While the illustrious astronomer, Tycho Brahe, lay on his death-bed, he had an interview which must ever rank as one of the important incidents in the history of science. The life of Tycho had been passed, as we have seen, in the accumulation of vast stores of careful observations of the positions of the heavenly bodies. It was not given to him to deduce from his splendid work the results to which they were destined to lead. It was reserved for another astronomer to distil, so to speak, from the volumes in which Tycho's figures were recorded, the great truths of the universe which those figures contained. Tycho felt that his work required an interpreter, and he recognised in the genius of a young man with whom he was acquainted the agent by whom the world was to be taught some of the great truths of nature. To the bedside of the great Danish astronomer the youthful philosopher was summoned, and with his last breath Tycho besought of him to spare no labour in the performance of those calculations, by which alone the secrets of the movements of the heavens could be revealed. The solemn trust thus imposed was duly accepted, and the man who accepted it bore the immortal name of Kepler. Kepler was born on the 27th December, 1571, at Weil, in the Duchy of Wurtemberg. It would seem that the circumstances of his childhood must have been singularly unhappy. His father, sprung from a well-connected family, was but a shiftless and idle adventurer; nor was the great astronomer much more fortunate in his other parent. His mother was an ignorant and ill-tempered woman; indeed, the ill-assorted union came to an abrupt end through the desertion of the wife by her husband when their eldest son John, the hero of our present sketch, was eighteen years old. The childhood of this lad, destined for such fame, was still further embittered by the circumstance that when he was four years old he had a severe attack of small-pox. Not only was his eyesight permanently injured, but even his constitution appears to have been much weakened by this terrible malady. It seems, however, that the bodily infirmities of young John Kepler were the immediate cause of his attention being directed to the pursuit of knowledge. Had the boy been fitted like other boys for ordinary manual work, there can be hardly any doubt that to manual work his life must have been devoted. But, though his body was feeble, he soon gave indications of the possession of considerable mental power. It was accordingly thought that a suitable sphere for his talents might be found in the Church which, in those days, was almost the only profession that afforded an opening for an intellectual career. We thus find that by the time John Kepler was seventeen years old he had attained a sufficient standard of knowledge to entitle him to admission on the foundation of the University at Tubingen. In the course of his studies at this institution he seems to have divided his attention equally between astronomy and divinity. It not unfrequently happens that when a man has attained considerable proficiency in two branches of knowledge he is not able to see very clearly in which of the two pursuits his true vocation lies. His friends and onlookers are often able to judge more wisely than he himself can do as to which Of the two lines it would be better for him to pursue. This incapacity for perceiving the path in which greatness awaited him, existed in the case of Kepler. Personally, he inclined to enter the ministry, in which a promising career seemed open to him. He yielded, however, to friends, who evidently knew him better than he knew himself, and accepted in 1594, the important Professorship of astronomy which had been offered to him in the University of Gratz. It is difficult for us in these modern days to realise the somewhat extraordinary duties which were expected from an astronomical professor in the sixteenth century. He was, of course, required to employ his knowledge of the heavens in the prediction of eclipses, and of the movements of the heavenly bodies generally. This seems reasonable enough; but what we are not prepared to accept is the obligation which lay on the astronomers to predict the fates of nations and the destinies of individuals. It must be remembered that it was the almost universal belief in those days, that all the celestial spheres revolved in some mysterious fashion around the earth, which appeared by far the most important body in the universe. It was imagined that the sun, the moon, and the stars indicated, in the vicissitudes of their movements, the careers of nations and of individuals. Such being the generally accepted notion, it seemed to follow that a professor who was charged with the duty of expounding the movements of the heavenly bodies must necessarily be looked to for the purpose of deciphering the celestial decrees regarding the fate of man which the heavenly luminaries were designed to announce. Kepler threw himself with characteristic ardour into even this fantastic phase of the labours of the astronomical professor; he diligently studied the rules of astrology, which the fancies of antiquity had compiled. Believing sincerely as he did in the connection between the aspect of the stars and the state of human affairs, he even thought that he perceived, in the events of his own life, a corroboration