ON THE SOURCES ANI> EFFECTS OF SOUND. 299 



division are also quiescent, while the intervening portions are in motion.* 

 1 (Pfete-XXV. Fig. 343.) 



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

 mental sound of the cord, and it is, therefore, necessary, in such cases, to 

 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 cord is susceptible ; for I 

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

 cord 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 reason of 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 cord, which is just sufficient to derange the perfect 

 coincidence of the actual motions with those which the theory indicates? 

 without producing a discordance capable of offending the ear. That a 

 cord irregularly 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 affecting 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 cord 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 

 cord 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 inter- 

 mediate direction, or a revolution in a circle or in an ellipsis. But besides 

 these compound vibrations of the whole cord, it is also frequently agitated 

 by subordinate vibrations, which constitute harmonic notes of different 

 kinds, so that the whole effect becomes very intricate ; as we may observe 

 by a microscopic inspection of any luminous point on the surface of the 

 cord, for instance the reflection of a candle in the coil of a fine wire wound 

 round it. The velocity of the motion is such that the path of the luminous 

 point is marked by a line of light, in the same manner as when a burning 

 coal is whirled round ; and the figures, thus described, are not only different 

 at different parts of the same chord, but they often pass through an amusing 

 variety of forms during the progress of the vibration ; they also vary con- 

 siderably according to the mode in which that vibration is excited. (Plate 

 XXV. Fig. 344, 345.) 



The vibrations immediately dependent on elasticity are those of rods, 

 * Wallis, Op. II. 466. Sauveur, Hist, et Mem. de 1'Acad. 1701. 



