234 



the two weights were employed. If the string be shortened, 

 (or only a portion of it permitted to vibrate), the tones will 

 be found strictly in proportion to the length vibrating. Thus 

 the tone produced by half the string will be the octave of 

 the note produced by the whole string. 



Not only do plates, strings, and solid bodies produce 

 regular vibrations, but also the air and gases. But to 

 produce regular and sensible vibrations, the air must be 

 confined to some extent ; for instance, in a tube either open 

 or closed at one end. The vibrations of a column of air 

 are very similar to those of strings in many respects, but 

 differ materially in others. An open diapason organ pipe 

 of 32 feet in length is found to give about 16 vibrations, — 

 a pipe of 16 feet gives 32 vibrations per second; and the 

 vibrations produced by shorter pipes are in like proportion. 



But the weight or volume of the air vibrated does not 

 materially affect the pitch; and if we take an organ pipe 

 of narrow bore, and take another pipe of larger bore but 

 of the same length, on blowing, a tone of nearly the same 

 pitch will be produced. If, however, the tube be sounded 

 by warm or rarer, instead of cold or denser air, the pitch 

 will be found higher. The density, therefore, of the air or 

 gas is analogous to the weight of the string. 



There are no correspondent phenomena of tension, and 

 the phenomena of actual mass and weight in the string and 

 in the column of air are quite incongruous ; but the apparent 

 discrepancies cease when we consider that a bar of iron is 

 capable of vibrating longitudinally as well as laterally, and 

 that it is most probable that the vibrations of a confined 

 column of air are altogether longitudinal, and not lateral, 

 as are the vibrations of the string. 



The vibrations of a body are disturbed or prevented by 

 a slight obstacle, but when the disturbing force is very 

 slight, the stopping of the vibrations may be partial, 



