here could be no tides, and
therefore no progress in the direction of tidal evolution. There is,
however, the profound difference of stability and instability between
the two cases; the most insignificant disturbance of the system at the
initial stage was sufficient to precipitate the revolving moon from
its condition of dynamical equilibrium, and to start the course of
tidal evolution in full vigour. If, however, any trifling derangement
should take place in the last condition of the system, so that the
month and the day departed slightly from equality, there would
instantly be an ebbing and a flowing of the tides; and the friction
generated by these tides would operate to restore the equality because
this condition is one of dynamical stability.

It will thus be seen with what justice we can look forward to the day
and month each of fourteen hundred hours as a finale to the progress
of the luni-tidal evolution. Throughout the whole of this marvellous
series of changes it is always necessary to remember the one constant
and invariable element--the moment of momentum of the system which
tides cannot alter. Whatever else the friction can have done, however
fearful may have been the loss of energy by the system, the moment of
momentum which the system had at the beginning it preserves unto the
end. This it is which chiefly gives us the numerical data on which we
have to rely for the quantitative features of tidal evolution.

We have made so many demands in the course of these lectures on the
capacity of tidal friction to accomplish startling phenomena in the
evolution of the earth-moon system, that it is well for us to seek for
any evidence that may otherwise be obtainable as to the capacity of
tides for the accomplishment of gigantic operations. I do not say
that there is any doubt which requires to be dispelled by such
evidence, for as to the general outlines of the doctrine of tidal
evolution which has been here sketched out there can be no reasonable
ground for mistrust; but nevertheless it is always desirable to widen
our comprehension of any natural phenomena by observing collateral
facts. Now there is one branch of tidal action to which I have as yet
only in the most incidental way referred. We have been speaking of the
tides in the earth which are made to ebb and flow by the action of the
moon; we have now to consider the tides in the moon, which are there
excited by the action of the earth. For between these two