[ 2.39 ] 



. The Extinction of Sound in a Viscous Atmosphere hy Small Obstacles of 

 (Cylindrical and Spherical Form. 



Ily C. J. T. SEWELL, B.A., Trinity College, Ca.mbridye. 



Communicated In/ Prof. H. LAMB, F.R.8. 



Received February 1, Head March 10, 1910. 



CONTENTS. 



Page 

 1. Expression obtained for the dissipation function in the case of aerial vibrations ... .241 



2. Solution of the equations of motion with reference to cylindrical surfaces 242 



3. Incidence of plane waves of sound upon obstructing cylinder. An expression is obtained 



for the secondary waves 214 



4. Determination of the lost energy. Discussion of results 24K 



5. Incidence of plane waves of sound upon a large number of cylindrical obstacles .... 25 I 

 556. Problems relating to spherical obstacles. A solution of the equations of motion suitable to 



such problems is obtained 257 



S 7. Incidence of plane waves of sound upon obstructing sphere. An expression is obtained for 



the secondary waves 25!) 



8. Determination of the lost energy. Discussion of results 262 



>5 9. Incidence of plane waves of sound upon a large number of spherical obstacles 205 



INTRODUCTION. The theory of the incidence of waves of sound in a non-viscous air 

 upon small obstacles of cylindrical or spherical form is well known to students of 

 mathematical physics ; it has been treated in Lord RAYLEIGH'S ' Theory of Sound,' 

 and in Prof. LAMB'S ' Treatise on Hydrodynamics.' The corresponding problems for a 

 viscous air have not, however, been worked out, and this paper is devoted to an 

 investigation of these problems. The solutions of the equations of vibration of a 

 viscous gas with reference to cylindrical and spherical surfaces were given by 

 Prof. LAMB in a paper entitled "On the Motion of a Viscous Fluid Contained in a 

 Spherical Vessel " and published in the ' Proceedings of the London Mathematical 

 Society' in 1884. It is easy to obtain solutions suitable to the case of divergent 

 waves ; the functions involved are Bessel functions with a complex argument. An 

 analytical expression for the secondary waves diverging from the obstacle is obtained 

 without difficxilty. It then remains to find an expression for the loss of energy to the 

 VOL. ccx. A 465. 4.5.10 



