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the diameters of the largest ones, naturally the earliest discovered, are only three or four hundred miles. The size of the smallest can be inferred only in a rough way from their brightness. They may be twenty or thirty miles in diameter.

The orbits of these bodies are for the most part very eccentric. In the case of Polyhymnia, the eccentricity is about 0.33, which means that at perihelion it is one third nearer the sun than its mean distance, and at aphelion one third more. It happens that its mean distance is just about three astronomical units; its least distance from the sun is therefore two, its greatest four, or twice as great as the least.

The large inclination of most of the orbits is also noteworthy. In several cases it exceeds twenty degrees, in that of Pallas it is twenty-eight degrees.

Olbers' idea that these bodies might be fragments of a planet which had been shattered by some explosion is now abandoned. The orbits range through too wide a space ever to have joined, as they would have done if the asteroids had once formed a single body. In the philosophy of our time these bodies have been as we see them since the beginning. On the theory of the nebular hypothesis the matter of all the planets once formed rings of nebulous substance moving round the sun. In the case of all the other planets the material of these rings gradually gathered around the densest point of the ring, thus agglomerating into a single body. But