374 



THE SPECIAL SENSES. 



obtained. In this way a great variety of forms of compound waves 

 may be supposed to be produced by the union of a series of simple 

 waves of different periods of vibration. That compound waves dif- 

 fer from simple ones in being composed of several series of vibrations 

 is indicated directly by our sensations. When we listen to the note 

 of a tuning-fork we hear only a single tone; when two or more 

 tuning-forks are sounded together the trained ear can detect the tone 

 due to each fork, and similarly when a single note is sounded by 

 the human voice, a violin, or any other instrument that has a char- 

 acteristic quality the trained ear can detect a series of higher tones, 



Fig. 167. Schema by Helmholtz to illustrate the formation of a compound wave 

 from two pendular waves: A and B, pendular vibrations, B being the octave of A. If 

 superposed so that e coincides with d and the ordinates are added algebraically, the non- 

 pendular curve C is produced. If superposed so that e coincides with d' the non-pendular 

 curve D is produced. 



the upper partial tones, or harmonics, or overtones, which indicate 

 that the note is really compound, and not simple. The formation 

 of these overtones is due to the fact that the sounding body vibrates 

 not only as a whole, but also in its aliquot parts, as may be repre- 

 sented in Fig. 168, illustrating the vibrations of a string. When 

 the string is plucked it vibrates as a whole (a), giving large waves 

 which produce what is called the fundamental tone, but at the same 

 time each half (b), third (c), fourth (d), etc., may vibrate, giving 

 each its own simple tone. The combination of all of these simple 

 waves forms a compound wave whose form or at least whose 



