thus displaced would have come
in contact with other cosmical particles of the same family with
itself--then, it may be assumed, more evenly scattered than now--would
have coalesced with them, and permanently left its original track. In
this way the regions of maximum perturbation would gradually have become
denuded of their occupants.

We can scarcely doubt that this law of commensurability has largely
influenced the present distribution of the asteroids. But its effects
must have been produced while they were still in an unformed, perhaps a
nebular condition. In a system giving room for considerable modification
through disturbance, the recurrence of conjunctions with a dominating
mass at the same orbital point need not involve instability.[1026] On
the whole, the correspondence of facts with Kirkwood's hypothesis has
not been impaired by their more copious collection.[1027] Some chasms of
secondary importance have indeed been bridged; but the principal stand
out more conspicuously through the denser scattering of orbits near
their margins. Nor is it doubtful that the influence of Jupiter in some
way produced them. M. de Freycinet's study of the problem they
present[1028] has, however, led him to the conclusion that they existed
_ab origine_, thus testifying rather to the preventive than to the
perturbing power of the giant planet.

The existence, too, of numerous asteroidal pairs travelling in
approximately coincident tracks, must date from a remote antiquity. They
result, Professor Kirkwood[1029] believed, from the divellent action of
Jupiter upon embryo pigmy planets, just as comets moving in pursuit of
one another are a consequence of the sundering influence of the sun.

Leverrier fixed, in 1853,[1030] one-fourth of the earth's mass as the
outside limit for the combined masses of all the bodies circulating
between Mars and Jupiter; but it is far from probable that this maximum
is at all nearly approached. M. Berberich[1031] held that the moon would
more than outweigh the whole of them, a million of the lesser bodies
shining like stars of the twelfth magnitude being needed, according to
his judgment, to constitute her mass. And M. Niesten estimated that the
whole of the 216 asteroids discovered up to August, 1880, amounted in
_volume_ to only 1/4000th of our globe,[1032] and we may safely
add--since they are tolerably certain to be lighter, bulk for bulk, than
the earth--that their proportionate _mass_ is smaller