244 Mr. Willis on the Vowel Sounds, 



will be formed which will run back again, be reflected from *the 

 bottom of the tube, and again present itself at the mouth where 

 a new echo will be produced, and so on in succession till the 

 motion is destroyed by friction and imperfect reflexion. If it be 

 a condensed pulsation that is echoed from the open end of a 

 tube, the echo will be a rarefied one and vice versd, but the direc- 

 tion of the velocity of translation of its particles will be the same. 

 On the other hand when the reflexion takes place from the stopped 

 end, the pulsation retains its density, but changes its velocity 

 of translation. The effect therefore will be the propagation from 

 the mouth of the tube of a succession of equidistant pulsations 

 alternately condensed and rarefied, at intervals corresponding to 

 the time required for the pulse to travel down the tube and back 

 again ; that is to say, a short burst of the musical note corres- 

 ponding to a stopped pipe of the length in question, will be 

 produced. 



' Let us now endeavour to apply this result of Euler's to the 

 case before us, of a vibrating reed, applied to a pipe of any 

 length, and examine the nature of the series of pulsations that 

 ought to be produced by such a system upon this theory. 



The vibrating tongue of the reed will generate a series of 

 pulsations of equal force, at equal intervals of time, but alternately 

 condensed and rarefied, which we may call the primary jjulsa- 

 tions; on the other hand each of these will be followed by a 

 series of secondary pulsations of decreasing strength, but also at 

 equal intervals from their respective primaries, the interval between 

 them being, as we have seen, regulated by the length of the at- 

 tached pipe. Take an indefinite line Af.^^ (No. 5) to represent 

 the time, and let ABC...&cc. be the primary pulsations, aa...bb... 

 their respective secondaries, and for simplicity we will suppose 

 that after the third they Ijecome insensible, also we will denote 

 a condensed pulse by a stroke above the line, and a rarefied one 



