374 Dr. J. W. Nicholson on the Scattering 



Retaining only the significant portions, 







M = 



= tt sech 2 f 







N= 



2 

 = ■= sech 2 f , 







and 



finally 







*= 



6r\ 2 J 



r \VA 



ikr 



,(30) 



which agrees with the result of Lord Rayleigh's analysis by 

 spherical harmonics and Bessel functions. This agreement 

 extends also to the first approximations for the spheroidal 

 obstacle. 



Prolate spheroidal obstacle of small ellipticity. 

 When e is small, 



v 



m =f( i+ S) 



and to the first power of the ellipticity e — - e 2 , 



k q a d /^ , 3 n \ ,, h x a° ( 32 3 >. 1 9 ,A _ ?Ar 

 f =-f (1+ - 2 CO^>-* + — (jgg + goOOS^gOOS' 6>)« 



+ -3r-( 1+ 5 C0S T - ~ (l89 + 50 COS ^- fl 008 »" lO 008 'M 



where a is the major axis. • • . -. (40 



Long thin blade. 



The effect of any thin obstacle placed with its length along 

 the direction of propagation of the incident waves, may be 

 estimated by considering a very prolate spheroid, in which 

 f is very small. If the greatest breadth is 2b, and length 2a, 



f=tanh-^ = ^l+^) 

 a a \ oa A ' 



h c= / a " ?r ^ s=a ( 1 -£)' 



since - is small. 

 a 



