278 POPULAR LECTURES AND ADDRESSES. 



matics for etherealising and illustrating common 

 sense, and you need not be disheartened in your 

 study of mathematics, but may rather be re- 

 invigorated when you think of the power which 

 mathematicians, devoting their whole lives to the 

 study of mathematics, have succeeded in giving to 

 that marvellous science. 



I spoke of the sense of sound being caused 

 by rapid variations of pressure. I had better 

 particularise, and say how rapid must be the 

 alternations from greatest pressure to least, and 

 back to greatest, and how frequently must that 

 period occur, to give us the sound of a musical 

 note. If the barometer varies once a minute 

 you would not perceive that as a musical note. 

 But suppose by any mechanical action in the 

 air, you could cause the barometric pressure 

 the air pressure to vary much more rapidly. 

 That change of pressure which the barometer 

 is not quick enough to show to the eye, the ear 

 hears as a musical sound if the period recurs 

 twenty times per second. If it recurs twenty, 

 thirty, forty, or fifty times per second, you hear 





