4:0 HISTOKY OF ACOUSTICS. 



laid down an hypothesis more special than was necessary. Lag-range' 

 considers the vibration of open flutes as " the oscillations of a fibre of 

 air," under the condition that its elasticity at the two ends is, during 

 the whole oscillation, the same as that of the surrounding atmosphere. 

 Bernoulli supposes 4 the whole inertia of the air in the flute to be col- 

 lected into one particle, and this to be moved by the whole elasticity 

 arising from this displacement. It may be observed that both these 

 modes of treating the matter come very near to what we have stated 

 as Newton's theory ; for though Bernoulli supposes all the air in the 

 flute to be moved at once, and not successively, as by Newton's pulse, 

 in either case the whole elasticity moves the whole air in the tube, and 

 requires more time to do this according to its quantity. Since that 

 time, the subject has received further mathematical developement from 

 Euler, 5 Lambert, 6 and Poisson ; 7 but no new explanation of facts has 

 arisen. Attempts have however been made to ascertain experimentally 

 the places of the nodes. Bernoulli himself had shown that this place 

 was affected by the amount of the opening, and Lambert 8 had examined 

 other cases with the same view. Savart traced the node in various 

 musical pipes under different conditions ; and very recently Mr. Hop- 

 kins, of Cambridge, has pursued the same experimental inquiry. 9 It 

 appears from these researches, that the early assumptions of mathema- 

 ticians with regard to the position of the nodes, are not exactly verified 

 by the facts. When the air in a pipe is made to vibrate so as to have 

 several nodes which divide it into equal parts, it had been supposed by 

 acoustical writers that the part adjacent to the open end was half of 

 the other parts ; the outermost node, however, is found experimentally 

 to be displaced from the position thus assigned to it, by a quantity 

 depending on several collateral circumstances. 



Since our purpose was to consider this problem only so far as it has 

 tended towards its mathematical solution, we have avoided saying 

 anything of the dependence of the mode of vibration on the cause by 

 which the sound is produced ; and consequently, the researches on 

 the effects of reeds, embouchures, and the like, by Chladni, Savart, 

 Willis, and others, do not belong to our subject. It is easily seen 

 that the complex effect of the elasticity and other properties of the 

 reed and of the air together, is a problem of which we can hardly 



3 Jfi'm. Turin, vol. ii. p. 154. 4 M!:m. Berlin, 1753, p. 446. 



6 Nov. Act. Petrop. torn. xvi. c Acad. Berlin, 1775. 



T Journ. EC. Polijt. cap. 14. 8 Acad. Berlin, 1775. 



9 Camb Trans, vol. v. p. 234. 



