less remarkable is the singular good fortune by which, while groping in the dark, among erroneous principles and erroneous assumptions, he was led, by careful observation of Mars, to discover the true form of its orbit, and the true law of its motion, and the motion of all planets, round the sun. These are enunciated in two of the three celebrated theorems known by the name of Kepler's Laws, beyond comparison the most important discoveries made in astronomy from the time of Copernicus to that of Newton, of which the first is, that the planets move in ellipses, in one of the foci of which the sun is placed: the second, that the time of describing any arc is proportional, in the same orbit, to the area comprised by the arc itself, and lines drawn from the sun to the beginning and end of it.

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About the year 1613, Kepler quitted Prague, after a residence of eleven years, to assume a professorship in the University of Linz. The year preceding his departure saw him involved in great domestic distress. Want of money, sickness, the occupation of the city by a turbulent army, the death of his wife and of the son whom he best loved; these, he says to a correspondent, were reasons enough why I should have overlooked not only your letter, but even astronomy itself." His first marriage, contracted early in life, had not been a happy one: but he resolved on a second venture, and no less than eleven ladies were successively the objects of his thoughts. After rejecting, or being rejected, by the whole number, he at last settled on her who stood fifth in the list; a woman of humble station, but, according to his own account, possessed of qualities likely to wear well in a poor man's house. He employed the judgment and the mediation of his friends largely in this delicate matter: and in a letter to the Baron Strahlendorf, he has given a full and amusing account of the process of his courtships, and the qualifications of the ladies among whom

his judgment wavered. He proposed to one lady whom he had not seen for six years, and was rejected: on paying her a visit soon after, he found, to his great relief, that she had not a single pleasing point about her. Another was too proud of her birth; another too old; another married a more ardent lover, while Kepler was speculating whether he would take her or not; and a fifth punished the indecision which he had shown towards others by alternations of consent and denial, until after a three months' courtship, the longest in the list, he gave her up in despair.

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Kepler did not long hold his professorship at Linz. Some religious opinions relative to the doctrine of transubstantiation gave offence to the Roman Catholic party, and he was excommunicated. In 1617 he received an invitation to fill the chair of mathematics at Bologna: this however he declined, pleading his German origin and predilections, and his German habits of freedom in speech and manners, which he thought likely to expose him to persecution or reproach in Italy. In 1618 he published his Epitome of the Copernican system, a summary of his philosophical opinions, drawn up in the form of question and answer. 1619 appeared his celebrated work 'Harmonice Mundi,' dedicated to King James I. of England; a book strongly illustrative of the peculiarities of Kepler's mind, combining the accuracy of geometric science with the wildest metaphysical doctrines, and visionary theories of celestial influences. The two first books are almost strictly geometrical; the third treats of music; for the fourth and fifth, we take refuge from explaining their subjects in transcribing the author's exposition of their contents. "The fourth, metaphysical, psychological, and astrological, on the mental essence of harmonies, and of their kinds in the world, especially on the harmony of rays emanating on the earth from the heavenly bodies, and on their effect

in nature, and on the sublunary and human soul; the fifth, astronomical and metaphysical, on the very exquisite harmonies of the celestial motions, and the origin of the eccentricities in harmonious proportions." This work, however, is remarkable for containing amid the varied extravagancies of its two last books, the third of Kepler's Laws, namely, that the squares of the periods of the planets' revolution vary as the cubes of their distances from the sun; a discovery in which he exulted with no measured joy. "It is now

eighteen months since I got the first glimpse of light, three months since the dawn, very few days since the unveiled sun, most admirable to gaze upon, burst out upon me. 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."

The substance of Kepler's astrological opinions is contained in this work. It is remarkable that one whose candour and good faith are so conspicuous, one so intent on correcting his various theories by observation and experience, should have given in to this now generally rejected system of imposture and credulity; nay, should profess to have been forced to adopt it from direct and positive observations. most unfailing experience (as far as can be hoped in natural phenomena), of the excitement of sublunary nature by the conjunctions and aspects of the planets, has instructed and compelled my unwilling belief." At the same time he professed through life a supreme contempt for the common herd of nativity casters, and

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claimed to be the creator of a "new and most true philosophy, a tender plant which, like all other novelties, ought to be carefully nursed and cherished." His plant was rooted in the sand, and it has perished; nor is it important to explain the fine-spun differences by which his own astrological belief was separated from another not more baseless. Poor through life, he relieved his ever recurring wants by astrological calculations; and he enjoyed considerable reputation in this line, and received ample remuneration for his predictions. It was principally as astrologers that both Tycho Brahe and Kepler were valued by the Emperor Rudolph; and it was in the same capacity that the latter was afterwards entertained by Wallenstein. One circumstance may suggest a doubt whether his predictions were always scrupulously honest. From the year 1617 to 1620, he published an annual Ephemeris, concerning which he writes thus: "In order to pay the expense of the Ephemeris for these two years, I have also written a vile prophesying almanac, which is hardly more respectable than begging; unless it be because it saves the Emperor's credit, who abandons me entirely, and, with all his frequent and recent orders in council, would suffer me to perish with hunger." Poverty is a hard task-master; yet Kepler should not have condescended to become the Francis Moore of his day.

In 1620, Kepler was strongly urged by Sir Henry Wotton, then ambassador to Venice, to take refuge in England from the difficulties which beset him. This invitation was not open to the objections which had deterred him from accepting an appointment in Italy: but love of his native land prevailed to make him decline it also. He continued to weary the Imperial Government with solicitations for money to defray the expense of the Rudolphine Tables, which were not printed until 1627. These were the first calculated

on the supposition of elliptic orbits, and contain, besides tables of the sun and planets, logarithmic and other tables to facilitate calculation, the places of one thousand stars as determined by Tycho, and a table of refractions. Similar tables of the planetary motions had been constructed by Ptolemy, and reproduced with alterations in the thirteenth century under the direction of Alphonso, King of Castile. Others, called the Prussian Tables, had been calculated after the discoveries of Copernicus, by two of that great astronomer's pupils. All these, however, were superseded in consequence of the observations of Tycho Brahe, observations far more accurate than had ever before been made; and for the publication of the Rudolphine Tables alone, which for a long time continued unsurpassed in exactness, the name of Kepler would deserve honourable remembrance.

Kepler was the first of the Germans to appreciate and use Napier's invention of logarithms; and he himself calculated and published a series, under the title of Chilias Logarithmorum,' in 1624. Not long after the Rudolphine Tables were printed, he received permission from the Emperor Ferdinand to attach himself to the celebrated Wallenstein, a firm believer in the science of divination by the stars. In him Kepler found a more munificent patron than he had yet enjoyed; and by his influence he was appointed to a professorship at the University of Rostock, in the Duchy of Mecklenburg. But the niggardliness of the Imperial Court, which kept him starving through life, was in some sense the cause of his death. He had claims on it to the amount of eight thousand crowns, which he took a journey to Ratisbon to enforce, but without success. Fatigue or disappointment brought on a fever which put an end to his life in November, 1630, in his 59th year. A plain stone, with a simple inscription, marked his grave in St.