PNEUMATICS. 283 



380. If L be the length of a musical string of 

 uniform thickness, B its weight, S the weight by 

 which it is stretched, or tne measure of its tension, 

 t the time of a double vibration, 



t 



t) as usual is measured in seconds, and g is the velo- 

 city acquired in 1" by a falling body, expressed in 

 the same measure with L. The most convenient 

 unit in this case is an inch ; so that g = 386 . 



The value of t may be made more convenient, by 

 supposing w to denote the weight of an inch of the 



string ; so that P = w L, then t = 3-^_ 



V# s 



If N be the number of vibrations in a given time, for 



instance in one second, N _^~L . 



2 L V w 



If the lengths and weights of two chords are the 

 same, their times of vibration will be inversely as 

 the square roots of the forces by which they are 

 stretched ; and the number of vibrations which they 

 perform in the same time, directly as those square 

 roots. 



So also, the tension and the weight remaining the 

 same, the celerity of the vibration is inversely as 

 the square-root of the length; or, the tension and 



weight 



