﻿Plane, 
  Cylindrical, 
  and 
  Spherical 
  Current-Sheets. 
  397 
  

  

  poles 
  or 
  an 
  unclosed 
  current 
  inside 
  the 
  sheet 
  it 
  is 
  necessary 
  

   from 
  physical 
  considerations 
  to 
  place 
  equal 
  and 
  opposite 
  

   poles 
  at 
  the 
  centre 
  or 
  to 
  close 
  the 
  circuit 
  by 
  axial 
  return 
  

   currents, 
  and 
  this 
  is 
  also 
  essential 
  for 
  the 
  success 
  of 
  the 
  image 
  

   method. 
  

  

  4. 
  The 
  relations 
  between 
  the 
  intensity 
  of 
  the 
  source 
  of 
  dis- 
  

   turbance 
  and 
  those 
  of 
  the 
  images 
  will 
  readily 
  be 
  found 
  to 
  be 
  

   in 
  every 
  case 
  expressible 
  in 
  terms 
  of 
  their 
  distances 
  from 
  the 
  

   centre. 
  The 
  results 
  expressed 
  in 
  this 
  way 
  may 
  be 
  tabulated 
  

   as 
  follows 
  : 
  — 
  

  

  Sheet. 
  Inducing 
  disturbance. 
  

  

  Cylinder. 
  Line 
  of 
  poles 
  parallel 
  to 
  axis. 
  

   „ 
  Current 
  parallel 
  to 
  axis. 
  

  

  „ 
  Line 
  of 
  magnets. 
  

  

  Sphere. 
  Magnet 
  radially 
  magnetized. 
  

  

  Concentric 
  magnetic 
  shell. 
  

   Current 
  on 
  concentric 
  sphere. 
  

   Magnetic 
  pole 
  {with 
  exception). 
  

  

  Law 
  of 
  variation. 
  

   Constant. 
  

  

  ?? 
  

   x 
  distance. 
  

   oc 
  (distance)?. 
  

  

  x 
  (distance)^. 
  

  

  x 
  (distance)^. 
  

  

  5. 
  The 
  last-named 
  exceptional 
  case 
  is 
  that 
  of 
  a 
  spherical 
  

   sheet 
  when 
  the 
  disturbance 
  is 
  due 
  to 
  the 
  generation 
  of 
  a 
  

   pole, 
  and 
  it 
  is 
  required 
  to 
  represent 
  by 
  images 
  the 
  potential 
  of 
  

   the 
  currents 
  on 
  the 
  same 
  side 
  as 
  the 
  disturbing 
  pole, 
  the 
  

   images 
  thus 
  being 
  on 
  the 
  opposite 
  side 
  of 
  the 
  sheet. 
  Here, 
  

   in 
  addition 
  to 
  the 
  single 
  pole 
  whose 
  intensity 
  and 
  position 
  

   are 
  given 
  by 
  the 
  above 
  statements, 
  the 
  image 
  consists 
  of 
  a 
  

   line-distribution 
  of 
  magnetism 
  of 
  opposite 
  sign, 
  extending 
  

   from 
  that 
  pole 
  along 
  the 
  radius 
  away 
  from 
  the 
  sheet, 
  and 
  

   having 
  its 
  line-density 
  equal 
  to 
  the 
  quantity 
  of 
  magnetism 
  

   in 
  the 
  pole 
  or 
  image 
  divided 
  by 
  its 
  distance 
  from 
  the 
  

   centre. 
  

  

  6. 
  When 
  the 
  source 
  of 
  disturbance 
  is 
  in 
  motion, 
  the 
  trails 
  

   of 
  images 
  can 
  be 
  built 
  up 
  synthetically 
  as 
  in 
  the 
  case 
  of 
  a 
  

   plane 
  sheet. 
  If 
  the 
  source 
  of 
  disturbance 
  is 
  rotating 
  uni- 
  

   formly 
  about 
  the 
  centre 
  of 
  the 
  cylinder 
  or 
  sphere, 
  the 
  

   curves 
  described 
  by 
  the 
  trails 
  of 
  images 
  will 
  be 
  equiangular 
  

   spirals. 
  

  

  Phil. 
  Mag. 
  S. 
  5. 
  Vol. 
  45. 
  No. 
  276. 
  May 
  1898. 
  

  

  2 
  E 
  

  

  