IN CYLINDRICAL TUBES. 269 



described in my own experiments, although the extent of excursion of 

 the reed was in this case less than in that in which no resonance was 

 produced. 



One discrepancy is observable between this experiment and mine, 

 inasmuch as the intensity of the sound, instead of increasing as the 



length of the tube approximated to the odd multiple of - , as in my 



experiments, gradually decreased*. The explanation, however, of this 

 fact, is easily found in the diminished excursion of the reed, and still 

 more, I suspect, in the irregularity of its vibration, by which the 

 undulations produced by it are probably rendered imperfectly sonorous^. 

 With this explanation of this apparent discrepancy, the general results 

 of Mr Willis's experiments afford as strong a corroboration of those 

 Avhich I have obtained, as the difference between our modes of experi- 

 menting will allow. The flexibility of the reed, however, and its 

 consequent ready obedience to the vibrations of the air, as compared 

 with the inflexible obstinacy of a glass plate, together with the partial 

 disturbance produced by the reed, render it a totally unfit agent in 

 obtaining experimental tests for our mathematical results, though it 

 presents to us in its own motions many interesting points of enquiry. 



Our theory will also perfectly account for one of the most striking 

 phenomena observable in wind instruments, viz. the rapidity with which 

 different states of vibration are assumed within the tube, corresponding 

 to different effective lengths of it, as determined by the opening or 

 closing of the finger holes. We have seen (Art. 22, VII. VIII.) that 



* For a very clear and distinct account of these experiments, I must refer the reader to the 

 excellent paper from which the above is taken. It will be observed, however, that the results 

 mentioned in the text were not the direct objects of Mr Willis's investigations, but were such as 

 naturally offered themselves in the course of his experiments on the production of the vowel 

 sounds. 



t I think it very possible that \heform of the aerial vibrations may have more to do with our 

 sense of the intensity of sound than has been generally supposed ; and perhaps some cases of 

 resonance may admit the most satisfactory explanation on this hypothesis. 



Vol, V. Part XL M m 



