KEPLER AND GALILEO.
Kepler followed Tycho, and in his hands astronomy underwent a change only second to that 'which it had undergone in the hands of Copernicus. He was born in• 1571. He early applied himself to study and observe the heavens, and was soon distinguished as an inventor. He -,began with taking a more accurate view of astronomical refraction than had been done, and he appears to have been the first who conceived that there mist be a certain fixed law which determined the quantity of it, corresponding to every alti tude,. from the horizon to the zenith.. The application of the principles of optics to as.. tronomy, and the accurate distinction betWeen the optical and real inequalities of the planets, are the work of the same astronomer. It was by the views thus presented that he was led to the method of constructing and calculating eclipses, by means of projec tions, without taking into consideration the diurnal parallax. These are valuable im provements, but they +were, however, obscured by the greatness of his future discove ries.
The planes of the orbits of the planets were naturally, in the Ptolemaic system, sup. posed to pass through the earth, and the reformation of Copernicus did not go so far as to change the notions on that subject which had generally been adopted. Kepler ob served that the orbits of the planets are in planes passing through the sun, and that, of consequence, the lines of their nodes all intersect in the centre of that luminary. This discovery contributed essentially to those which followed.
The oppositions of the planets, or their places when they pass the meridian at mid night, offer the most favourable opportunities for observing them, both because they are at that time nearest to the earth, and because their places seen from thence is the same as if they were seen from the sun. The true time of the opposition had, however, been till now mistaken by astronomers, who held it to be at the moment when the appa rent place of the planet was opposite to the mean place of the sun. It ought, however, 10 to have been, when the apparent places of both were opposed to one another. This re formation was proposed by Kepler, and, though strenuously resisted by Tycho, was finally received.
Having undertaken to examine the orbit of Mars, in which the irregularities are most considerable, Kepler discovered, by comparing together seven oppositions of that planet, that its orbit is elliptical ; that the sun is placed in one of the foci ; and that there is no point round which the angular motion is uniform. In the pursuit of this inquiry he found that the same thing is true of the earth's orbit round the sun ; hence by analogy it was reasonable to think, that all the planetary orbits are elliptical, having the sun in their common focus.
The industry and patience of Kepler, in this investigation, were not less remarkable than his ingenuity and invention. Logarithms were not yet known, so that arithmeti cal computation, when pushed to great accuracy, was carried on at a vast expence of time and labour. In the calculation of every opposition of Mars, the work filled ten folio pages, and Kepler repeated each calculation ten times, so that the whole work for each opposition extended to one hundred such pages ; seven oppositions thus calculated pro duced a large folio volume.
Though the angular motion of the planet was not found to be uniform, it was discover ed that a very simple law connected. that motion with the rectilineal distance from the sun, the inner being every where inversely as the square of the latter ; and hence it was easy to prove, that the area described by the line drawn from the planet to the sun increased at a uniform rate, and, therefore, that any two such areas were proportional to the times in which they were described. The picture presented of the heavens was thus, for the first time, cleared of every thing hypothetical.