Sec TYCHO.
Kepler was born at Niel, in the duchy of Wirtemberg, on the 27th December 1571. In the 18th year of his age he went to study philosophy at Tubinger, and was instructed in mathematics and astronomy by Michael Mxstlin, who first explained the secondary light of the moon. Misled by the ardour of his fancy, Kepler was perpetually seeking after harmonies and anologics in the system ; but during his stay with Tycho at Prague, this youthful propensity was in some measure corrected, and he was taught to check the flights of his imagination by the results ofpractical astronomy, and by the most rigid severity of investigation. At the death of Tycho, Kepler was put in possession of his valuable observa tions on the planets. Those which he had made upon the planet Mars were particularly numerous, and were the means of conducting his pupil to the most important discoveries in astronomy. Kepler attempted in vain to represent the motions of this planet on the hypothesis of a circular orbit, and by means of the numerous circles which Copernicus had employed to explain its inequali ties. After trying seTeral other curves, he at last found every difficulty removed by supposing that Mars revolv ed in an elliptical orbit, and that the sun was placed in one of its foci. He then determined the dimensions of his orbit, and by comparing together the times employ ed by the planet in completing a whole revolution, or any part of a revolution, he discovered that the times in which Mars described any arch of the elliptic, were always to one another as the areas contained by lines drawn from the focus to the extremities og the respective arches, or in other words, that the radius vector described equal areas in equal times. The same law was found to exist in the orbits of all the other planets, and in those of the satellites with regard to their primary ; and in the year 1626, Kepler published his Rodolphine Tables, comput ed on the true laws of the planetary motions. Induced by the mysterious analogies of the Pythagoreans, Kep ler endeavoured to explain the arrangements of the solar system by the laws or musical harmony. He imagined that the mean distances of the planets ought to vary in some regular progression ; and he sought for this ima ginary law, by comparing them with the regular geome trical solids, and with the intervals of tones. After seven teen years labour, he at last succeeded, by comparing the powers of the numbers which represented the periods and distances of the planets, and discovered that the squares of the periodic times of the planets were as the cubes of the major axes of their orbits ; a law which he found to prevail in the orbits both of the primary and secondary planets. These laws of Kepler, which he has explained at great length in his Astronomic Nova, celestis tradita CUM Commenta-riis de motibus stell,e Martis, banish ed from astronomy the epicycles of Ptolemy, laid the foundation of physical astronomy, and paved the way for the great discoveries of Newton. Had he proceeded in
the prosecution of these interesting discoveries, he might have extended the same laws to the motions of the co mets ; but he unfortunately imagined that these bodies were transient meteors, generated in xther ; and was thus prevented, by this erroneous opinion, from pursuing the brilliant career which he had begun. The prejudices of Kepler, respecting the harmony of the universe,'did not forsake him even towards the close of his life. Con sidering the mysterious analogies of Pythagoreans as es tablished principles, we find him, even in his latest works, deducing the earth's eccentricity, and the density and parallax of the sun, from these imaginary data. These philosophical delusions, the creatures of a lively fancy, have vanished in the progress of science, and astrono mers now look back to them as beacons to check the temerity of speculation, and to guide the theorist into that path of rigid investigation, which can alone conduct him to the establishment of general laws. The specula tions of Kepler, on the cause of the planetary motions, exhibit the same genius which we have already admired in his other discoveries. Ile considered gravity as a mutual and corporeal affection between similar bodies ; and he maintained that heavy bodies do not tend to the centre of the world, but to that of the round body to which they belonged ; and that if the earth were not spherical, heavy bodies would not fall towards its centre, but to M'erent points in the solid. He likewise sup posed.that the tides were produced by the attraction of the moon, and that the lunar inequalities were occasion ed by the united action of the earth and the sun. 'The pleasure which we feel in retracing the discoveries and the sagacious anticipations of this illustrious astronomer, is painfully alloyed by the recollection of the misery in which he lived. While magicians and conjurers were rewarded by the munificence of kings, Kepler could, with difficulty, obtain payment of the trifling-pension on which he was doomed to subsist; and it was in conse quence of his journey to Ratisbon to solicit his arrrears from the diet, that this great man, worn out with age and fatigue, terminated his valuable life. It is fortunate for science, that genius, like virtue, has its own reward. Had the progress of the human mind been entrusted to the generosity of princes, it might have yet been struggling with the ignorance and prejudices of its sa vage state.