PART B - MEASURING ANGLES
3-11. Triangulation. Triangulation affords a rapid and accurate method of surveying a large area by
eliminating the necessity of measuring the length of every line. In any triangle, if we know the values of
all three angles and the length of one side of the triangle, we can calculate the length of the other two
sides. Having calculated the length of the unknown sides, we can use them as sides of known length for
adjacent triangles. With this simple procedure, we could continue and calculate lengths throughout the
entire series of connected triangles. However, we need not measure all three angles. The properties of a
triangle are such that if we can measure any two angles, we can compute the value of the third.
a. This procedure does not guarantee that the calculated value of the unknown angle will be its true
value. Any error in the original measurement will be reflected in the calculated angle; therefore, there
would be no tangible reference for adjusting the triangulation on completion of the survey. Certain
instruments and field techniques are employed which greatly reduce the possibility of error. Many of
these techniques will be brought to your attention during the remainder of this lesson. Certain
mathematical computations are applied to the data so that any error is distributed throughout the entire
system. This is the primary task of the data computer. The persistent elimination of conditions likely to
cause errors makes their occurrences rare and allows for isolation and immediate remedy.
b. Accuracy should be maintained throughout the triangulation. Use care when operating
instruments, and pay strict attention to the methods. Observing the proper methods ensures that
systematic and accidental errors are kept within the prescribed limits and that no part of the system
exhibits undue weakness.
3-12. Theodolites. A theodolite is a precision surveying instrument used for the accurate measurement
of angles. It consists of an alidade with a telescope. It is mounted on a base carrying an accurately
graduated horizontal circle and equipped with necessary levels and reading devices. The alidade usually
carries a graduated vertical circle. There are two general types of theodolites, repeating and direction.
A repeating theodolite is designed so that successive measures of an angle may be accumulated on a
graduated circle. The reading of the accumulated sum is divided by the number of repetitions to obtain
the observed angle. On a direction theodolite, the circle remains fixed while the telescope is pointed on
a number of signals in succession. The circle is read for each direction. The direction theodolite is the
preferred instrument used in higher-order triangulation. The quality of a theodolite is not measured by
its size or the minutes on the least reading of the micrometers, but by the beat measure of excellence in
its performance in actual fieldwork.
3-13. Wild T-3 Precision Theodolite. Refer to Figure 3-4, page 3-16. The wild T-3 precision
theodolite is a 0.2-second, prism microscope type of direction theodolite and is a satisfactory first-order
instrument. The principal operating characteristic of this type of instrument is the method of reading the
circles by means of an auxiliary telescope (microscope) alongside the sighting telescope. Both sides of
the circle are reflected simultaneously in this reading microscope through a chain of prisms. A
3-15
EN0593
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