IN CYLINDRICAL TUBES. 261 



The best method therefore of determining the positions of the 

 nodes in tubes considerably smaller than those I have mentioned, is 

 that by which the value of \ is determined, as described in the 

 last Article. 



Thus, suppose / to be the length of tube, with which it is found 

 most difficult to make the plate vibrate ; then (the tube being open) 

 we shall have 



l={2m + l)^-C, 



where m is a whole number, which will be known when \ is de- 

 termined by either of the methods pointed out above. The quantity 

 C evidently shews how much the distance between the open ex- 

 tremity, and the nearest node differs from — , or it expresses the 

 displacement. 



From the above equation, 



C={2m + l))-l, 



4 



and the displacement is thus determined. 



36. The following table exhibits the magnitude of this displace- 

 ment in a tube of given diameter, as determined experimentally for 



different values of - . The positions of the nodes were in these cases 



carefully ascertained by means of the membrane suspended in the 

 tube. 



Vol. V. Paet II. L i. 



