A theodolite is a device used to measure horizontal and vertical angles, traditionally with a pointing instrument and calibrated circular plates. It is commonly used in surveying to determine distance and height of features. The first theodolite, called a dioptra, dates back to ancient Greece. Modern theodolites have improved accuracy and portability, with electronic versions incorporating infrared devices and software for calculations and data storage.
A theodolite is a device for measuring horizontal and vertical angles. The traditional theodolite consists of a pointing instrument that can be rotated horizontally and vertically and two calibrated circular plates positioned to measure the amount of horizontal or vertical rotation in degrees. By aiming the pointing instrument, which can be a telescope, on an object, it is possible to measure its horizontal and vertical angles with respect to appropriate reference points. Normally, these would be true north for horizontal angles and horizon for vertical angles. Theodolites have been used in navigation and astronomy and are today most commonly employed in surveying, both for building and construction as well as geographic surveying.
When used for geographic surveying, a theodolite can help determine the distance and height of a feature, such as a hill or mountain. By measuring the horizontal angle, relative to true north, of the feature from two different locations at a known distance, the distance can be calculated by trigonometry. Once the distance is known, the height can be determined in the same way by measuring the vertical angle of the feature with respect to the horizon.
It is difficult to pinpoint the date when the first theodolite was built, as a variety of devices with varying degrees of similarity to a modern theodolite have been introduced throughout history. The first evidence of a device of this type dates back to about 150 BC in ancient Greece; it was called a dioptra and had two metal plates that could be rotated horizontally and vertically, along with a leveling method that involved pipes containing water. It was used for astronomical observations. The term “theodolite” first appeared in 1571 when the English mathematician Leonard Digges described an instrument for measuring angles called the “theoloditus”; however, it appears that it only measured horizontal angles. In 1653, William Leybourn, an English surveyor and author, gave a detailed description of a theodolite that could measure angles both horizontally and vertically and incorporated a compass and a sight.
Modern theodolites work on the same principles as their predecessors, but with improvements in accuracy and portability. They have telescopic sights and can measure angles to an accuracy of up to a tenth of an arc second. An electronic theodolite often incorporates an infrared device for measuring distances and may have a processor and software to perform calculations and store the results internally or download them to a laptop or PC. This type of system is sometimes called a “total station”.
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