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Any line from which points and objects are located is a control
line. Horizontal control surveys are conducted to establish
supplementary control stations for use in construction surveys.
Supplementary control stations usually consist of one or more short

traverses run close to or across a construction area to afford easy tie-
ins for various projects. These stations are established to the degree of
accuracy needed for the purpose of the survey. Direction, like

horizontal location itself, is relative; that is, the direction of a line can
only be stated relative to a reference line (or sometimes of assumed)
direction. In true geographical direction, the reference line is the
meridian passing through the point where the observer is located; and

the direction of a line passing through that point is described in terms
of the horizontal angle between that line and the meridian. In magnetic
geographical direction, the reference line is the magnetic meridian

instead of the true meridian.
The direction of a traverse line is commonly given by bearing. In
field traversing, however, turning deflection angles with a transit is

more convenient than orienting each traverse line to a meridian.
As horizontal control surveys generally determine geodetic
latitudes and geodetic longitudes of points. To explain geodetic

latitude and longitude, it is necessary to first define the geoid, and the
ellipsoid (sometimes called the spheroid). The geoid is an
equipotential gravitational surface located approximately at mean sea
level, which is everywhere perpendicular to the direction of gravity.

Because of variations in the Earth’s mass distribution and the rotation
of the Earth, the geoid has an irregular shape.
The ellipsoid is a mathematical surface obtained by revolving an

ellipse about the Earth’s polar axis. The dimensions of the ellipse are
selected to give a good fit of the ellipsoid to the geoid over a large
area and are based upon surveys made in the area.
A two-dimensional view, which illustrates conceptually the geoid

and ellipsoid, is shown in Figure 12.3.1. 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.

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