KEPLER as laid down by Ptolemy and Cardan. He, moreover, sought in the events of his own life a verification of the theory of planetary influences; and it is to this practice that we owe the summary record of each year's occurrences which, continued almost to his death, affords for his biography a slight but sure foundation. He was convinced that for the actual disposition of the solar system some abstract intelligible reason must exist, and this, after much meditation, he believed himself to have found in relation between the "five regular solids" and the number and distances of the planets. His views, published in Prodromus Dissertationum Cos mographicarum seu Mysterium Cosmographicum (Tubingen, 1596) procured him much fame, and a friendly correspondence with the two most eminent astronomers of the time, Tycho Brahe and Galileo.
Kepler met at Gratz, Barbara von Miihleck, a wealthy heiress, and married her on April 27, 1597. Religious disturbances caused Kepler to leave Gratz, and to accept Tycho Brake's offer to be come assistant in his observatory near Prague. By Tycho's unex pected death (Oct. 24, i6oi) a brilliant career seemed to be thrown open to Kepler. The emperor Rudolph II. immediately appointed him to succeed his patron as imperial mathematician, although at a reduced salary of 500 florins; the invaluable treasure of Tycho's observations was placed at his disposal ; and the laborious but congenial task was entrusted to him of completing the tables to which Tycho had already affixed the title of Rudolphine. The first works executed by him at Prague were, nevertheless, a homage to the astrological proclivities of the emperor. In De fundamentis astrologiae certioribus (Prague, 1602) he declared his purpose of preserving and purifying the grain of truth which he believed the science to contain. He drew the horoscopes of the emperor and Wallenstein as well as of a host of lesser magnates ; he made neces sity his excuse for a compromise with superstition. "Nature," he wrote, "which has conferred upon every animal the means of subsistence, has given astrology as an adjunct and ally to astro nomy." He dedicated to the emperor in 1603 a treatise on the
"great conjunction" of that year (Judicium de trigono igneo); and he published his observations on a brilliant star which ap peared suddenly (Sept. 30, 1604), and remained visible for seven teen months, in De stella nova in pede Serpentarii (Prague, 1606).
The main task of his life was not meanwhile neglected. This was nothing less than the foundation of a new astronomy, in which physical cause should replace arbitrary hypothesis. A preliminary study of optics led to the publication, in 1604, of his Astronomiae pars optica, containing important discoveries in the theory of vision, and a notable approximation towards the true law of re fraction. From the time of his first introduction to Tycho he had devoted himself to the investigation of the orbit of Mars, which, on account of its relatively large eccentricity, had always been especially recalcitrant to theory, and the results appeared in As tronomia nova airuAcrynT6s, seu Physica coelestis tradita coin mentariis de motibus stellae Martis (Prague, 1609). In this, the most memorable of Kepler's multifarious writings, two of the cardinal principles of modern astronomy—the laws of elliptical or bits and of equal areas—were established (see ASTRONOMY : His tory) ; important truths relating to gravity were enunciated, and the tides ascribed to the influence of lunar attraction ; while an at tempt to explain the planetary revolutions in the then backward condition of mechanical knowledge produced a theory of vor tices closely resembling that afterwards adopted by Descartes. Having been provided in 1610 with one of the new Galilean instruments, Kepler began to observe the wonders revealed by it. In his Dioptrice (Augsburg, 161i), he expounded the theory of re fraction by lenses, and suggested the principle of the "astronomi cal" or inverting telescope. Indeed the work may be said to have founded the branch of science to which it gave its name.