Now so great a displacement could certainly not have escaped observation, especially since it might have been doubled by reversing the current.
The following would be the results of the calculation according to the hypothesis of Fresnel:—
Now a displacement equal to
of the breadth of a band could not be observed; it might, in fact, be a hundred times greater and still escape observation. Thus the apparent immobility of the bands in the experiment made with moving air may be explained by the theory of Fresnel, according to which the displacement in question, although not absolutely zero, is so small as to escape observation.
After having established this negative fact, and seeking, by means of the several hypotheses respecting æther, to explain it as well as the phenomenon of aberration and the experiment of Arago, it appeared to me to be necessary to admit, with Fresnel, that the motion of bodies changes the velocity with which light traverses them, but that this change of velocity varies according to the energy with which the traversed medium refracts light; so that the change is great for highly refracting bodies, but small for feebly refracting ones such as air.
I was thus led to anticipate a sensible displacement of the bands by means of the motion of water, since its index of refraction greatly exceeds that of air.