Beyond 300 meters, the effect of curvature and refraction must be considered and the necessary
4-11. Methods of Trigonometric Leveling. The difference
between two stations, whose
distance apart is known, can be determined using one of the following methods:
a. Reciprocal Observations. During the method of reciprocal observations, observations are
performed at both stations, either simultaneously or not simultaneously. First, determine the difference
in elevation from vertical angles observed from one station to the other. The object of such reciprocal
observations is to remove the effect of uncertainty regarding the value of the coefficient of refraction.
This effect will balance out when the observations are taken in both directions and are more complete if
the observations are taken simultaneously. On triangulation work where each station is occupied
consecutively and additional observers are not available, this method of reciprocal observations is
usually used, but no attempt is made to observe in both directions simultaneously. The measurements
are sometimes made at the time of minimum refraction on different days but with less accurate results.
b. Nonreciprocal Observations. During nonreciprocal observations, the difference of elevation
from the vertical angle measured at only one of the stations is commuted. The value of the refraction
must be known. This method is available to determine the elevation of the station occupied by
observation to a point of known elevation and elevations of inaccessible and intersected points.
4-12. Zenith Distances With the T-3 Theodolite. In first- and second-order triangulation, zenith
distances are obtained using a Wild T-3 theodolite or a theodolite of similar accuracy.
a. The zenith is an imaginary point overhead where an extension of the plumb line intersects an
assumed sphere on which the stars appear projected. The equivalent point that is directly below the
zenith is called the nadir. The zenith distance is the vertical angle from the zenith, or a point directly
overhead, to the sighted point. The zenith permits reading angles in a vertical plane without using a plus
or minus. Vertical-angle measurements with the T-3 read elevation (plus) angles as values less than 900
and depression (minus) angles as values greater than 900.
b. Observe zenith distances between 1200 and 1600 hours whenever possible, as vertical refraction
is at its minimum and more constant during these hours. Confine angle observations to this period, the
duration of which varies in area. In general, good observations are possible from 1000 to 1600 hours.
c. Over longer distances, the preferred method of obtaining observations is with heliotropes or
other visible objects at the stations. When it is not possible to observe zenith distances during the
recommended hours, make observations at night using lights. To obtain the best results, make reciprocal
observations from two