﻿28 
  i 
  On 
  Equipotential 
  Curves 
  and 
  Surfaces, 
  fyc. 
  [Feb. 
  25, 
  

  

  A 
  rectangular 
  box 
  was 
  taken, 
  and 
  the 
  battery-electrodes 
  attached 
  to 
  

   pieces 
  of 
  wood, 
  which 
  could 
  be 
  clamped 
  at 
  the 
  centre 
  of 
  the 
  end 
  of 
  the 
  

   box, 
  and 
  could 
  be 
  brought 
  to 
  any 
  required 
  point 
  in 
  the 
  line 
  joining 
  the 
  

   middle 
  points 
  of 
  the 
  end 
  of 
  the 
  box. 
  The 
  galvanometer-electrodes 
  were 
  

   attached 
  to 
  "J* 
  pieces 
  which 
  rest 
  on 
  the 
  ends 
  and 
  side 
  of 
  the 
  box, 
  and 
  

   the 
  position 
  of 
  the 
  electrodes 
  was 
  read 
  off 
  by 
  a 
  millimetre-scale 
  placed 
  on 
  

   the 
  ends 
  and 
  sides 
  of 
  the 
  box. 
  

  

  In 
  the 
  sulphate-of-copper 
  experiments, 
  covered 
  wire 
  with 
  the 
  end 
  ex- 
  

   posed 
  was 
  immersed 
  to 
  half 
  the 
  depth 
  of 
  the 
  liquid 
  ; 
  in 
  the 
  experiments 
  

   with 
  sulphate 
  of 
  zinc, 
  the 
  zinc 
  electrodes 
  were 
  just 
  immersed 
  below 
  the 
  

   surface 
  of 
  the 
  liquid. 
  The 
  close 
  coincidence 
  between 
  the 
  experimental 
  

   curves 
  traced 
  out 
  and 
  the 
  theoretical 
  curves 
  and 
  surfaces 
  in 
  space 
  is 
  

   shown 
  by 
  a 
  comparison 
  of 
  the 
  numbers 
  given 
  in 
  the 
  paper 
  for 
  several 
  of 
  

   the 
  curves 
  which 
  have 
  been 
  traced 
  out 
  ; 
  it 
  also 
  shows 
  that, 
  by 
  reversing 
  

   currents 
  alternately, 
  it 
  is 
  easy 
  to 
  keep 
  the 
  polarization 
  very 
  small, 
  and 
  of 
  

   constant 
  amount, 
  on 
  the 
  galvanometer-electrodes. 
  

  

  When 
  the 
  electrodes 
  are 
  parallel 
  lines 
  extending 
  throughout 
  the 
  depth 
  

   of 
  the 
  liquid, 
  the 
  equipotential 
  surfaces 
  are 
  cylindrical, 
  and 
  their 
  sections 
  

   are 
  given 
  by 
  the 
  equation 
  

  

  log(rr' 
  . 
  ..^(logr^' 
  . 
  . 
  .) 
  = 
  logc, 
  

  

  where 
  there 
  are 
  several 
  positive 
  and 
  several 
  negative 
  electrodes, 
  r 
  .r' 
  . 
  . 
  . 
  

   &c. 
  being 
  measured 
  from 
  the 
  points 
  where 
  the 
  electrodes 
  cut 
  the 
  plane 
  

   of 
  the 
  section. 
  

  

  Hence 
  the 
  forms 
  of 
  these 
  equipotential 
  curves 
  are 
  the 
  same 
  as 
  in 
  a 
  

   plane 
  sheet 
  ; 
  so 
  that 
  the 
  forms 
  traced 
  out 
  in 
  tinfoil 
  will 
  be 
  the 
  same 
  as 
  

   the 
  corresponding 
  forms 
  in 
  space 
  for 
  line 
  electrodes. 
  These 
  forms 
  may 
  

   be 
  traced 
  out 
  in 
  sulphate 
  of 
  copper 
  with 
  copper 
  electrodes, 
  or 
  in 
  sulphate 
  

   of 
  zinc 
  with 
  amalgamated 
  zinc 
  electrodes 
  ; 
  and 
  for 
  these 
  experiments, 
  

   with 
  cylindrical 
  and 
  other 
  vessels, 
  the 
  polar 
  coordinates 
  may 
  be 
  mea- 
  

   sured 
  directly. 
  One 
  of 
  the 
  battery- 
  electrodes 
  is 
  made 
  the 
  origin 
  of 
  

   coordinates, 
  and 
  a 
  lath, 
  or 
  brass 
  wire, 
  resting 
  on 
  the 
  edges 
  of 
  the 
  vessel 
  

   has 
  a 
  slot 
  along 
  it, 
  the 
  origin 
  being 
  at 
  one 
  end 
  or 
  at 
  some 
  point 
  of 
  the 
  

   slot. 
  In 
  the 
  slot 
  is 
  a 
  sliding 
  piece 
  of 
  wood 
  or 
  ivory 
  which 
  carries 
  one 
  of 
  the 
  

   galvanometer-electrodes, 
  and 
  the 
  lath 
  is 
  capable 
  of 
  turning 
  about 
  the 
  

   battery-electrode 
  on 
  which 
  it 
  is 
  placed. 
  Around 
  this 
  electrode 
  is 
  a 
  gra- 
  

   duated 
  circle 
  for 
  measuring 
  the 
  angles 
  about 
  the 
  origin, 
  and, 
  on 
  the 
  sides 
  

   of 
  the 
  slot, 
  is 
  a 
  millimetre-scale 
  for 
  measuring 
  the 
  distances 
  from 
  the 
  

   origin. 
  

  

  The 
  other 
  galvanometer-electrode 
  may 
  be 
  fixed- 
  in 
  a 
  manner 
  which 
  is 
  

   most 
  suitable 
  in 
  each 
  case. 
  

  

  The 
  results 
  of 
  these 
  investigations 
  show 
  how 
  closely 
  the 
  experimental 
  

   determination 
  of 
  equipotential 
  surfaces 
  and 
  lines 
  of 
  force 
  agrees 
  with 
  

   the 
  theory 
  of 
  electrical 
  distribution 
  in 
  space. 
  

  

  