Si56 Mr HOPKINS ON AERIAL VIBRATIONS 



parts of the tube where the motion is most sensible. In all cases, 

 however, the distances of the nodes from B is independent of the 

 length of the tube. 



28. If we take a tube closed at B instead of the open one, we 



observe the same alternations of points of greatest and least vibration, 



and (the plate being made to vibrate in the same manner as before) 



at exactly the same distances from each other as in the closed tube; 



but the distance of the upper node from the closed extremity of the 



X I 



tube is now observed to be -, the same as the distance between the 



2 



nodes. Proceeding as in the former case, it is found also that the 



strongest vibrations are excited when the length of the tube is about equal 



to a multiple of - ; and the least vibrations when the length = an odd 



multiple of - . I find also that in the open tube stronger vibrations exist 

 4 



in the nodal points than for corresponding cases of the closed tube. 



29. In performing the above experiments with reference to the 

 intensity of the vibrations in the tube, care must of course be taken 

 to prevent the influence of any other cause than that of which I have 

 spoken, viz. the length of the tube with respect to X. It has been as- 

 sumed that the vibration of the part of the plate immediately in contact 

 with the mouth of the tube is in all cases the same, which requires 

 that the tvibe should always be placed over exactly the same portion 

 of the plate. This portion also should be included in one and the same 

 ventral segment; for if a nodal line on the plate pass across the mouth 

 of the tube, the vibrations transmitted from opposite sides of this line 

 will be in exactly opposite phases, and will consequently neutralize each 

 other in a degree depending on the ratio which the intensity of one 

 of these undulations bears to the other. If the nodal line divides the 

 part of the plate in contact with the mouth of the tube into two 

 equal portions, parts of similar ventral segments, the interference 

 will be so complete as to destroy all sensible motion in the 



