268 Mr HOPKINS ON AERIAL VIBRATIONS 



resonance will be heard, though extremely feeble as compared with 

 that I have found in my experiments. This is, in fact, the kind of 

 resonance which has been observed by all experimenters. It does not 

 appear to me to admit of the same obvious explanation which the 

 other admits of ; that which is usually received being, as I conceive, 

 in itself insufficient, when subjected to those restrictions which must 

 be imposed upon it by the general laws which govern the communication 

 of motion from one particle of matter to another. At present, however, 

 it is not my object to enter on the discussion of this and of some 

 other points relative to this part of the subject. It is sufficient for 

 me now to have shewn that that powerful resonance which I have 

 observed in my experiments is exactly accordant with the results of 

 our mathematical investigations, when the conditions assumed in those 

 investigations are fully satisfied. I hope to return to the careful examina- 

 tion of other cases at a future period. 



I have already alluded* to a paper by Mr Willis, published in the 

 Transactions of this Society, in which he has described some experiments 

 bearing on this subject, and affiarding a general corroboration of some 

 of the results above stated. He fixed a reed to a sliding tube, and 

 observed the intensity of the sound, when the reed was made to speak, 

 produced by different lengths of the tube, and by means of a microscope 

 carefully adjusted, he was able to observe the excursions of the reed 

 in its vibration, and to obtain micrometer admeasurements of them. 

 He thus found that when the length of the tube equalled about an 



even multiple of - , it gave the exact note of the reed with no perceptible 



resonance. As the tube was gradually lengthened, the tone was flattened, 



and as the length approximated to about an odd multiple of -, the 



extent of the reed's excursions was diminished, its vibrations became 

 irregular and convulsive, till at length it ceased to produce any musical 

 tone. When the tube, however, was a little lengthened beyond this 

 point, the reed suddenly assumed its original form of vibration, 

 producing a note of painful intensity, similar to that which I have 



* See page 260. 



