the sea first rises and then falls; and so, with respect to the
place, it does. Thus the succession of high and low water, and the two
high tides every twenty-four hours, are easily understood in their
easiest and most elementary aspect. A more complete account of the
matter it will be wisest not to attempt: suffice it to say that the
difficulties soon become formidable when the inertia of the water, its
natural time of oscillation, the varying obliquity of the moon to the
ecliptic, its varying distance, and the disturbing action of the sun are
taken into consideration. When all these things are included, the
problem becomes to ordinary minds overwhelming. A great many of these
difficulties were successfully attacked by Laplace. Others remained for
modern philosophers, among whom are Sir George Airy, Sir William
Thomson, and Professor George Darwin.

I may just mention that the main and simplest effect of including
the inertia or momentum of the water is to dislocate the obvious
and simple connexion between high water and high moon; inertia
always tends to make an effect differ in phase by a quarter period
from the cause producing it, as may be illustrated by a swinging
pendulum. Hence high water is not to be expected when the
tide-raising force is a maximum, but six hours later; so that,
considering inertia and neglecting friction, there would be low
water under the moon. Including friction, something nearer the
equilibrium state of things occurs. With _sufficient_ friction the
motion becomes dead-beat again, _i.e._ follows closely the force
that causes it.

Returning to the elementary discussion, we see that the rotation of the
earth with respect to the humps will not be performed in exactly
twenty-four hours, because the humps are travelling slowly after the
moon, and will complete a revolution in a month in the same direction as
the earth is rotating. Hence a place on the earth has to catch them up,
and so each high tide arrives later and later each day--roughly
speaking, an hour later for each day tide; not by any means a constant
interval, because of superposed disturbances not here mentioned, but on
the average about fifty minutes.

We see, then, that as a result of all this we get a pair of humps
travelling all over the surface of the earth, about once a day. If the
earth were all ocean (and in the southern hemisphere it is nearly all
ocean), then th