156 Mr. C. S. Whitehead on the Effect of a 



Let &> = mngnetic induction tangential to a meridian, 

 u = magnetic induction along a radius. 



Then from the theorem that the line integral of the electro- 

 motive intensity round a circuit is equal to the rate of decrease 

 of the magnetic induction through the circuit, we obtain 



dm _ _ 1 d(<£>r) 

 dt r dr ' 



dv_ 1 c/(<E> sin ) 

 dt ~ r sin dO 

 But <f> varies as e ipt , 



1 d(®r) 



0)= — 



ipr dr ' 

 1 1 d(® sin 0) 

 cpr sin dd 



Since -j& = 0, % n satisfies 



^ (tii&\ + -Li ("sin *£\ = 

 dr\ r dr J + sin0 M dO ) U ' 



.'. from (5) 



cpr T v ar \ of?' / 

 But rf Xn 



•'. |(^) =W(n + 1) ^ 

 where a f\«w <*• ^"M _, . ,* \ 



...•M^J^J 



(6) 

 (7) 



