On a surveying crew, the instrument man is the person who uses the transit, theodolite, level or other instrument to measure angles, elevations or distances.
These instruments are typically set up on a tripod, often precisely over a point on the ground marked by a nail or spike. The tripod usually has a bubble level to make it possible to exactly level the instrument.
Transits and theodolites are most often used to measure (or "turn", in the jargon) angles. The instrument man sights through the telescopic instrument and lines up the cross hairs on a target (often a rod, held by the rodman over some distant point). The scales are then locked and the instrument turned to sight on another point. When the second point is perfectly lined up in the cross hairs, the angle between the points can be read off of the vernier scales (or electronic display for modern instruments). In the case of a transit, this angle is usually accurate to one minute of arc. In the case of a modern theodolite, the angle can be accurate to as little as a half of a second of arc (1/3600'th of a degree, the width of a quarter seen at a distance of about three miles).
A level is used to measure elevations. It has a very precise internal mechanism to level the cross hairs inside so that the instrument itself only needs to be marginally level. The instrument man sights on a level rod held by the rodman, which is marked in feet and hundredths of a foot. The level rod is first held over a benchmark whose exact elevation is known. The number of feet read off the rod is added to the known elevation of the benchmark to determine the elevation of the instrument. As the level rod is subsequently held over additional points, their elevation is the height of the instrument minus the number read of off the level rod.
All operations conducted by the instrument man must be exact. To insure this, various procedures are used. For angles, it is possible to turn an angle several times in one direction, locking and unlocking the scales to "wind up" a sum of several turns of the same angle. Then, the angle is unwound, by turning the angle back the other direction. When finished, there will often be a very small error (say a couple of seconds) that is then distributed back over the measurements to correct them. This not only insures that no mistakes were made reading the angles off of the scales or sighting the targets, but it also gets the maximum precision out of the instrument. For elevation measurement, a loop is run, starting from the benchmark and carrying through all subsequent points. At the end, the loop checks back in to the benchmark again. Any error can be detected by the difference between the known elevation of the benchmark and the deduced elevation at the end of the run. If the error is small, it is distributed along the various points "shot" during the loop.
In modern times, the instrument man can also measure distances. Modern theodolites have electronics built in that can very accurately measure distances by bouncing microwave or laser radiation off of a distant reflector. On a still day, under good conditions, these instruments can measure distances to within one part per million (say, one millimeter per kilometer).
See: land surveying.