the apparent velocity of B will for him be 400,000 kilometers. If A knows the new mechanics he will say: "B has a velocity he cannot attain, therefore I also am in motion." It seems he could decide about his absolute state. But he must be able to observe the motion of B himself. To make this observation A and B commence by setting their watches, then B sends telegrams to A to indicate to him his successive positions; putting them together A can reckon B's motion and trace the curve of this motion. Now the signals go with the speed of light. The watches which mark the apparent time vary at each instant and everything will happen as if B's watch went too fast. B will think himself going much less rapidly and the apparent velocity he will have relatively to A will not surpass the limit it should not attain. Nothing can reveal to A whether he is in motion or at absolute rest.
It is still necessary to make a third hypothesis, which is much more surprising, much more difficult to admit, and which greatly disturbs our present modes of thought. A body in motion of translation undergoes a deformation in the direction of its displacement; a sphere, for instance, becomes like a species of flattened ellipsoid with the short axis parallel to the translation. If we do not perceive such a transformation every day this is because it is so small as to render it almost imperceptible. The earth, borne along in its revolution through its orbit, is deformed about 1⁄200 000 000. To observe such a phenomenon would require measuring instruments of extreme precision, but if their precision were infinite it would not avail, because they also are borne along in the motion and would undergo the same transformation. We should perceive nothing; the meter we could use would shorten like the length to be measured. We could not learn anything except by comparing the length of one of these bodies to the velocity of light.
