This result was afterwards compared with those which have been deduced by calculation from the different hypotheses relative to the æther.
According to the supposition that the æther is entirely free and independent of the motion of bodies, the displacement ought to be null.
According to the hypothesis which considers the æther united to the molecules of matter in such a way as to participate in its motions, calculation gives for the double displacement the value 0.92. Experiment gave a number only half as great, or 0.46.
According to the hypothesis by which the æther is partially carried along, the hypothesis of Fresnel, calculation gives 0.40, that is to say, a number very near to that which was found by experiment; and the difference between the two values would very probably be still less if it had been possible to introduce into the calculation of the velocity of the water a correction which had to be neglected from the want of sufficiently precise data, and which refers to the unequal velocity of the different threads of fluid; by estimating the value of that correction in the most probable manner, it is seen that it tends to augment a little the theoretical value and to approach the value of the observed result.
An experiment similar to that which I have just described had been made previously with air in motion, and I have demonstrated that the motion of the air does not produce any sensible displacement in the fringes. In the circumstances in which that experiment was made, and with a velocity of 25 metres a second, which was that of the motion of the air, it is found that according to the hypothesis by which the æther is considered to be carried along with the bodies, the double displacement ought to be 0.82.
According to the hypothesis of Fresnel, the same displacement ought to be only 0.000465, that is to say, entirely imperceptible. Thus the apparent immobility of the fringe in the experiment made with air in motion is completely in accordance with the theory of Fresnel. It was after having demonstrated this negative fact, and while seeking for an explanation by the different hypotheses relating to the æther in such a way as to satisfy at the same time the phænomena of aberration and the experiment of M. Arago, that it appeared to me to be necessary to admit with Fresnel that the motion of a body occasions an alteration in the velocity of light, and that this alteration of velocity is greater or less for different mediums, according to the energy with which those mediums refract light, so that it is considerable in bodies which are strongly refractive and very feeble in those which refract but little, as the air. It follows from this, that if the fringes are not displaced when light traverses air in motion, there should, on the contrary, be a sensible displacement when the experiment is made with water, the index of refraction of which is very much greater than that of air.
An experiment of M. Babinet, mentioned in the ninth volume of the Comptes Rendus, seems to be opposed to the hypothesis of an alteration of velocity in conformity with the law of Fresnel, But