IN CYLINDRICAL TUBES. SSS 



with which the fluid at the extremity of the tube is in immediate 

 contact. This condition is manifestly less restrictive than those of 

 Euler, since it involves no supposition of the perfect rigidity of bodies, 

 and leaves room for a certain degree of condensation and rarefaction 

 of the fluid at the extremity of the open tube, thus removing the 

 difficulty above-mentioned respecting the maintaining of aerial pulsations 

 from the open end, in the circumambient air ; while it enables us also 

 to account in some measure for the rapid cessation of sound with the 

 cessation of the cause producing the vibratory motion of the air in 

 the tube. 



2. The two authors above-mentioned have written elaborately on 

 this subject of the vibrations of elastic fluids in tubes. Mr Challis 

 also in his paper published in the Transactions of this Society, (Vol. III.), 

 has been led to the consideration of the conditions which hold at the 

 closed or open extremity of the tube in which the air is in a state 

 of sonorous vibration, though the determination of this point forms 

 with him a collateral rather than a principal object. He assumes that 

 a pulse proceeding along a cylindrical tube will be reflected from the 

 further extremity if the tube be stopped, the intensity of the reflected 

 pulse being equal to that of the incident one; and that if the extremity 

 of the tube be open, it will pass into the circumambient air, sending 

 back no reflected wave within the tube. If this were the case, it 

 would immediately account for the apparently instantaneous cessation 

 of sound above-mentioned ; but there are other equally obvious 

 phenomena, for which this hypothesis appears to offer no adequate 

 solution. 



3. It will be observed, that Euler has supposed either the velocity 

 of the particles or their condensation to have, at the extremity of the 

 tube, a constant value, independently of the time ; while M. Poisson 

 has supposed this constancy of value to belong to the quantity ex- 

 pressing the relation between the velocity and condensation. It does not 

 however appear to me probable that any such conditions, independently 

 of the time, should hold. All the above assumptions are equally 

 arbitrary, and equally require to be put to the test of experiment. In 



