A German astronomer, born at Magstatt, near Weil, Wurtemberg, Dec. 27, 1571, died in Ratisbon, Nov. 15, 1630. He was a sickly child, and during his whole life suffered periodically from fevers and other ailments. His father, a man of noble origin and at one time a soldier in the Netherlands under the duke of Alva, having been reduced by the loss of his property to the condition of an innkeeper, young Kepler was during a portion of his childhood employed by him in a menial capacity. In 1586 he entered the monastic school of Maulbronn, whence he was transferred to the university of Tubingen, where in 1591 he took his degree of master. Subsequently he devoted himself to the study of astronomy under Mostlin, a disciple of Copernicus, and in 1594 was called to the professorship of mathematics in the university of Gratz in Styria. Here in the same year appeared his first publication, an almanac for 1595, followed in 1596 by his " Cosmographical Mystery," containing a fanciful theory regulating the order of the heavenly bodies.

In 1597 he married a young widow named Barbara Muller von Mulech, and soon after, in consequence of domestic dissensions, and of religious troubles which threatened the safety of the Protestant professors in Gratz, of whom he was one, he accepted Tycho Brahe's invitation to go to Prague and assist him in the preparation of a new set of astronomical tables. The work was done by order of the emperor Rudolph II., who intended to substitute tables having his own name for those calculated on the Ptolemaic and Copernican systems. Tycho shortly afterward died, and Kepler succeeded him as principal mathematician. He was thenceforth constantly involved in pecuniary difficulties, in consequence of the inability or neglect of the emperor to pay him the full amount of his salary. For this reason he was obliged to eke out a subsistence by casting nativities and writing popular almanacs. In his "Principles of Astrology" (1602) he describes the power of certain harmonious configurations of suitable planets to control human impulses. In his day such a belief was regarded as in accordance with just conceptions of the attributes of the planets, and Kepler's most profitable employment at this time was drawing the horoscopes of the princes.

In his optical treatise, "A Supplement to Vitellio," published in 1604 at Prague, although unable to discover the precise law of refraction, he was nevertheless singularly successful in his inquiries respecting vision, and in analyzing the structure of the eye. In this work he also described the mode of calculating eclipses which obtains at the present day. In his subsequent work on optics, entitled "Dioptrics" (Augsburg, 1611; reprinted in London, 1653), which, according to Sir David Brewster, "laid the foundation of the science," he explained the method of tracing the progress of rays through transparent bodies with convex and concave surfaces, and of determining the foci of lenses, and of the relative positions of the images which they form and the objects from which the rays proceed. Hence he was led to describe the astronomical telescope, having two convex lenses, by which objects are seen inverted. These discoveries, however, are obscured by the greatness of those announced in his " New Astronomy, or Commentaries on the Motions of Mars" (Prague, 1609), which were founded on the astronomical data prepared by Tycho. After many fruitless attempts to represent the orbit of Mars by combinations of uniform circular motion (that is, by epicyclic curves), he discovered, by comparing together seven oppositions of that planet, that its orbit is elliptical, whence he concluded that the orbit of each planet is an ellipse, with the sun placed in one of its foci.

Having next ascertained the dimensions of the orbit of Mars, he found that the radius vector, or line joining the planet and the sun, described equal areas in equal times, and that the same was true of the other planets. These results constitute the first two of the three great laws of planetary motion known as Kepler's laws, the third of which was discovered nine years later. The labor and patience with which Kepler conducted these investigations will be best appreciated when it is considered that the calculations were made without the assistance of logarithms, which were a later invention, and that each calculation of an opposition of Mars, filling 10 folio pages, was repeated 10 times, so that 7 oppositions produced a folio volume of 700 pages. In view of such difficulties, the remark of Prof. Play-fair is particularly pertinent, "that the discoveries of Kepler were secrets extorted from nature by the most profound and laborious research." Notwithstanding the reputation which these brilliant discoveries gained for him, his worldly circumstances showed no signs of improvement.

Not only did his arrears of salary remain unpaid, but the emperor Rudolph refused to allow him to accept the professorship of mathematics at Linz; and to add to his embarrassments, his wife died and his children were attacked by the smallpox, which proved fatal to the eldest. At this time also Prague was occupied by Austrian troops, and the plague devastated the city. Upon the accession of the emperor Matthias, in 1612, he was allowed to accept the professorship at Linz, and three years later he was married for the second time, chiefly for the sake of his children. It has been well remarked by Sir David Brewster, that the narrative of Kepler's search for a wife "is one of the most curious chapters in his history. No fewer than eleven ladies were presented to his choice," his patient scrutiny of their respective claims being comparable with his analysis and successive rejection of the epicyclic theories of Mars. In a jocular letter to Baron Strahlendorf he describes their various characters, and the negotiations preceding his marriage. During the preparations for the wedding, his wine-merchant having incorrectly measured the contents of the wine-casks, Kepler investigated the matter and produced his work on gauging; the first in which the modern analysis is employed.

