A two-dimensional view, which illustrates conceptually the geoid and ellipsoid,
is shown in Figure 19.1. As illustrated, the geoid contains nonuniform undulations
(which are exaggerated in the figure for clarity) and is therefore not
readily defined mathematically. Ellipsoids, which approximate the geoid and can
be defined mathematically, are therefore used to compute positions of widely
spaced points that are located through control surveys. The Clarke Ellipsoid of
1866 approximates the geoid in North America very well and from 1879 until the
1980s it was the ellipsoid used in NAD 27 as a reference surface for specifying