## Theodolite Surveys

The theodolite, sometimes referred to in the United States as a surveyor's transit, is the surveying instrument that is most useful in determining the astronomical potential of structural alignments at archaeological sites such as prehistoric monuments. Although the designs of theodolites vary considerably, as they have throughout the century or so that they have been manufactured, their fundamental components remain invariable. These consist of a telescope that can be pointed in any direction, together with two graduated circles, mounted horizontally and vertically, which enable that direction to be defined quantitatively. In order to determine the astronomical po tential of (say) a point on the horizon as viewed from a given observing position—in other words, to determine the apparent positions of the distant celestial bodies in relation to that closer feature—the direction of that point from the observer is precisely what we need.

Any direction can be defined in terms of two angles: a horizontal angle measured around from some suitable zero point, and a vertical angle measured up or down from level. Determining the second of these is straightforward. When a theodolite is first set up on its tripod, a leveling process involving various bubbles ensures that the vertical circle is properly zeroed and will give us the required angle, which is known as the altitude. The situation regarding the horizontal angle is more complicated. The leveling process ensures that the horizontal circle is truly horizontal, but the zero point on this scale will be pointing in an arbitrary direction. What we actually want is the angle measured clockwise around from true north, which is known as the azimuth. However, generally we can't know the direction of true north (at least, to the required accuracy) in advance. What is normally done in practice is to measure what is called the horizontal plate bearing: the clockwise angle around from the arbitrary zero point. We must make the adjustment from plate bearings to azimuths in retrospect. This will involve making the same correction to each reading, by adding the actual azimuth of the zero point, sometimes known as plate bearing zero or PBZ.

But how do we determine PBZ once we have set up the theodolite? One way is to take a series of timed observations of the sun (it is very important not to look through the telescope when it is pointing at the sun, but the sun's image can be projected on to a piece of paper). The plate bearing of each reading can then be compared with the sun's actual azimuth as determined using published or on-line ephemerides. Each direction we measure (e.g., of a point on the horizon) will eventually be defined in terms of azimuth and altitude, from which we can calculate the declination and hence know what rises and sets there, or would have risen and set there at any given era in the past.

A modern theodolite will typically measure the azimuth and altitude of a distant object to a precision of twenty arc seconds or better. For work that does not warrant anything like this sort of accuracy, it may be possible to obtain the necessary information on site using a magnetic compass and a clinometer, or by using large-scale topographic maps or digital topographic data.

In addition to determining the directions of horizon points, etc., it is important to fix the position of the theodolite in space, for example, in relation to a monument. This can be done using a tape, but modern surveying instruments are very useful for this. Theodolites incorporating an electronic distance measurement device (EDM) provide a convenient way of determin ing the distance between the instrument and a reflector placed within a range of distances appropriate for most site surveys. Total Stations combine this technology with a computer chip that can convert direction-and-distance determinations of measured points into positions in space expressed in a chosen coordinate system. They can also store measurements for downloading directly to a computer, which not only allows the surveyor to dispense with the task of recording measurements manually on site, but also allows for a quick display of the results, using appropriate software.

Compass and Clinometer Surveys; Field Survey; Precision and Accuracy.

Altitude; Azimuth; Declination.