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The stadia marks are set a specific length apart. This length is chosen so that there is a fixed, integer ratio between the difference of the rod readings and the distance from the telescope to the rod. This ratio is known as the stadia constant or stadia interval factor. Thus the formula for distance is D = kS. where
Stadia readings used in surveying can be taken with modern instruments such as transits, theodolites, plane-table alidades and levels. When using the stadia measuring method, a level staff or stadia rod is held so that it appears between two stadia marks visible on the instrument's reticle.
In both parts of the pattern, the squares, lines or spaces are precisely one centimetre high. When viewed through an instrument's telescope, the observer can visually interpolate a 1 cm mark to a tenth of its height, yielding a reading with precision in mm. Usually readings are recorded with millimetre precision. On this side of the rod, the ...
The rod is then held on an unknown point and a reading is taken in the same manner, allowing the elevation of the new (foresight) point to be computed. The difference between these two readings equals the change in elevation, which is why this method is also called differential levelling. The procedure is repeated until the destination point is ...
The surveyor rotates the telescope until the graduated staff is in the crosshairs and records the reading. This is repeated for all sightings from that datum. Should the instrument be moved to another position within sighting distance, it is re-levelled, and a sighting taken of a known level in the previous survey.
Alternatively, also by readings of the staff indicated by two fixed stadia wires in the diaphragm of the telescope. The difference of height Δh is computed from the angle of depression z or angle of elevation α of a fixed point on the staff and the horizontal distance S already obtained.
The division of the device in two sliding sections are devised for ease of transport. Readings of 7 ft (2.1 m) or less, and up to 13 ft (4.0 m), can be measured. It has a rear section that slides on the front section. The rod must be fully extended, when higher measurements are needed to avoid reading errors.
From these readings a plan can be drawn, or objects can be positioned in accordance with an existing plan. The modern theodolite has evolved into what is known as a total station where angles and distances are measured electronically, and are read directly to computer memory.