formed the basis of the ‘Rudolphine Tables,’ and were of invaluable assistance to Kepler in his investigation of the laws relating to planetary motion.

Tycho Brahé declined to accept the Copernican theory, and devised a system of his own, which he called the ‘Tychonic.’ By this arrangement the Earth remained stationary, whilst all the planets revolved round the Sun, who in his turn completed a daily revolution round the Earth. All the phenomena associated with the motions of those bodies could be explained by means of this system; but it did not receive much support, and after the Copernican theory became better understood it was given up, and heard of no more.

We now arrive at the name of Kepler, one of the very greatest of astronomers, and a man of remarkable genius, who was the first to discover the real nature of the paths pursued by the Earth and planets in their revolution round the Sun. After seventeen years of close observation, he announced that those bodies travelled round the Sun in elliptical or oval orbits, and not in circular paths, as was believed by Copernicus. In his investigation of the laws which govern the motions of the planets he formulated those famous theorems known as ‘Kepler’s Laws,’ which will endure for all time as a proof of his sagacity and surpassing genius. Prior to the discovery of those laws the Sun, though acknowledged to be the centre of the system, did not appear to occupy a central position as regards the motions of the planets; but Kepler, by demonstrating that the planes of the orbits of all the planets, and the lines connecting their apsides, passed through the Sun, was enabled to assign the orb his true position with regard to those bodies.

John Kepler was born at Weil, in the Duchy of Wurtemberg, December 21, 1571. His parents, though of noble family, lived in reduced circumstances, owing to causes for which they were themselves chiefly responsible. In his youth Kepler suffered so much from ill-health that his education had to be neglected. In 1586 he was sent to a monastic school at Maulbronn, which had been established at the Reformation, and was under the patronage of the Duke of Wurtemberg. Afterwards he studied at the University of Tubingen, where he distinguished himself and took a degree. Kepler devoted his attention chiefly to science and mathematics, but paid no particular attention to the study of astronomy. Maestlin, the professor of mathematics, whose lectures he attended, upheld the Copernican theory, and Kepler, who adopted the views of his teacher, wrote an essay in favour of the diurnal rotation of the Earth, in which he supported the more recent astronomical doctrines. In 1594, a vacancy having occurred in the professorship of astronomy at Gratz consequent upon the death of George Stadt, Kepler was appointed his successor. He did not seek this office, as he felt no particular desire to take up the study of astronomy, but was recommended by his tutors as a man well fitted for the post. He was thus in a manner compelled to devote his time and talents to the science of astronomy. Kepler directed his attention to three subjects—viz. ‘the number, the size, and the motion of the orbits of the planets.’ He endeavoured to ascertain if any regular proportion existed between the sizes of the planetary orbits, or in the difference of their sizes, but in this he was unsuccessful. He then thought that, by imagining the existence of a planet between Mars and Jupiter, and another between Venus and Mercury, he might be able to attain his object; but he found that this assumption afforded him no assistance. Kepler then imagined that as there were five regular geometrical solids, and five planets, the distances of the latter were regulated by the size of the solids described round one another. The discovery afterwards of two additional planets testified to the absurdity of this speculation. A description of these extraordinary researches was published, in 1596, in a work entitled ‘Prodromus of Cosmographical Dissertations; containing the cosmographical mystery respecting the admirable proportion of the celestial orbits, and the genuine and real causes of the number, magnitude, and periods of the planets, demonstrated by the five regular geometrical solids.’ This volume, notwithstanding the fanciful speculations which it contained, was received with much favour by astronomers, and both Tycho Brahé and Galileo encouraged Kepler to continue his researches. Galileo admired his ingenuity, and Tycho advised him ‘to lay a solid foundation for his views by actual observation, and then, by ascending from these, to strive to reach the causes of things.’ Kepler spent many years in these fruitless endeavours before he made those grand discoveries in search of which he laboured so long.

The religious dissensions which at this time agitated Germany were accompanied in many places by much tumult and excitement. At Gratz the Catholics threatened to expel the Protestants from the city. Kepler, who was of the Reformed faith, having recognised the danger with which he was threatened, retired to Hungary with his wife, whom he had recently married, and remained there for near twelve months, during which time he occupied himself with writing several short treatises on subjects connected with astronomy. In 1599 he returned to Gratz and resumed his professorship.

In the year 1600 Kepler set out to pay Tycho Brahé a visit at Prague, in order that he might be able to avail himself of information contained in observations made by Tycho with regard to the eccentricities of the orbits of the planets. He was received by Tycho with much cordiality, and stayed with him for four months at his residence at Benach, Tycho in the meantime having promised that he would use his influence with the Emperor Rudolph to have him appointed as assistant in his observatory. On the termination of his visit Kepler returned to Gratz, and as there was a renewal of the religious trouble in the city, he resigned his professorship, from which he only derived a small income, and, relying on Tycho’s promise, he again journeyed to Prague, and arrived there in 1601. Kepler was presented to the Emperor by Tycho, and the post of Imperial Mathematician was conferred upon him, with a salary of 100 florins a year, upon condition that he should assist Tycho in his observatory. This appointment was of much value to Kepler, because it afforded him an opportunity of obtaining access to the numerous astronomical observations made by Tycho, which were of great assistance to him in the investigation of the subject which he had chosen—viz. the laws which govern the motions of the planets, and the form and size of the planetary orbits.

As an acknowledgment of the Emperor’s great kindness, the two astronomers resolved to compute a new set of astronomical tables, and in honour of his Majesty they were to be called the ‘Rudolphine Tables.’ This project pleased the Emperor, who promised to defray the expense of their publication. Logomontanus, Tycho’s chief assistant, had entrusted to him that portion of the work relating to observations on the stars, and Kepler had charge of the part which embraced the calculations belonging to the planets and their orbits. This important work had scarcely been begun when the departure of Logomontanus, who obtained an appointment in Denmark, and the death of Tycho Brahé in October 1601, necessitated its suspension for a time. Kepler was appointed Chief Mathematician to the Emperor in succession to Tycho—a position of honour and distinction, and to which was attached a handsome salary, that was paid out of the Imperial treasury. But owing to the continuance of expensive wars, which entailed a