SYMPATHETIC RESONANCE. 549 



tones when proceeding from one instrument, and that the 

 ripper partial s, not rising into consciousness as definite 

 tones, but present as subdued sensations, give its char- 

 acter to the whole tone and determine its timbre. It 

 might be, however, that the composition of non-pendular 

 vibrations from pendular was a mere mathematical possibil- 

 ity, having no real existence in nature. Before we can ac- 

 cept the above explanation of timbre, we must see if there 

 is any evidence that, as a matter of fact, non-pendular vibra- 

 tions, not only may be, but are, made up by the combination 

 of pendular. 



/ Sympathetic Besonance. Imagine slight taps to be 

 ugffen to a pendulum ; n these be repeated at such intervals 

 of time as to always help the swing and never to retard it, I 

 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 move- 

 ment, 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 

 given 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 powerful vibrations to cause 

 it to emit an audible note. By using such strings we 

 might hope to detect the separate pendular vibrations in 

 any non-pendular aerial periodic movement if such really 

 existed; certain strings would pick out the pendular com- 

 ponent agreeing in rate with their own vibrational period 

 and be soon set in powerful movement; while those not 

 vibrating in the same period as any of the pendular compo- 

 nents, would remain practically at rest, like the pendulum 

 getting taps which sometimes helped and sometimes impeded 

 its swing. If the dampers of a piano be raised and a note 

 be sung to it, it will be found that several strings are set in 

 vibration, such vibrations being called sympathetic. The 

 human voice emits compound tones which can be mathe- 

 matically analyzed into simple vibrations, and if the piano 



