ether _transversal_.

The most familiar illustration of the interference of sound-waves is
furnished by the _beats_ produced by two musical sounds slightly out
of unison. When two tuning-forks in perfect unison are agitated
together the two sounds flow without roughness, as if they were but
one. But, by attaching with wax to one of the forks a little weight,
we cause it to vibrate more slowly than its neighbour. Suppose that
one of them performs 101 vibrations in the time required by the other
to perform 100, and suppose that at starting the condensations and
rarefactions of both forks coincide. At the 101st vibration of the
quicker fork they will again coincide, that fork at this point having
gained one whole vibration, or one whole wavelength, upon the other.
But a little reflection will make it clear that, at the 50th
vibration, the two forks condensation where the other tends to produce
a rarefaction; by the united action of the two forks, therefore, the
sound is quenched, and we have a pause of silence. This occurs where
one fork has gained _half a wavelength_ upon the other. At the 101st
vibration, as already stated, we have coincidence, and, therefore,
augmented sound; at the 150th vibration we have again a quenching of
the sound. Here the one fork is _three half-waves_ in advance of the
other. In general terms, the waves conspire when the one series is an
_even_ number of half-wave lengths, and they destroy each other when
the one series is an _odd_ number of half-wave lengths in advance of
the other. With two forks so circumstanced, we obtain those
intermittent shocks of sound separated by pauses of silence, to which
we give the name of beats. By a suitable arrangement, moreover, it is
possible to make one sound wholly extinguish another. Along four
distinct lines, for example, the vibrations of the two prongs of a
tuning-fork completely blot each other out.[12]

The _pitch_ of sound is wholly determined by the rapidity of the
vibration, as the _intensity_ is by the amplitude. What pitch is to
the ear in acoustics, colour is to the eye in the undulatory theory of
light. Though never seen, the lengths of the waves of light have been
determined. Their existence is proved _by their effects_, and from
their effects also their lengths may be accurately deduced. This may,
moreover, be done in many ways, and, when the different determinations
are compared, the strictest harmony is found to exist between them.
This c