About the same time he presented to the diet at Ratisbon his views on the reformation of the calendar, the substance of which he published in a short essay. In 1616 appeared his Ephemerides 1617-1620, the expense attending the preparation of which he confessed he had been obliged to defray "by composing a vile, prophesying almanac, which is scarcely more respectable than begging, unless from its saving the emperor's credit, who abandons me entirely, and would suffer me to perish from hunger." He nevertheless declined an invitation to fill the mathematical chair in Bologna, preferring poverty and the limited degree of freedom of speech and opinion he enjoyed in Germany, to the prospect of bettering his fortune in Italy. Between 1618 and 1622 appeared the seven books of his " Epitome of the Copernican Astronomy," which was placed by the inquisition on the list of prohibited books; and in 1619 he published his "Harmonies of the World," dedicated to James I. of England, which is memorable in the history of science as containing the third of his celebrated laws, viz.: that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun.

Such was the transport with which this discovery, which for 17 years had baffled all his skill and patience, filled him, that he marked the day and year. May 15, 1618, when it became known to him; and, speaking of the book which promulgated it, he said: "It may well wait a century for a reader, as God has waited 6,000 years for an observer." The accession in 1619 of the emperor Ferdinand II., who promised to pay the arrears of his salary, and to furnish the means of publishing the Rudolphine tables, seemed to open a more favorable era for the prosecution of Kepler's scientific labors; but such were the drains upon the imperial treasury caused by the religious wars which then began to convulse Germany, that it was not until several years afterward that he was enabled to collect even a part of the sums promised him. In 1620 he was strongly urged by Sir Henry Wotton, the English ambassador at Venice, to take up his residence in England, but declined the offer. Finally in 1627, after more than a quarter of a century's delay and amid difficulties of all kinds, the Rudolphine tables were published in Ulm. They were the first ever calculated on the theory of the ellip-ticity of the planetary orbits, and are so remarkable a monument of patience and industry, that had Kepler done nothing more than compute them, he would be regarded as one of the benefactors of science.

In 1629, for the sake of avoiding the religious dissensions which distracted Linz, at the invitation of Wallenstein, he removed with his family to Sagan in Silesia, and soon afterward secured a professorship in the university of Rostock. In the following year he went to Ratisbon, and made a final but fruitless effort to obtain from the imperial assembly his arrears, which now amounted to 8,000 crowns. The vexation which this occasioned, combined with.fatigue of mind and body, brought on a fever which proved fatal. His remains were interred in St. Peter's churchyard, Ratisbon, and in 1803 a monumental temple to his memory was erected on the spot by the prince bishop of Constance. The following epitaph, composed by himself, was engraved on his tombstone:

Mensus eram coelos. nunc temp metior umbras: Mens coelestis erat, corporis umbra jacet.

- The ardor and patience with which Kepler pursued science have found few parallels among modern philosophers. Ever prone to indulge in fanciful theories, he never lost sight of the precise object of his search, and ingenuously renounced any hypothesis that he could not reconcile with his advancing knowledge of phenomena. Of his manifold attempts in various branches of science Delambre says: "Those which have failed seem to us only fanciful, while those which have been more fortunate appear sublime." The history of science presents no discoveries more original, or which were deduced with so little assistance from the speculations of preceding philosophers, as his three celebrated laws, from which the discoveries of Newton subsequently sprung, thus completing the great chain of truths which constitute the laws of the planetary system. He computed correctly the transit of Mercury on Nov. 7, 1631 (observed by Gassendi), and announced a transit of Venus in the same year, which was not observed, as it occurred during the night. (Sir David Brewster is mistaken in asserting that "the transit did not take place.") The transit of Venus in 1639 Kepler failed to announce, but that of 1761 he predicted.

It is a sufficient evidence of his industry as an author that between 1594 and 1630 he published 33 works, besides leaving 22 volumes of manuscripts, 7 of which contain his epistolary correspondence. The latter was published in 1 vol. fol. in 1718, by Gottlieb Hansen; but the enterprise proving unsuccessful, he was obliged to part with the remaining volumes, which are now in the possession of the imperial library of sciences in St. Petersburg. A complete edition of the works of Kepler, including all his unedited manuscripts, was published at Frankfort (8 vols., 1858-70.)