240 MR. C. J. T. SEWELL : EXTINCTION OF SOUND IN A VISCOUS ATMOSPHERE 



primary waves. In calculating this loss of energy it is necessary to consider the 

 dissipation of energy by friction in the immediate neighbourhood of the obstacle in 

 addition to the energy which is carried away to a distance by the secondary waves. 

 This was pointed out to me by Prof. LAMB, at whose suggestion this paper was 

 written. In obtaining an expression for the energy dissipated by friction I at first 

 made use of the dissipation function. This method led to exactly the same results as 

 that finally adopted, but the mathematics involved were cumbrous, and the physical 

 ideas, on which they were based, were somewhat obscure. Another disadvantage of 

 this method was that it was necessary to calculate separately the scattered and the 

 dissipated energy. I have to thank Prof. LAMB for his kindness in pointing out to 

 me the method of calculating the lost energy adopted in this paper. The result has 

 been to make the paper more clear and readable. 



I have succeeded in obtaining expressions for the energy lost to the primary waves 

 in the case of spherical and cylindrical obstacles. As might be expected, the problem 

 of the cylindrical obstacle presents greater analytical difficulty than that of the 

 spherical obstacle, and in the former case it is necessary to obtain different 

 approximate expressions according to the diameter of the obstacle. The results for 

 wires of 10" 1 cm. radius and for wires of 10~ 3 cm. radius can be obtained without 

 much difficulty, but when the radius of the wire is of order 10~ a cm. it is necessary 

 to perform very laborious calculations in order to arrive at intelligible results. The 

 energy lost to the primary waves is, in all cases, very great compared with what 

 would be lost in a non-viscous air, but the ratio of the lost energy to that incident 

 upon the obstacle is at most of order 10~ 2 . 



In the case of spherical obstacles the difficulties of approximation are not so great, 

 as in the case of cylindrical obstacles the loss of energy is far greater than in a non- 

 viscous air, but, as before, the ratio of the lost energy to that incident upon the 

 obstacle is at most of order 10~ 2 . 



It is possible to extend the results obtained for a single obstacle to the case when 

 the waves of sound are incident upon a large number of similar obstacles. This has 

 been done by Lord HAYLEIGH for the corresponding problem in a non-viscous air ; the 

 same method has been adopted in this paper. It should, however, be borne in mind 

 that the results so obtained are valid only when the obstacles are so sparsely 

 distributed that the space occupied by the obstacles is a small fraction of the total 

 volume. The investigation has some practical interest. It has been asserted that 

 the suspension of a large number of parallel wires in a hall or lecture room will 

 improve the acoustic properties of the room. According to the ordinary theory of a 

 non-viscous air the effect of any such arrangement of wires would be inappreciable. 

 From the results of this paper it also appears that the viscosity of the air is not 

 sufficient to account for the alleged phenomenon. 



The results in the case of spherical obstacles are of greater interest, since they are 

 .applicable to the consideration of the effect of foggy weather upon the propagation 



