us spheroid which is concentrating into a planet,
there are at work two antagonist mechanical tendencies--the centripetal
and the centrifugal. While the force of gravitation draws all the atoms
of the spheroid together, their tangential momentum is resolvable into
two parts, of which one resists gravitation. The ratio which this
centrifugal force bears to gravitation, varies, other things equal, as
the square of the velocity. Hence, the aggregation of a rotating
nebulous spheroid will be more or less hindered by this resisting force,
according as the rate of rotation is high or low: the opposition, in
equal spheroids, being four times as great when the rotation is twice as
rapid; nine times as great when it is three times as rapid; and so on.
Now the detachment of a ring from a planet-forming body of nebulous
matter, implies that at its equatorial zone the increasing centrifugal
force consequent on concentration has become so great as to balance
gravity. Whence it is tolerably obvious that the detachment of rings
will be most frequent from those masses in which the centrifugal
tendency bears the greatest ratio to the gravitative tendency. Though it
is not possible to calculate what ratio these two tendencies had to each
other in the genetic spheroid which produced each planet, it is possible
to calculate where each was the greatest and where the least. While it
is true that the ratio which centrifugal force now bears to gravity at
the equator of each planet, differs widely from that which it bore
during the earlier stages of concentration; and while it is true that
this change in the ratio, depending on the degree of contraction each
planet has undergone, has in no two cases been the same; yet we may
fairly conclude that where the ratio is still the greatest, it has been
the greatest from the beginning. The satellite-forming tendency which
each planet had, will be approximately indicated by the proportion now
existing in it between the aggregating power, and the power that has
opposed aggregation. On making the requisite calculations, a remarkable
harmony with this inference comes out. The following table shows what
fraction the centrifugal force is of the centripetal force in every
case; and the relation which that fraction bears to the number of
satellites.[18]

Mercury. 1/360
Venus. 1/253
Earth. 1/289 1 Satellite.
Mars. 1/127 2 Satellites.
Jupiter. 1/11.4 4 Satellites.
Saturn.