KEPLER 47 in which he reviews the qualifications of eleven candidates for his hand, and explains the reasons which decided his choice in favour of a portionless orphan girl named Susanna Reutlinger. The marriage was celebrated at Linz, October 30, 1613, and seems to have proved a happy and suitable one. The abundant vintage of that year drew his attention to the defective methods in use for estimating the cubical contents of vessels, and his essay on the subject (Nova Stereometria Doliorum, Linz, 1613) entitles him to rank among those who prepared the discovery of the infinitesimal calculus. His observations on the three comets of 1618 were published in De Cometis, contemporaneously with the Harmonica Jfuncli (Augsburg, 1619), of which the first lineaments had been traced twenty years previously at Gratz. This extraordinary production is memorable as having announced the discovery of the " third law " that of the sesquiplicate ratio between the planetary periods and distances. But the main purport of the treatise was the exposition of an elaborate system of celestial harmonies depending on the various and varying velocities of the several planets, of which the sentient soul animating the sun was the solitary auditor, The work exhibiting this fantastic emulation of extravagance with genius was dedi cated to James I. of England, and the compliment was acknowledged with an invitation to that island, conveyed through Sir Henry "Wotton. Notwithstanding the dis tracted state of his own country, however, he refused to abandon it, as he had previously, in 1617, declined the post of successor to Magini in the mathematical chair of Bologna. The insurmountable difficulties presented by the lunar theory forced Kepler, after an enormous amount of fruitless labour, to abandon his design of comprehending the whole scheme of the heavens in one great work to be called Ilipparchus, and he then threw a portion of his materials into the form of a dialogue intended for the instruction of general readers. The Epitome Astronomies Copernicanx (Linz and Frankfort, 1618-21), a lucid and attractive text book of Copernican science, was remarkable for the pro minence given to " physical astronomy," as well as for the extension to the Jovian system of the laws recently dis covered to regulate the motions of the planets. The first of a series of ephemerides, calculated on these principles, was published by him at Linz in 1617 ; and in that for 1620, dedicated to Napier, he for the first time employed logarithms. This important invention was eagerly wel comed by him, and its theory formed the subject of a treatise entitled Chilias Logarithmorum, printed in 1624, but circulated in manuscript three years earlier, which largely contributed to bring the new method into general use in Germany. His studies, were, however, interrupted by a painful family trouble. The restless disposition and unbridled tongue of Catherine Kepler his mother created for her numerous enemies in the little town of Leonberg; while her unguarded conduct exposed her to a species of calumny at that time but too readily circulated and believed. As early as 1615 suspicions of sorcery began to be spread against her, which she, with more spirit than prudence, met with an action for libel. The suit was, by the con nivance of the judicial authorities, purposely protracted, and at length, August 5, 1620, the unhappy woman, then in her seventy -fourth year, was arrested on a formal charge of witchcraft. Kepler immediately hastened to Wurtem- berg, and devoted a whole year to the zealous advocacy of her cause. It was owing to his indefatigable exertions that, contrary to general expectation, she was acquitted after having suffered thirteen months imprisonment, and endured with undaunted courage the formidable ordeal of " territion," or examination under the imminent threat of torture. She survived her release only a few months, dying April 13, 1622. Kepler s whole attention was now devoted to the produc tion of the new tables. " Germany," he wrote, " does not long for peace more anxiously than I do for their publica tion." Financial difficulties, however, combined with civil and religious convulsions, long delayed the accomplishment of his desires. From June 24 to August 29, 1626, Linz was besieged, and its inhabitants reduced to the utmost straits by bands of insurgent peasants. The pursuit of science needed a more tranquil shelter ; and accordingly, on the raising of the blockade, Kepler obtained permission to transfer his types to Ulm, where, in September 1627, the RiidolpMne Tables were at length given to the world. Although by no means free from errors, their value appears from the fact that they ranked for a century as the best aid to astronomy. Appended were tables of logarithms and of refraction, together with Tycho s catalogue of 777 stars, enlarged by Kepler to 1005. The work of Kepler s life was now virtually completed, but not so its vicissitudes. His claims upon the insolvent imperial exchequer amounted by this time to 12,000 florins. The emperor Ferdinand IT., too happy to transfer the burden, countenanced an arrangement by which Kepler entered the service of the duke of Friedland (Wallenstein), who assumed the full responsibility of the debt. Tn July 1628 Kepler accordingly arrived with his family at Sagan in Silesia, where he applied himself to the printing of his ephemerides up to the year 1636, and whence he issued, in 1629, a Notice to the Curious in Things Celestial, warning astronomers of approaching transits. That of Mercury was actually seen by Gassendi in Paris, November 7, 1631 (being the first passage of a planet across the sun ever ob served) ; that of Venus, predicted for the 6th of December following, was invisible in western Europe. Wallen stein s promises to Kepler were but imperfectly fulfilled. In lieu of the sums due, he offered him a professorship at Rostock, which Kepler declined, being unwilling to com promise his claim. An expedition to Ratisbou, undertaken for the purpose of representing his case to the Diet, termi nated his life. Shaken by the journey, which he had per formed entirely on horseback, he was attacked with fever, and died at Ratisbon, November 15 (N. S.), 1630, in the fifty-ninth year of his age. An inventory of his effects found among his papers showed him to have been possessed of no inconsiderable property at the time of his death. It is true that he had often been severely straitened ; but there is reason to believe that his complaints on the subject were to some extent exaggerated. By his first wife he had five, and by his second seven children, of whom only two, a son and a daughter, reached maturity. The character of Kepler s genius was one of which it is especially difficult to arrive at a just estimate. His irresistible tendency towards mystical speculation formed a not less fundamental quality of his mind than its strong grasp of positive scientific truth. Without assigning to each element its due value, no sound compre hension of his modes of thought can be attained. His idea of the universe was essentially Pythagorean and Platonic. He started with the conviction that the arrangement of its parts must correspond with certain abstract conceptions of the beautiful and harmonious. His imagination, thus kindled, animated him to those severe labours of which his great discoveries were the fruit. His demonstra tion that the planes of all the planetary orbits pass through the centre of the sun, coupled with his clear recognition of the sun as the moving power of the system, entitles him to rank as the founder of physical astronomy. But the fantastic relations imagined by him of planetary movements and distances to musical intervals and geometrical constructions seemed to himself discoveries no less admirable than the achievements which have secured his lasting fame. Outside the boundaries of the solar system, the metaphysical side of his genius, no longer held in check by experience, fully asserted itself. The Keplerian like the Pythagorean cosmos was threefold, consisting of the centre, or sun, the surface, being the sphere of the fixed stars, and the intermediate space, filled with
