﻿392 
  Br. 
  Gr. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

  

  would 
  be 
  produced 
  by 
  a 
  magnet 
  of 
  moment 
  — 
  Me 
  dm/2a 
  a 
  3 
  /b 
  3 
  at 
  

   a 
  distance 
  from 
  the 
  centre 
  of 
  e 
  m 
  ' 
  a 
  a 
  2 
  /b. 
  

  

  As 
  before, 
  the 
  intensities 
  of 
  tbe 
  several 
  magnets 
  vary 
  as 
  the 
  

   t| 
  power 
  of 
  their 
  distance 
  from 
  the 
  centre. 
  

  

  Images 
  due 
  to 
  Generation 
  of 
  Circular 
  Currents 
  coaxial 
  with 
  

   a 
  Spherical 
  Sheet 
  , 
  fyc. 
  

  

  10. 
  A 
  circular 
  current 
  whose 
  axis 
  passes 
  through 
  the 
  centre 
  

   of 
  the 
  sphere 
  is 
  equivalent 
  to 
  a 
  magnetic 
  shell 
  forming 
  a 
  spheri- 
  

   cal 
  cap 
  on 
  the 
  surface 
  of 
  a 
  concentric 
  sphere, 
  this 
  cap 
  being 
  

   bounded 
  by 
  the 
  current. 
  It 
  is 
  thus 
  evident 
  that 
  the 
  images 
  

   due 
  to 
  the 
  sudden 
  generation 
  of 
  such 
  a 
  current 
  are 
  also 
  circular 
  

   currents, 
  which 
  move 
  in 
  the 
  manner 
  described 
  in 
  the 
  pre- 
  

   ceding 
  sections. 
  There 
  is 
  no 
  need 
  to 
  restrict 
  the 
  results 
  to 
  

   circular 
  currents 
  as 
  the 
  same 
  arguments 
  are 
  equally 
  applicable 
  

   when 
  the 
  inducing 
  current 
  flows 
  in 
  any 
  closed 
  curve 
  traced 
  on 
  

   a 
  spherical 
  surface 
  concentric 
  with 
  the 
  sheet, 
  the 
  images 
  in 
  

   this 
  case 
  being 
  currents 
  in 
  similar 
  curves. 
  It 
  remains 
  to 
  state 
  

   the 
  relation 
  between 
  the 
  intensities 
  of 
  the 
  currents 
  in 
  the 
  

   images 
  and 
  that 
  of 
  the 
  inducing 
  current. 
  

  

  (i.) 
  Let 
  A 
  A 
  7 
  (fig. 
  4) 
  be 
  the 
  wire 
  in 
  which 
  an 
  inducing 
  

  

  Fio% 
  4. 
  

  

  current 
  of 
  intensity 
  I 
  is 
  suddenly 
  generated 
  outside 
  the 
  sheet. 
  

   Then 
  at 
  time 
  t 
  the 
  image 
  for 
  inside 
  points 
  will 
  be 
  a 
  current 
  in 
  

   PP'and 
  for 
  outside 
  points 
  a 
  current 
  in 
  QQ', 
  where 
  OP=^ 
  R/a 
  OA 
  

   and 
  OQ 
  = 
  e~* 
  R/a 
  a 
  2 
  /OA. 
  Suppose 
  the 
  currents 
  replaced 
  by 
  

   their 
  equivalent 
  magnetic 
  shells 
  on 
  spherical 
  surfaces 
  centred 
  

   at 
  0, 
  and 
  let 
  corresponding 
  elements 
  of 
  these 
  shells 
  be 
  taken. 
  

   The 
  magnetic 
  moments 
  of 
  the 
  elements 
  of 
  PP', 
  QQ', 
  and 
  AA' 
  

   are 
  respectively 
  as 
  OP! 
  : 
  OQI 
  : 
  OA* 
  ; 
  and 
  the 
  areas 
  of 
  these 
  

   elements 
  areas 
  OP 
  2 
  : 
  OQ 
  2 
  : 
  OA 
  2 
  ; 
  hence 
  the 
  strengths 
  of 
  the 
  

   shells 
  are 
  as 
  OP~* 
  : 
  OQ 
  - 
  * 
  : 
  OA 
  - 
  *, 
  and 
  the 
  current-intensities 
  

  

  