facts concerning sound that have been alluded to on
the preceding pages, it is easy to see how such an opinion should arise,
and also the fallacy of it. It is proved conclusively that the ability
to hear high sounds decreases as one grows older. As the violin gives a
very great number of overtones, even up to the limits of audibility, it
is plain that if such an instrument should not change in its quality of
tone in the least degree, yet to a man who played upon it for a number
of years it would seem to change by subtracting some of the higher
overtones from the sound; that is, it would seem to become mellower.
There is no evidence that such a physical change takes place in the
instrument. It is not here affirmed that no change does take place. It
may be probable; but all the evidence we have is the opinions of
individuals whose hearing we know does change; and this change is
competent to modify the judgment as to the quality of the sound in the
same direction. Before it can be affirmed that such a physical change
does take place in the violin as to make a perceptible difference in the
quality of its tone, it will be needful to determine accurately the
number and intensity of the overtones at intervals during many years,
and then to compare them. This has not yet been done.

FORM OF A COMPOUND SOUND-WAVE IN AIR.

Upon p. 63 is given a picture of the form of a simple sound-wave in air,
which, as described, consists of two parts, a condensation and a
rarefaction. All simple sound-waves have such a form; but when two or
more sound-waves that stand in some simple ratio to each other, as do
the sounds of musical instruments, are formed in air, the resulting wave
is more or less complex in structure; and where there are many
components, as there are where a number of different kinds of
instruments are all sounding at once, it is well-nigh impossible to
figure even approximately the form of such wave-combinations. It is
generally given in treatises upon sound with ordinates representing the
factors with their relative intensities. When the extremities of the
ordinates are connected, there is drawn a curved line with regularly
recurring loops. This cannot give a correct idea of the form of the
wave, because the motion of a particle of air is not up and down like a
floating body upon waving water, but it is forward and back, in the
direction of the motion of the wave.

In Fig. 10 three simple sound-waves are thus represente