In surveying, a telescope is set up at one end of a base-line and pointed first at the other end of the base-line and then at the distant object. A scale with which the instrument is provided gives us the size of the angle between the two. Then the same thing is done at the other end of the "base" and the similar angle there is obtained. The length of the base being known, the distance of the remote object can then be calculated.
In the same way two observations can be made, one at each end of a ship, the length of the ship forming the base-line. Or an instrument can be made by which two observations can be made simultaneously by the same man.
This is done by means of mirrors which are turned so that the same object is seen in both of them, apparently in a straight line. The extent to which one of them has to be turned gives the angle, and the instrument forms the base.
Anyone with the slightest geometrical experience will perceive at once that the best results are obtained when the base-line is of considerable length, and hence small portable range-finding instruments such as can be easily carried and used by one man are necessarily less accurate than an arrangement such as has been suggested above, where two observers work simultaneously from the two ends of a ship.
In many cases, however, the self-contained instrument is the only one which it is possible to use, and when the instrument is well made and in experienced hands the results are surprisingly good.
As used in surveying, for example, where the base-line may be anything, according to circumstances, and the angles may likewise vary at both ends, elaborate trigonometrical calculations have to be performed to arrive at the desired result. If, however, the base-line be always the same, and one of the angles be always a right angle, the distance of the distant object will vary with the remaining angle. Indeed the scale by which that angle is measured can be made to give not degrees, but the distance of the object. Portable range-finders, therefore, in many cases have one reflector set for a right angle and only one of the reflectors movable. The instrument then shows the distance of the object at a glance.
This is impossible in the case of two separate observations on a ship. In that case the base is always the same, but since the ship cannot be set at right angles to the object whenever a range has to be found, both angles have to be measured. There is, however, a beautifully simple little mechanism in which two pointers are set one to each of the two angles, and the distance is then shown instantly.