410 POPULAR LECTURES AND ADDRESSES. 



quality of the sound represented by the sharp- 

 topped and flat-hollowed curve from that repre- 

 sented by the flat-topped and sharp-hollowed 

 curve. In the one case the pressure of air close 

 to the car rises very suddenly to, and falls very 

 suddenly from, its maximum, and (as in cases of 

 tides in which there is a long hanging on low 

 water) there is a comparatively slow variation of 

 pressure for a few ten-thousandths of a second on 

 each side of the instant of minimum pressure ; in 

 the opposite phase-relation there is a slow change 

 before and after the time of maximum pressure, 

 and a rapid change before and after the time of 

 minimum pressure. In the former case the dif- 

 ference of maximum from mean exceeds the 

 difference of minimum from mean ; in the hitter 

 the difference of the minimum from mean exceeds 

 the difference of maximum from mean. If the ear 

 could not distinguish between two such sounds, 

 but could distinguish between cither of them and 

 the sounds represented by the first and third 

 quarter-cycle curves, the number of beats would 

 be twice the error of frequency of the higher note. 



