266 Mr HOPKINS ON AERIAL VIBRATIONS 



The experimental deductions in the preceding part of this section 

 are based on the evidence afforded by the exploring membrane, because 

 it is more direct than any other evidence which the phenomena appear 

 to admit of, and therefore better calculated to supply those decisive 

 and positive tests for ascertaining the accuracy or fallacy of our theoretical 

 results, which it is my object to supply. We have seen the perfect 

 accordance of these results with the general indications of the membrane, 

 and also with the striking and well-defined phenomenon of the im- 

 possibility of making the plate vibrate in a certain manner with tubes 

 of certain lengths. It remains for us to consider also how far our 

 theory agrees with the phenomena of resonance, in those cases in 

 which the conditions assumed in our mathematical investigations are 

 satisfied, viz. where the communication between the external air and 

 that in the tube at the surface of the plate is prevented, and the 

 disturbance extends uniformly over the whole orifice. In such cases 

 it will appear from the following enunciation, that the intensity of 

 the sound is proportional to that of the aerial vibrations, as indicated 

 by the membrane, and by the difficulty or facility with which the 

 vibrations of the plate may be maintained. (See Arts. 27, 31.) 



The resonance of the open tube is scarcely perceptible when the length 

 of it does not differ much from something less than an even multiple 



of -, or 2m • j - C ; but as it approximates to something less than an odd 



multiple of that quantity, or (2m'+ 1)- — C, the resonance increases, and 



at length becomes of painful intensity, increasing till it is no longer possible 

 to maintain the same mode of vibration of the plate. Whether the length 

 of the tube be gradually increased or diminished in approximating to 

 the above-mentioned lengths, the phenomena are precisely the same. 



I was the better pleased to obtain this result, inasmuch as those 

 which I first obtained (when the precaution of preventing communication 

 with the external air was not attended to*), as well as those of previous 



* In such cases the resonance was always greatest (as in the case considered in the text) 

 when the difficulty of making the plate vibrate was greatest. The corresponding lengths of the 

 tube may be seen in Art. 30. 



