Robert S. Ball

Contrast between Uranus and the other great Planets—William Herschel—His Birth and Parentage—Herschel's Arrival in England—His Love of Learning—Commencement of his Astronomical Studies—The Construction of Telescopes—Construction of Mirrors—The Professor of Music becomes an Astronomer—The Methodical Research—The 13th March, 1781—The Discovery of Uranus—Delicacy of Observation—Was the Object a Comet?—The Significance of this Discovery—The Fame of Herschel—George III. and the Bath Musician—The King's Astronomer at Windsor—The Planet Uranus—Numerical Data with reference thereto—The Four Satellites of Uranus—Their Circular Orbits—Early Observations of Uranus—Flamsteed's Observations—Lemonnier saw Uranus—Utility of their Measurements—The Elliptic Path—The Great Problem thus Suggested.

To the present writer it has always seemed that the history of Uranus, and of the circumstances attending its discovery, forms one of the most pleasing and interesting episodes in the whole history of science. We here occupy an entirely new position in the study of the solar system. All the other great planets were familiarly known from antiquity, however erroneous might be the ideas entertained in connection with them. They were conspicuous objects, and by their movements could hardly fail to attract the attention of those whose pursuits led them to observe the stars. But now we come to a great planet, the very existence of which was utterly unknown to the ancients; and hence, in approaching the subject, we have first to describe the actual discovery of this object, and then to consider what we can learn as to its physical nature.

We have, in preceding pages, had occasion to mention the revered name of William Herschel in connection with various branches of astronomy; but we have hitherto designedly postponed any more explicit reference to this extraordinary man until we had arrived at the present stage of our work. The story of Uranus, in its earlier stages at all events, is the story of the early career of William Herschel. It would be alike impossible and undesirable to attempt to separate them.

William Herschel, the illustrious astronomer, was born at Hanover in 1738. His father was an accomplished man, pursuing, in a somewhat humble manner, the calling of a professor of music. He had a family of ten children, of whom William was the fourth; and it may be noted that all the members of the family of whom any record has been preserved inherited their father's musical talents, and became accomplished performers. Pleasing sketches have been given of this interesting family, of the unusual aptitude of William, of the long discussions on music and on philosophy, and of the little sister Caroline, destined in later years for an illustrious career. William soon learned all that his master could teach him in the ordinary branches of knowledge, and by the age of fourteen he was already a competent performer on the oboe and the viol. He was engaged in the Court orchestra at Hanover, and was also a member of the band of the Hanoverian Guards. Troublous times were soon to break up Herschel's family. The French invaded Hanover, the Hanoverian Guards were overthrown in the battle of Hastenbeck, and young William Herschel had some unpleasant experience of actual warfare. His health was not very strong, and he decided that he would make a change in his profession. His method of doing so is one which his biographers can scarcely be expected to defend; for, to speak plainly, he deserted, and succeeded in making his escape to England. It is stated on unquestionable authority that on Herschel's first visit to King George III., more than twenty years afterwards, his pardon was handed to him by the King himself, written out in due form.

At the age of nineteen the young musician began to seek his fortunes in England. He met at first with very considerable hardship, but industry and skill conquered all difficulties, and by the time he was twenty-six years of age he was thoroughly settled in England, and doing well in his profession. In the year 1766 we find Herschel occupying a position of some distinction in the musical world; he had become the organist of the Octagon Chapel at Bath, and his time was fully employed in giving lessons to his numerous pupils, and with his preparation for concerts and oratorios.

Notwithstanding his busy professional life, Herschel still retained that insatiable thirst for knowledge which he had when a boy. Every moment he could snatch from his musical engagements was eagerly devoted to study. In his desire to perfect his knowledge of the more abstruse parts of the theory of music he had occasion to learn mathematics; from mathematics the transition to optics was a natural one; and once he had commenced to study optics, he was of course brought to a knowledge of the telescope, and thence to astronomy itself.

