242 ME. C. J. T. SEWELL : EXTINCTION OF SOUND IN A VISCOUS ATMOSPHEEE 



same in all planes perpendicular to this direction, the expression (2) for the dissipation 

 of energy per unit length of the axis of z takes the form 



2F = $vp 



+ '2vp (lu + mv) (a+b)ds vp ^-ds + ^vp^ (lvmu)ds ... (4) 



where ds is an element of the curve bounding the region in question. 



2. We now proceed to obtain a solution of the equations of motion which shall be 

 applicable to the case when the motion in all planes perpendicular to the axis of z is 

 the same, and when further there is no motion parallel to this axis. 



In this case the equations of motion take the form 



Bu _ 1 cp ^ 2 _i 3& ] 



dt p a dx ' dx I 



^L- L& + VW 1 *- 

 dt p a By By J 



\ <^ ^O "^Q 



where ^ = - + , and V/ denotes the operator ?-- + = 5- 

 Bx dy Bx* dif 



The equation of continuity takes the form 



where squares of the velocity and other quantities of the same order have been 

 ignored, and ,s denotes the condensation. 



If we neglect the effects of conduction and radiation of heat, we may write 



(3), 



where p is the equilibrium pressure and c is the velocity of sound. 



Eliminating p and .s from equations (l) with the help of (2) and (3), we obtain 



....... (4). 



These equations will be satisfied by 



Bx By ' By 



