THE EAR, HEARING, TASTE AND SMELL 225 



and intense enough. The actual form of air wave which proceeds 

 from a body vibrating thus depends upon the particular com- 

 ponents which make it, and it has been shown that any complex 

 periodic vibration can be analyzed mathematically into its con- 

 stituents, and these unerringly determined. The timbre of a tone 

 depends, then, according to our former definition, upon the form of 

 air wave which enters the ear. A tone composed of a fundamental 

 and three overtones will come to the ear as a wave having quite a 

 different form from one having in addition to the fundamental 

 five partials. 



Whereas we ordinarily hear compound tones merely as tones of 

 certain quality, the trained ear is able to hear and pick out the 

 overtones by which the quality is determined. It is evident, 

 therefore, that the ear is able to analyze compound tones into their 

 individual constituents. 



Sympathetic Resonance. Imagine slight taps to be given to a 

 pendulum; if these be repeated at such intervals of time as al- 

 ways to help the swing and never to retard it, the pendulum will 

 soon be set in powerful movement. If the taps are irregular, or 

 when regular come at such intervals as sometimes to promote and 

 sometimes retard the movement, no great swing will be produced; 

 but if they always push the pendulum in the way it is going at that 

 instant, they need not come every swing in order to set up a power- 

 ful vibration; once in two, three, or four swings will do. A stretched 

 string, such as that of a piano, is so far like a pendulum that 

 it tends to vibrate at one rate and no other; if aerial waves hit 

 it at exactly the right times they soon set it in sufficiently power- 

 ful vibrations to cause it to emit an audible note. By using such 

 strings we can analyze compound tones and thus prove objectively 

 that they are made up of partials. If the dampers of a piano be 

 raised and a note be sung loudly to it, it will be found that several 

 strings are set in vibration, such vibrations being called sympa- 

 thetic. The human voice emits compound tones which can be 

 mathematically analyzed into simple vibrations, and if the piano 

 strings set in movement by it be examined, they will be found to 

 be exactly those which answer to these vibrations and to no 

 others. We thus get experimental grounds for believing that com- 

 pound tones are really made up of a number of simple vibrations, 

 and get an additional justification for the supposition that in 



