254 Mr. Willis on the Vowel Sounds, 



case the direct portions AB, AB, &c. will be exactly similar to 

 AB, also all the retrograde portions AB, AB will be exactly similar 

 whatever portion of the wave is issuing from A, therefore all 

 the direct waves will unite and assist each other, and in like 

 manner all the retrograde waves, so that the column of air in 

 the pipe will vibrate in the well known manner of a common 

 organ-pipe. We should obtain a similar result if the pipe had 

 been taken equal to any multiple of the wave. 



But if B be open, the alternate portions BB, BB^ &c. will 

 be inverted: in this case AB being exactly similar to AB, but 

 on the opposite side of the axis, will tend to counteract it; again 

 AB destroys AB and so on, and in like manner the retrograde 

 waves alternately tend to neutralize each other, so that, in fact, 

 were it not for the gradual decay of the secondary pulsations, 

 there ought to be no sound at all in this case. 



Again, if we consider a tube ab equal in length to half a 

 wave, we shall find, in a similar way, that when b is stopped, 

 the secondary pulses mutually interfere and destroy each other, 

 and when open that they streng:then each other, and the same 

 results would be found if the length of the pipe were taken 

 equal to any odd multiple of the half wave. In the same way 

 we may examine the case of pipes open at both ends, and so 

 generally we find, that in pipes stopped or open at both ends, 

 the pulsations strengthen each other when the pipe equals a 

 wave or its multiple, and destroy each other when the pipe 

 equals a half wave or its odd multiple, and that in pipes stopped 

 at one end, the reverse is the case. 



This mutual destruction of the jjulsations, when the pipe is 

 a multiple of the wave is confirmed by experiment. It has been 

 shewn that such a pipe rather weakens than strengthens the 

 tone of the reed. 



^V'e may now be partly able to see how the reed is affected 



