254 Mr. H. M. Macdonald. The Bending of [Jan. 21, 



The calculation of the electric forces at a point not on the surface of 

 the sphere presents difficulties, but when the wave-length is small 

 compared with the radius of the sphere, the electric force at the surface 

 of the sphere can be obtained in a simple form. The electric force at 

 the surface of the sphere is normal to the surface, and denoting it by F r 



— —is the real part ot when r = ft. JNow 



V 2 dt F « 2 3> 



and, when the wave-length is small compared with a, this becomes 



1 gf 



ft 2 3/v=«, 



a * r «-* 3 i 3p, 



= + — £ {«» J»+» («») } J a - > 



that is, writing ^ x = /(?'), 



i 3^ l 3 r _ . . 13 



a 2 djjt r =a u 2 3/x 

 From the above 



/(fl) = (1-/*-) (a- - /ir- ^p— , 

 \ Oft 0/x/ -Ko 



where R 2 = ^ 2 + r r - 2arifi t that is 

 /(fl) = ( l_ r) ^_ 



/((() = ^a-M 8 ) g 



R 3R Rq ? 



therefore 



l 3f _ l 3 r fft 2 3 f-^ E o l 3 ft 2 3 g-^ R o |-| 

 ft 2 3/x r = ft ft 2 3/xL ( -^LKoSRo Ro + ^^Ro3R K J j 



which gives 



i 3f c 3 r . - ft 2 a cosKm.-vn 



