﻿396 
  Dr. 
  G. 
  H. 
  Bryan 
  on 
  Electromagnetic 
  Induction 
  in 
  

  

  together 
  with 
  a 
  line-distribution 
  of 
  magnetism 
  of 
  linear 
  

   density 
  —me~ 
  ml2a 
  la 
  extending 
  from 
  distance 
  p 
  to 
  infinit}\ 
  

   This 
  linear 
  density 
  is 
  equal 
  to 
  the 
  strength 
  of 
  the 
  pole-image 
  

   divided 
  by 
  its 
  distance 
  p. 
  

  

  Other 
  Images 
  in 
  a 
  Spherical 
  Sheet. 
  

  

  13. 
  When 
  the 
  inducing 
  potential 
  is 
  due 
  to 
  a 
  small 
  magnet 
  

   whose 
  axis 
  does 
  not 
  pass 
  through 
  the 
  centre 
  of 
  the 
  sphere 
  we 
  

   could 
  of 
  course 
  find 
  the 
  images 
  by 
  considering 
  the 
  positive 
  

   and 
  negative 
  poles 
  separately. 
  If 
  the 
  axis 
  of 
  the 
  magnet 
  

   makes 
  an 
  angle 
  a, 
  with 
  the 
  radius-vector 
  the 
  simplest 
  plan 
  

   would 
  be 
  to 
  replace 
  it 
  by 
  two 
  magnets 
  of 
  moment 
  M 
  cos 
  a 
  

   and 
  M 
  sin 
  a 
  along 
  and 
  perpendicular 
  to 
  the 
  radius. 
  

  

  14. 
  The 
  images 
  due 
  to 
  a 
  pole 
  of 
  constant 
  strength 
  moving 
  

   along 
  the 
  radius-vector 
  and 
  initially 
  at 
  rest 
  will 
  be 
  trails 
  of 
  

   magnets 
  which 
  can 
  be 
  worked 
  out 
  by 
  employing 
  the 
  simpler 
  

   images 
  of 
  §§ 
  10 
  and 
  11. 
  If, 
  initially, 
  the 
  pole 
  were 
  suddenly 
  

   generated, 
  we 
  should 
  have 
  to 
  introduce 
  the 
  more 
  complicated 
  

   images 
  of 
  §§11 
  and 
  12, 
  but 
  this 
  may 
  be 
  avoided 
  by 
  considering 
  

   the 
  problem 
  in 
  which 
  the 
  pole 
  is 
  supposed 
  to 
  have 
  remained 
  

   at 
  rest 
  from 
  an 
  infinite 
  time 
  past 
  (or, 
  at 
  any 
  rate, 
  so 
  long 
  that 
  

   all 
  currents 
  in 
  the 
  sheet 
  have 
  died 
  out), 
  and 
  investigating 
  only 
  

   the 
  effects 
  due 
  to 
  its 
  motion. 
  As 
  usual, 
  any 
  small 
  displacement 
  

   may 
  be 
  represented 
  by 
  putting 
  down 
  a 
  magnet 
  of 
  which 
  one 
  

   pole 
  cancels 
  the 
  moving 
  pole 
  in 
  its 
  old 
  position, 
  while 
  the 
  

   other 
  is 
  identical 
  with 
  the 
  moving 
  pole 
  in 
  its 
  new 
  position. 
  If 
  

   the 
  pole 
  moves 
  in 
  a 
  direction 
  other 
  than 
  radial, 
  the 
  more 
  com- 
  

   plicated 
  images 
  of 
  §§ 
  11 
  and 
  12 
  will 
  of 
  course 
  be 
  introduced. 
  

  

  General 
  Conclusions. 
  

  

  1. 
  The 
  phenomena 
  of 
  two-dimensional 
  induction 
  in 
  cylin- 
  

   drical 
  sheets 
  and 
  of 
  induction 
  in 
  spherical 
  sheets 
  due 
  to 
  a 
  

   sudden 
  disturbance 
  in 
  the 
  magnetic 
  field 
  can 
  be 
  represented 
  

   by 
  moving 
  trails 
  of 
  images 
  which 
  are 
  generally 
  not 
  much 
  

   more 
  complicated 
  than 
  those 
  obtained 
  with 
  a 
  pLme 
  sheet. 
  

  

  2. 
  The 
  images 
  in 
  every 
  case 
  start 
  from 
  the 
  source 
  of 
  dis- 
  

   turbance 
  and 
  its 
  inverse, 
  and 
  move 
  away 
  from 
  the 
  sheet 
  

   radially 
  with 
  velocities 
  varying 
  directly 
  as 
  the 
  distance, 
  the 
  

   constant 
  of 
  variation 
  being 
  such 
  as 
  to 
  make 
  the 
  velocity 
  at 
  

   the 
  surface 
  of 
  the 
  sheet 
  become 
  equal 
  to 
  R, 
  the 
  corresponding 
  

   velocity 
  for 
  a 
  plane 
  sheet 
  of 
  the 
  same 
  thickness 
  and 
  conduc- 
  

   tivity. 
  The 
  image 
  which 
  initially 
  coincides 
  with 
  the 
  source 
  of 
  

   disturbance 
  initially 
  neutralizes 
  its 
  effect 
  on 
  the 
  opposite 
  side 
  

   of 
  the 
  sheet. 
  

  

  3. 
  Where 
  the 
  source 
  of 
  disturbance 
  is 
  a 
  distribution 
  of 
  

  

  