Small Vibratory Motions of Elastic Fluids. 303 



been observed, that if a tin tube be applied to the ear, its 

 fundamental note will at all times be distinctly heard, without 

 any apparent cause, but if a paper tube be applied, no note is 

 heard. But whatever be the causes which define the length 

 of X, they appear not to be of a very strict nature, for it is 

 possible by skill and practice, to modify the notes of the series 

 1, 2, 3, 4, &c., and to produce notes intermediate to them. (Biot. 

 pp. 128, 130.) When in the common the6ry, the values of X are 

 accounted for by saying that the density of the air at the extremities 

 of the tube must be the mean, to be in equilibrium with the ex- 

 ternal air, a cause is assigned, which is perhaps of too determinate 

 a nature. Besides that it seems in contradiction to the fact, that 

 the sound ceases immediately that the cause which produces it 

 ceases. M. Poisson felt the force of these objections, and a con- 

 siderable portion of his Memoir {Acad. Scien. Ann. 1817.) is 

 employed in obviating them. The above theory, by ascribing 

 the length of X entirely to the mode of disturbance, leaves a 

 latitude in this respect, and admits the possibility of inserting 

 notes between those of the regular series. When the tube has 

 holes in the .side, like a flute, X is seldom equal to the length, 

 but appears to be determined both by the side holes, and by 

 that at the extremity. The fundamental note being so deter- 

 mined, an alteration of the disturbance in degree, will produce 

 as in other cases, the series i, 2, 3, &c. in order. (See Lambert, 

 Berlin JMcmoirs, 1775.) And here I will observe, that supjiosing 

 the condensations and rarefactions generated at one end of the 

 flute, to chase each other towards the other end, the eflfect of 

 a side hole will be to diminish them by a quantity depending 

 on its size, and in such a manner that the type of the waves 

 after passing the hole is diflerent from their previous type, only 

 in having the ordinates diminished in a given ratio. (Art. 11.) 

 The condensations and rarefactions act on the external air at the 



