[Footnote 2:  Though, indeed, a century hence it may be premature
    to offer an opinion on such a point.]

To attempt to give any idea of the drift of progress in all the directions which I have hastily mentioned, to attempt to explain the beginnings of the theories of elasticity and of matter, would take too long, and might only result in confusion.  I will limit myself chiefly to giving some notion of what we have gained in knowledge concerning electricity, ether, and light.  Even that is far too much.  I find I must confine myself principally to light, and only treat of the others as incidental to that.

For now well nigh 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, seven times the circumference of the earth per second, taking 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 medium is competent to transmit waves at anything like 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.

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 the shore in which it is possible to bathe.  But if you ask a mathematician what he means by a wave, he will probably reply that the simplest wave is

  y = a sin (p t — n x),

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 “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, are comprehended in the definition.