78 ON THE PHYSIOLOGICAL CAUSES OF 



tones, and feels the tone due to each separate simple wave sepa- 

 rately, whether the compound wave originally proceeded from a 

 source capable of generating it, or became compounded on the 

 way. 



For example, on striking a string, it will give a tone correspond- 

 ing, as we have seen, to a wave-form widely different from that of a 

 simple tone. When the ear analyses this wave-form into a sum of 

 simple waves, it hears at the same time a series of simple tones cor- 

 responding to these waves. 



Strings are peculiarly favourable for such an investigation, be- 

 cause they are themselves capable of assuming extremely different 

 forms in the course of their vibration, and these forms may also be 

 considered, like those of aerial undulations, as compounded of simple 

 waves. Fig. 4, p. 66, shows the consecutive forms of a string struck by 

 a simple rod. Fig. 11, p. 79, gives a number of other forms of vibration 

 of a string, corresponding to simple tones. The continuous line shows 

 the extreme displacement of the string in one direction, and the 

 dotted line in the other. At a the string produces its fundamental 

 tone, the deepest simple tone it can produce, vibrating in its whole 

 length, first on one side and then on the other. At b it falls into 

 two vibrating sections, separated by a single stationary point |3, called 

 a node (knot). The tone is an octave higher, the same as each of the 

 two sections would separately produce, and it performs twice as many 

 vibrations in a second as the fundamental tone. At c we have two 

 nodes, y 3 and y v and three vibrating sections, each vibrating three 

 times as fast as the fundamental tone, and hence giving its^twelfth. 

 At dj there are three nodes, 8 lf S 2 , 8 3 , and four vibrating sections, 

 each vibrating four times as quickly as the fundamental tone, and 

 giving the second octave above it. 



In the same way forms of vibration may occur with 5, 6, 7, &c., 

 vibrating sections, each performing respectively 5, 6, 7, &c., times as 

 many vibrations in a second as the fundamental tone, and all other 

 vibrational forms of the string may be conceived as compounded of a 

 sum of such simple vibrational forms. 



The vibrational forms with stationary points or nodes may be 

 produced by gently touching the string at one of these points either 

 with the finger or a rod, and rubbing the string with a violin bow, 

 plucking it with the finger, or striking it with a pianoforte hammer. 

 The bell-like harmonics or flageolet-tones of strings, so much used in 

 violin playing, are thus produced. 



