Eq. (82) represents, in effect, the gross shape of the
geoid with the value of r at 
being 
(Table 2.01-Ia),
and a is really 
.
The mean radius of the geoid 
is defined by
where V is the volume of the geoid. The latter can be computed from the relation
Making use of Eq. (82) and carryin gout the indicated integration yields
In view of Eq. (83) this gives for the mean radius
The second term in parentheses is very small compared with unity and consequently the root can be taken as simply the first two terms of the binomial expansion. This leads to
Inserting
and
gives
which confirms the value given in Table 2.01-I.
The geoidal surface can be conveniently described in terms of
the radial anomaly from a sphere of radius 
. If
we let 
represent this radial anomaly, then
or
The value of is zero at the latitude
Numerical values of for different latitudes are given
in Table 2.07-I below. The overall range of
is 21,500 meters and the mean value for all latitudes is zero.
Because of gravitational anomalies assocated with topographic features of the earth, the shape of the reference geoid will depart slightly from the mean distribution represented by Table 2.07-I. The departure is most pronounced near coastlines, as already mentioned in Art. 2.03.