In the period considered four great novel ideas were introduced into theoretical science. Of course, it is possible to show good cause for increasing my list far beyond the number _four_. But I am keeping to ideas which, if taken in their broadest signification, are vital to modern attempts at reconstructing the foundations of physical science. Two of these ideas are antithetical, and I will consider them together. We are not concerned with details, but with ultimate influences on thought. One of the ideas is that of a field of physical activity pervading all space, even where there is an apparent vacuum. This notion had occurred to many people, under many forms. We remember the medieval axiom, nature abhors a vacuum. Also, Descartes’ vortices at one time, in the seventeenth century, seemed as if established among scientific assumptions. Newton believed that gravitation was caused by something happening in a medium. But, on the whole, in the eighteenth century nothing was made of any of these ideas. The passage of light was explained in Newton’s fashion by the flight of minute corpuscles, which of course left room for a vacuum. Mathematical physicists were far too busy deducing the consequences of the theory of gravitation to bother much about the causes; nor did they know where to look, if they had troubled themselves over the question. There were speculations, but their importance was not great. Accordingly, when the nineteenth century opened, the notion of physical occurrences pervading all space held no effective place in science. It was revived from two sources. The undulatory theory of light triumphed, thanks to Thomas Young and Fresnel. This demands that there shall be something throughout space which can undulate. Accordingly, the ether was produced, as a sort of all pervading subtle material. Again the theory of electromagnetism finally, in Clerk Maxwell’s hands, assumed a shape in which it demanded that there should be electromagnetic occurrences throughout all space. Maxwell’s complete theory was not shaped until the eighteen-seventies. But it had been prepared for by many great men, Ampère, Oersted, Faraday. In accordance with the current materialistic outlook, these electromagnetic occurrences also required a material in which to happen. So again the ether was requisitioned. Then Maxwell, as the immediate first-fruits of his theory, demonstrated that the waves of light were merely waves of his electromagnetic occurrences. Accordingly, the theory of electromagnetism swallowed up the theory of light. It was a great simplification, and no one doubts its truth. But it had one unfortunate effect so far as materialism was concerned. For, whereas quite a simple sort of elastic ether sufficed for light when taken by itself, the electromagnetic ether has to be endowed with just those properties necessary for the production of the electromagnetic occurrences. In fact, it becomes a mere name for the material which is postulated to