Small Vibratory Motions of Elastic Fluids. 301 



length will transmit rather than all others. Since, therefore, it 

 is found that tubes produce a certain series of notes in preference 

 to all others, the cause is to be sought in the mode and circum- 

 stances of the disturbance, and unless these be exactly known, 

 the fact cannot be explained theoretically. It is necessary to 

 distinguish between those cases in which the vibrations arise out 

 the elastic nature of the fluid itself, as for instance, when they 

 are caused by blowing across a hole ; and the cases in which 

 the vibrations are immediately impressed on the fluid by an 

 elastic substance, as in Keed Organ-Pipes. To the former I 

 shall direct my attention, having" in view the experiments de- 

 scribed by Biot. [Traite de Physique, Tom. II.) AVhen a musical 

 sound is caused by a continuous and equable disturbance of this 

 nature, we may conclude, because it is musical, (see Art. 5.) 

 that the type of the wave is given generally by the equation, 



, r . irX ^ , . SttT , „ . 37r.X- .1 



?/ = X {tn Sin — — \-m sni F m sin h &c.' . 



^ X X X J 



Suppose the disturbance to be made at the extremity of a tube 

 open at both ends. Experience shews that when the lowest note 

 possible, the fundamental note, is sounded, x is equal to the length 

 of the tube. This note, which may be called i, and is expounded 

 by the first term, is heard, because the coefficient m of this 

 term, becomes by the nature of the disturbance, large compared 

 to those of the other terms; not however to the exclusion of 

 the sounds 2, .3, 4, &c. which correspond to these terms, for they 

 are heard as harmonics with the first. By a change of cir- 

 cumstances each of the coefficients m', m", &c. may be made 

 in order prominent above the rest, and the sounds 2, 3, 4, &c. 

 be generated. Accordingly in practice it is found that this 

 effect is produced by altering the disturbance in degree, its 

 particular natiue remaining the same. (Biot, pp. 125, 138) 

 M. Biot states, (p. 131.) that he has ascertained in the most con- 



