THE SIX GA TE WA YS OF KNO WLEDGE. 275 



the condition of the air, how it is lacerated some- 

 times in a complicated effect. Think of the 

 smooth gradual increase and diminution of pres- 

 sure smooth and gradual though taking place 

 several hundred times in a second when a piece 

 of beautiful harmony is heard ! Whether how- 

 ever it be the single note of the most delicate 

 sound of a flute, or the purest piece of harmony of 

 two voices singing perfectly in tune ; or whether 

 it be the crash of an orchestra, and the high notes, 

 sometimes even screechings and tearings of the 

 air, which you may hear fluttering above the 

 sound of the chorus think of all that, and yet 

 that is not too complicated to be represented 

 by Professor Cayley, with a piece of chalk in 

 his hand, drawing on the blackboard a single 

 line. A single curve, drawn in the manner of 

 the curve of prices of cotton, describes all that 

 the ear can possibly hear, as the result of the 

 most complicated musical performance. How is 

 one sound more complicated than another ? It 

 is simply that in the complicated sound the 

 variations of our one independent variable, pres- 



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