﻿390 
  Dr. 
  G. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

   and 
  when 
  r>b 
  we 
  have 
  in 
  like 
  manner 
  

  

  ^C?J 
  p 
  ' 
  ( 
  10 
  ) 
  

  

  Considering 
  the 
  case 
  where 
  the 
  magnet 
  is 
  outside 
  the 
  sphere, 
  

   we 
  must 
  take 
  the 
  first 
  expression, 
  since 
  at 
  the 
  surface 
  of 
  the 
  

   sphere 
  r<b. 
  

  

  Let 
  the 
  potentials 
  due 
  to 
  the 
  induced 
  currents 
  at 
  points 
  

   inside 
  and 
  outside 
  the 
  sphere 
  be 
  assumed 
  of 
  the 
  form 
  

  

  0'=S(n 
  + 
  l)A 
  ^P,, 
  (inside), 
  . 
  . 
  (11) 
  

  

  (At 
  

  

  n"=-XnAn 
  ~V 
  n 
  (outside), 
  . 
  . 
  (12) 
  

  

  where 
  the 
  coefficients 
  A„ 
  are 
  functions 
  of 
  the 
  time 
  t 
  ; 
  the 
  

   assumed 
  forms 
  being 
  such 
  as 
  to 
  satisfy 
  the 
  surface-condition 
  

   dn 
  / 
  /dr 
  = 
  cM"/dr. 
  

  

  Substituting 
  the 
  expressions 
  for 
  the 
  potential, 
  f2 
  + 
  fl' 
  and 
  

   flo 
  + 
  fl" 
  for 
  Ili 
  and 
  I2 
  2 
  in 
  the 
  surface-conditions 
  (2), 
  

  

  d 
  I 
  JUa 
  d 
  / 
  ..attlA 
  R 
  d 
  2 
  d 
  N 
  

  

  diV* 
  "* 
  ) 
  = 
  *r 
  IF) 
  = 
  "i 
  £ 
  •**t°»-°^ 
  

  

  we 
  find, 
  on 
  equating 
  coefficients 
  of 
  P 
  ,' 
  

  

  dk 
  n 
  (2;t4l)R 
  , 
  _ 
  , 
  v 
  , 
  a 
  n+1 
  

   dt 
  + 
  2a 
  "~ 
  / 
  W*"*' 
  

  

  _JA 
  ^2n+l)fR/2aj_/V/*\,(2» 
  + 
  l)*B/2a 
  ?!!__, 
  

  

  ... 
  A. 
  = 
  f 
  /' 
  (T) 
  e 
  -^"+i)(^T)R/2a 
  rf 
  T 
  . 
  ^ 
  . 
  

  

  Now 
  let 
  the 
  inducing 
  system 
  be 
  a 
  magnet 
  of 
  moment 
  M 
  

   suddenly 
  generated 
  at 
  the 
  time 
  £ 
  = 
  0, 
  so 
  that 
  

  

  /(*)=0 
  when 
  £<0, 
  

   f(t) 
  = 
  M 
  when 
  t 
  > 
  0. 
  

  

  Then 
  by 
  a 
  similar 
  artifice 
  to 
  that 
  used 
  for 
  the 
  cylindrical 
  

   sheet, 
  we 
  have 
  

  

  A 
  _ 
  M>-(2»+l)*E/2a 
  ^ 
  

  

  .n* 
  — 
  au.e 
  £n+2' 
  

  

  