IN CYLINDRICAL TUBES. 259 



to the surface of the plate, without interfering with its vibrating 

 motion, and then putting round the edge of the tube, a small 

 quantity of fluid which by its adherence to the tube and the plate 

 fills up the interstice between them, and prevents communication with 

 the external air. When this precaution is taken, the lengths of the 

 tube which correspond to the above mentioned phenomena exactly agree 

 with theory; that is — 



The .vibration of the plate is unaffected by the presence of the open 

 tube, Avhen its length is equal to something less than an even multiple 



of — , or 2 m. J— C, and of the closed one when its length is equal to 



4 4 



an odd multiple of -; but as the lengths of the tubes approximate 



respectively to quantities differing by - , from the above lengths it 



becomes almost impossible to make the plate assume the same vi- 

 bratory motion. (Art. 22, VI.) 



32. It might at first appear probable that the neglect of this 

 precaution might have some effect on the position of the nodes, as 

 well as on the phenomena above mentioned. This however is not 

 the case; and the reason will be obvious if we recollect that the 

 position of the nodes depends on the periodicity of the vibrations, or 

 the value of X, which is unaffected by the communication with the 

 external air at A ; whereas the force opposing the vibration of the 

 plate depends on the condensations and rarefactions of the air, at the 

 surface of the plate within the tube, which will necessarily be much 

 affected by the communication just mentioned.* 



33. If we take a closed tube, a similar discrepancy or accordance 

 in the results of theory and experiment will be found under the 

 same circumstances as above described. 



* It does not appear so easy to account for the phenomena as above described, when the 

 influence of external air is not prevented. This, however, does not immediately belong to the 

 object I have proposed to myself in this paper, which is, to establish as accurately as possible the 

 identity of the results of theory and of experiment in those cases in which the conditions assumed 

 in our mathematical investigations are experimentally satisfied. 



