How does a theodolite work?

A theodolite is a precision instrument that measures angles in both the vertical and horizontal planes. It uses a movable telescope that can be rotated, a graduated circle (or circle divided into degrees), and one or two spirit levels. The procedure involves setting up the theodolite over a point on the ground and adjusting its level. This leveling is achieved by rotating the telescope and watching the bubble in the spirit levels.

The angles of the target point relative to the theodolite point are then measured by orienting the telescope toward the target point and rotating it until the cross-hairs in the eyepiece of the telescope line up with the target point. The motion of the telescope is recorded by the graduated circle. The readings from both the vertical and horizontal circles are noted and used to determine the angle between the two points.