354 HISTORY OF ACOUSTICS. 



in closed tubes, while the whole series, 1, 2, 3, 4, 5, 

 &c., occurs in open ones. Both views of the nature 

 of the vibration appear to be nearly the same ; 

 though Lagrange's is expressed with an analytical 

 generality which renders it obscure, and Bernoulli 

 has perhaps laid down an hypothesis more special 

 than was necessary. Lagrange 3 considers the vibra- 

 tion 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. Ber- 

 noulli supposes 4 the whole inertia of the air in the 

 flute to be collected into one particle, and this 

 to be moved by the whole elasticity arising from 

 its 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 mathe- 

 matical developement from Euler 5 , Lambert 6 , and 

 Poisson 7 ; but no new explanation of facts has 

 arisen. Attempts have however been made to-as- 



3 Mem. Turin, vol. ii. p. 154. 4 Mem. Berlin. 1753, p. 446. 

 5 Nov. Act. Petrop. torn. xvi. a Acad. Berlin, 1775. 

 7 Journ. EC. Polyt. cap. 14. 



