of March 1618; but, having made an erroneous calculation, he was obliged to reject it. He resumed the subject on the 15th of May; and having discovered his former error, recognised with transport the absolute truth of a principle which for seventeen years had been the object of his incessant labours. The delight which this grand discovery gave. him had no bounds. "Nothing holds me," says he; "I will indulge in my sacred fury; I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God, far away from the confines of Egypt. If you forgive me, I rejoice; if you are angry, I can bear it. The die is cast, the book is written, to be read either now or by posterity, I care not which. It may well wait a century for a reader, as God has waited six thousand years for an observer."(P. 240.)

The Rudolphine Tables,' in the preparation of which Kepler had been engaged for twenty-six years, after having been long delayed for want of funds to defray the expenses of the printing, and subsequently from the disturbed state of Germany during the wars of the Reformation, were at length published in 1628. This work is remarkable in the history of Astronomy, as containing the first tables which were calculated on the hypothesis of elliptic orbits, and as exhibiting the science under the form in which it appears in our modern treatises. The labour which Kepler bestowed on its preparation was enormous; and it is curious to observe, that it was increased by the discovery of the logarithms; in consequence of which, he was under the necessity of giving a different form to several of the tables, in order to adapt them to the new method of calculation.

Kepler had continued to reside at Linz since 1622; but, about the time of the appearance of the Rudolphine Tables,' he was invited by the Duke of Friedland, a great patron of Astrology, to take up his abode at Sagan, in Silesia. Having solicited permission from the Emperor to accept of this invitation, the Em'peror did not hesitate to grant the request, and would gladly have transferred Kepler's arrears as well as himself to the ser'vice of a foreign prince.' Kepler accordingly removed his family to Sagan in 1629, and was favourably received by the Grand Duke, who treated him with distinction and liberality, and procured for him a Professorship in the university of Rostock. But it would seem as if no change had the power of producing any amelioration of Kepler's fortunes:

"In this remote situation, Kepler found it extremely difficult to obtain payment of the imperial pension, which he still retained. The arrears had accumulated to 8000 crowns; and he resolved to go to the imperial assembly at Ratisbon to make a final effort to obtain them. His attempts, however, were fruitless. The vexation which this occasioned, and the great fatigue which he had undergone, threw him into a

VOL. LXXX. NO. CLXI.

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violent fever, which is said to have been one of cold, and to have been accompanied with an imposthume in the brain, occasioned by two much study. This disease baffled the skill of his physicians, and carried him off on the 5th of November, O. S., 1630, in the sixtieth [fifty-ninth] year of his age.'-(P. 249.)

6

Kepler's name will always be associated with the discovery of the Three Laws which regulate the planetary motions; by which he effected a greater revolution in theoretical Astronomy than ever had fallen, or can fall again, to the lot of any individual. But he has many other claims upon our consideration. The Rudolphine Tables' were a most important contribution to practical Astronomy, and would alone have sufficed to place him in the first rank among the promoters of that science; and various methods of observation and computation suggested by him are still in use. His physical speculations, though frequently fanciful, and sometimes extravagant, always give evidence of enlarged views and great acuteness; and he nearly anticipated two of Newton's most important discoveries-the law of gravitation, and the theory of the prismatic colours. In mathematics his knowledge was neither systematie nor very profound; and the circumstance was unfortunate for himself, for greater proficiency in this science would have saved him an immensity of unnecessary calculations. Nevertheless, even here he has left the impress of his genius. His method of solving the problem which goes by his name, is perhaps as well adapted for practical purposes as any of the numerous solutions which have since been given; and his treatise on Gauging contains principles near akin to those on which the infinitesimal calculus was afterwards built. sooner had he heard of the invention of the Logarithms than he perceived its immense importance in Astronomy; and immediately set about improving the theory, and computing and publishing new tables.

No

Kepler's works are composed in a very singular style; for he not only gives the process of reasoning through which he arrived at the conclusions ultimately adopted, but also a detailed account of all his previous trials and failures. This frankness has perhaps been injurious to his reputation, and occasioned his being represented as working in some measure in the dark, and arriving at important results by accident. Thus, in a recent biography, we meet with such remarks as the following :— It is impossible ' not to admire Kepler's singular good fortune in arriving at this correct result, in spite, or rather through the means, of his erroneous principles;'-' if he had exerted his ingenuity in this direction, he might have wasted his life in useless labour;'— if the orbit of Mars had been less oval, he would not have de

'tected the true orbit by the method he followed;'-it is extraordinary that a supposition made for such a reason should have 'the luck to be the right one; if the laws of the planetary 'orbits had chanced to have been any other than those which 'cause them to describe ellipses, this last singular confirma'tion of an erroneous theory would not have taken place." Whether Kepler would have discovered the laws of the planetary motions had they been different from what they are, is a question of extremely little importance. It is sufficient for his glory, and was sufficient for the wants of Astronomy, that he discovered the actually existing laws; and although the liveliness of his imagination-some prepossessions in favour of occult qualities and mystical properties, together with a want of method and system in his investigations-led him to give expression to many conjectures which would never have occurred to a mind otherwise constituted, or at least would have been suppressed when found to be erroneous-his laws of the planets were discovered, according to our apprehension, in the only way by which such discoveries could be made; namely, by deducing them (after his own fashion, indeed) from the observations which were at his command, and proving, by laborious calculations, that they accurately represented those observations. Sir David Brewster has placed this matter in its proper light :--

