ch turning, with its own proper rotation rate, around the
central planet. It is singular that Herschel, who, though not versed in
the methods of the higher mathematics, had considerable native power as
a mathematician, was unable to perceive the force of Laplace's
reasoning. Indeed, this is one of those cases where clearness of
perception rather than profundity of mathematical insight was required.
Laplace's equations of motion did not express all the relations
involved, nor was it possible to judge, from the results he deduced, how
far the stability of the Saturnian rings depended on the real structure
of these appendages. One who was well acquainted with mechanical
matters, and sufficiently versed in mathematics to understand how to
estimate generally the forces acting upon the ring-system, could have
perceived as readily the general conditions of the problem as the most
profound mathematician. One may compare the case to the problem of
determining whether the action of the moon in causing the tidal wave
modifies in any manner the earth's motion of rotation. We know that as a
mathematical question this is a very difficult one. The Astronomer
Royal, for example, not long ago dealt with it analytically, and deduced
the conclusion that there is no effect on the earth's rotation,
presently however, discovering by a lucky chance a term in the result
which indicates an effect of that kind. But if we look at the matter in
its mechanical aspect, we perceive at once, without any profound
mathematical research, that the retardation so hard to detect
mathematically must necessarily take place. As Sir E. Beckett says in
his masterly work, _Astronomy without Mathematics_, 'the conclusion is
as evident without mathematics as with them, when once it has been
suggested.' So when we consider the case of a wide flat ring surrounding
a mighty planet like Saturn, we perceive that nothing could possibly
save such a ring from destruction if it were really one solid structure.

To recognise this the more clearly, let us first notice the dimensions
of the planet and rings.

We have in Saturn a globe about 70,000 miles in mean diameter, an
equatorial diameter being about 73,000 miles, the polar diameter 66,000
miles. The attractive force of this mighty mass upon bodies placed on
its surface is equal to about one-fifth more than terrestrial gravity if
the body is near the pole of Saturn, and is almost exactly the same as
terrestrial gravity i