On May 23, 1611, Matthias, brother of the emperor, assumed the Bohemian crown in Prague, compelling Rudolph to take refuge in the citadel, where he died early in 1612. Kepler's fidelity in re maining with him to the last did not deprive him of the favour of his successor. Payment of arrears was not, however, in the condi tion of the imperial finances, to be hoped for; and he was glad, while retaining his position as court astronomer, to accept (in 1612) the office of mathematician to the states of Upper Austria. In 1613 he appeared with the emperor Matthias before the diet of Ratisbon to advocate the introduction into Germany of the Gregorian calendar ; but the attempt was for the time frustrated by anti-papal prejudice. About this period he published several essays in which he sought to prove that the birth of Christ took place five years earlier than the commonly accepted date. His wife died in 1611, and in 1613 he married Susanna Reutlinger, a poor orphan girl.
The abundant vintage of 1613 drew his attention to the defec tive methods in use for estimating the cubical contents of vessels, and his essay on the subject (Nova Stereometria Doliorum, Linz, 1615) entitles him to rank among those who prepared the discov ery of the infinitesimal calculus. His observations on the three comets of 1618 were published in De Cometis, contemporaneously with De Harmonice Mundi (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 connection between the planetary periods and distances. But the main purport of the treatise was the exposition of a system of celestial harmonies de pending on the various and varying velocities of the several planets, of which the sentient soul animating the sun was the solitary audi tor. The work was dedicated to James I. who invited Kepler to England, but, notwithstanding the distracted state of his own coun try, he refused to abandon it.
The insurmountable difficulties presented by the lunar theory forced Kepler, after much fruitless labour, to abandon his design of comprehending the whole scheme of the heavens in one great work. The Epitome Astronomiae Copernicanae (Linz and Frank fort, 1618-1621), a lucid and attractive textbook of Copernican science, was remarkable for the prominence given to "physical astronomy," as well as for the extension to the Jovian system of the laws recently discovered 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, dedi cated to Napier of Merchiston (q.v.), he for the first time em ployed logarithms. This important invention was eagerly wel comed by him, and its theory formed the subject of a treatise en titled Chilias Logarithorum, 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 interrupted by family trouble. In 1620 his mother was arrested on a formal charge of witchcraft. Kepler immediately hastened to Wiirttemberg, and owing to his exertions she was acquitted after having suffered thirteen months' imprison ment, and endured with undaunted courage the formidable ordeal of "territion," or examination under the imminent threat of tor ture. She survived her release only a few months, dying in 1622.
Kepler's whole attention was now devoted to the production of the new tables. But financial difficulties, combined with civil and religious convulsions, caused delay. From June 24 to Aug. 29, Linz was besieged, and its inhabitants reduced to the utmost straits by bands of insurgent peasants. In 1626 he obtained permission to transfer his types to Ulm, where, in Sept. 1627, the Rudolphine 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 1,005. In July 1628 Kepler went with his family to 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 on Nov. 7, 1631 (being the first passage of a planet across the sun ever observed) ; that of Venus, predicted for Dec. 6, following, was invisible in western Europe. Kepler died at Ratisbon on Nov. 15 (N.S.), 1630.
Kepler's demonstration that the planes of all the planetary orbits pass through the centre of the sun, coupled with his clear recogni tion of the sun as the moving power of the system, entitles him to rank as the founder of physical astronomy. But the relations imagined by him of planetary movements and distances to musical intervals and geometrical constructions seemed to himself discov eries no less admirable than the achievements which have secured his lasting fame.
Kepler's extensive literary remains, purchased by the empress Catherine II. in 1724 from some Frankfort merchants, and long inaccessibly deposited in the observatory of Pulkowa, were fully brought to light, under the able editorship of Dr. Ch. Frisch, in the first complete edition of his works. This important publication (Joannis Kepleri opera omnia, Frankfort, 1858-1871, 8 vols. 8vo) contains, besides the works already enumerated and several minor treatises, a posthumous scientific satire entitled Joh. Keppleri Somnium (first printed in 1634) and a vast mass of his correspondence. A care ful biography is appended, founded mainly on his private notes and other authentic documents. His correspondence with Herwart von Hohenburg, unearthed by C. Anschiltz at Munich was printed at Prague in 1886.