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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 severe drain upon the resources of the country, the public funds became very low, and Kepler’s salary was always in arrear. This condition of things involved him in serious pecuniary difficulties, and the responsibility of having to maintain an increasing family added to his anxieties. It was with the greatest difficulty that he succeeded in obtaining payment of even a portion of his salary, and he was reduced to such straits as to be under the necessity of casting nativities in order to obtain money to meet his most pressing requirements.

      In 1609 Kepler published his great work, entitled ‘The New Astronomy; or, Commentaries on the Motions of Mars.’ It was by his observation of Mars, which has an orbit of greater eccentricity than that of any of the other planets, with the exception of Mercury, that he was enabled, after years of patient study, to announce in this volume the discovery of two of the three famous theorems known as Kepler’s Laws. The first is, that all the planets move round the Sun in elliptic orbits, and that the orb occupies one of the foci. The second is, that the radius-vector, or imaginary line joining the centre of the planet and the centre of the Sun, describes equal areas in equal times. The third law, which relates to the connection between the periodic times and the distances of the planets, was not discovered until ten years later, when Kepler, in 1619, issued another work, called the ‘Harmonies of the World,’ dedicated to James I. of England, in which was contained this remarkable law. These laws have elevated astronomy to the position of a true physical science, and also formed the starting-point of Newton’s investigations which led to the discovery of the law of gravitation. Kepler’s delight on the discovery of his third law was unbounded. He writes: ‘Nothing holds me. I will indulge in my sacred fury. I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God far away from the confines of Egypt. If you forgive me, I rejoice; if you are angry, I can bear it. The die is cast; the book is written, to be read either now or by posterity I care not which. It may well wait a century for a reader, as God has waited six thousand years for an observer.’

      When Kepler presented his celebrated book to the Emperor, he remarked that it was his intention to make a similar attack upon the other planets, and promised that he would be successful if his Majesty would undertake to find the means necessary for carrying on operations. But the Emperor had more formidable enemies to contend with nearer home than Jupiter and Saturn, and no funds were forthcoming to assist Kepler in his undertaking.

      The chair of mathematics in the University of Linz having become vacant, Kepler offered himself as a candidate for the appointment, which he was anxious to obtain; but the Emperor Rudolph was averse to his leaving Prague, and encouraged him to hope that the arrears of his salary would be paid. But past experience led Kepler to have no very sanguine expectations on this point; nor was it until after the death of Rudolph, in 1612, that he was relieved from his pecuniary embarrassments.

       On the accession of Rudolph’s brother, Matthias, to the Austrian throne, Kepler was reappointed Imperial Mathematician; he was also permitted to hold the professorship at Linz, to which he had been elected. Kepler was not loth to remove from Prague, where he had spent eleven years harassed by poverty and other domestic afflictions. Having settled with his family at Linz, Kepler issued another work, in 1618, entitled ‘Epitome of the Copernican Astronomy,’ in which he gave a general account of his astronomical observations and discoveries, and a summary of his opinions with regard to the theories which in those days were the subject of controversial discussion. Almost immediately after its publication it was included by the Congregation of the Index, at Rome, in the list of prohibited books. This occasioned Kepler considerable alarm, as he imagined it might interfere with the sale of his works, or give rise to difficulties in the issue of others. He, however, was assured by his friend Remus that the action of the Papal authorities need cause him no anxiety.

      The Emperor Matthias died in 1619, and was succeeded by Ferdinand III., who not only retained Kepler in his office, but gave orders that all the arrears of his salary should be paid, including those which accumulated during the reign of Rudolph; he also expressed a desire that the ‘Rudolphine Tables’ should be published without delay and at his cost. But other obstacles intervened, for at this time Germany was involved in a civil and religious war, which interfered with all peaceful vocations. Kepler’s library at Linz was sealed up by order of the Jesuits, and the city was for a time besieged by troops. This state of public affairs necessitated a considerable delay in the publication of the ‘Tables.’

      The ‘Rudolphine Tables’ were published at Ulm in 1627. They were commenced by Tycho Brahé, and completed by Kepler, who made his calculations from Tycho’s observations, and based them upon his own great discovery of the ellipticity of the orbits of the planets. They are divided into four parts. The first and third parts contain logarithmic and other tables for the purpose of facilitating astronomical calculations; in the second are tables of the Sun, Moon, and planets; and in the fourth are indicated the positions of one thousand stars as determined by Tycho. Kepler made a special journey to Prague in order to present the ‘Tables’ to the Emperor, and afterwards the Grand Duke of Tuscany sent him a gold chain as an acknowledgment of his appreciation of the completion of this great work.

      Albert Wallenstein, Duke of Friedland, an accomplished scholar and a man fond of scientific pursuits, made Kepler a most liberal offer if he would take up his residence in his dominions. After duly considering this proposal, Kepler decided to accept the Duke’s offer, provided it received the sanction of the Emperor. This was readily given, and Kepler, in 1629, removed with his family from Linz to Sagan, in Silesia. The Duke of Friedland treated him with great kindness and liberality, and through his influence he was appointed to a professorship in the University of Rostock. Though Kepler was permitted to retain the pension bestowed upon him by the late Emperor Rudolph, he was unable after his removal to Silesia to obtain payment of it, and there was a large accumulation of arrears. In a final endeavour to recover the amount owing to him he travelled to Ratisbon, and appealed to the Imperial Assembly, but without success. The fatigue which Kepler endured on his journey, combined with vexation and disappointment, brought on a fever, which terminated fatally. He died on November 15, 1630, when in the sixtieth year of his age, and was interred in St. Peter’s churchyard, Ratisbon.

      Kepler was a man of indomitable energy and perseverance, and spared neither time nor trouble in the accomplishment of any object which he took in hand. In thinking over the form of the orbits of the planets, he writes: ‘I brooded with the whole energy of my mind on this subject—asking why they are not other than they are—the number, the size, and the motions of the orbits.’ But many fanciful ideas passed through Kepler’s imaginative brain before he hit upon the true form of the planetary orbits. In his ‘Mysterium Cosmographicum’ he asserts that the five kinds of regular polyhedral solids, when described round one another, regulated the distances of the planets and size of the planetary orbits. In support of this theory he writes as follows: ‘The orbit of the Earth is the measure of the rest. About it circumscribe a dodecahedron. The sphere including this will be that of Mars. About Mars’ orbit describe a tetrahedron; the sphere containing this will be Jupiter’s orbit. Round Jupiter’s describe a cube; the sphere

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