234 Mr HOPKINS ON AERIAL VIBRATIONS 



applying this test, I find that the deductions from the results, derived 

 from any of the three hypotheses above-mentioned, do not sufficiently 

 accord with the observed phenomena to be perfectly satisfactory. This 

 discrepancy is more particularly observable in the position of the nodes 

 or points of minimum vibration in the open tube. According to Euler's 

 hypothesis, these nodes would be places of perfect rest ; and they would 



be distant from the open end by an exact odd multiple of -, where 



\ = length of a whole undulation. From the hypothesis of M. Poisson, 

 their positions would be the same as in the above case, but they would 

 become points of minimum vibration, and not of perfect rest. Mr 

 Challis's supposition would lead to the conclusion that no nodes existed 

 in this case, except they should be produced by some vibration of the 

 tube itself, a cause the total inadequacy of which to produce any appre- 

 ciable effect, must be immediately recognized by every one who has 

 made experiments on this subject. The facts, as determined by experi- 

 ment, are very obvious ; and it appears that there are nodes, which 

 are points of minimum vibration and not of perfect rest ; that they are 



equidistant, but that denoting this distance by -, the distance between 



the open extremity and the nearest node is considerably less than -. 



I shall not in this place proceed further with the detail of experimental 

 facts ; but shall first shew how the theory of this subject may be 

 generalized by the assumption of conditions less restrictive than those 

 which have been made by the writers I have mentioned. In the second 

 section, I shall describe the experiments which have suggested these 

 assumptions ; and shall conclude with some observations on the resonance 

 of tubes, so far, more particularly, as it is allied to the investigations 

 contained in this paper. 



The form under which I shall consider the problem, is that under 

 which it presents itself, as nearly as possible, in the experiments I have 

 to describe. 



