at a small change in the outer rings must balance a
great change in the inner one. It is possible, however, that some of the
observed changes may be due to the existence of a resisting medium.
If the changes already suspected should be confirmed by repeated
observations with the same instruments, it will be worth while to
investigate more carefully whether Saturn's rings are permanent or
transitory elements of the solar system, and whether in that part of
the heavens we see celestial immutability or terrestrial corruption
and generation, and the old order giving place to the new before our
eyes."(4)

Studies of the Moon

But perhaps the most interesting accomplishments of mathematical
astronomy--from a mundane standpoint, at any rate--are those that refer
to the earth's own satellite. That seemingly staid body was long ago
discovered to have a propensity to gain a little on the earth, appearing
at eclipses an infinitesimal moment ahead of time. Astronomers were
sorely puzzled by this act of insubordination; but at last Laplace and
Lagrange explained it as due to an oscillatory change in the earth's
orbit, thus fully exonerating the moon, and seeming to demonstrate the
absolute stability of our planetary system, which the moon's misbehavior
had appeared to threaten.

This highly satisfactory conclusion was an orthodox belief of celestial
mechanics until 1853, when Professor Adams of Neptunian fame, with whom
complex analyses were a pastime, reviewed Laplace's calculation, and
discovered an error which, when corrected, left about half the moon's
acceleration unaccounted for. This was a momentous discrepancy, which at
first no one could explain. But presently Professor Helmholtz, the great
German physicist, suggested that a key might be found in tidal friction,
which, acting as a perpetual brake on the earth's rotation, and
affecting not merely the waters but the entire substance of our planet,
must in the long sweep of time have changed its rate of rotation. Thus
the seeming acceleration of the moon might be accounted for as actual
retardation of the earth's rotation--a lengthening of the day instead of
a shortening of the month.

Again the earth was shown to be at fault, but this time the moon could
not be exonerated, while the estimated stability of our system, instead
of being re-established, was quite upset. For the tidal retardation is
not an oscillatory change which will presently correct itself, like the
orb