﻿388 
  Dr. 
  G. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

  

  negative 
  poles 
  at 
  A' 
  (fig. 
  2), 
  the 
  image 
  at 
  time 
  t 
  for 
  inside 
  points 
  

   will 
  be 
  the 
  oppositely 
  magnetized 
  line 
  PP', 
  and 
  for 
  outside 
  

   points 
  the 
  line 
  QQ' 
  having 
  its 
  positive 
  magnetism 
  at 
  Q. 
  Prom 
  

   the 
  properties 
  of 
  similar 
  triangles 
  and 
  of 
  inversion, 
  PP 
  f 
  is 
  

  

  Fig. 
  2. 
  

  

  P' 
  

  

  A' 
  ... 
  ----^ 
  

  

  :^i 
  

  

  A 
  

  

  parallel 
  and 
  QQ'is 
  antiparallel 
  to 
  A 
  A', 
  also, 
  since 
  the 
  strengths 
  

   of 
  the 
  poles 
  are 
  constant, 
  tlie 
  magnetic 
  moments 
  of 
  the 
  images 
  

   are 
  to 
  one 
  another 
  and 
  to 
  that 
  of 
  the 
  inducing 
  system 
  as 
  

   PF 
  : 
  QQ' 
  : 
  A 
  A', 
  that 
  is 
  as 
  OP 
  : 
  OQ' 
  : 
  OA 
  or, 
  in 
  the 
  limiting 
  

   case 
  (when 
  Q 
  and 
  Q' 
  are 
  infinitely 
  near 
  together), 
  as 
  the 
  

   distances 
  OP 
  : 
  OQ 
  : 
  OA. 
  

  

  Hence 
  if 
  M 
  be 
  the 
  magnetic 
  moment 
  generated 
  in 
  AA', 
  

   those 
  of 
  the 
  images 
  PP' 
  and 
  QQ 
  / 
  at 
  time 
  t 
  are 
  — 
  Me 
  m/a 
  and 
  

   Me-WW/b 
  2 
  , 
  where 
  b 
  = 
  OA. 
  

  

  (ii.) 
  Similarly, 
  if 
  a 
  line 
  of 
  magnets 
  of 
  moment 
  M 
  be 
  suddenly 
  

   generated 
  at 
  BB' 
  inside 
  the 
  cylinder, 
  the 
  images 
  at 
  time 
  / 
  

   for 
  outside 
  points 
  will 
  be 
  the 
  oppositely 
  magnetized 
  line 
  QQ' 
  

   of 
  magnetic 
  moment 
  — 
  Me 
  - 
  ' 
  , 
  and 
  for 
  inside 
  points 
  the 
  

   magnetized 
  line 
  PP' 
  having 
  its 
  positive 
  poles 
  at 
  P 
  and 
  of 
  

   magnetic 
  moment 
  Me* 
  /a 
  a 
  2 
  /h 
  2 
  , 
  b 
  being 
  now 
  taken 
  = 
  OB. 
  

  

  7. 
  If 
  a 
  line 
  of 
  poles 
  of 
  strength 
  m 
  suddenly 
  changes 
  position 
  

   from 
  A' 
  to 
  A 
  the 
  effect 
  is 
  equivalent 
  to 
  the 
  superposition 
  of 
  

   — 
  m 
  at 
  A' 
  and^H- 
  m 
  at 
  A, 
  and 
  is 
  thus 
  equivalent 
  to 
  the 
  

   generation 
  of 
  a 
  line 
  of 
  magnets 
  in 
  the 
  direction 
  AA', 
  the 
  

   images 
  of 
  which 
  have 
  just 
  been 
  found. 
  

  

  Fig. 
  3 
  shows 
  the 
  application 
  of 
  this 
  method 
  to 
  construct 
  

   the 
  trails 
  of 
  images 
  of 
  a 
  line 
  of 
  poles 
  revolving 
  uniformly 
  

   about 
  the 
  centre 
  and 
  passing 
  in 
  succession 
  through 
  the 
  

   positions 
  A 
  x 
  , 
  A 
  2 
  , 
  A 
  3 
  , 
  A 
  4 
  , 
  . 
  . 
  ., 
  at 
  equal 
  small 
  intervals 
  of 
  time, 
  

   the 
  actual 
  trails 
  are 
  of 
  course 
  the 
  limits 
  of 
  the 
  series 
  of 
  moving 
  

   poles 
  thus 
  plotted 
  out. 
  By 
  supposing 
  the 
  line 
  of 
  poles 
  to 
  

   remain 
  fixed 
  and 
  the 
  cylinder 
  to 
  rotate, 
  we 
  get 
  a 
  kind 
  of 
  

  

  