It is now of interest to inquire into the matter of how much
the mean sea level at a given latitude would be effected by a
relatively small alteration in the speed of the earth's rotation.
In the development of Eq. (88) we have seen that only half of the
magnitude of 
can be attributed directly to the
effect of the earth's rotation. Half of the effect is due to the
variation of 
with latitude associated with the distorted
shape of the lithosphere, and thus indirectly related to
the centrifugal force of the earth's rotation.
In attempting to predict how much the sea level will be altered
with a given change in 
, the question arises as to whether
or not the earth's solid mantle will be altered as well and, if so, by
how much? An alteration of the shape of the earth's mantle would
have a two-fold effect: (1) the redistribution of mass would alter
the latitudinal variation of and thus influence the shape of
the sea level in addition to the direct effect of the altered
centrifugal force on the water; and (2) the change is shape of
the solid crust will tend to reduce the apparent change in water
lwvel which can only be measured relative to the earth's crust.
It is conceivable that for the very slow secular reductino
of which results from the frictional influences
of the earth and sea tides the mantle is altered in about the
same manner as the sea surface. However, for the relatively
rapid variations of which are known to occur
during the year and even over periods of a few
weeks ( (), Munk and Miller (1950),
Lawford and Veley (1951)), it would seem reasonable to expect
that the earth's crust cannot respond commensurate with
the varying centrifugal force, and that only the sea itself
will be fully responsive.
For the latter situation, if we assume no change in the mantle
then the distribution of should remain essentially unaltered
except for the second order effect due to the altered distribution
of the mass of the sea itself. Consequently, we must regard Eq. (88)
as of the the form
where 
meters is invariant. It can then be shown that
where T is the period of rotation of the earth about its axis.
On the basis of Eq. (90) and Table 2.07-I we see that the increase
of at the equator corresponding to a decrease of the
length of the day of one second is
The corresponding drop of sea level at the North pole would be
16.6 cm (or about 6.5 inches). At latitude 35.1 
N or S
the sea level would be unaffected.
The variations in the length of the day are actually of the order
of milliseconds and the associated changes in sea level are therefore
only fractions of a millimeter. However, the important aspect
of the above considerations with respect to the earth is the effect
of the alterations in the position and magnitude of the solar tidal
bulge during the course of a year. The varying declination of the
sun induces a slight shift in the mass of water above or below
the equatoar which, in turn, alters the length of the
day (Mintz and Munk (1951), Munk and Revelle (1952)). This
effect must therefore be taken into account when interpreting
observations of the changes in the length of the day before
drawing any conclusions as regards changes in the atmospheric
circulation.