830 SPECIAL SENSES. 



will remain undisturbed, while riders placed at any other portion of the string will be 

 thrown off. This experiment shows that the three-fourths of the string have been di- 

 vided, as we have sounded the second octave above the fundamental tone. This may be 

 illustrated by connecting one end of the string with a tuning-fork. When this is done, 

 and the string is brought to the proper degree of tension, it will first vibrate as a whole, 

 then, when a little tighter, will spontaneously divide into two equal parts, and, under 

 increased tension, into three, four, and so on. By damping a string with the light touch 

 of a feather, we suppress the fundamental tone and bring out the overtones, which exist 

 in all vibrating strings, but are usually concealed by the fundamental. The points which 

 mark the subdivisions of the string into segments of secondary vibrations are called 

 nodes. When we damp the string at its centre, we quench the fundamental tone and 

 have overtones an octave above ; damping it at a distance of one-fourth, we have the 

 second octave above, and so on. When we damp it at a distance of one-fifth from the 

 end, we have the four-fifths sounding the 3d of the fundamental, with the second octave 

 of the 3d. If we damp it at a distance of two-thirds, we have the 5th of the fundamen- 

 tal, with the octave of the 5th. 



Every vibrating string possesses, thus, a fundamental tone and overtones. We have, 

 qualifying the fundamental, first, as the most^ simple, a series of octaves ; next, a series 

 of 5ths of the fundamental and their octaves ; and next, a series of 3ds. These are the 

 most powerful overtones, and they form the common chord of the fundamental ; but they 

 are so far concealed by the greater intensity of the fundamental, that they cannot be easily 

 distinguished by the unaided ear, unless the fundamental be quenched in some such way 

 as we have indicated. In the same way, the harmonic 5ths and 3ds overpower other 

 overtones; for we have the string subdividing again and again into overtones, which are 

 not harmonious like the notes of the common chord of the fundamental. 



The presence of overtones, resultant tones, and additional tones, which latter will be 

 described hereafter, can be demonstrated, without damping the strings, by the resonators, 

 invented by Helmholtz. It is well known that, if a glass tube, closed at one end, which 

 ^contains a column of air of a certain length, be brought near a resounding body emitting 

 V a note identical with that produced by the vibrations of the column of air, the air in the 

 tube will resound in consonance with the note. If, for example, we have a tube sounding 

 C, a tuning-fork of the same pitch sounded near the tube will throw the air in the tube 

 into action and will produce a powerful sound, while no other note will have this effect. 

 The resonators of Helmholtz are constructed upon this principle. A glass globe or tube 

 (Fig. 262) is constructed so as to produce a certain note. This has a larger opening (a) 

 and a smaller opening (b) which latter is fitted in the ear by warm sealing-wax, the other 

 ear being closed. When the proper note is sounded, it is reenforced by the resonator 

 and is greatly increased in intensity, while all other notes are heard very faintly. Sup- 

 pose, now, that we apply this to the detection of overtones. We fix in the ear a resonator 

 adjusted to G, and sound the fundamental (0). The fundamental (C) is imperfectly heard, 

 but the overtone (G) is reenforced, and we have a loud and distinct sound of the 5th. By 

 using resonators graduated to the musical scale, we can easily analyze a note and distin- 

 guish the overtones. In the same way, if we place in the ear a resonator tuned to a par- 

 ticular note and strike a succession of chords on the piano, the general sound is imper- 

 fectly heard ; but, whenever we strike the note of the resonator, this is clearly distin- 

 guished, to the practical exclusion of all others; and we can thus analyze complicated 

 chords into each of their constituent parts. This experiment shows the similarity between 

 chords, resolved into their constituent parts, and single notes, resolved into their harmonics, 

 or overtones. The resonators of Helmholtz, which are open at the larger extremity, are 

 infinitely more delicate than those in which this is closed by a membrane. 



A very striking and instructive point in the present discussion is the following : All 

 the overtones are produced by vibrations of segments of the string included between the 

 comparatively still points, called nodes ; and, if we cause a string to vibrate by plucking 



