son is this: The condensations sent forth from each of
the two strings occur exactly together; the rarefactions, which, of
course, alternate with the condensations, are also simultaneous. It
necessarily follows, therefore, that the condensations from each of
the two strings travel with the same velocity. Now, while this
condition prevails, it is evident that the two strings assist each
other, making the condensations more condensed, and, consequently, the
rarefactions more rarefied, the result of which is, the two allied
forces combine to strengthen the tone.

In opposition to the above, if two strings, tuned to produce the same
tone, could be so struck that the condensation of one would occur at
the same instant with the rarefaction of the other, it is readily seen
that the two forces would oppose, or counteract each other, which, if
equal, would result in absolute silence.[G]

[G] When the bushing of the center-pin of the hammer butt becomes
badly worn or the hammer-flange becomes loose, or the condition of
the hammer or flange becomes so impaired that the hammer has too
much play, it may so strike the strings as to tend to produce the
phenomenon described in the above paragraph. When in such a
condition, one side of the hammer may strike in advance of the other
just enough to throw the vibrations in opposition. Once you may get
a strong tone, and again you strike with the same force and hear but
a faint, almost inaudible sound. For this reason, as well as that of
preventing excessive wear, the hammer joint should be kept firm and
rigid.

If one of the strings vibrates 100 times in a second, and the other
101, there will be a portion of time during each second when the
vibrations will coincide, and likewise a portion of time when they
will antagonize each other. The periods of coincidence and of
antagonism pass by progressive transition from one to the other, and
the portion of time when exactitude is attained is infinitesimal; so
there will be two opposite effects noticed in every second of time:
the one, a progressive augmentation of strength and volume, the other,
a gradual diminution of the same; the former occurring when the
vibrations are coming into coincidence, the latter, when they are
approaching the point of antagonism. Therefore, when we speak of one
beat per second, we mean that there will be one period of augmentation
and one period of diminution in one seco