Figure 13-14.-Vertical angles and zenith distances.
on the vertical limb by means of the vertical
vernier.
On a transit with a movable vertical vernier,
the vernier is equipped with a control level. The
telescope is centered on the point as described
above, but the vernier bubble is centered before
the angle is read.
The ZENITH is an imaginary point overhead
where the extension of the plumb line will intersect
an assumed sphere on which the stars appear
projected. The equivalent point, directly below
the zenith, is the NADIR. Use of the zenith
permits reading angles in a vertical plane without
using a plus or a minus. Theodolites have a
vertical scale reading zero when the telescope is
pointed at the zenith instead of in a horizontal
plane. With the telescope in a direct position and
pointed straight up, the reading is 0°; on a
horizontal line, the reading is 90°; and straight
down, 180°. When measuring vertical angles with
the theodolites (fig. 13-14, view B), you should
read the angle of elevation with values less than
90°and the angle of depression with values greater
than 90°. These angle measurements with the
zenith as the zero value are called the ZENITH
DISTANCES. DOUBLE ZENITH DISTANCES
are observations made with the telescope direct
and reversed to eliminate errors caused by the
inclination of the vertical axis and the collimation
of the vertical circle.
Zenith distance is used in measuring vertical
angles involving trigonometric leveling (discussed
in the next chapter) and in astronomical
observations. (See Engineering Aid 1 & C,
NAVEDTRA 10635-C.)
Measuring Angles by Repetition
You may recall, from a previous discussion,
the distinction between precision and accuracy.
A transit on which angles can be measured to the
nearest 20 sec is more precise than one that can
measure only to the nearest 1 min. However, this
transit is not necessarily more accurate.
The inherent angular precision of a transit can
be increased by the process of REPETITION. To
illustrate this principle, suppose that with a 1-min
transit you turn the angle between two lines in the
field and read 45°00´. The inherent error in the
transit is 1´; therefore, the true size of this angle
is somewhere between 44°59´30´´ and 45°00´30´´.
For example, when using repetition, you leave
the upper motion locked but release the lower
motion. The horizontal limb will now rotate with
the telescope, holding the reading of 45°00´. You
plunge the telescope, train again on the initial line
of the angle, and again turn the angle. You have
now doubled the angle. The A vernier should read
approximately 90°00´.
For this second reading, the inherent error in
the transit is still 1 min, but the angle indicated
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