| Historically, distances were measured using a variety of means, such as chains with links of a known length, for instance a Gunter's Chain, or measuring tapes made of steel or invar. |
In order to measure horizontal distances, these chains or tapes would be pulled taut, to reduce sagging and slack. Additionally, attempts to hold the measuring instrument level would be made. In instances of measuring up a slope, the surveyor might have to "break" the measurement- that is, raise the rear part of the tape upward, plumb from where the last measurement ended.
Horizontal angles were historically measured using compasses, which would provide a magnetic bearing, from which deflections could be measured. This type of instrument was later improved upon, through more carefully scribed discs, providing better angular resolution, as well as through mounting telescopes with reticles for more precise sighting atop the disc. Additionally, levels and calibrated circles allowing measurement of vertical angles were added, along with verniers for measurement down to a fraction of a degree- such as a turn-of-the-century Transit (surveying).
The simplest method for measuring height is with an altimeter — basically a barometer — using air pressure as an indication of height. But for surveying more precision is needed. Toward this end, a variety of means, such as precise levels have been developed, which are calibrated to provide a precise plane from which differentials in height between the instrument and the point in question, typically through the use of a vertical measuring rod.
The basic tool is a theodolite, set on a tripod, with which one can measure angles (horizontal and vertical), combined with triangulation. Starting from a benchmark, a position with known location and elevation, the distance and angles to the unknown point are measured. A more modern instrument is a total station, which is basically a theodolite with an electronic distance measurement device (EDM). Still more modern is the use of satellite positioning systems, such as a Global Positioning System (GPS). Though GPS systems have increased the speed of surveying, they are still only accurate to about 20 mm. It is because of this that EDMDs have not been completely phased out. Robotics allows surveyors to gather precise measurements without extra workers to look through and turn the telescope or record data. A faster way to measure (no obstacles) is with a helicopter with laser echolocation, combined with GPS to determine the height of the helicopter. To increase precision, beacons are placed on the ground (about 20 km apart). This method reaches a precision of about 5 cm.
With the triangulation method, first, one needs to know the horizontal distance to the object. If this is not known or cannot be measured directly, it is determined as explained in the triangulation article. Then the height of an object can be determined by measuring the angle between the horizontal plane and the line through that point at a known distance and the top of the object. In order to determine the height of a mountain, one should do this from sea level (the plane of reference), but here the distances can be too great and the mountain may not be visible. So it is done in steps, first determining the position of one point, then moving to that point and doing a relative measurement, and so on until the mountaintop is reached.
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