What

Kepler,' he observes, has fortunately left behind him a full account of the methods by which he arrived at his great discoveries. other philosophers have studiously concealed, Kepler has openly avowed and minutely detailed; and we have no hesitation in considering these details as the most valuable present that has ever been given to science, and as deserving the careful study of all who seek to emulate his immortal achievements. It has been asserted that Newton made his discoveries by following a different method; but this is a mere assumption, as Newton has never favoured the world with any account of the erroneous speculations, and the frequent failures, which must have preceded his ultimate success. Had Kepler done the same, by recording only the final steps of his enquiries, his method of investigation would have obtained the highest celebrity, and would have been held up to future ages as a pattern for their imitation. But such was the candour of his mind, and such his inordinate love of truth, that he not only recorded his wildest fancies, but emblazoned even his greatest errors. If Newton had indulged us with the same insight into his physical enquiries, we should have witnessed the same processes which were employed by Kepler, modified only by the different characters and intensities of their imaginative powers.'—(P. 264.)

The personal character of Kepler has been very fully developed by himself, in his various works and epistolary correspon

dence; and the incidents of his life, collected chiefly from the same sources, have been succinetly narrated in the Memoirs prefixed to the Collection of Letters published by Hansch. History presents to our consideration few more remarkable characters. His struggles with the world excite our sympathy; his ardour and enthusiasm our admiration. It is, no doubt, an afflicting consideration, that a man whose genius and indomitable energy have done so much for the advancement of human knowledge, should have encountered so unpropitious a fate; yet if we dispassionately consider the circumstances, we may see reason to doubt whether science was in any respect the cause of his misfortunes. If his salary was irregularly paid, the irregularity was owing to political causes, and the unfavourable circumstances of the times. Religious controversies, domestic misfortunes, war, and the plague, are calamities to which the learned and the illiterate are subject indiscriminately. No doubt all his misfortunes were aggravated by the narrowness of his circumstances; but it is by no means certain that his circumstances would have been more prosperous had he followed any other pursuit, though it is probable that in that case the world would never have heard of them. His condition, hard as it was, was not without its shades of light. His lofty title of Imperial Mathematician gave him official consequence among those with whom he lived; and to an enthusiast like Kepler, the consciousness that his discoveries would occupy a prominent place in the future history of science, was a compensation for many evils. Of the importance he attached to his successful labours, he gives us a proof in his declaration, that he would not exchange his discovery of the analogy of the planetary orbits with the five regular solids for the whole Electorate of Saxony. We see no just ground for imputing a disregard of science to Rudolph and his successors, who certainly were in no condition to appreciate Kepler's merits, and whose favour was conferred on him in his character of Astrologer. It is, indeed, remarkable how little Kepler's merits were understood in his own age. Galileo had no conception of the importance of his discoveries: they were little considered by Gassendi-they were undervalued by Riccioli-they were never mentioned by • Descartes. It was an honour reserved for Newton to estimate ' them at their true value.' Such are the words of the late Professor Playfair; yet it is satisfactory to observe, that even before the time of Newtor their merit was perceived and acknowledged by one Astronomer at least in our own country. Horrox describes them as not only valuable, but as more valuable than those of all other Astronomers put together Pergo igitur ad As

tronomiæ principem, J. Keplerum; cujus unius viri inventis, non est harum artium peritus qui neget plus debere astronomiam 'quam ceteris in universum.'

The misfortunes of Galileo, Tycho, and Kepler, arose from peculiar and accidental circumstances; and the sovereigns under whom they lived deserve the praise of having been munificent patrons of science. The following incident in the life of Kepler, gives Sir David Brewster an opportunity of glancing at the encouragement held out to scientific pursuits in our own country. Kepler, it seems, upon one occasion received a visit from Sir Henry Wotton, Ambassador from England to the States of Ve nice, and was invited by him to take up his residence in England. Sir David thinks it probable that the invitation proceeded from the Sovereign, who made Kepler a distinct offer through his Ambassador; and upon this supposition he thus expresses himself: If the imperial mathematician had no other assurance of a comfortable home in England than that of Sir Henry Wotton, he acted a wise part in distrusting it; and we rejoice 'that the sacred name of Kepler was thus withheld from the long list of distinguished characters whom England has starved and dishonoured.'-(P. 343.) w

It would far exceed the limits we have now left, and it is not by any means within the scope of our intention, to enter upon a discussion of the question pointed at in this startling allegation. In the long list of distinguished characters whose names have shed a lustre on British science during the last two or three centuries, there are, indeed, many whose success in the world has fallen far short of their merits; but to represent them as having been dishonoured in not being the recipients of pecuniary supplies from the public treasury, is to make use of a strong, if not a perverse figure of speech. Science in England, has not, it is true, been fostered by state provisions: yet if we look to results, our system (if it may be so called) cannot be pronounced to have been unsuccessful; for on reference to the history of the great and fundamental discoveries by which the various sciences have been advanced to their present state, it will not assuredly be found that England has any reason to blush for her share of them. That science has derived some important benefits from the pensioned Academies which have been instituted and maintained by some of the Continental governments, is a proposition which it would be idle to dispute: but such establishments are little in harmony with our political institutions; and in proportion as wealth and intelligence are more generally diffused, they become more and more unnecessary. A British Institute, maintained at the public