Theodolite Employed for Tacheometry by Stadia System

The stadia system is a method used in tacheometry for measuring distances and elevations. It involves using a theodolite with a stadia diaphragm, which is specially designed for this purpose. The stadia diaphragm consists of a pair of horizontal hairs or stadia hairs that are fixed in the focal plane of the objective lens of the theodolite.

Comparison with an Ordinary Transit

The theodolite employed for tacheometry by the stadia system differs from an ordinary transit in terms of the diaphragm configuration. While an ordinary transit typically has a single horizontal hair and a single vertical hair, the theodolite used for tacheometry by the stadia system has two additional horizontal hairs.

Reason for Additional Horizontal Hairs

The additional horizontal hairs in the stadia system theodolite serve a specific purpose. They are used to measure the subtense or stadia intercept, which is the distance between the two horizontal hairs as observed in the field of view. This distance is directly proportional to the distance between the instrument and the target.

Measurement of Distance

To measure the distance using the stadia system, the theodolite is set up at a known position and the two horizontal hairs are aligned with two points on the target whose distance is to be determined. The subtense or stadia intercept is then read from the graduated stadia rod held at the target point.

Relation between Subtense and Distance

The relation between the subtense and the distance can be expressed by the stadia formula: Distance = K x subtense, where K is a constant factor that depends on the focal length of the objective lens and the distance between the instrument and the target.

Advantages of Stadia System

The stadia system offers several advantages in tacheometry. It allows for the rapid measurement of distances and elevations without the need for additional equipment such as chains or tapes. It is particularly useful for large-scale surveys and topographical mapping.

In summary, the theodolite employed for tacheometry by the stadia system differs from an ordinary transit by having two additional horizontal hairs. These additional hairs are used to measure the subtense or stadia intercept, which is directly proportional to the distance between the instrument and the target. The stadia system provides a convenient and efficient method for measuring distances and elevations in tacheometry.