His beginnings were made on a very modest scale. It was through a small and imperfect telescope that the great astronomer obtained his first view of the celestial glories. No doubt he had often before looked at the heavens on a clear night, and admired the thousands of stars with which they were adorned; but now, when he was able to increase his powers of vision even to a slight extent, he obtained a view which fascinated him. The stars he had seen before he now saw far more distinctly; but, more than this, he found that myriads of others previously invisible were now revealed to him. Glorious, indeed, is this spectacle to anyone who possesses a spark of enthusiasm for natural beauty. To Herschel this view immediately changed the whole current of his life. His success as a professor of music, his oratorios, and his pupils were speedily to be forgotten, and the rest of his life was to be devoted to the absorbing pursuit of one of the noblest of the sciences.

Herschel could not remain contented with the small and imperfect instrument which first interested him. Throughout his career he determined to see everything for himself in the best manner which his utmost powers could command. He at once decided to have a better instrument, and he wrote to a celebrated optician in London with the view of making a purchase. But the price which the optician demanded seemed more than Herschel thought he could or ought to give. Instantly his resolution was taken. A good telescope he must have, and as he could not buy one he resolved to make one. It was alike fortunate, both for Herschel and for science, that circumstances impelled him to this determination. Yet, at first sight, how unpromising was the enterprise! That a music teacher, busily employed day and night, should, without previous training, expect to succeed in a task where the highest mechanical and optical skill was required, seemed indeed unlikely. But enthusiasm and genius know no insuperable difficulties. From conducting a brilliant concert in Bath, when that city was at the height of its fame, Herschel would rush home, and without even delaying to take off his lace ruffles, he would plunge into his manual labours of grinding specula and polishing lenses. No alchemist of old was ever more deeply absorbed in a project for turning lead into gold than was Herschel in his determination to have a telescope. He transformed his home into a laboratory; of his drawing-room he made a carpenter's shop. Turning lathes were the furniture of his best bedroom. A telescope he must have, and as he progressed he determined, not only that he should have a good telescope, but a very good one; and as success cheered his efforts he ultimately succeeded in constructing the greatest telescope that the world had up to that time ever seen. Though it is as an astronomer that we are concerned with Herschel, yet we must observe even as a telescope maker also great fame and no small degree of commercial success flowed in upon him. When the world began to ring with his glorious discoveries, and when it was known that he used no other telescopes than those which were the work of his own hands, a demand sprang up for instruments of his construction. It is stated that he made upwards of eighty large telescopes, as well as many others of smaller size. Several of these instruments were purchased by foreign princes and potentates.[29] We have never heard that any of these illustrious personages became celebrated astronomers, but, at all events, they seem to have paid Herschel handsomely for his skill, so that by the sale of large telescopes he was enabled to realise what may be regarded as a fortune in the moderate horizon of the man of science.

Up to the middle of his life Herschel was unknown to the public except as a laborious musician, with considerable renown in his profession, not only in Bath, but throughout the West of England. His telescope-making was merely the occupation of his spare moments, and was unheard of by most of those who knew and respected his musical attainments. It was in 1774 that Herschel first enjoyed a view of the heavens through an instrument built with his own hands. It was but a small one in comparison with those which he afterwards fashioned, but at once he experienced the advantage of being his own instrument maker. Night after night he was able to add the improvements which experience suggested; at one time he was enlarging the mirrors; at another he was reconstructing the mounting, or trying to remedy defects in the eye-pieces. With unwearying perseverance he aimed at the highest excellence, and with each successive advance he found that he was able to pierce further into the sky. His enthusiasm attracted a few friends who were, like himself, ardently attached to science. The mode in which he first made the acquaintance of Sir William Watson, who afterwards became his warmest friend, was characteristic of both. Herschel was observing the mountains in the moon, and as the hours passed on, he had occasion to bring his telescope into the street in front of his house to enable him to continue his work. Sir William Watson happened to pass by, and was arrested by the unusual spectacle of an astronomer in the public street, at the dead of night, using a large and quaint-looking instrument. Having a taste for astronomy, Sir William stopped, and when Herschel took his eye from the telescope, asked if he might be allowed to have a look at the moon. The request was readily granted. Probably Herschel found but few in the gay city who cared for such matters; he was quickly drawn to Sir W. Watson, who at once reciprocated the feeling, and thus began a friendship which bore important fruit in Herschel's subsequent career.