of the doctrine which affirmed the influence of the planets upon the fate of individuals. [PLATE: KEPLER'S SYSTEM OF REGULAR SOLIDS.] But quite independently of astrology there seem to have been many other delusions current among the philosophers of Kepler's time. It is now almost incomprehensible how the ablest men of a few centuries ago should have entertained such preposterous notions, as they did, with respect to the system of the universe. As an instance of what is here referred to, we may cite the extraordinary notion which, under the designation of a discovery, first brought Kepler into fame. Geometers had long known that there were five, but no more than five, regular solid figures. There is, for instance, the cube with six sides, which is, of course, the most familiar of these solids. Besides the cube there are other figures of four, eight, twelve, and twenty sides respectively. It also happened that there were five planets, but no more than five, known to the ancients, namely, Mercury, Venus, Mars, Jupiter, and Saturn. To Kepler's lively imaginations this coincidence suggested the idea that the five regular solids corresponded to the five planets, and a number of fancied numerical relations were adduced on the subject. The absurdity of this doctrine is obvious enough, especially when we observe that, as is now well known, there are two large planets, and a host of small planets, over and above the magical number of the regular solids. In Kepler's time, however, this doctrine was so far from being regarded as absurd, that its announcement was hailed as a great intellectual triumph. Kepler was at once regarded with favour. It seems, indeed, to have been the circumstance which brought him into correspondence with Tycho Brahe. By its means also he became known to Galileo. The career of a scientific professor in those early days appears generally to have been marked by rather more striking vicissitudes than usually befall a professor in a modern university. Kepler was a Protestant, and as such he had been appointed to his professorship at Gratz. A change, however, having taken place in the religious belief entertained by the ruling powers of the University, the Protestant professors were expelled. It seems that special influence having been exerted in Kepler's case on account of his exceptional eminence, he was recalled to Gratz and reinstated in the tenure of his chair. But his pupils had vanished, so that the great astronomer was glad to accept a post offered him by Tycho Brahe in the observatory which the latter had recently established near Prague. On Tycho's death, which occurred soon after, an opening presented itself which gave Kepler the opportunity his genius demanded. He was appointed to succeed Tycho in the position of imperial mathematician. But a far more important point, both for Kepler and for science, was that to him was confided the use of Tycho's observations. It was, indeed, by the discussion of Tycho's results that Kepler was enabled to make the discoveries which form such an important part of astronomical history. Kepler must also be remembered as one of the first great astronomers who ever had the privilege of viewing celestial bodies through a telescope. It was in 1610 that he first held in his hands one of those little instruments which had been so recently applied to the heavens by Galileo. It should, however, be borne in mind that the epoch-making achievements of Kepler did not arise from any telescopic observations that he made, or, indeed, that any one else made. They were all elaborately deduced from Tycho's measurements of the positions of the planets, obtained with his great instruments, which were unprovided with telescopic assistance. To realise the tremendous advance which science received from Kepler's great work, it is to be understood that all the astronomers who laboured before him at the difficult subject of the celestial motions, took it for granted that the planets must revolve in circles. If it did not appear that a planet moved in a fixed circle, then the ready answer was provided by Ptolemy's theory that the circle in which the planet did move was itself in motion, so that its centre described another circle. When Kepler had before him that wonderful series of observations of the planet, Mars, which had been accumulated by the extraordinary skill of Tycho, he proved, after much labour, that the movements of the planet refused to be represented in a circular form. Nor would it do to suppose that Mars revolved in one circle, the centre of which revolved in another circle. On no such supposition could the movements of the planets be made to tally with those which Tycho had actually observed. This led to the astonishing discovery of the true form of a planet's orbit. For the first time in the history of astronomy the principle was laid down that the movement of a planet could not be represented by a circle, nor even by combinations of circles, but that it could be represented by an elliptic path. In this path the sun is situated at one of those two points in the ellipse which are known as its foci. [PLATE: KEPLER.] Very simple apparatus is needed for the drawing of one of those ellipses which Kepler has shown to possess such astonishing astronomical significance. Two pins are stuck through a sheet of paper on a board, the