Theory of the Sextant

The same distant object being seen directly through the clear glass, and indirectly after being reflected twice.

A ray of light from an object subtending an angle of 60 degrees with the first object does not reach the eye. To do so the reflected ray must be turned round through 60 degrees.

To do this the mirror has to be turned through half the angle (30 degrees). The observer now sees the two objects, side by side, one direct and the other after two reflections.

The scale on which the rotation of the mirror is read is specially calibrated, each degree being equal to two degrees, so that the angle between the objects is found without multiplying by two.