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How does a theodolite measure horizontal and vertical angles?

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surveying Figure 1: Photogrammetric photographs from two short, overlapping flight strips arranged for supplying mapping details. Photo-control points are shown on only one photograph; shading indicates a typical terrain feature such as a lake (see text).

In civil engineering, the theodolite measures horizontal and vertical angles by utilizing a telescope that is mounted to swivel around both horizontal and vertical axes.12

To operate the instrument, a surveyor first ensures it is properly leveled using a spirit level. Once the telescope is aligned with a target using internal crosshairs, the angle is determined by reading the instrument's two accompanying graduated circles—one for horizontal angles and one for vertical angles. These circles are marked in degrees and smaller intervals, such as 10 or 20 minutes.12

To achieve high precision, the exact position of the index mark between these graduations is measured using a vernier or a micrometer. In modern geodetic instruments, these measurements can be accurate to within one second of arc. For increased accuracy, surveyors may repeat the measurement multiple times and average the results. This process is fundamental for establishing the precise framework required for mapping, road building, and tunnel alignment.21