ON THE SOURCES AXD EFFECTS OF SOUND. 383 



feathers or pieces of paper on the string, that the remaining points of divi- 

 sion are also quiescent, while the intervening portions are in motion. (Plate 

 X^V. Fig. 343.) 



These harmonic sounds are also generally heard together with the funda- 

 mental sound of the chord, and it is, therefore, necessary, in such cases, tQ^ 

 consider the subordinate vibrations as combined with a general one. It is 

 not, however, universally true that the fundamental sound must always be 

 accompanied by all the harmonics of which the chord is susceptible; for I 

 have found that by inflecting the chord exactly at any point in which the 

 cliord might be divided into a number of equal parts, and then suffering 

 it to vibrate, we lose the effect of the corresponding harmonic. There is 

 some difficulty in explaining the reasonof the distinct production of these 

 sounds, in cases where the theory appears to indicate a single and simple 

 vibration only ; but it appears to be most probable that they usually become 

 audible in consequence of some imperceptible irregularity in the form or 

 weight of the chord, which is just sufficient to derange the perfect coinci- 

 dence of the actual motions with those which the theory indicates, without 

 producing a discordance capable of offending the ear. That a chord ir- 

 regularly loaded may have the relations of its harmonics disturbed, may 

 easily be understood by considering the effect of a small weight placed at 

 one of the points of division, which will obviously retard the principal 

 vibration, without materially afi'ecting that of the portions terminated by it. 

 An abrupt and irregular agitation appears also in many cases to make the 

 secondary notes more audible, while a gradual and delicate impulse, like 

 that of the wind on the strings of an Aeolian harp, produces a sound almost' 

 entirely free from subordinate harmonics. 



It usually happens that the vibration of a chord deviates from the plane 

 of its first direction, and becomes a rotation or revolution, which may be 

 considered as composed of various vibrations in different planes, and which 

 is often exceedingly complicated. These vibrations may be combined in the 

 first instance in a manner similar to that which has been already ex- 

 plained respecting the vibrations of pendulums; and if the motion 

 of the chord be supposed to follow the same law as that of a pendulum, the 

 result of two entire vibrations thus united, may be either a vibration in an 



