At the former of these distances an asteroid's period would be one-third of Jupiter's, and at the latter, three-fifths. That part of the zone included between the distances 2.30 and 2.70 contains one hundred and ten intervals, exclusive of the maximum at the critical distance 2.50. This gap--between Thetis and Hestia--is not only much greater than any other of this number, but is more than sixteen times greater than their average. The distance 3.70 falls in the wide hiatus interior to the orbit of Ismene. III.--Chasms corresponding to the Third Order.--The Distances 2.82, 3.58, and 3.80. As the order of commensurability becomes less simple, the corresponding breaks in the zone are less distinctly marked. In the present case conjunctions with Jupiter would occur at angular intervals of 120°. The gaps, however, are still easily perceptible. Between the distances 2.765 and 2.808 we find twenty minor planets. In the next exterior space of equal breadth, containing the distance 2.82, there is but one. This is No. 188, Menippe, whose elements are still somewhat uncertain. The space between 2.851 and 2.894--that is, the part of equal extent immediately beyond the gap--contains thirteen asteroids. The distances 3.58 and 3.80 are in the chasm between Andromache and Ismene. IV.--The Distances 2.95, 3.51,[10] and 3.85, corresponding to the Fourth Order of Commensurability. The first of these distances is in the interval between Psyche and Clytemnestra; the second and third, in that exterior to Andromache. The nine cases considered are the only ones in which the conjunctions with Jupiter would occur at less than five points of an asteroid's orbit. Higher orders of commensurability may perhaps be neglected. It will be seen, however, that the distances 2.25, 2.70, 3.03, and 3.23, corresponding to the ratios of the fifth order, 2/7, 3/8, 4/9, and 6/11, still afford traces of Jupiter's influence. The first is in the interval between Augusta and Feronia; the last falls in the same gap with 3.277; and the second and third are in breaks less distinctly marked. It may also be worthy of notice that the rather wide interval between Prymno and Victoria is where ten periods of a minor planet would be equal to three of Jupiter. The distance of Medusa is somewhat uncertain. The FACT of the existence of well-defined gaps in the designated parts of the ring has been clearly established. But the theory of probability applied in a single instance gives, as we have seen, but one chance in 300,000,000,000 that the distribution is accidental. This improbability is increased many millions of times when we include all the gaps corresponding to simple cases of commensurability. We conclude, therefore, that those discontinuities cannot be referred to a chance arrangement. What, then, was their physical cause? and what has become of the eliminated asteroids?