Introduction

A number of visual optical instruments are designed to measure the angles between two distant objects or the distance of an object. The determination of the angle between two distant objects is frequently done in surveying. Using simple rules of trigonometry, the location of any point can be determined if the direction of two other points and the distances between any two pairs of points are known. The determination of the elevation of celestial objects combined with astronomical tables and an accurate clock can be used to determine a position on the earth's surface, for surveying and navigation.

In many applications, these instruments have been superseded by other quicker or more accurate means. For example distance measurement can now be done with laser rangefinders and satellites are used for routine navigation. However, visual optical instruments are still used in some applications and are still worthy of some attention.

Angle measuring instruments

The theodolite

The theodolite is in essence a telescope of medium magnification with an eyepiece containing an alignment graticule. It is mounted such that it can rotate through horizontal and vertical circles, so that its horizontal and vertical direction of pointing can be measured. The theodolite is fitted with a levelling bubble so that the horizontal scale or table can be accurately made horizontal. If the vertical scale is zero for this horizontal scale then the elevation of an object can be absolutely read from the vertical scale.