point of a pencil is inserted in a loop of string which passes over the pins, and as the pencil is moved round in such a way as to keep the string stretched, that beautiful curve known as the ellipse is delineated, while the positions of the pins indicate the two foci of the curve. If the length of the loop of string is unchanged then the nearer the pins are together, the greater will be the resemblance between the ellipse and the circle, whereas the more the pins are separated the more elongated does the ellipse become. The orbit of a great planet is, in general, one of those ellipses which approaches a nearly circular form. It fortunately happens, however, that the orbit of Mars makes a wider departure from the circular form than any of the other important planets. It is, doubtless, to this circumstance that we must attribute the astonishing success of Kepler in detecting the true shape of a planetary orbit. Tycho's observations would not have been sufficiently accurate to have exhibited the elliptic nature of a planetary orbit which, like that of Venus, differed very little from a circle. The more we ponder on this memorable achievement the more striking will it appear. It must be remembered that in these days we know of the physical necessity which requires that a planet shall revolve in an ellipse and not in any other curve. But Kepler had no such knowledge. Even to the last hour of his life he remained in ignorance of the existence of any natural cause which ordained that planets should follow those particular curves which geometers know so well. Kepler's assignment of the ellipse as the true form of the planetary orbit is to be regarded as a brilliant guess, the truth of which Tycho's observations enabled him to verify. Kepler also succeeded in pointing out the law according to which the velocity of a planet at different points of its path could be accurately specified. Here, again, we have to admire the sagacity with which this marvellously acute astronomer guessed the deep truth of nature. In this case also he was quite unprovided with any reason for expecting from physical principles that such a law as he discovered must be obeyed. It is quite true that Kepler had some slight knowledge of the existence of what we now know as gravitation. He had even enunciated the remarkable doctrine that the ebb and flow of the tide must be attributed to the attraction of the moon on the waters of the earth. He does not, however, appear to have had any anticipation of those wonderful discoveries which Newton was destined to make a little later, in which he demonstrated that the laws detected by Kepler's marvellous acumen were necessary consequences of the principle of universal gravitation. [PLATE: SYMBOLICAL REPRESENTATION OF THE PLANETARY SYSTEM.] To appreciate the relations of Kepler and Tycho it is necessary to note the very different way in which these illustrious astronomers viewed the system of the heavens. It should be observed that Copernicus had already expounded the true system, which located the sun at the centre of the planetary system. But in the days of Tycho Brahe this doctrine had not as yet commanded universal assent. In fact, the great observer himself did not accept the new views of Copernicus. It appeared to Tycho that the earth not only appeared to be the centre of things celestial, but that it actually was the centre. It is, indeed, not a little remarkable that a student of the heavens so accurate as Tycho should have deliberately rejected the Copernican doctrine in favour of the system which now seems so preposterous. Throughout his great career, Tycho steadily observed the places of the sun, the moon, and the planets, and as steadily maintained that all those bodies revolved around the earth fixed in the centre. Kepler, however, had the advantage of belonging to the new school. He utilised the observations of Tycho in developing the great Copernican theory whose teaching Tycho stoutly resisted. Perhaps a chapter in modern science may illustrate the intellectual relation of these great men. The revolution produced by Copernicus in the doctrine of the heavens has often been likened to the revolution which the Darwinian theory produced in the views held by biologists as to life on this earth. The Darwinian theory did not at first command universal assent even among those naturalists whose lives had been devoted with the greatest success to the study of organisms. Take, for instance, that great naturalist, Professor Owen, by whose labours vast extension has been given to our knowledge of the fossil animals which dwelt on the earth in past ages. Now, though Owens researches were intimately connected with the great labours of Darwin, and afforded the latter material for his epoch-making generalization, yet Owen deliberately refused to accept the new doctrines. Like Tycho, he kept on rigidly accumulating his facts under the influence of a set of ideas as to the origin of living forms which are now universally admitted to be erroneous. If, therefore, we liken Darwin to Copernicus, and Owen to Tycho, we may liken the biologists of the present day to Kepler, who interpreted the results of accurate observation upon sound theoretical principles. In reading the works of Kepler in the light of our modern knowledge we are often struck by the extent to which his