and Electric Waves upon Small Obstacles. 47 



so that (103), (104) may be written 



- 7 K'-K k 2 a 3 e- ikr r xz yz ^+f \ , 1ftgN 



a, /3,y _ K'-K yA-^ /y _.* n \ „ 



4ttV ~K / + 2K r \r' »■' V " l U ° 



These equations give the values of the functions for a 

 disturbance radiating from a small spherical obstacle, so far 

 as it depends upon (K' — K). We have to add a similar 

 solution dependent upon the change from fi to fx . In this 

 (103), (104) are replaced by 



^72TT ... J2TT 



(108) 



(109) 



where II = Be~~** r /r, corresponding to an impressed magnetic 

 force parallel to y. In the neighbourhood of the origin (1 08) 

 becomes 



V 2- dxdxj V 2 ~~ dy 2 > V 2 "" dzdtf 



so that ^ in (99) is to be identified with —Y 2 dU/dy. Thus 



»--¥££ ("0) 



At a great distance we have 



/j,'—fik 2 a z e- ikr /z x\ ..... 



\2 = 



dm 



dxdy' 



y3 </ 2 n d 2 n 



V 2 ~ f/.i- 2 + dz 2 ~' 



7 dm 



V 2 ~ dsrfy' 





4tt/= 



dm 

 -dJdt> v =0 > 



47r// = T- , 



dxdV 



4?t V /a' + 2/a 



-(-%^. -?>("?) 



By addition of (111) to (106) and of (112) to (107) we 

 obtain the complete values of f, g, h, a, ft, <y when both the 

 dielectric constant and the permeability undergo variation. 

 The disturbance corresponding to the primary waves h = e ikx 

 is thus determined. 



When the changes in the electric constants are small, (106), 

 (111) may be written 



