48 Lord Bayleigh on the Incidence of Aerial 



h= ^ e -*r(^l+t-^*\ . . (115) 



where T = |7ra 3 , # = 27r/A. These are the results given 

 formerly * as applicable in this case to an obstacle of volume 

 T and of arbitrary form. When the obstacle is spherical 

 and AK/K is not small, it was further shown that AK/K 

 should be replaced by (K' — K)/(K' + 2K), and similar 

 reasoning would have applied to A//,//*> 



The solution for the case of a spherical obstacle having the 

 character of a perfect conductor may be derived from the 

 general expressions by supposing that K' = <x>, and (in order 

 that V may remain finite) p' = 0. We get from (106), (111), 



/-■--- r-(? + p> • • (116) 



k 2 a z e~ ikr yz 



9 1 • • • • 



r r 



(117) 



7/= + 



tfah-^/x 2 



r 



C-^+0 • • (H8) 



in agreement with the results of Prof. J. J. Thomson f. As 

 was to be expected, in every case the vectors (/, g, h), (a, /3, 7), 

 (%, y, z) are mutually perpendicular. 



Obstacle in the Form of an Ellipsoid. 

 The case of an ellipsoidal obstacle of volume T, whose 

 principal axes are parallel to those of a, y, z, i. e. parallel to 

 the directions of propagation and of vibration in the primary 

 waves, is scarcely more complicated. The passage from the 

 values of the disturbance in the neighbourhood of the 

 obstacle to that at a great distance takes place exactly as in 

 the case of the sphere. The primary magnetic potential in 

 the neighbourhood of the obstacle is 4.7rVy, and thus, as 

 before, u = 0, t> = 47rV, w = in (1). Accordingly, by (14), 

 A=0, = ; and (28) gives 



* "Electromagnetic Theory of Light," Phil. Mag. vol. xii. p. U0 (1881). 

 t ' Recent Researches/ § 377. 



