178 Mr. C. S. Whitehead on the Effect of a Solid 



Rd is the magnetic induction perpendicular to the surface 



of the plate. 

 Td the magnetic induction tangential to the surface along p. 



Let the point be on the axis of the circuit, so that p = 0. 

 Therefore 



Ei = 

 T*=0 



Qir<yp, df 2 



*■ (d 2 +f 2 )* 



cos I vt — 



&-?}; . 



(26) 



Let p be greater than / and large compared with d, so that 

 d 2 may be neglected. 

 We have 



(l + 27tcosv + /i 2 )~2 = (l+he a, )~2 (l + he-' v )~* 



= (l+A 1 he LV + A<Ji 2 t? lv + +A m h m e™+ . 



x (l + AA^ + A^V 2 ^ • • • • + A m h™e~™ + , 



where 



s(s + 2) (2m + s-2) 



0- 



2 m . m! 



k=(-v 



A =l. 



The coefficient of h m 



= 2A m cos mv 4- 2A 1 A ni _ 1 cos (m — 2) y + 2A 2 A m _ 2 cos (m —4) y 



+ 



the last term =A 2 m, if in be even 



2 



= 2A m _i A TO+ i cos v, if m be odd. 

 2 ~T~ 



We hence find 



+ (^1(/y + ....} 



Hence approximately when ^ is small compared with / 



I 



>■ CT 



