and Electric Waves upon Small Obstacles. 49 



corresponding to (99) for the sphere. In like manner the 

 electric potential is 



K 7 — K Tz M9fh 



X ~ 4ttK + (K'-K)N r 3 ' " ' * { J 



These potentials give by differentiation the values of a, fB, y 

 and/, g, h respectively in the neighbourhood of the ellipsoid. 

 Thus at a great distance we obtain for the part dependent on 

 (K/— K), as generalizations of (106), (107), 



- , _ K'-K k 2 Te~ ikr / xz yz_ x 2 + y 2 \ 



:9 > 4ttK + (K / -K)N r \ r 2 > > r 2 ) ; 



. . . (121) 



«.j8,7 _ K/ ~ K STg-gy y _f ft \ n99y 



4ttV ~4ttK + (K , -K)N r \r r' )' ' ^ iZZj 



To these are to be added corresponding terms dependent 

 upon (fjJ—fx), viz. : — 



a, £, 7_ fJ — p k 2 Te~ ikr / xy w 2 + z 2 zy\ 



4ttV - 47T/i + (/A'-/i)M r \ f 5 * ~^~' ~*?/« 



. . . (124) 



The sum gives the disturbance at a distance due to the 

 impact of the primary waves, 



h 9 =e ikx , P =47rYe ikx , . . . . (125) 



upon the ellipsoid T of dielectric capacity K/ and of permea- 

 bility //. 



As in the case of the sphere, the result for an ellipsoid of 

 perfect conductivity is obtained by making K/ = oo, fi' = 0. 

 Thus 



*V*/T«* T z\ 



f- — (jv + 4^M r) ' (126 > 



k 2 e~ ikr Tyz ,. % 



" + f l» r 2 + 4tt-M;> ' C12bj 



Next to the sphere the case of greatest interest is that of a 

 flat circular disk (radius = R). The volume of the obstacle 

 then vanishes, but the effect remains finite in certain cases 



Phil. Mag. S. 5. Vol. 44. No. 266. July 1897. E 



