em to the bones of the upper jaw, and by these to
the auditory nerve. In this way a person born deaf, and having no
power of hearing through the medium of the air, may become sensible
of the pleasures of music.

That sound may be propagated by vibrations, independent of pulses of
the air, is evident from the experiment with the string and poker.

There is, strictly speaking, no such thing existing as sound; it
being only a sensation of the mind, caused by tremors of the air, or
vibrations of the sounding body.

In order to understand more clearly how pulses, or waves are caused
by the vibration of bodies, and the manner in which vibrating bodies
are affected, I shall just enumerate some of the properties of
pendulums, which however I shall not stop to demonstrate here, as
that would consume much time.

When two pendulums vibrate which are exactly of the same length,
their vibrations are performed in equal times; if they set out
together to describe equal arcs, they will agree together in their
motions, and the vibrations will be performed in equal times.

But if one of these pendulums be four times as long as the other, the
vibrations of the longer will be twice as slow as those of the
shorter; the number of vibrations being as the square roots of their
lengths.

A pendulum is fixed to one point, but a musical string is extended
between two points, and in its vibrations may be compared to a double
pendulum vibrating in a very small arc, hence we see how strings of
different lengths may agree in their motions after the manner of
pendulums; but we must observe that it is not necessary to quadruple
the length of a musical string, in order to make the time of
vibration twice as long; it will be sufficient merely to double it.
We know that from whatever height a pendulum falls on one side, to
the same height will it rise on the other. In the same manner will an
elastic string continue to vibrate from one side to the other for
some time, till its motion be destroyed by the resistance of the air,
and friction about its fixed points, and each of its small
vibrations, like those of a pendulum, will, for the same reason, be
performed in times exactly equal to each other.

Thus we gain from the analogy between a pendulum and a musical
string, a more adequate conception of a subject which was never
understood till this analogy was discovered. It explains to us why
every musical string preserves the same pitch from the begi