4^0 PHYSIOLOGICAL PHYSICS. [Chap. xxxn. 



air in a second of time, and the note produced by the 

 box will be sharpened. If, however, the box be 

 turned in the same direction as the disc, the two sets 

 of holes will coincide less speedily, and a flattening of 

 the note will result. Now suppose both boxes to be 

 producing the same number of vibrations in a second 

 of time, i.e. sounding the same note, let the upper 

 box be turned in either direction, a slight difference 

 will be produced between the number of vibrations of 

 each box ; and this difference will announce itself by 

 the appearance of what are called BEATS, alternate rising 

 and falling of the sound, or intensification and diminu- 

 tion of the sound. This occurrence may be explained 

 in the following way. Suppose two men walking 

 side by side, and keeping step. Consider only the 

 right foot of each. The right foot of each will ad- 

 vance and touch the ground in front at the same 

 instant of time. With the forward movement of the 

 body and the advance of the left feet, the right feet 

 will come to be behind, and as the advance continues 

 will leave the ground at the same instant. The foot 

 may be considered as oscillating with each step 

 between two extremes from its middle position, and 

 the movement from the place where the foot touches 

 the ground in front to the place where it leaves the 

 ground behind, and forwards again to the position in 

 front as a complete wave movement, one complete 

 vibration or oscillation. The distance, then, between 

 the extreme position in front and the extreme position 

 behind will be half a wave length ; and, in the lan- 

 guage of wave motion, the foot in its extreme position 

 in front and its extreme position behind may be said to 

 be in opposite phases. Suppose now that the two men 

 start by each touching the ground in front with the 

 right foot at the same instant, but suppose that one 

 walks very slightly faster than the other. If he is 

 not to go ahead of his neighbour his steps must be 



