in this manner I have been able to observe with the telescope C, with sufficient clearness, countless circular fringes, even for l = 32 cm. But for these researches I have limited the difference of path to l = 13 cm., or still less.
The disposition described above is particularly suitable for detecting very small differences in the value of the incident wave-length; in fact, the value of l being large a very great number of wave-lengths is comprised in this length (e.g., 200,000 if λ = 0.5μ, and l = 10 cm.), and correspondingly for the same variations very sensible displacements can be observed in the position of a fringe.
With the apparatus disposed as above, let us note with the micrometer wire of the telescope the position of a fringe, for instance the first central bright one, when R is in the position shown in the figure, or, still better, when it revolves with a negligible velocity (one turn per second). If, now, this velocity be increased to sixty turns per second a displacement of the fringe under observation is distinctly visible; if the mirrors are moving against the incident ray this displacement indicates a diminution of λ, and it changes sign when the direction of rotation of the wheel is reversed, and this indicates an increase of λ. In order to define the sense of the displacement, I will say that on examining the system of circular fringes with the telescope focussed for infinite distance the diameter of each of these increases when the mirrors move against the incident ray, and the fringes themselves crowd together as those of large diameter are very little displaced; at the same time some new fringes come out from the centre of the system. On the other hand, when the mirrors are moving in the sense of propagation of the incident light the diameter of each fringe diminishes; they become more widely separated, and some of them are as it were swallowed up by the centre.
Before stating the measure of the displacement observed we will see what it should amount to, making the hypothesis that the velocity of the light reflected from a mirror is the same as that of the incident light. Let g be the number of revolutions of R per second and d its diameter, reckoned between the centres of two opposite mirrors M, then πdg will be the instantaneous velocity of translation of the latter. Since the mirrors are inclined at an angle α to the radius of the wheel passing through each of them, the component of the given velocity in the direction normal to the plane of each mirror will be
v = πdg cos α.
