The Theodolite

The theodolite is an instrument used in surveying for measuring angles in both the horizontal and vertical planes. Its invention, in around 1571, is accredited to the English mathematician and surveyor Leonard Digges of Kent (1515-1559), although arguably its origins can be traced back considerably further. The Greeks used an instrument called a dioptra for measuring the position of stars in the night sky. This instrument was later adapted by the Romans for the purpose of measuring angles during surveying, and in this more evolved form had started to resemble its sixteenth century counterpart. Digges called his instrument a theodelitus, and it consisted of a divided circle and square with a compass in the centre, as illustrated below. Although equipped with a sighting device, it was missing the telescopic tube found in more modern versions. Digges' original design is believed to have been for an instrument capable of measuring horizontal angles only.

The instrument originally designed by Digges consisted of a circular plate, marked around its circumference with graduations at one degree intervals, and having a compass at its centre. The whole assembly had to be carefully positioned so that the plate lay in the horizontal plane, and the compass was then used to orient the plate correctly. A rotating alidade (see above) enabled the user to establish the line of site between themselves and some distant target object. Its position relative to the graduated plate was then used to determine the angle of the target object relative to the user's position.

As you can see from the illustration above, a second alidade mounted on a semi-circular plate attached to the instrument in the vertical plane and capable of rotating around its vertical axis, was later added. This enabled an observer to measure vertical angles as well. By the middle of the eighteenth century, the alidades had been replaced by a single telescope, mounted on the vertical arc, which could be used to measure both horizontal and vertical angles. The use of a telescope also increased both the range and accuracy of the instrument.

The theodolite is generally considered to have become the modern, accurate instrument most contemporary surveyors are familiar with in 1787, when English mathematician and instrument maker Jesse Ramsden (1735-1800) built his famous Great Theodolite. The instrument was subsequently purchased by the Royal Society, and used to facilitate the calculation of the relative locations of the observatories at Greenwich and Paris by using a technique known as triangulation. Ramsden is notable for the fact that he created one of the first high-quality dividing engines. These devices enabled the graduations on navigational instruments to be marked with a degree of accuracy that had not previously been possible. In the years that followed, theodolites designed by Ramsden, which were capable of measuring angles to an accuracy of within a second of arc, were employed by the British Ordnance Survey to map most of southern Britain.

As we have already mentioned, the use of the theodolite in surveying relies on a technique known as triangulation. The technique is accredited to the Dutch mathematician, cartographer and instrument maker Gemma Frisius (1508-1555), and involves the establishment of a baseline between two points. The length of the baseline (which can be several miles in length) must be measured very precisely. A theodolite is then used to measure the angles between the baseline and the line of sight between each end of the baseline and the target point. Once these angles are known, and since the length of the baseline itself is already known, the position of the target point in relation to the baseline can be precisely calculated using basic trigonometry.

From the early part of the nineteenth century until the middle of the twentieth century, the techniques used to carry out geodetic surveys (i.e. surveys used to map large areas of land) remained relatively unchanged. From the 1950s onwards, significant advances in theodolite technology were made possible thanks to the availability of advanced electronic components, and the design of the instrument became increasingly sophisticated. Features such as automated targeting and distance measurement began to appear, culminating in the appearance of the modern "intelligent" theodolite. Theodolites are still used in many applications including, of course, construction, although the adoption of survey techniques involving satellite-based global positioning systems (GPS) in the early 1980s has largely obviated the need for the use of theodolites in geodetic surveys.

As an aside, and for those interested in such things, we came across what the authors describe as:

"a multi-function augmented reality app that combines a compass, GPS, map, photo/movie camera, rangefinder, and two-axis inclinometer into one indispensable app. Theodolite overlays real time information about position, altitude, bearing, range, and inclination on the iPhone's live camera image, like an electronic viewfinder."

The app is one of several navigationally oriented apps marketed by Hunter Research and Technology, run by mechanical/aerospace engineer Dr. Craig Hunter, and is apparently available for iPhones and iPads on iTunes for just a few dollars – pretty amazing if it can do everything they say it can!