190 DYNAMICAL THEOKY OF SOUND 



whichever side of that position the piston may happen to be, is 

 greater than it would have been had the temperature remained 

 unaltered. 



"Now the first case is analogous to that of the sonorous 

 vibrations of air when the heat and cold produced by sudden 

 condensation and rarefaction are supposed to pass away with 

 great rapidity. For we are evidently concerned only with the 

 relative rates at which the phase of vibration changes, and the 

 heat causing the excess of temperature passes away, so that 

 it is perfectly immaterial whether we suppose the change of 

 motion to be very slow, or the cooling of heated air to be very 

 rapid. The second case is analogous to that of sound, when we 

 suppose the constants q* and n comparable with each other; and 

 we thus see how it is, that, on such a supposition, labouring force 

 would be so rapidly consumed, and the sound so rapidly stifled. 

 The third case is analogous to that of sound when we make the 

 usual supposition, that the alternations of condensation and 

 rarefaction take place with too great rapidity to allow a given 

 portion of air to acquire or lose any sensible portion of heat by 

 radiation. The increase in the force of restitution of the piston, 

 arising from the alternate elevation and depression of tempera- 

 ture, is analogous to the increase in the forces of restitution 

 of the particles of air arising from the same cause, to which 

 corresponds an increase in the velocity of propagation of 

 sound." 



66. Damping of Waves in Narrow Tubes and Crevices. 



A somewhat greater effect of viscosity may be looked for 

 when the air is in contact with a solid body, as at the walls of 

 a pipe or resonator, owing to the practically infinite resistance 

 which the surface opposes to the sliding of the fluid immedi- 

 ately in contact with it. It seems in fact to be well-established 

 that the relative velocity vanishes at the surface, whereas in 

 our theoretical investigations we assume for the most part that 

 sliding takes place quite freely. A closer examination shews 

 however that in the case of rapid vibrations, such as we are 

 concerned with in acoustics, the effect is mainly local, being 



* [q is a constant of radiation.] 



