purpose, and Kepler arose to lay the foundations of physical astronomy. John Kepler was born at Wiel, in Wirtemberg, in 1571. He was educated for the church, and discharged even some of the clerical functions; but his devotion to science withdrew him from the study of theology. Having received mathematical instruction from the celebrated Mæstlinus, he had made such progress in the science, that he was invited in 1594 to fill the mathematical chair of Gratz in Styria. Endowed with a fertile imagination, his mind was ever intent upon subtle and ingenious speculations. In the year 1596 he published his peculiar views in a work on the Harmonies and Analogies of Nature. In this singular production, he attempts to solve what he calls the great cosmographical mystery of the admirable proportion of the planetary orbits; and by means of the six regular geometrical solids, * he endeavours to assign a reason why there are six planets, and why the dimensions of their orbits and the time of their periodical revolutions were such as Copernicus had found them. If a cube, for example, were inserted in a sphere, of which Saturn's orbit was one of the great circles, it would, he supposed, touch by its six planes the lesser sphere of Jupiter; and, in like manner, he proposes to determine, by the aid of the other geometrical solids, the magnitude of the spheres of the other planets. A copy of this work was presented by its author to Tycho Brahe, who had been too long versed in the severe realities of observation to attach any value to such wild theories. He advised his young friend “ first 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;" and there is reason to think that, by the aid of the whole Baconian philosophy, thus compressed * The cube, the sphere, the tetrahedron, the octohedron, the dodecahedron, and the icosahedron. by anticipation into a single sentence, he abandoned for a while his visionary inquiries. In the year 1598 Kepler suffered persecution for his religious principles, and was compelled to quit Gratz; but though he was recalled by the States of Styria, he felt his situation insecure, and accepted of a pressing invitation from Tycho to settle at Prague, and assist him in his calculations. Having arrived in Bohemia in 1600, he was introduced by his friends to the Emperor Rodolph, from whom he ever afterward received the kindest attention. On the death of Tycho in 1601, he was appointed mathematician to the emperor,-a situation in which he was continued during the successive reigns of Matthias and Ferdinand; but what was of more importance to science, he was put in possession of the valuable collection of Tycho's observations. These observations were remarkably numerous; and as the orbit of Mars was more oval than that of any of the other planets, they were peculiarly suitable for determining its real form. The notions of harmony and symmetry in the construction of the solar system, which had filled the mind of Kepler, necessarily led him to believe that the planets revolved with a uniform motion in circular orbits. So firm, indeed, was this conviction, that he made numerous attempts to represent the observations of Tycho by this hypothesis. The deviations were too great to be ascribed to errors of observation; and in trying various other curves, he was led to the discovery that Mars revolved round the sun in an elliptical orbit, in one of the foci of which the sun itself was placed. The same observations enabled him to determine the dimensions of the planet's orbit, and by comparing together the times in which Mars passed over different portions of its orbit, he found that they were to one another as the areas described by the lines drawn from the centre of the planet to the centre of the sun, or, in more technical terms, that the radius vector describes equal areas in equal times. These two remarkable discoveries, the first that were ever made in physical astronomy, were extended to all the other planets of the system, and were communicated to the world in 1609, in his 6 Commentaries on the Motions of the Planet Mars, as deduced from the observations of Tycho Brahe.” Although our author was conducted to these great laws by the patient examination of well-established facts, his imagination was ever hurrying him among the wilds of conjecture. Convinced that the mean distances of the planets from the sun bore to one another some mysterious relation, he not only compared them with the regular geometrical solids, but also with the intervals of musical tones; an idea which the ancient Pythagoreans had suggested, and which had been adopted by Archimedes himself. All these comparisons were fruitless; and Kepler was about to abandon an inquiry of about seventeen years' duration, when, on the 8th March, 1618, he conceived the idea of comparing the powers of the different members which express the planetary distances, in place of the numbers themselves. He conipared the squares and the cubes of the distances with the same powers of the periodic times ; nay, he tried even the squares of the times with the cubes of the distances; but his hurry and impatience led him into an error of calculation, and he rejected this law as having no existence in nature ! On the 15th May, his mind again reverted to the same notion, and upon making the calculations anew, and free from error, he discovered the great law, that the squares of the periodic times of any two planets are to one another as the cubes of their distances from the sun. . Enchanted with this unexpected result, he could scarcely trust his calculations; and, to use his own language, he at first believed that he was dreaming, and had taken for granted the very truth of which he was in search. This brilliant discovery was pub lished in 1619, in his “Harmony of the World;" a work dedicated to James VI. of Scotland. Thus were established what have been called the three laws of Kepler,-the motion of the planets in elliptical orbits,—the proportionality between the areas described and their times of description,—and the relations between the squares of the periodic times and the cubes of the distances. The relation of the movements of the planets to the sun, as the general centre of all their orbits, could not fail to suggest to Kepler that some power resided in that luminary by which these various motions were produced ; and he went so far as to conjecture that this power diminishes as the square of the distance of the body on which it was exerted; but he immediately rejects this law, and prefers that of the simple distances. In his work on Mars, he speaks of gravity as a mutual and corporeal affection between similar bodies. He maintained that the tides were occasioned by the moon's attraction, and that the irregularities of the lunar motions, as detected by Tycho, were owing to the joint actions of the sun and the earth; but the relation between gravity, as exhibited on the earth's surface, and as conducting the planets in their orbits, required more patience of thought than he could command, and was accordingly left for the exercise of higher powers. * The misery in which Kepler lived forms a painful contrast with the services which he performed to science. The pension on which he subsisted was always in arrears, and though the three emperors whose reigns he adorned directed their ministers to be more punctual in its payment, the disobedience of their commands was a source of continued vexation to Kepler. When he retired to Sagan, in Silesia, to spend in retirement the remainder of his days, his pecuniary difficulties became still more harassing. Necessity at last compelled him to apply personally for the arrears which were due ; and he accordingly set out in 1630 for Ratisbon; but in consequence of the great fatigue which so long a journey on horseback produced, he was seized with à fever, which carried him off on the 30th November, 1630, in the 59th year of his age. While Kepler was thus laying the foundation of physical astronomy, Galileo was busily employed in extending the boundaries of the solar system. This distinguished philosopher was born at Pisa in 1564. He was the son of a Florentine nobleman, and was educated for the medical profession; but a passion for geometry took possession of his mind, and called forth all his powers. Without the aid of a master, he studied the writings of Euclid and of Archimedes; and such were his acquirements, that he was appointed by the Grand-duke of Tuscany to the mathematical chair of Pisa in the twenty-fifth year of his age. His opposition to the Aristotelian philosophy gained him many enemies, and at the end of three years he quitted Pisa, and accepted of an invitation to the professorship of mathematics at Padua. Here he continued for eighteen years adorning the university by his name, and diffusing around him a taste for the physical sciences. With the exception of some contrivances of inferior importance, Galileo had distinguished himself by no discovery till he had reached the forty-fifth year of his age. In the year 1609, the same year in which Kepler published his celebrated commentary on Mars, Galileo paid a visit to Venice, where he heard, in the course of conversation, that a Dutchman of the name of Jansens had constructed and presented to Prince Maurice an instrument through which he saw distant objects magnified and rendered more distinct, as if they had been brought nearer to the observer. This report was credited by some and disbelieved by others; but, in the course of a few days, Galileo received a letter from James Badovere at Paris, |