because the most natural explanation of such differences would seem to
be that they arose from variations in the roughness or smoothness of
the reflecting surface, which would be characteristic of fragmentary
bodies. In the case of a large planet alternating expanses of land and
water, or of vegetation and desert, would produce a notable variation
in the amount of reflection, but on bodies of the size of the
asteroids neither water nor vegetation could exist, and an atmosphere
would be equally impossible.

One of the strongest objections to Olbers' hypothesis is that only a
few of the first asteroids discovered travel in orbits which
measurably satisfy the requirement that they should all intersect at
the point where the explosion occurred. To this it was at first
replied that the perturbations of the asteroidal orbits, by the
attractions of the major planets, would soon displace them in such a
manner that they would cease to intersect. One of the first
investigations undertaken by the late Prof. Simon Newcomb was directed
to the solution of this question, and he arrived at the conclusion
that the planetary perturbations could not explain the actual
situation of the asteroidal orbits. But afterward it was pointed out
that the difficulty could be avoided by supposing that not one but a
series of explosions had produced the asteroids as they now are. After
the primary disruption the fragments themselves, according to this
suggestion, may have exploded, and then the resulting orbits would be
as ``tangled'' as the heart could wish. This has so far rehabilitated
the explosion theory that it has never been entirely abandoned, and
the evidence which we have just cited of the probably abnormal shapes
of Eros and other asteroids has lately given it renewed life. It is a
subject that needs a thorough rediscussion.