Before considering these bodies individually, we may well look upon them _en bloc_, inasmuch as one attribute of the asteroids concerns them generically rather than specifically, and is of great interest both from a mechanical and an historical point of view. For, in fact, it is what led to their discovery. Titius of Wittenburg, about the middle of the eighteenth century, noticed a curious relation between the distances from the Sun of the then known planets. It consisted in a sort of regular progression, but with one significant gap. Bode was so struck by the gap that he peopled it with a supposed planet, and so brought the relation into general regard in 1772. In consequence, it usually bears his name. It is this: if we take the geometrical series, 3, 6, 12, 24, 48, 96 and add 4 to each term, we shall represent to a fair degree of precision the distances of the several planets, beginning with Mercury at 4 and ending with Saturn at 100, which was the outermost planet then known. All the terms were represented except 24 + 4, or 28—a gap lying between Mars and Jupiter. When Uranus was discovered by Sir William Herschel in 1781 and was found to be travelling at what corresponded to the next outer term 192 + 4, or 196, the opinion became quite general that the series represented a real law and that 28 must be occupied by a planet. Von Zach actually calculated what he called its analogical elements, and finally got up in 1800 a company to look for it which he jocularly described as his celestial police. Considering that Bode’s law is not a law at all, but a curious coincidence, as Gauss early showed in its lack of precision and in its failure to mark the place of Mercury with any approach to accuracy, and as the discovery of Neptune amply bore out, it was perhaps just in fate that the honor of filling the gap did not fall to any of the “celestial police,” but to an Italian astronomer, Piazzi, at the time engaged on a new star chart. An illness of Piazzi caused it to be lost almost as soon as found. In this plight an appeal was made to the remarkable Gauss, just starting on his career. Gauss undertook the problem and devised formulæ by which its place was predicted and the planet itself recovered. It proved to fit admirably the gap. But it had hardly been recovered before another planet turned up equally filling the conditions. Ceres, the first, lay at 26.67 astronomical units from the Sun; Pallas, the second, at 27.72. Two claimants were one too many. But the inventive genius of Olbers came to the rescue. By a bold hypothesis he suggested that since two had appeared where only one was wanted, both must originally have formed parts of a single exploded planet. He predicted that others would be detected by watching the place where the explosion had occurred, to wit: where the orbits of Ceres and Pallas nearly intersected in the signs of the Virgin and the Whale.