IN CYLINDRICAL TUBES. 255 



26. If the membrane be rendered very sensitive by being exactly 

 tuned to the note produced by the vibrating plate, it will not indicate 

 perfect rest at the nodal points, shewing them in fact to be points of 

 minimum vibration, which agrees with our theory, (Art. 22, III.). 

 With such a membrane it will be difficult to determine the position of 

 these points with accuracy, and its sensibility should be diminished, 

 till the sand appears perfectly at rest when it is placed exactly at the 

 node. If the membrane be rendered still less sensitive, it will appear 

 at rest for a space on each side of the node, the position of which will 

 in such case, be determined by observing those points immediately 

 above, and below the node at which the motion of the sand is just 

 sensible. The middle point between them will of course be the 

 node. 



27. Now suppose the length of the tube to be any odd multiple 



of -, and the membrane to have such a degree of sensibility, as just 



to remain at rest only when placed in a node or within a very small 

 distance of it. After it has been placed in this position, let the brass 

 tube sliding within the upper part of the glass one be raised through a 



space less than - . While the whole tube is thus lengthened, let the 



distance of the membrane from the upper end B remain the same; 

 the membrane will consequently be still in a node. The plate being 

 now put in vibration, the membrane will remain perfectly at rest, not 

 only in this position, but also when moved to one considerably above 

 or below the node, the new length of the tube remaining the same. 

 This indicates a less degree of motion in the tube than in the former 

 case, and we find that the intensity of the vibration in the open tube 

 is least when its length is equal to something less than an even 



multiple of -T, or 2m.j — C; and becomes greater as the length 



approximates to rather less than an odd multiple of -, or {2m' + 1)-—C, 



m and m' being any whole numbers. (Art. 22. V.). This diminution of 

 motion is also very obvious when the membrane is placed in those 



KK2 



