264 Mr HOPKINS ON AERIAL VIBRATIONS 



kind, and are too small both in the large and' small tube. They can 

 leave no doubt of the fact of the magnitude of the displacement being 

 dependent on the diameter of the tube. 



It is important to observe, that the values of X determined in the 

 large tube and the small one, from the consideration that the distance 



between any two nodes must equal some multiple of - , was exactly 



the same, being for the first case in the table 2.05, very nearly agreeing 

 with the accurate value 2.044. This proves that the distance between 

 the nodes is independent of the diameter of the tube, provided the dis- 

 turbance take place uniformly throughout its extreme section. 



37. I have before remarked, that there can be nothing arbitrary 

 or indeterminate in the vibratory motion of the air at the extremity 

 of the open tube when the vibrations in it are excited according to 

 some known law ; and consequently, if our theoretical knowledge of 

 the subject were complete, we should undoubtedly find in our investiga- 

 tions the cause of the retardation of phase, of which I have spoken, 

 in the reflected wave of the open tube, supposing it to be the actual 

 cause of that displacement of the whole system of nodes which I have 

 established as an experimental fact. Our knowledge at present, how- 

 ever, is totally inadequate to this purpose, and therefore we can only 

 conjecture what may be the probable cause of this retardation in the 

 reflected wave; but at all events, our formulse, with the modifications 

 1 have introduced into them, do become perfect representations of all 

 those phenomena which we can distinctly determine by experiment, 

 in the cases to which our mathematical investigations apply. The fact 

 too, of a retardation of phase in the reflected wave may not be very 

 difficult to conceive, or appear improbable, if we suppose the undulation 

 proceeding from the open end of the tube to advance through a certain 

 space before it assumes that form in diverging into free space, which 

 it must ultimately assume when it sends back no reflected wave from 

 any point of its path. Before it reaches this state, a partial wave may 

 be reflected in its course from each point towards the tube; and an 

 indefinite number of these reflected waves will form a general reflected 



