order, with a spacing of not more than 60 miles between arcs. The main effort today is
toward this goal.
The length closure in Class III is 1 part in 25,000, which corresponds to the classification
formerly accepted as the most precise triangulation and used as a basis for extension of all
surveys of the same and lower order. Old work in this class is being strengthened by
additional baselines and by connection and adjustment to new Class I or Class II work.
However, some Class III triangulation is still in demand in remote areas of the world.
(1) All first-order triangulation must start from stations of known position, baselines, and
azimuths that have been established with the appropriate degree of accuracy. These nets must tie to
baselines and azimuths of the same or higher order. Starting from and tying to two adjacent stations in a
previously established and adjusted net of the same or higher order may meet these requirements. The
criteria for length closures, after all side and angle conditions have been satisfied, have been previously
given. Other criteria that should be considered are the maximum strength of figure (R1), side checks,
inside equation tests, and the probable error and frequency of a check azimuth.
(2) The instrument used in running first-order triangulation should be a 0.2-second optical
reading, direction theodolite, or equivalent. Since first-order triangulation is normally performed at
night, signal lights (which will be discussed in a future chapter) are used as targets. In Class II
triangulation, it is permissible to make daylight observations using the heliotrope or signal lights in areas
where atmospheric conditions are stable. Daylight observations on standard cloth or wooden targets are
not normally accepted.
(3) The methods used in observing first-order triangulation are designed to give a maximum
triangle closure of 3 seconds of arc and an average triangle closure for the net not exceeding 1
second. This requirement can be met by observing the horizontal circle using a 0.2-second theodolite or
equivalent. The rejection limit should be 4 seconds from the mean for any individual direction, with a
set of 16 positions observed each of two nights, with a minimum of 2-hour separation between the two
sets. The mean of the sets must agree within 1.5 seconds, or additional sets must be observed until two
sets agree within 1.5 seconds.
b. Second-Order Triangulation. There are two classes of second-order triangulation.
Second-order, Class I triangulation is used to subdivide areas between first-order control. It
provides area networks and supplementary cross arcs in the primary scheme to be used in the
extension of control for mapping, cadastral, and local land surveys.
Second-order, Class I triangulation must start from and tie to lines of a first-order
triangulation net or two adjacent stations of an adjusted