In order to accurately express the configuration of the equigeopotential surfaces in the sea and air relative to the sea level geoid we can make use of Eqs. (66) and (26):
or
The value
is 0.00259 as deduced from pendulum measurements;
has the value
cm
for the
sea; and
has the value 980.62 cm/sec
. The
variable z is vertical distance measured upward along the
plumbline from the sea level geoid reference.
Eq. (91) applies accurately to the gross distribution of
throughout
the practical limits of the sea and atmosphere. At very great
distances away from the earth's surface (say, greater than 100
km) Eq. (91) is not accurate since Eq. (26), upon which Eq. (91)
is based, no longer accurately describes the variation
of g with elevation. For great positive values of z the
development given in Article 2.07 corrected for the effect of
the variation of
with latitude must be used.
The elevation of a particular equigeopotential surface in the sea or atmosphere can be evaluated from Eq. (91). If the binomial expansion is employed in evaluating the quadratic roots and second order terms neglected, we find
This holds within the practical limits of the sea and atmosphere as does Eq. (91).