perception of the sublimest truths in nature was associated with the most extravagant errors and absurdities. But, of course, it must be remembered that he wrote in an age in which even the rudiments of science, as we now understand it, were almost entirely unknown. It may well be doubted whether any joy experienced by mortals is more genuine than that which rewards the successful searcher after natural truths. Every science-worker, be his efforts ever so humble, will be able to sympathise with the enthusiastic delight of Kepler when at last, after years of toil, the glorious light broke forth, and that which he considered to be the greatest of his astonishing laws first dawned upon him. Kepler rightly judged that the number of days which a planet required to perform its voyage round the sun must be connected in some manner with the distance from the planet to the sun; that is to say, with the radius of the planet's orbit, inasmuch as we may for our present object regard the planet's orbit as circular. Here, again, in his search for the unknown law, Kepler had no accurate dynamical principles to guide his steps. Of course, we now know not only what the connection between the planet's distance and the planet's periodic time actually is, but we also know that it is a necessary consequence of the law of universal gravitation. Kepler, it is true, was not without certain surmises on the subject, but they were of the most fanciful description. His notions of the planets, accurate as they were in certain important respects, were mixed up with vague ideas as to the properties of metals and the geometrical relations of the regular solids. Above all, his reasoning was penetrated by the supposed astrological influences of the stars and their significant relation to human fate. Under the influence of such a farrago of notions, Kepler resolved to make all sorts of trials in his search for the connection between the distance of a planet from the sun and the time in which the revolution of that planet was accomplished. It was quite easily demonstrated that the greater the distance of the planet from the sun the longer was the time required for its journey. It might have been thought that the time would be directly proportional to the distance. It was, however, easy to show that this supposition did not agree with the fact. Finding that this simple relation would not do, Kepler undertook a vast series of calculations to find out the true method of expressing the connection. At last, after many vain attempts, he found, to his indescribable joy, that the square of the time in which a planet revolves around the sun was proportional to the cube of the average distance of the planet from that body. The extraordinary way in which Kepler's views on celestial matters were associated with the wildest speculations, is well illustrated in the work in which he propounded his splendid discovery just referred to. The announcement of the law connecting the distances of the planets from the sun with their periodic times, was then mixed up with a preposterous conception about the properties of the different planets. They were supposed to be associated with some profound music of the spheres inaudible to human ears, and performed only for the benefit of that being whose soul formed the animating spirit of the sun. Kepler was also the first astronomer who ever ventured to predict the occurrence of that remarkable phenomenon, the transit of a planet in front of the sun's disc. He published, in 1629, a notice to the curious in things celestial, in which he announced that both of the planets, Mercury and Venus, were to make a transit across the sun on specified days in the winter of 1631. The transit of Mercury was duly observed by Gassendi, and the transit of Venus also took place, though, as we now know, the circumstances were such that it was not possible for the phenomenon to be witnessed by any European astronomer. In addition to Kepler's discoveries already mentioned, with which his name will be for ever associated, his claim on the gratitude of astronomers chiefly depends on the publication of his famous Rudolphine tables. In this remarkable work means are provided for finding the places of the planets with far greater accuracy than had previously been attainable. Kepler, it must be always remembered, was not an astronomical observer. It was his function to deal with the observations made by Tycho, and, from close study and comparison of the results, to work out the movements of the heavenly bodies. It was, in fact, Tycho who provided as it were the raw material, while it was the genius of Kepler which wrought that material into a beautiful and serviceable form. For more than a century the Rudolphine tables were regarded as a standard astronomical work. In these days we are accustomed to find the movements of the heavenly bodies set forth with all desirable exactitude in the NAUTICAL ALMANACK, and the similar publication issued by foreign Governments. Let it be remembered that it was Kepler who first imparted the proper impulse in this direction. [PLATE: THE COMMEMORATION OF THE RUDOLPHINE TABLES.] When Kepler was twenty-six he married an heiress from Styria, who, though only twenty-three years old, had already had some experience in matrimony. Her first husband had died; and it was after her