ular 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.

What properties are essential to a medium capable of transmitting wave
motion? Roughly we may say two--_elasticity_ and _inertia_. Elasticity
in some form, or some equivalent of it, in order to be able to store
up energy and effect recoil; inertia, in order to enable the disturbed
substance to overshoot the mark and oscillate beyond its place of
equilibrium to and fro. Any medium possessing these two properties can
transmit waves, and unless a medium possesses these properties in some
form or other, or some equivalent for them, it may be said with
moderate security to be incompetent to transmit waves. But if we make
this latter statement, one must be prepared to extend to the terms
elasticity and inertia their very largest and broadest signification,
so as to include any possible kind of restoring force and any possible
kind of persistence of motion respectively.

These matters may be illustrated in many ways, but perhaps a simple
loaded lath or spring in a vise will serve well enough. Pull aside one
end, and its elasticity tends to make it recoil; let it go, and its
inertia causes it to overshoot its normal position; both causes
together cause it to swing to and fro till its energy is exhausted. A
regular series of such springs at equal intervals in space, set going
at regular intervals of time one after the other, gives you at once a
wave motion and appearance which the most casual observer must
recognize as such. A series of pendulums will do just as well. Any
wave-transmitting medium must similarly possess some form of
elasticity and of inertia.

But now proceed to ask what is this ether wh