188 DYNAMICAL THEORY OF SOUND 



If on the other hand the alternations of density were to 

 take place with extreme slowness, as in the case of very long 

 waves of simple-harmonic type, there would be time for 

 practical equalization of temperature, and the dissipative 

 influence of conduction as well as viscosity would again be 

 insignificant. Since the expansions are here nearly isothermal, 

 the wave-velocity will approximate to the Newtonian value 



(I 59 (10))- 



In intermediate cases the theory shews that the wave- 

 velocity would no longer be constant, but perceptibly dependent 

 on the frequency. Since no such effect is observed, we infer 

 that in all ordinary cases the conditions are practically adiabatic. 

 It appears also that in such intermediate cases the dissipation 

 would be very greatly increased. The investigation of Stokes 

 (1851), which is here referred to, relates to the effect of 

 radiation ; the extension to conduction was made independently 

 by Kirchhoff and Lord Rayleigh. It is probable that the 

 effects of radiation alone are of subordinate importance. 



The detailed calculation must be passed over, but the 

 general explanation of the manner in which thermal processes 

 may operate to produce dissipation of energy has been stated 

 with such admirable clearness by Stokes that it is worth while 

 to reproduce the passage in question. The explicit reference is 

 to radiation, but the same principles are involved in the case of 

 conduction also. 



" Conceive a mass of air contained in a cylinder in which an 

 air-tight piston fits, which is capable of moving without friction, 

 and which has its outer face exposed to a constant atmospheric 

 pressure ; and suppose the air alternately compressed and 

 rarefied by the motion of the piston. If the motion take place 

 with extreme slowness, there will be no sensible change of 

 temperature, and therefore the work done on the air during 

 compression will be given out again by the air during expansion, 

 inasmuch as the pressure on the piston will be the same when 

 the piston is at the same point of the cylinder, whether it be 

 moving forwards or backwards. Similarly, the work done in 

 rarefying the air will be given out again by the atmosphere as 

 the piston returns towards its position of equilibrium, so that 



