164 M. V. Regnault on the Velocity of the 



second reflexion at B and a second return to A, the wave has tra- 

 velled 6360 metres ; the percussion is still heard very distinctly. 

 Finally, it is only after another reflexion at B that] the third 

 return to A becomes inaudible, and perfect silence reigns in 

 the tube. The entire course is then 9540 metres. 

 7 Thus the discharge in a pistol of 1 gramme of powder gives a 

 vibration in the air (son) which becomes inaudible when it has 

 traversed 



1150 metres in a tube of the diameter 0*108 metre. 

 3810 „ „ 0-300 „ 



9540 „ „ 1-100 „ 



These lengths are sensibly proportional to the diameters. It 

 is nevertheless probable that the path would be longer were 

 not the wave subjected to successive reflexions which continu- 

 ally diminish it. 



When the wave has no longer sufficient intensity to pro- 

 duce the sensation of sound upon the ear, or when it has been 

 so far modified as to be unable to do so, it may nevertheless, 

 even after a very prolonged course, still mark its arrival upon 

 the membranes. 



Thus when the wave is produced by a charge of 1 grm. of 

 powder, it makes its last impression upon a membrane when it 

 has passed over the following courses : — 



4056 metres in a tube of diameter 0*108 metre. 

 11430 „ „ 0-300 „ 



19851 „ „ 1-100 „ 



But in a pipe of 1*100 metre diameter, which forms the grand 

 service-pipe of Villemonble, I have observed paths of much 

 greater length, — the charge of powder, it is true, being raised 

 in this case to 2*40 grms. Thus in the Table showing the re- 

 sults of one of the series of experiments made with this large 

 tube, the last mark corresponds to a wave which had traversed 

 58641 metres ; and if the bands of paper were allowed to remain, 

 it was easy to detect as many as ten returns of the wave to the 

 membrane A. This is, in effect, a path equivalent to 97735 

 metres, or nearly 100 kilometres ; but the bands of blackened 

 paper were then so long that I found it impossible to collect the 

 indications of more than six returns ; the band of paper with 

 this number had already reached the length of 27 metres. 



What are the causes which thus weaken a plane wave when 

 it is propagated in a straight cylindrical tube ? They are of 

 several kinds • but the chief one undoubtedly depends upon the 

 continual loss by the wave of a part of its vis viva by the reac- 

 tion of the elastic sides of the tube. This is shown distinctly 

 in the great tube of the Saint Michel sewer, which is supported 



