their regularity. If we shake a number of nails in a
tin box, we get only a series of superimposed and chaotic sensations. On
the other hand, if we strike a tuning-fork, the air is agitated a
certain number of times a second, with a pleasant result which we call a
note.

We will begin our excursion into the region of musical instruments with
an examination of that very familiar piece of furniture,

THE PIANOFORTE,

which means literally the "soft-strong." By many children the piano is
regarded as a great nuisance, the swallower-up of time which could be
much more agreeably occupied, and is accordingly shown much less respect
than is given to a phonograph or a musical-box. Yet the modern piano is
a very clever piece of work, admirably adapted for the production of
sweet melody--if properly handled. The two forms of piano now generally
used are the _upright_, with vertical sound-board and wires, and the
_grand_, with horizontal sound-board.[27]

THE VIBRATION OF STRINGS.

As the pianoforte is a stringed instrument, some attention should be
given to the subject of the vibration of strings. A string in a state of
tension emits a note when plucked and allowed to vibrate freely. The
_pitch_ of the note depends on several conditions:--(1) The diameter of
the string; (2) the tension of the string; (3) the length of the string;
(4) the substance of the string. Taking them in order:--(1.) The number
of vibrations per second is inversely proportional to the diameter of
the string: thus, a string one-quarter of an inch in diameter would
vibrate only half as often in a given time as a string one-eighth of an
inch in diameter. (2.) The length remaining the same, the number of
vibrations is directly proportional to the _square root_ of the
_tension_: thus, a string strained by a 16-lb. weight would vibrate four
times as fast as it would if strained by a 1-lb. weight. (3.) The number
of vibrations is inversely proportional to the _length_ of the string:
thus, a one-foot string would vibrate twice as fast as a two-foot
string, strained to the same tension, and of equal diameter and weight.
(4.) Other things being equal, the rate of vibration is inversely
proportional to the square root of the _density_ of the substance: so
that a steel wire would vibrate more rapidly than a platinum wire of
equal diameter, length, and tension. These facts are important to
remember as the underlying principles of stringed instruments.

Now, i