IN CYLINDRICAL TUBES. 265 



wave, of which the period will be the same as that of each of its 

 component waves, but the phase of which will be retarded as compared 

 with that of a wave reflected immediately from the extremity of the 

 tube. This is equivalent to our supposing a certain space beyond the 

 extremity of the tube as subject to a disturbance (acting at consecutive 

 instants along this space) such as to produce a wave diverging in all 

 directions, and consequently sending a portion of this general wave 

 back along the tube. 



To give generality to the investigations of the preceding section, 

 I have considered the effect on the position of the nodes which would 

 be produced by any retardation of the phase of the wave reflected from 

 the stopped end of a tube. It appears, however, that there is not in 

 this case any displacement of the nodes appreciable by the mode of 

 experimenting I have described. The only reason, in fact, for supposing 

 any retardation of phase in this case, is founded in the imperfect 

 analogy between the cases of the open tube and the tube closed with 

 an elastic substance. The cases are far too different, however, to admit 

 of any thing but vague inferences from such analogy ; and it is 

 manifest that no reasoning similar to that above applied to the open 

 tube, can be applied to the closed one. If any retardation do exist in 

 this case, I can only conceive it to arise from a cause similar to that 

 suggested by Mr Willis*, viz. that time must be necessary for the 

 action between the elastic stop and the air to produce its effect. This, 

 however, appears much less probable in this case than in that which 

 suggested the idea to Mr Willis, in which the action between the air 

 and the vibrating body (a membrane) was lateral instead of being direct, 

 as in the present instance. I have not been able to detect any indica- 

 tion of such law of force in a displacement of the nodes in the closed 

 tube, though I have examined the case with great care, conceiving 

 that any facts bearing directly upon the nature of the mutual action 

 of two elastic media at their common surface must necessarily be of 

 importance. 



* Cambridge Transactions, Vol. IV. Part III. p. 346. 



