The Geoid and Different Height Systems - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 143

Fig. 4.7 Level surface

In ( 4.20 ), if s is directed against the direction of gravity g, denoted by h, in this
case, cos(g, h) ¼ 1, yields:

dW
dh ¼

g,

also written as:

dW
g

dh ¼ , ð 4 : 22 Þ

where dW represents the potential difference of two infinitely close level surfaces,
and dh is the vertical distance between the two level surfaces. Equation ( 4.22 )
indicates that the distance between level surfaces is inversely proportional to
gravity.
Because g varies everywhere on a level surface, the level surfaces are
non-parallel. Figure 4.7 is a general description of the level surface. In the mean-
time, the value of g is finite and dh cannot possibly be zero, so the level surfaces do
not intersect. However, within a small area the gravity value does not change much,
and the two level surfaces can be considered parallel; for instance, the two level
surfaces at each point, where the leveling rods are held, are considered parallel to
each other in leveling. Hence, the distance observed between the level surfaces is
considered to be the height difference between the two points.

4.2 Earth Ellipsoid and Normal Ellipsoid

4.2.1 Earth Ellipsoid

The geoid is an irregular surface that approximates the shape of the Earth. Its
undulations are mainly generated by the inhomogeneous distribution of mass within
the Earth's crust. Given the fact that the mass of the Earth's crust is only one sixty-