1st. That the planets move in ellipses, of which the sun is in one of the foci. 2nd. The spaces described by the ideal radius which joins each planet to the sun are proportional to the times of their description. In other words, the nearer a planet is to the sun, the faster it moves. 3rd. The squares of the times of revolution are as the cubes of the major axes of the orbits. Such were the laws of Kepler, the basis of modern astronomy, which led in the hands of Newton to the simple explanation by universal gravitation, which itself is now asking to be explained. We are not to suppose that the system of Copernicus was universally accepted even by astronomers of note. By some an attempt was made to invent a system which should have all the advantages of this, and yet if possible save the immobility of the earth. Such was that of Tycho Brahe, who was born three years after the death of Copernicus, and died in 1601. He was one of the most laborious and painstaking observers of his time, although by the peculiarity of fate he is known generally only by his false system. [Illustration: FIG. 21.--TYCHO BRAHE'S SYSTEM.] In 1577, Tycho Brahe wrote a little treatise, _Tychonis Brahe, Dani, De Mundi AEtherei Recentioribus phenomenis, a propos_ of a comet that had lately appeared. He speaks at length of his system as follows:--"I have remarked that the ancient system of Ptolemy is not at all natural, and too complicated. But neither can I approve of the new one introduced by the great Copernicus after the example of Aristarchus of Samos. This heavy mass of earth, so little fit for motion, could not be displaced in this manner, and moved in three ways, like the celestial bodies, without a shock to the principles of physics. Besides, it is opposed to Scripture! I think then," he adds, "that we must decidedly and without doubt place the earth immovable in the centre of world, according to the belief of the ancients and the testimony of Scripture. In my opinion the celestial motions are arranged in such a way that the sun, the moon, and the sphere of the fixed stars, which incloses all, have the earth for their centre. The five planets turn about the sun as about their chief and king, the sun being constantly in the centre of their orbits, and accompany it in its annual motion round the earth." This system perfectly accounts for the apparent motions of the planets as seen from the earth, and is essentially a variation on the Copernican, rather than on the Ptolemaic system, but it lent itself less readily to future discoveries. It simply amounts, as far as the solar system is concerned, to impressing upon all the rest of it the motions of the earth, so as to leave the latter at rest; and were the sun only as large with respect to the earth as it seems, were the planets really smaller than the moon, and the stars only at a short distance, and smaller than the planets, it might seem more natural that they should move than the earth; but when