Page:Deux Mémoires de Henri Poincaré.djvu/2

 is determined by the "coefficient of Fresnel" $$1\tfrac{1}{n^ {2}}$$, in which $$N$$ is the index of refraction of the medium.

When, thanks to the work of Clerk Maxwell, our views on the nature of light had been profoundly changed, it was natural to try a deduction of this coefficient based on the principles of the electromagnetic theory. That's the goal I set myself, which could be achieved without too much difficulty in the theory of electrons.

The majority of the phenomena which are connected to aberration, and in particular the absence of an influence of the earth's motion in all the experiments where the collective system of devices is at rest in respect to our planet, could now be explained in a satisfactory way. It was only necessary to make the restriction, that the considered effects were of first order of magnitude compared to the speed of the Earth divided by the speed of light, terms of the second order have been neglected in calculations.

However, in 1881 Mr. Michelson succeeded to interfere two light rays, that were departed from a single point and came back after following rectilinear and mutually perpendicular paths of equal length. He found that the observed phenomena are again insensitive to the earth's motion; the interference fringes preserved the same positions, whatever were the directions of the arms of the device.

This time it was indeed an effect of the second order and it was easy to see that the hypothesis of the stationary aether alone is not sufficient for the explanation of the negative result. I was obliged to make a new assumption which consists in admitting, that the translation of a body through the aether produces a slight contraction of the body in the direction of motion. This assumption was indeed the only possibility; it had also been imagined by Fitzgerald and it found the approval of Poincaré, who however did not conceal the lack of satisfaction that the theories gave him in which one multiplies special assumptions invented for particular phenomena. This criticism was for me an additional reason to seek a general theory, in which the same principles would lead to the explanation of the experiment of Mr. Michelson and all those that were undertaken after him to discover effects of the second order. In the theory that I proposed, the absence of phenomena due to the collective motion of a system should be demonstrated for any value of speed less than that of light.

The method to be followed was indeed indicated. It was obviously necessary to demonstrate that