ON THE SOURCES AND EFFECTS OF SOUND. 381 



tension, derived from the operation of a weight, or of some other external 

 force, or by tlie natural elasticity of the substance. The vibrations of ex- 

 tended substances resemble most in their properties those of elastic fluids, 

 and they occur the most frequently in practice, although the vibrations 

 produced by the elasticity of the substance may be considered as the mo&t 

 natural. 



Vibrations derived from tension are either those of chords or musical 

 strings, or those of membranes; but the vibrations of membranes afford 

 little variety, and have not hitherto been very accurately investigated, the 

 drum being almost the only instrument in which they are concerned ; they 

 do not however appear to diifer materially in their properties from the vibra- 

 tions of strings. A musical string or chord is supposed to be perfectly 

 flexible, and of uniform thickness, to be stretched between two fixed point^ 

 by a force incomparably greater than its own weight, and to vibrate in a 

 single plane through a minute space on each side of its natural position. 

 Its motions may then be traced through all their stages, by comparing the 

 chord to a portion of an elastic medium of the same length, contained be- 

 tween two bodies capable of reflecting any impulse at each end; for example, 

 to a portion of air situated between two walls, or inclosed in a pipe stopped 

 at both ends; for the vibration of such a medium will be performed in the 

 time occupied by any impulse in travelling through twice its length; 

 and the vibration of the chord will be performed in the same time, suppos- 

 ing the height or depth of the medium equal to the length of a portion of 

 the chord, of which the weight is equivalent to the force applied to stretch 

 it, and which may be called with propriety the modulus of the tension. If 

 the chord be at first bent into a figure of any kind, and then set at liberty, 

 the place of any part of it at every subsequent time will be such, that it will 

 always be in a right line between two points moving along the figure each 

 way with the appropriate velocity; but in order to pursue this determination,^ 

 we must repeat the figure of the chord on each side of the fixed points in an 

 inverted position, changing the ends as well as the sides. Hence it appears 

 that, at the end of a single vibration, the whole chord will assume a similar 

 figure on the opposite side of its natural place, but iu an inverted position, 

 and after a complete or double vibration, it will return precisely to the form 

 which it had in the beginning. The truth of this result is easily shown by 



