﻿382 
  Dr. 
  Gr. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

   For 
  a 
  spherical 
  sheet 
  we 
  found 
  in 
  like 
  manner 
  

  

  involving, 
  as 
  before, 
  the 
  condition 
  dSl-Jdr—dflzldr, 
  

  

  Before 
  determining 
  the 
  images 
  which 
  repi'esent 
  the 
  effect 
  

   of 
  the 
  currents 
  induced 
  by 
  the 
  introduction 
  of 
  a 
  given 
  pole, 
  

   magnet, 
  or 
  current 
  in 
  the 
  presence 
  of 
  such 
  sheets, 
  it 
  will 
  be 
  

   convenient 
  to 
  think, 
  for 
  a 
  moment, 
  of 
  the 
  images 
  which 
  occur 
  

   in 
  hydrodynamical 
  problems 
  relating 
  to 
  the 
  cylinder 
  and 
  

   sphere. 
  In 
  two-dimensional 
  fluid 
  motion, 
  the 
  image 
  of 
  a 
  line- 
  

   source 
  outside 
  and 
  parallel 
  to 
  the 
  axis 
  of 
  a 
  cylinder 
  is 
  an 
  equal 
  

   line-source 
  through 
  the 
  inverse 
  point 
  together 
  with 
  an 
  equal 
  

   line-sink 
  through 
  the 
  centre 
  (t. 
  e. 
  along 
  the 
  axis) 
  ; 
  similarly 
  

   the 
  image 
  of 
  a 
  line-source 
  inside 
  the 
  sphere 
  together 
  with 
  an 
  

   equal 
  line-sink 
  along 
  the 
  axis 
  is 
  an 
  equal 
  line-source 
  through 
  

   the 
  inverse 
  point. 
  The 
  image 
  of 
  a 
  vortex-filament 
  parallel 
  to 
  

   the 
  axis 
  of 
  a 
  cylinder, 
  whether 
  inside 
  or 
  outside 
  the 
  cylinder, 
  is 
  

   an 
  equal 
  and 
  opposite 
  vortex 
  through 
  the 
  inverse 
  point. 
  In 
  

   the 
  case 
  of 
  a 
  sphere, 
  the 
  image 
  of 
  a 
  doublet 
  whose 
  axis 
  passes 
  

   through 
  the 
  centre 
  is 
  a 
  certain 
  doublet 
  at 
  the 
  inverse 
  point, 
  

   whether 
  the 
  original 
  doublet 
  be 
  inside 
  or 
  outside 
  the 
  sphere. 
  

   The 
  image 
  of 
  a 
  source 
  in 
  a 
  sphere, 
  on 
  the 
  other 
  hand, 
  is 
  more 
  

   complicated, 
  consisting 
  not 
  only 
  of 
  a 
  source 
  but 
  also 
  of 
  a 
  sink 
  

   extending 
  to 
  the 
  centre 
  if 
  the 
  original 
  source 
  was 
  outside 
  the 
  

   sphere, 
  and 
  to 
  infinity 
  if 
  inside. 
  

  

  We 
  may 
  therefore 
  expect 
  by 
  analogy 
  that 
  the 
  images 
  in 
  a 
  

   spherical 
  sheet 
  due 
  to 
  the 
  motion 
  or 
  generation 
  of 
  magnetic 
  

   poh's 
  in 
  its 
  neighbourhood 
  will 
  be 
  less 
  simple 
  than 
  those 
  pro- 
  

   duced 
  by 
  magnets 
  whose 
  axes 
  pass 
  through 
  the 
  centre 
  of 
  the 
  

   sphere 
  ; 
  and 
  such 
  we 
  shall 
  find 
  to 
  be 
  actually 
  the 
  case. 
  

  

  Image 
  due 
  to 
  Generation 
  of 
  a 
  Line 
  of 
  Poles 
  parallel 
  to 
  the 
  

   Axis 
  outside 
  a 
  Cylindrical 
  Sheet. 
  

  

  2. 
  We 
  first 
  consider 
  the 
  two-dimensional 
  problem 
  in 
  which 
  

   the 
  currents 
  ;tre 
  induced 
  by 
  the 
  generation 
  or 
  destruction 
  of 
  

   a 
  linear 
  distribution 
  of 
  magnetism 
  parallel 
  to 
  the 
  axis 
  of 
  the 
  

   cylinder 
  at 
  A 
  (tig. 
  1) 
  in 
  the 
  line 
  whose 
  polar 
  (cylindrical) 
  

   coordinates 
  are 
  r 
  = 
  b, 
  6 
  = 
  0, 
  where 
  b 
  is 
  greater 
  than 
  a 
  the 
  

   radius 
  of 
  the 
  cylinder. 
  To 
  cover 
  all 
  cases 
  we 
  commence 
  by 
  

   assuming 
  at 
  the 
  outset 
  that 
  the 
  line-denshy 
  of 
  this 
  line 
  of 
  

   poles, 
  as 
  it 
  may 
  be 
  called, 
  is/(7) 
  a 
  function 
  of 
  the 
  time. 
  

  

  The 
  magnetic 
  potential 
  of 
  this 
  distribution 
  at 
  the 
  point 
  

   (r, 
  t)) 
  is 
  therefore 
  

  

  n 
  (say) 
  =/*/(*){const.-log 
  s/(r 
  2 
  + 
  b 
  2 
  -2rbcost))l, 
  

  

  