376 Scattering of Sound by Spheroids and Disks. 



Approximately spherical planetary body. 

 If e be the small eccentricity of the axial section, 

 tan -1 cosech f = sin -1 e, 

 and it appears that 



eM. = zm~ l e-e^l^~e 2 



^N = 3 v /I^" 2 sm- 1 ^-<3~6 2 ), . . . (45) 

 and for small values of e 



and finally, if a is the unequal axis, and e the ellipticity, 



t=-^(i + ! > cos4-* + ^ e /' 1+ 9 co ^y* 



or \ 2 J Ar V 10 / 



, Pa'/ 32 3 „ 1 , A \ , 

 ■ f ^(i35 + 20 CO ^-9 Cos2 T"'" 



- k ^Xi + kr sd -!2 cos ' e+ k^ d y' kr - ■ (i ^ 



Circular disk. 



The case of the circular disk may be deduced from that of 

 the oblate spheroid by making the axis zero. 



Thus £=0, and c becomes the radius of the disk. The 

 result is 



2 PaU ^ 7 Pa 2 k 2 a 2 „ A „ , ,.„. 



yb= — - 1— — - + — s cos 2 0)cos0<?-^. (17) 



37r r \ 2d 10 / v 



If the disk thickens towards the centre it may be roughly 

 treated as an oblate spheroid of small minor axis 26, where 

 2b is the maximum thickness. 



In this case, T it b 



~ J " 2 ~~a* 



f ' =tt ( i_ y ; 



