CHAPTER XVI. 



FREE PATH PHENOMENA (CONTINUED). 



THE PROPAGATION OF SOUND. 



359. AT the end of Chapter X. (p. 228), it was pointed out that the 

 problem of the propagation of sound requires special investigation from the 

 point of view of the Kinetic Theory. In any gas for which 7, the ratio of the 

 two specific heats, is less than If, the propagation of sound is dependent 

 on a transfer of internal energy through collisions, and if this energy is not 

 transferred with sufficient rapidity to keep pace with the transfer of trans- 

 lational energy, complications will arise which are not contemplated by a 

 simple theory of the kind which is given in books on Sound or Hydro- 

 dynamics. This simple theory deals only with the mass motion of a gas on 

 the assumption that it may be regarded as a homogeneous fluid : it is the 

 province of the Kinetic Theory to investigate what modifications, if any, are 

 required when the molecular structure of the gas is taken into account. 



We shall work out the problem in detail in the special case in which the 

 molecules of the gas are loaded spheres. We shall be able to infer the 

 nature of the general solution from the special solution obtained in this way. 



The molecules are loaded spheres. 



360. At any point in the gas we suppose as usual that the mass 

 motion is so small that squares of its components may be neglected. Also 

 the mass motion is in one dimension, so that if we choose this direction for 

 the axis of x, the components of mass velocity may be taken to be U Q , 0, 0, 

 and w 2 may be neglected. 



Along the path of the wave, the quantities u , v, H and K will vary, 

 differing only slightly from their values in the undisturbed state. The 