At length the year 1781 approached, which was to witness his great achievement. Herschel had made good use of seven years' practical experience in astronomy, and he had completed a telescope of exquisite optical perfection, though greatly inferior in size to some of those which he afterwards erected. With this reflector Herschel commenced a methodical piece of observation. He formed the scheme of systematically examining all the stars which were above a certain degree of brightness. It does not quite appear what object Herschel proposed to himself when he undertook this labour, but, in any case, he could hardly have anticipated the extraordinary success with which the work was to be crowned. In the course of this review the telescope was directed to a star; that star was examined; then another was brought into the field of view, and it too was examined. Every star under such circumstances merely shows itself as a point of light; the point may be brilliant or not, according as the star is bright or not; the point will also, of course, show the colour of the star, but it cannot exhibit recognisable size or shape. The greater, in fact, the perfection of the telescope, the smaller is the telescopic image of a star.

How many stars Herschel inspected in this review we are not told; but at all events, on the ever-memorable night of the 13th of March, 1781, he was pursuing his self-allotted task among the hosts in the constellation Gemini. Doubtless, one star after another was admitted to view, and was allowed to pass away. At length, however, an object was placed in the field which differed from every other star. It was not a mere point of light; it had a minute, but still a perfectly recognisable, disc. We say the disc was perfectly recognisable, but we should be careful to add that it was so in the excellent telescope of Herschel alone. Other astronomers had seen this object before. Its position had actually been measured no fewer than nineteen times before the Bath musician, with his home-made telescope, looked at it, but the previous observers had only seen it in small meridian instruments with low magnifying powers. Even after the discovery was made, and when well-trained observers with good instruments looked again under the direction of Herschel, one after another bore testimony to the extraordinary delicacy of the great astronomer's perception, which enabled him almost at the first glance to discriminate between it and a star.

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 surpassed in bulk by Jupiter and by Saturn. This superb new planet was plunged into space to such a depth that, notwithstanding its noble 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 entitled 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 substitute. 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 Uranus was the discovery of Herschel's unrivalled powers of observation. Uranus must, sooner or later, have been found. Had Herschel not lived, we would still, no doubt, have known Uranus 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 Uranus secured all this, and accordingly obtained for astronomy all Herschel's future labours.[30]

Uranus 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 Uranus must be about sixty-four times as great as that of the earth. We also find that, like the other giant planets, Uranus 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, Uranus is only fifteen times as heavy. If we may trust to the analogies of what we see everywhere else in our system, we can feel but little doubt that Uranus 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 Uranus.

There is, however, one feature about Uranus which presents many points of interest to those astronomers who are possessed of telescopes of unusual size and perfection. Uranus 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 Uranus 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, Titania, 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 latitude 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 Uranus 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 circumstance that the orbits of the satellites of Uranus 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 circumstance 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 Uranus 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 Uranus lie in a plane nearly at right angles to the orbit of Uranus. We are not in a position to give any satisfactory explanation of this circumstance. 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 Uranus, in 1781, sufficient observations were accumulated 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. Uranus 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 Uranus 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 Uranus 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? Uranus 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 illustrious 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 Uranus 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 Uranus 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 Uranus. An object was found in the "Historia Coelestis" which occupied a position identical with that which Uranus must have filled on the same date. Could this be Uranus? 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 Uranus could hardly be for a moment doubted. Speedily other confirmation flowed in. It was shown that Uranus had been observed by Bradley and by Tobias Mayer, and it also became apparent that Flamsteed had observed Uranus 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 Uranus 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 Uranus would have been discovered, and William Herschel would have been anticipated. 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 Uranus 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 Uranus 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 Uranus. 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 Uranus; 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 Uranus. 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 Uranus?

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. Uranus does not move solely in consequence of the sun's attraction and that of the planets of our system interior to Uranus; there must therefore be some further influence acting upon Uranus besides those already known. To the development of this subject the next chapter will be devoted.