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 compared 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 published 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.