﻿Anomalous 
  Conduction 
  in 
  a 
  Solid 
  Dielectric. 
  689 
  

  

  ordinates 
  of 
  the 
  curves 
  in 
  fig. 
  2. 
  It 
  will 
  be 
  seen 
  that 
  the 
  

  

  relation 
  is 
  very 
  far 
  from 
  a 
  linear 
  one, 
  and 
  the 
  deviation 
  

  

  from 
  the 
  linear 
  law 
  is 
  enormously 
  greater 
  than 
  can 
  be 
  

  

  accounted 
  for 
  by 
  errors 
  of 
  observation. 
  

  

  It 
  is 
  interesting 
  to 
  inquire 
  as 
  to 
  the 
  extent 
  of 
  the 
  departure 
  

  

  from 
  Ohm's 
  law. 
  Applying 
  equation 
  (1) 
  and 
  putting 
  in 
  

  

  G 
  

   the 
  measured 
  value 
  of 
  ~ 
  — 
  ^- 
  and 
  a, 
  we 
  find 
  that 
  corre- 
  

  

  sponding 
  to 
  the 
  first 
  observation 
  of 
  the 
  first 
  table 
  on 
  p. 
  681, 
  

   f\) 
  At) 
  =1'07x 
  10~ 
  12 
  ampere 
  per 
  sq. 
  cm. 
  

  

  This 
  is 
  obtained 
  taking 
  k 
  as 
  2*3. 
  If, 
  as 
  is 
  probably 
  the 
  

   case, 
  the 
  effective 
  value 
  of 
  k 
  is 
  larger, 
  the 
  corresponding- 
  

   value 
  of 
  the 
  above 
  quantity 
  would 
  also 
  be 
  larger. 
  Hence 
  

  

  fl 
  — 
  ) 
  , 
  w 
  T 
  hich 
  measures 
  the 
  current 
  density 
  between 
  C 
  and 
  

  

  A, 
  is 
  greater 
  than 
  1*07 
  x 
  10" 
  12 
  . 
  Taking 
  3 
  X 
  10 
  18 
  as 
  the 
  

   specific 
  resistance 
  of 
  paraffin-wax 
  for 
  small 
  fields, 
  we 
  find, 
  

   on 
  the 
  assumption 
  of 
  a 
  linear 
  law, 
  that 
  the 
  part 
  of 
  the 
  

   current 
  density 
  obeying 
  Ohm's 
  law 
  comes 
  out 
  as 
  1'7 
  X 
  10 
  _1 
  \ 
  

   This 
  is 
  taking 
  the 
  potential 
  difference 
  between 
  C 
  and 
  A 
  to 
  

   be 
  10,000 
  volts, 
  which 
  is, 
  if 
  anything, 
  too 
  high, 
  since 
  this 
  

   is 
  approximately 
  the 
  potential 
  to 
  which 
  C 
  was 
  originally 
  

   charged. 
  Thus 
  the 
  portion 
  of 
  the 
  current 
  which 
  our 
  

   apparatus 
  records, 
  and 
  which 
  does 
  not 
  obey 
  Ohm's 
  law, 
  is 
  

   for 
  the 
  above 
  potential 
  gradient 
  (50,000 
  volts 
  per 
  centimetre) 
  

   at 
  least 
  60 
  times 
  as 
  great 
  as 
  the 
  part 
  not 
  recorded 
  by 
  the 
  

   apparatus, 
  and 
  calculated 
  on 
  the 
  assumption 
  of 
  Ohm's 
  law. 
  

  

  (3) 
  Reasons 
  for 
  the 
  departure 
  from 
  Ohm's 
  Law. 
  — 
  We 
  have 
  

   already 
  seen 
  that 
  the 
  experiments 
  are 
  not 
  to 
  be 
  explained 
  as 
  

   arising 
  from 
  a 
  departure 
  from 
  Ohm's 
  law 
  such 
  as 
  w 
  T 
  ould 
  

   be 
  accounted 
  for 
  by 
  an 
  approach 
  to 
  the 
  condition 
  where 
  

   saturation 
  currents 
  are 
  obtained. 
  The 
  bearings 
  of 
  the 
  

   phenomena 
  of 
  residual 
  charge 
  on 
  the 
  matter 
  are 
  rather 
  

   complicated, 
  but 
  we 
  can 
  see 
  in 
  a 
  general 
  way 
  that 
  it 
  is 
  very 
  

   unlikely 
  that 
  the 
  experiments 
  can 
  be 
  explained 
  by 
  an 
  appeal 
  

   to 
  these 
  phenomena. 
  We 
  may 
  consider 
  dielectric 
  strain 
  of 
  

   two 
  kinds. 
  In 
  the 
  first, 
  the 
  dielectric 
  may 
  be 
  considered 
  to 
  

   be 
  strained, 
  and 
  to 
  be 
  continually 
  giving 
  way 
  permanently 
  

   after 
  the 
  manner 
  of 
  a 
  number 
  of 
  elastic 
  threads 
  which 
  are 
  

   stretched, 
  and 
  break 
  one 
  by 
  one. 
  There 
  is 
  nothing 
  except 
  

   the 
  complication 
  of 
  the 
  phenomenon, 
  however, 
  to 
  distinguish 
  

   this 
  from 
  true 
  conduction, 
  so 
  that 
  we 
  need 
  only 
  concern 
  

  

  