For in the case of an explosion the various parts, unless perturbed, must all return in time to the scene of the catastrophe. By following his precept, two more were in fact detected in the next two years, Juno and Vesta. His hypothesis seemed to be confirmed. No new planets were discovered, and the old fulfilled fairly what was required of them. Lagrange on calculation gave it his mathematical assent. Nevertheless, it was incorrect, as events eventually showed, though for forty years it slept in peace, no new asteroids being found. We now know that this was because the rest were all much smaller, and for such nobody looked. It was not till 1845 that Hencke, an ex-postmaster of Driessen in Prussia, after fifteen years of search detected another, Astræa, of the 11th magnitude. After this discoveries of them came on apace, until now more than six hundred are known, and their real number seems to be legion. But those discovered are smaller each year on the average, showing that the larger have already been found. Their orbits are such that they cannot possibly ever have all formed part of a pristine whole. The idea, not the body, was exploded. For they are now recognized as having always been much as they are to-day. [Illustration: ASTEROIDS. _MAJOR AXES OF ORBITS._] They prove to be thickest at nearly the point where Bode’s law required, the spot where Ceres and Pallas were found. The mean of their distances is less, being 2.65 instead of 2.8 astronomical units, probably simply because the nearer ones are easier discovered. The fact that they are clustered most thickly just inside 2.8 astronomical units implies that there of all points within the space between Mars and Jupiter a planet would have formed if it could. A definite reason exists for its failure to do so—Jupiter’s disturbing presence. Throughout this whole region Jupiter’s influence is great; so great that his scattering effect upon the particles exceeds their own tendency to come together. We see this in the arrangement of the orbits. If we plot the orbits of the asteroids, we shall be struck by the emergence of certain blanks in the ribbon representing sections of their path. It is the woof of a plaid of Jupiter’s weaving. The gaps are where asteroids revolving about the Sun would have periods commensurate with his, ²/₅, ¹/₂, ³/₅, ⁴/₇, and the like. Such bodies would return after a few revolutions, five of theirs, for instance, to Jupiter’s two, into the same configurations with him at the same points of their orbits. Thus the same perturbation would be repeated over and over again until the asteroid’s path was so changed that commensurability ceased to exist. And it would be long before perturbation brought it back again. Thus the orbits are constantly swinging out and in, all of them within certain limits, but those are most disturbed which synchronize with his. In this manner he has fashioned their arrangement and even prevented any large planet from forming in the gap.