IN CYLINDRICAL TUBES. 251 



21. If e and e' be the distances through which the nodes are moved 

 by a supposed given retardation of phase, the same for each, at the 

 extremities of the open and closed tubes respectively, 



e = — kki e ; 



6 will consequently be much larger than e'. 



The quantities m' i- in the open tube, and m- + -^ in the 



4 2 ^ 4 2« 



closed one, must be determined by experiment. 



22. I will recapitulate the principal inferences from this theory. 



I. In the tube AB, open at the extremity B opposite to that at 

 which the vibrations are produced, there will be a series of nodes 



equidistant from each other by -, or half a whole undulation, the 



distance of the nearest node from the open extremity being considerably 



less than -, the whole system of nodes being thus brought nearer to 



the open end than the position assigned to it by the investigations of 

 Euler or of M. Poisson. The distance of each node from the open 

 end will be independent of the length of the tube. (Art. 20.) 



II. If the tube be closed at B, the nodes will still be equidistant as 

 X 

 2 



before by - . The distance from B of the node nearest that extremity 



will be - , or a quantity rather greater than that, if we suppose a cause 



of displacement of the whole system of nodes to exist in this case of 

 the closed tube, similar to that which exists in the open one ; the dis- 

 placement however being necessarily much smaller in the former than 

 in the latter case, and in the opposite direction. (Art. 18.) 



III. These nodes are not places in which the air is perfectly at 

 rest, but points of minimum vibration. (See Art. 16.) 



