396 POPULAR LECTURES AND ADDRESSES. 



point moving uniformly in a circle. Considering 

 the actual sensibility of the human car to musica 

 sounds, we must introduce farther as a practica 

 restriction that the period of the variation of the 

 pressure must be less than ..^ of a second, and 

 greater than lTn n 7T7 or .^^ f a second. The 

 vibrations of the air produced by a simple 

 harmonic vibrator are either simple harmonic, 01 

 are in circular or elliptic orbits, resulting from the 

 composition of two simple harmonic motions ; and 

 the consequent change of air-pressure in the 

 neighbourhood of the car follows the simple 

 harmonic law, provided the maximum velocity 

 of the vibrator and of the air in its neighbourhood 

 be infinitely small in comparison with the velocity 

 of sound. Hence the more nearly this condition 

 is fulfilled the more exactly a simple tone is the 

 sound heard ; but it is far from being fulfilled when 

 the vibrator, though itself performing simple 

 harmonic motion, has sharp edges round which 

 the air is forced to rush with great velocity, 

 or when, as in the case of free-reed organ pipes 

 or the reeds of a harmonium, the vibrator is 



