Are not Einstein’s theories, as some imperfectly informed writers have suggested, only a play of mathematical formulæ (taking the word in the meaning given to it by both mathematicians and philosophers)? If they were only a towering mathematical structure in which the _x_’s shoot out their volutes in bewildering arabesques, with swan-neck integrals describing Louis XV patterns, they would have no interest whatever for the physicist, for the man who has to examine the nature of things before he talks about it. They would, like all coherent schemes of metaphysics, be merely a more or less agreeable system of thought, the truth or falseness of which could never be demonstrated. Einstein’s theory is very different from that, and very much more than that. It is based upon facts. It also leads to facts—new facts. No philosophical doctrine or purely formal mathematical construction ever enabled us to discover new phenomena. It is precisely because it has led to such discovery that Einstein’s theory is neither the one nor the other. That is the difference between a scientific theory and a pure speculation, and it is that which, I venture to say, makes the former so superior. Like some suspension bridge boldly thrown across an abyss, Einstein’s theory rests, on the one side, on experimental phenomena, and it leads, at the other side, to other, and hitherto unsuspected, phenomena, which it has enabled us to discover. Between these two solid experimental columns the mathematical reasoning is like the marvellous network of thousands of steel bars which represent the elegant and translucent structure of the bridge. It is that, and nothing but that. But the arrangement of the beams and bars might have been different, and the bridge—though less light and graceful, perhaps—still have been able to join together the two sets of facts on which it rests. In a word, mathematical reasoning is only a kind of reasoning in a special language, from experimental premises to conclusions which are verifiable by experience. Now there is no language which cannot in some degree be translated into another language. Even the hieroglyphics of Egypt had to give way before Champollion. I am therefore convinced that the mathematical difficulties of Einstein’s theories will some day be replaced by simpler and more accessible formulæ. I believe, indeed, that it is even now possible to give by means of ordinary speech an idea, rather superficial perhaps, but accurate and substantially complete, of this wonderful Einsteinian structure which ranges all the conquests of science, as in some well-ordered museum, in a new and superb unity. Let us try. * * * * * We may resume in the few following words the story of the origin, the starting-point, of Einstein’s system. 1. Observation of the stars proves that interplanetary space is not empty, but is filled with a special medium, ether, in which the waves of light travel.