ura.n.u.s.

We have already alluded to the difficulties which were experienced when it was sought to reconcile the early observations of Ura.n.u.s with those made since its discovery. We have shown that the path in which this planet revolved experienced change, and that consequently Ura.n.u.s 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 Ura.n.u.s could not be accounted for by the attraction of the other planets. Ura.n.u.s revolves just outside Saturn. The ma.s.s of Saturn is much larger than the ma.s.s of Ura.n.u.s. Could it not be that Saturn draws Ura.n.u.s 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 Ura.n.u.s. In a similar manner Jupiter, with his mighty ma.s.s, acts on Ura.n.u.s, and produces a disturbance which the mathematician calculates.

When the figures had been worked out for all the known planets they were applied to Ura.n.u.s, 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, Ura.n.u.s was still shown to be influenced by some further agent; and hence the conclusion was established that Ura.n.u.s must be affected by some unknown body. What could this unknown body be, and where must it be situated? a.n.a.logy 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 Ura.n.u.s 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...o...b..t must lie outside the orbit of Ura.n.u.s. This was necessary, because the unknown planet must be a large and ma.s.sive one to produce the observed irregularities. If, therefore, it were nearer than Ura.n.u.s, 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 Ura.n.u.s were caused by the attraction of a planet, that body must revolve outside the globe discovered by Herschel. The general a.n.a.logies 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...o...b..t.

The measured deviations of Ura.n.u.s at the different points of its...o...b..t 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 ma.s.s of the planet itself, in such a way as to account for the various perturbations. Let us, for instance, a.s.sume a certain distance for the hypothetical body, and try if we can a.s.sign both an orbit and a ma.s.s for the planet, at that distance, which shall account for the perturbations.

Our first a.s.sumption 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 ma.s.s of the body can be also determined. We a.s.sume a certain value, and calculate the perturbations. If the results seem greater than those obtained by observations, then the a.s.sumed ma.s.s is too great. We amend the a.s.sumption, and recompute with a lesser amount, and so on until at length we determine a ma.s.s 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 Ura.n.u.s could be completely explained if the unknown planet had a certain ma.s.s, and moved in an orbit which had a certain position, while it was also manifest that no very different orbit or greatly altered ma.s.s 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 Ura.n.u.s, 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 Ura.n.u.s 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 un.o.bserved 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 inst.i.tuted 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 Ura.n.u.s, 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 Ura.n.u.s 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 Ura.n.u.s.

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 Ura.n.u.s. With exhaustive a.n.a.lysis 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 a.s.signed 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 a.n.a.lysis 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 inc.u.mbent 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 inst.i.tuted. 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 antic.i.p.ated 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 a.s.sociation 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 sh.o.r.es of Spain.

Its movements have been felt trembling along the far-reaching line of our a.n.a.lysis, 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 antic.i.p.ated 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.