260 Mr. Willis on the Vowel Sounds, 



of density, at different parts of the pipe. We have seen, that 

 when the pipe was equal to the half wave, or its odd multiples, 

 that the variation of density took ijlace as in a common organ- 

 pipe, being nothing at the mouth, or at a multiple of the wave 

 from it, where our flattening nearly disai)i)ears, and greatest 

 at the distance of the half wave, or its odd multiples, where 

 our flattening is greatest. Now as it has been shewn, that this 

 alteration of i^itch is occasioned by the reaction of the secondary 

 pulses which disturb the motion of the reed by a periodic variation 

 of density, it is clear, that if in the stratum of air S, (Figs. 9, and 10,) 

 where the reed is placed, this variation is destroyed or diminished 

 by the pulses returning from BD, that the effect on the reed's 

 motion will be proportionally diminished. 



Lastly, if instead of presenting a stopped pipe to a reed, 

 as in Fig. 10, we substitute one open at both ends, such as 

 a telescope without the glasses, or for shorter lengths, tin 

 tubes, the flattening takes place when the tube equals the 

 wave, or a multiple of it, and the vowels at double the length 

 they did with stopped pipes. That this ought to happen is plain 

 from what has been already said, and from the explanation of 

 Nos. 9, and 10, which it will he easily seen, are the vowel dia- 

 grams for this case. 



Some useful hints may now be deduced, for improving the 

 construction of the reed-pipes of organs. Organ builders have 

 been in the habit of attaching pipes to reeds, for two purposes. 

 First, as in the ordinary reed stops, by applying to the reed a 

 conical pipe, giving the same note, they hoped that the vibra- 

 tions of reed and pipe would assist each other, and the whole 

 effect be improved, and this view of the matter has always been 

 taken by the theorists : the builders however have been perplexed 

 by finding the motion of the reed obstructed, and its note flat- 

 tened by such a pipe, and have therefore always made the pipe 



