In order to measure very small rotations, e.g. of the suspended parts of a galvanometer or magnetometer, two methods are commonly employed. We may either observe with a magnifier the motion of a material pointer; or, following Gauss, cause the rotating parts to carry round a mirror in which a scale is seen by reflection. In a modification of Gauss's method, well known from Sir W. Thomson's galvanometers, the image of a dark or bright line is thrown objectively upon the scale. In deciding which arrangement to adopt in any particular case, various circumstances would have to be taken into account, but still a comparison of capabilities from a purely optical point of view is not without interest.

In the mirror method the optical limit depends upon the horizontal breadth of the mirror itself. The easiest road to the desired conclusion, as well as the most instructive, is by a direct application of the principles of the wave theory. To take the simplest case, we will suppose the mirror rectangular. Consider, then, a luminous point, and its image after reflection, whether in the focal plane of a telescope, or formed directly upon a scale. The optical work being perfect, the secondary rays from every part of the mirror agree in phase at the focal point. Now suppose that the mirror rotates through such an angle that one vertical edge advances a quarter of a wave-length (¼λ), while the other retreats to the same amount, and consider the effect on the phase-relations at the point in question.