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

 where T? /n 



and square brackets are, as before, used to denote that the real part only of the 

 expression so enclosed is being considered. 



Hence we have 



[A,] = -iorAV (D 2 E -D E 2 ) | Do | ~\ 



Now [iA ] = -jJjjTT^AV* 4 , and consequently it may be neglected in comparison 

 with [A,J. 



Hence the loss of energy to the primary waves is given by 



(D U E 2 -D 2 E,,) | D ( , | ~\ 



The ratio of this to p^a/c is 



(10), 



which therefore represents the proportion of the incident energy, which is lost to the 

 primary waves. 



On p. 253 will be found a table giving the ratio of the lost energy to that incident 

 upon the cylindrical obstacle in a number of different cases. For wires and 

 cylindrical rods of comparatively large radius it is necessary to use the formula (9) ; 

 the results for wires of radii 10 cm., 1 cm., and - 1 cm. have been deduced from this 

 formula. The formula (8) is applicable when the radius of the obstacle is very small, 

 and the results for wires of radius 10~ 3 cm. have been obtained from it. When the 

 radius of the wire is of order 10~ 2 cm., neither of these approximate formulae is 

 applicable, and it becomes necessary to calculate the results directly from (10) ; the 

 value of the ratio of the lost energy to that incident upon the wire has been worked 

 out in this case for only a few values of the wave-length on account of the laborious 

 nature of the work involved. 



It should be added that in the table given on p. 253 X denotes the wave-length of 

 the incident sound measured in centimetres, and K denotes the ratio of the lost 

 energy to that incident upon, the obstacle. 



I have also worked out the values of K for wires of different diameters in the case 

 when the wave-length of the incident sound is 250 cm. The results are arranged 

 below : 



A, = 250 cm. 



