For now wellnigh a century we have had a wave theory of light; and a wave theory of light is quite certainly true. It is directly demonstrable that light consists of waves of some kind or other, and that these waves travel at a certain well-known velocity,--achieving a distance equal to seven times the circumference of the earth every second; from New York to London and back in the thirtieth part of a second; and taking only eight minutes on the journey from the sun to the earth. This propagation in time of an undulatory disturbance necessarily involves a medium. If waves setting out from the sun exist in space eight minutes before striking our eyes, there must necessarily be in space some medium in which they exist and which conveys them. Waves we cannot have, unless they be waves in something. No ordinary matter is competent to transmit waves at anything like the speed of light: the rate at which _matter_ conveys waves is the velocity of sound,--a speed comparable to one-millionth of the speed of light. Hence the luminiferous medium must be a special kind of substance; and it is called the ether. The _luminiferous_ ether it used to be called, because the conveyance of light was all it was then known to be capable of; but now that it is known to do a variety of other things also, the qualifying adjective may be dropped. But, inasmuch as the term 'ether' is also applied to a familiar organic compound, we may distinguish the ultra-material luminiferous medium by calling it the Ether of Space. Wave-motion in ether, light certainly is; but what does one mean by the term wave? The popular notion is, I suppose, of something heaving up and down, or perhaps of something breaking on a shore. But if you ask a mathematician what he means by a wave, he will probably reply that the most general wave is such a function of _x_ and _y_ and _t_ as to satisfy the differential equation d²y/dt² = v² d²y/dx²; while the simplest wave is y = a sin (x-vt). And he might possibly refuse to give any other answer. And in refusing to give any other answer than this, or its equivalent in ordinary words, he is entirely justified; that _is_ what is meant by the term wave, and nothing less general would be all-inclusive. Translated into ordinary English the phrase signifies, with accuracy and comprehensive completeness, the full details of "a disturbance periodic both in space and time." Anything thus doubly periodic is a wave; and all waves--whether in air as sound waves, or in ether as light waves, or on the surface of water as ocean waves--can be comprehended in the definition.