﻿394 
  Dr. 
  Gr. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

  

  (i.) 
  Hence 
  we 
  find 
  for 
  the 
  potentials 
  of 
  the 
  induced 
  currents 
  

   at 
  points 
  inside 
  the 
  sphere 
  at 
  time 
  t 
  

  

  = 
  -^ 
  R/2 
  ^P^T 
  1 
  P». 
  • 
  • 
  • 
  (16) 
  

  

  This 
  is 
  the 
  potential 
  of 
  a 
  pole 
  of 
  intensity 
  —me 
  tR 
  l 
  2a 
  at 
  a 
  

   distance 
  from 
  the 
  centre 
  of 
  be 
  mia 
  . 
  

  

  (ii.) 
  For 
  points 
  inside 
  the 
  sphere 
  the 
  corresponding 
  

   potential 
  is 
  

  

  n+1 
  i,n+i 
  r 
  n+i 
  

  

  = 
  m 
  j 
  e 
  - 
  m 
  ? 
  2a 
  S 
  — 
  -r 
  v 
  — 
  f 
  2 
  - 
  P„ 
  . 
  

  

  o 
  n 
  + 
  1 
  r 
  n+i 
  

  

  Let 
  p 
  = 
  e- 
  m 
  < 
  la 
  a 
  2 
  /b. 
  Then 
  

  

  ?_^ 
  Pip 
  _*_/?! 
  P 
  _ 
  1 
  v 
  p' 
  1 
  * 
  1 
  p 
  

  

  1 
  1 
  f 
  <//0' 
  

  

  - 
  i 
  /(r 
  2 
  -2rpcos^f 
  /3 
  2 
  ) 
  pj 
  v/ 
  (r- 
  2 
  -2y 
  cos 
  + 
  p 
  /2 
  ) 
  

  

  . 
  o//- 
  me-W'a/b 
  _ 
  m 
  C? 
  dp' 
  

  

  ' 
  ' 
  </{r 
  2 
  -2rp 
  cos 
  d 
  + 
  p 
  2 
  ) 
  a 
  Jo 
  n/(> 
  2 
  - 
  2^' 
  cos 
  6> 
  + 
  p 
  /2 
  )* 
  

  

  . 
  . 
  . 
  (17) 
  

  

  The 
  first 
  part 
  represents 
  the 
  potential 
  of 
  a 
  pole 
  of 
  strength 
  

   me~ 
  mi2a 
  alb 
  at 
  a 
  distance 
  p 
  from 
  the 
  centre, 
  i.e. 
  at 
  the 
  point 
  

   Q 
  of 
  the 
  previous 
  sections, 
  and 
  the 
  second 
  represents 
  the 
  

   potential 
  of 
  a 
  line-distribution 
  of 
  magnetism 
  of 
  uniform 
  linear 
  

   density 
  —me 
  m 
  ^ 
  2a 
  /a 
  extending 
  from 
  the 
  centre 
  to 
  Q 
  ; 
  this 
  being- 
  

   equal 
  to 
  the 
  strength 
  of 
  the 
  pole 
  divided 
  by 
  p 
  or 
  OQ, 
  it 
  follows 
  

   that 
  the 
  total 
  quantity 
  of 
  magnetism 
  on 
  this 
  line 
  OQ 
  is 
  equal 
  

   and 
  opposite 
  to 
  that 
  in 
  the 
  pole 
  Q 
  (fig. 
  5). 
  This 
  distribution 
  

   of 
  images 
  is 
  related 
  to 
  the 
  image 
  on 
  the 
  opposite 
  side 
  in 
  the 
  

   same 
  manner 
  as 
  the 
  hydrodynamic 
  image 
  of 
  a 
  source 
  in 
  a 
  

   sphere 
  is 
  related 
  to 
  the 
  source, 
  except 
  in 
  the 
  matter 
  of 
  algebraic 
  

   sign. 
  The 
  reason 
  for 
  the 
  resemblance 
  is 
  that 
  the 
  two 
  potentials 
  

   here 
  have 
  to 
  make 
  dfl'/dr^dW/drnt 
  the 
  surface, 
  while 
  in 
  the 
  

  

  