second husband had divorced her that she received the addresses of Kepler. It will not be surprising to hear that his domestic affairs do not appear to have been particularly happy, and his wife died in 1611. Two years later, undeterred by the want of success in his first venture, he sought a second partner, and he evidently determined not to make a mistake this time. Indeed, the methodical manner in which he made his choice of the lady to whom he should propose has been duly set forth by him and preserved for our edification. With some self-assurance he asserts that there were no fewer than eleven spinsters desirous of sharing his joys and sorrows. He has carefully estimated and recorded the merits and demerits of each of these would-be brides. The result of his deliberations was that he awarded himself to an orphan girl, destitute even of a portion. Success attended his choice, and his second marriage seems to have proved a much more suitable union than his first. He had five children by the first wife and seven by the second. The years of Kepler's middle life were sorely distracted by a trouble which, though not uncommon in those days, is one which we find it difficult to realise at the present time. His mother, Catherine Kepler, had attained undesirable notoriety by the suspicion that she was guilty of witchcraft. Years were spent in legal investigations, and it was only after unceasing exertions on the part of the astronomer for upwards of a twelvemonth that he was finally able to procure her acquittal and release from prison. It is interesting for us to note that at one time there was a proposal that Kepler should forsake his native country and adopt England as a home. It arose in this wise. The great man was distressed throughout the greater part of his life by pecuniary anxieties. Finding him in a strait of this description, the English ambassador in Venice, Sir Henry Wotton, in the year 1620, besought Kepler to come over to England, where he assured him that he would obtain a favourable reception, and where, he was able to add, Kepler's great scientific work was already highly esteemed. But his efforts were unavailing; Kepler would not leave his own country. He was then forty-nine years of age, and doubtless a home in a foreign land, where people spoke a strange tongue, had not sufficient attraction for him, even when accompanied with the substantial inducements which the ambassador was able to offer. Had Kepler accepted this invitation, he would, in transferring his home to England, have anticipated the similar change which took place in the career of another great astronomer two centuries later. It will be remembered that Herschel, in his younger days, did transfer himself to England, and thus gave to England the imperishable fame of association with his triumphs. The publication of the Rudolphine tables of the celestial movements entailed much expense. A considerable part of this was defrayed by the Government at Venice but the balance occasioned no little trouble and anxiety to Kepler. No doubt the authorities of those days were even less Willing to spend money on scientific matters than are the Governments of more recent times. For several years the imperial Treasury was importuned to relieve him from his anxieties. The effects of so much worry, and of the long journeys which were involved, at last broke down Kepler's health completely. As we have already mentioned, he had never been strong from infancy, and he finally succumbed to a fever in November, 1630, at the age of fifty-nine. He was interred at St. Peter's Church at Ratisbon. Though Kepler had not those personal characteristics which have made his great predecessor, Tycho Brahe, such a romantic figure, yet a picturesque element in Kepler's character is not wanting. It was, however, of an intellectual kind. His imagination, as well as his reasoning faculties, always worked together. He was incessantly prompted by the most extraordinary speculations. The great majority of them were in a high degree wild and chimerical, but every now and then one of his fancies struck right to the heart of nature, and an immortal truth was brought to light. I remember visiting the observatory of one of our greatest modern astronomers, and in a large desk he showed me a multitude of photographs which he had attempted but which had not been successful, and then he showed me the few and rare pictures which had succeeded, and by which important truths had been revealed. With a felicity of expression which I have often since thought of, he alluded to the contents of the desk as the "chips." They were useless, but they were necessary incidents in the truly successful work. So it is in all great and good work. Even the most skilful man of science pursues many a wrong scent. Time after time he goes off on some track that plays him false. The greater the man's genius and intellectual resource, the more numerous will be the ventures which he makes, and the great majority of those ventures are certain to be fruitless. They are in fact, the "chips." In Kepler's case the chips were numerous enough. They were of the most extraordinary variety and structure. But every now and then a sublime discovery was made of such a character as to make us regard even the most fantastic of Kepler's chips with the greatest veneration and respect.