Surveying

Measure lengths by chaining (applying slope and other corrections) and directions by compass bearings, then adjust the traverse’s closing error by the Bowditch rule to distribute it among the sides.

Reduce staff readings to reduced levels by either the height-of-instrument method (RL = HI − staff reading) or the rise-and-fall method, and verify the work by the arithmetic checks on the sums of back sights and fore sights.

Measure the traverse angles and lengths with the theodolite, check the angular misclosure against (2n − 4) × 90°, compute latitudes and departures, and balance the closing error by the Bowditch rule before computing coordinates.

Use stadia tacheometry (D = ks + c from the staff intercept) for rapid distance measurement, and compute simple-curve elements (tangent length T = R tan(Δ/2), curve length L = πRΔ/180) for setting out horizontal curves.

Use the total station’s electronic distance and angle measurement to compute coordinates directly (E = E₀ + D sin θ, N = N₀ + D cos θ), and GPS/GNSS (especially RTK) for datum-referenced positioning, mindful of its error sources.