will be sixteen waves, giving a length of
about 70 feet to each wave. This is the lowest sound that the human
ear can appreciate as a musical note, and is, what may be called, the
fourth Octave above one vibration in one second. When the number of
vibrations in a second sinks below sixteen, the ear no longer
appreciates them as a musical sound, but is able to hear them as
separate vibrations or beats. The easiest way of illustrating this is
by means of a revolving disc, with sixteen holes pierced at regular
intervals round the edge, and a jet of high-pressure air, which is
forced through each of the holes successively as they revolve. When
the disc does not quite complete one revolution in a second, only
fifteen puffs come to the ear in a second of time, and they are heard
as puffs; but when the rate reaches one revolution in a second, the
sound, as if by magic, changes into the lowest musical sound. The same
result may be obtained in a more pronounced form by means of
explosions or pistol shots; when these are slow and heard separately,
they are painful and almost unbearable to the ear, but, as soon as
their rapidity, namely, at sixteen per second, gets beyond the power
of the ear to differentiate between the explosions, the impression, as
if by magic, changes into a continuous or musical sound, like a
thirty-foot pipe note of an organ.

To go back to our disc. The octave above this lowest musical note is
obtained by doubling the rate of puffs, namely, by revolving the disc
twice in one second, and the next octave by revolving four times in a
second, and so on, doubling each time, until, at about the thirteenth
octave, the sound has become so high that the majority of listeners
cannot hear it, and fancy it must have stopped, whereas a few will
still be saying: "How shrill it is!" At last, at about the fourteenth
octave, when there are 20,000 beats to the second and each wave is
about half an inch long, it passes beyond human audition, and,
although we can show that the air is still vibrating, all is silent,
the human ear being incapable of hearing so many beats in a second
even as a continuous sound, though I have evidence to show that many
insects can hear probably considerably beyond this limit. It is,
however, possible to make these higher vibrations perceptible to our
senses by means of what are called sensitive flames: we can actually,
by these, measure the length of these silent waves, and as we know the
rate a