Plotting theodolite traverse; repetition errors

Methods of plotting a theodolite traverse

1. Angle and distance (polar) method: the stations are plotted one after another from the measured angles and lengths, using a protractor (or the tangent or chord method for greater accuracy) and a scale. It is easy, but errors accumulate because each angle is plotted from the previous line.
2. Coordinate method: the latitudes and departures of all the lines are computed and adjusted (for example by Bowditch's rule), and the total (independent) coordinates of every station are found from a chosen origin. The stations are then plotted from their coordinates, so errors do not accumulate. This is the more accurate method and is used for large traverses.

In the tangent method, each angle is laid off using its tangent (offset = base length × tan of the angle), which is more accurate than using a protractor.

Errors eliminated by the repetition method

• Reading errors (least count error): the angle is added several times, so the error of a single reading is divided by the number of repetitions.
• Errors due to imperfect graduation of the horizontal circle, since different parts of the circle are used.
• Error of eccentricity of the verniers and centres (when both verniers are read and averaged).
• The errors removed by changing face (line of collimation and trunnion axis errors), when the repetitions are made on both faces.
• Errors of inaccurate bisection of the signals, which are reduced to some extent because the target is bisected many times and the errors tend to compensate.

It does not remove errors due to bad centering, or due to the vertical axis not being truly vertical (imperfect levelling).