﻿684 
  Dr. 
  W. 
  F. 
  G. 
  Swann 
  on 
  a 
  Case 
  of 
  

  

  the 
  present 
  problem, 
  we 
  see 
  that 
  the 
  potential 
  o£ 
  the 
  plate 
  A 
  

   will 
  have 
  altered 
  at 
  the 
  end 
  of 
  the 
  time 
  8t 
  by 
  the 
  amount 
  

  

  k 
  \ 
  a 
  b 
  ) 
  

  

  An 
  analogous 
  remark 
  applies 
  to 
  the 
  plate 
  B. 
  

  

  If 
  in 
  the 
  case 
  of 
  ordinary 
  conduction 
  by 
  ions 
  the 
  fields 
  are 
  

   so 
  great 
  as 
  to 
  approach 
  saturation 
  values 
  for 
  the 
  currents, 
  

   the 
  transference 
  would 
  be 
  less 
  than 
  the 
  amount 
  calculated 
  

   from 
  the 
  normal 
  conductivity; 
  but 
  the 
  transference 
  from 
  C 
  

   to 
  A 
  would 
  be 
  reduced 
  in 
  greater 
  proportion 
  than 
  the 
  trans- 
  

   ference 
  from 
  C 
  to 
  B, 
  owing 
  to 
  the 
  greater 
  field 
  in 
  the 
  former 
  

   case 
  ; 
  and 
  the 
  result 
  would 
  be 
  that 
  if 
  C 
  were 
  positively 
  

   charged 
  A 
  would 
  gradually 
  fall 
  in 
  potential 
  while 
  B 
  would 
  

   rise, 
  which 
  is 
  opposite 
  to 
  the 
  results 
  of 
  the 
  present 
  

   experiments. 
  

  

  It 
  seems 
  rather 
  startling 
  at 
  first 
  sight 
  that 
  on 
  the 
  hypothesis 
  

   of 
  a 
  constant 
  ionization 
  the 
  plates 
  A 
  and 
  B 
  should 
  remain 
  

   at 
  zero 
  potential 
  as 
  the 
  electricity 
  leaks 
  across; 
  but 
  it 
  is 
  

   nevertheless 
  true, 
  and 
  was 
  verified 
  experimentally 
  by 
  per- 
  

   forming 
  experiments 
  with 
  paraffin 
  oil, 
  in 
  which 
  case 
  we 
  

   know 
  that 
  the 
  main 
  effects 
  are 
  to 
  be 
  attributed 
  to 
  the 
  

   presence 
  of 
  ions 
  existing 
  in 
  constant 
  amount 
  in 
  the 
  oil. 
  

  

  The 
  results 
  obtained 
  above 
  for 
  paraffin-wax 
  are 
  not 
  readily 
  

   explained 
  by 
  an 
  appeal 
  to 
  the 
  phenomenon 
  of 
  residual 
  charge, 
  

   as 
  will 
  appear 
  later. 
  They 
  may, 
  however, 
  be 
  explained 
  if 
  we 
  

   assume 
  that 
  the 
  current 
  is 
  not 
  proportional 
  to 
  the 
  potential 
  

   gradient. 
  Let 
  us 
  write 
  the 
  current 
  density 
  i 
  as 
  a 
  function 
  

  

  of 
  the 
  potential 
  gradient 
  r~— 
  in 
  the 
  form 
  

  

  OjtJu 
  

  

  J 
  \dxJ 
  

  

  The 
  current 
  density 
  between 
  C 
  and 
  A 
  is 
  

  

  <-/© 
  

  

  * 
  A 
  difference 
  in 
  the 
  quality 
  of 
  the 
  wax 
  on 
  the 
  two 
  sides 
  of 
  the 
  

   plate 
  would 
  result 
  in 
  hv 
  being 
  different 
  from 
  zero. 
  In 
  the 
  apparatus 
  

   used 
  there 
  was 
  no 
  chance 
  of 
  this 
  occurring, 
  however, 
  as 
  the 
  wax 
  was 
  

   stirred 
  and 
  run 
  in 
  hot. 
  Moreover, 
  observations 
  were 
  taken 
  with 
  different 
  

   pieces 
  of 
  apparatus. 
  

  

  A 
  variation 
  of 
  k 
  with 
  the 
  field 
  would 
  also 
  result 
  in 
  8v 
  being 
  different 
  

   from 
  zero. 
  We 
  should, 
  however, 
  expect 
  k 
  to 
  increase 
  with 
  the 
  field 
  if 
  it 
  

   altered 
  at 
  all, 
  which 
  would 
  result 
  in 
  dv 
  being 
  negative 
  instead 
  of 
  positive 
  

   as 
  found. 
  

  

  