﻿280 
  

  

  Prof. 
  W. 
  G. 
  Adams 
  on 
  the 
  Forms 
  of 
  [Feb. 
  25, 
  

  

  The 
  Bakerian 
  Lecture 
  was 
  delivered 
  by 
  Prof. 
  W. 
  G. 
  Adams, 
  

   M.A., 
  F.R.S., 
  " 
  On 
  the 
  Forms 
  of 
  Equipotential 
  Curves 
  and 
  

   Surfaces 
  and 
  Lines 
  of 
  Electric 
  Force" 
  The 
  following 
  is 
  an 
  

   Abstract 
  : 
  — 
  

  

  This 
  paper 
  contains 
  an 
  account 
  of 
  certain 
  experimental 
  verifications 
  

   of 
  the 
  laws 
  of 
  electrical 
  distribution 
  in 
  space 
  and 
  in 
  a 
  plane 
  conducting 
  

   sheet. 
  

  

  The 
  potential 
  at 
  any 
  point 
  of 
  an 
  unlimited 
  plane 
  sheet 
  due 
  to 
  a 
  charge 
  

   of 
  electricity 
  at 
  any 
  other 
  point 
  of 
  the 
  plane 
  at 
  distance 
  r 
  from 
  it 
  is 
  pro- 
  

   portional 
  to 
  the 
  logarithm 
  of 
  the 
  distance, 
  and 
  the 
  potential 
  due 
  to 
  two 
  

   or 
  more 
  charges 
  at 
  different 
  points 
  of 
  the 
  plane 
  is 
  the 
  sum 
  of 
  the 
  poten- 
  

   tials 
  due 
  to 
  the 
  several 
  charges 
  ; 
  so 
  that 
  when 
  there 
  are 
  two 
  points 
  in 
  a 
  

   plane 
  conducting 
  sheet 
  connected 
  with 
  the 
  poles 
  of 
  a 
  battery, 
  as 
  there 
  

   are 
  equal 
  currents 
  flowing 
  at 
  those 
  two 
  points, 
  one 
  into 
  and 
  the 
  other 
  

   out 
  of 
  the 
  sheet, 
  the 
  potential 
  at 
  any 
  point 
  of 
  the 
  sheet 
  is 
  proportional 
  

   to 
  the 
  difference 
  of 
  the 
  logarithms 
  of 
  its 
  distances 
  from 
  the 
  two 
  points 
  

   or 
  electrodes 
  where 
  the 
  current 
  enters 
  and 
  leaves 
  the 
  sheet. 
  

  

  The 
  potential 
  is 
  constant 
  for 
  a 
  series 
  of 
  points 
  if 
  the 
  difference 
  of 
  the 
  

   logarithms 
  of 
  the 
  distances 
  of 
  each 
  of 
  those 
  points 
  from 
  the 
  electrodes 
  

   remains 
  constant, 
  i. 
  e. 
  if 
  the 
  ratio 
  of 
  the 
  distances 
  of 
  each 
  of 
  those 
  points 
  

   from 
  the 
  electrodes 
  remains 
  constant. 
  

  

  The 
  curve 
  joining 
  this 
  series 
  of 
  points 
  is 
  an 
  equipotential 
  curve. 
  

  

  If 
  r 
  and 
  i\ 
  are 
  the 
  distances 
  of 
  any 
  point 
  in 
  the 
  curve 
  from 
  the 
  two 
  

   electrodes, 
  and 
  c 
  a 
  constant, 
  then 
  

  

  Hence 
  the 
  equipotential 
  curves 
  are 
  circles 
  with 
  their 
  centres 
  on 
  the 
  line 
  

   joining 
  the 
  two 
  electrodes 
  ; 
  and 
  the 
  lines 
  of 
  force 
  which 
  cut 
  the 
  equipo- 
  

   tential 
  curves 
  at 
  right 
  angles 
  are 
  also 
  arcs 
  of 
  circles 
  passing 
  through 
  the 
  

   two 
  electrodes. 
  

  

  The 
  lines 
  of 
  force 
  may 
  be 
  regarded 
  as 
  distinct 
  from 
  one 
  another, 
  but 
  

   as 
  filling 
  up 
  all 
  the 
  space 
  on 
  the 
  conductor 
  between 
  the 
  two 
  electrodes 
  ; 
  

   and 
  the 
  distribution 
  would 
  not 
  be 
  altered 
  if 
  we 
  conceive 
  of 
  them 
  as 
  

   divided 
  from 
  one 
  another 
  like 
  separate 
  wires 
  conducting 
  currents 
  side 
  by 
  

   side. 
  By 
  taking 
  out 
  any 
  space 
  bounded 
  by 
  lines 
  of 
  force, 
  we 
  shall 
  increase 
  

   the 
  quantity 
  flowing 
  along 
  the 
  other 
  lines 
  of 
  force, 
  but 
  shall 
  not 
  alter 
  the 
  

   distribution 
  of 
  the 
  current 
  among 
  them. 
  Hence 
  we 
  may 
  cut 
  out 
  a 
  disk 
  

   from 
  an 
  unlimited 
  sheet 
  without 
  altering 
  the 
  form 
  of 
  the 
  hues 
  of 
  force, 
  

   if 
  the 
  boundary 
  of 
  the 
  disk 
  be 
  arcs 
  of 
  circles 
  passing 
  through 
  the 
  two 
  

   electrodes 
  ; 
  so 
  that 
  for 
  a 
  circular 
  disk 
  with 
  the 
  electrodes 
  on 
  the 
  edge 
  of 
  

   it, 
  the 
  equipotential 
  curves 
  are 
  circles 
  having 
  their 
  centres 
  on 
  the 
  straight 
  

   line 
  joining 
  the 
  electrodes. 
  

  

  