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