﻿Anomalous 
  Conduction 
  in 
  a 
  Solid 
  Dielectric. 
  685 
  

  

  so 
  that, 
  as 
  far 
  as 
  this 
  effect 
  is 
  concerned, 
  there 
  will 
  be 
  a 
  rise 
  

  

  2ira 
  /V\ 
  

   in 
  the 
  potential 
  of 
  the 
  plate 
  A 
  at 
  the 
  rate 
  o£ 
  • 
  = 
  — 
  /( 
  — 
  i 
  units 
  

  

  K 
  \Ql 
  J 
  

  

  per 
  second. 
  On 
  the 
  other 
  hand, 
  the 
  transference 
  from 
  C 
  to 
  

   B 
  results 
  in 
  a 
  fall 
  of 
  potential 
  of 
  the 
  plate 
  A 
  at 
  the 
  rate 
  

  

  2-irb 
  ,/V\ 
  

  

  fl 
  y- 
  1 
  units 
  per 
  second. 
  Hence 
  if 
  v 
  a 
  represents 
  the 
  net 
  

  

  rise 
  in 
  potential 
  which 
  the 
  plate 
  A 
  begins 
  to 
  experience 
  

   in 
  j 
  mediately 
  after 
  it 
  has 
  been 
  released 
  from 
  earth, 
  

  

  dv 
  a 
  

   dt 
  

  

  --^{O-m- 
  

  

  By 
  an 
  exactly 
  similar 
  process 
  of 
  reasoning, 
  the 
  alteration 
  in 
  

   the 
  potential 
  of 
  the 
  plate 
  B 
  will 
  take 
  place 
  according 
  to 
  the 
  

  

  relation 
  

  

  s-=?{»/(?H©}- 
  

  

  If 
  A 
  rises, 
  B 
  must 
  fall 
  at 
  an 
  equal 
  rate; 
  and 
  it 
  will 
  further 
  

   be 
  observed 
  that 
  if 
  in 
  the 
  expansion 
  of 
  f(x) 
  there 
  are 
  any 
  

   terms 
  of 
  the 
  form 
  mx 
  where 
  m 
  is 
  a 
  constant, 
  these 
  terms 
  (which 
  

   in 
  fact 
  correspond 
  to 
  the 
  Ohm's 
  law 
  part 
  of 
  the 
  current] 
  

   contribute 
  nothing 
  to 
  the 
  alteration 
  of 
  the 
  potential 
  of 
  the 
  

   plates 
  A 
  or 
  B. 
  

  

  In 
  view 
  of 
  the 
  fact 
  that 
  the 
  plates 
  have 
  to 
  be 
  connected 
  

   to 
  an 
  electrometer 
  of 
  appreciable 
  capacity, 
  it 
  is 
  necessary 
  to 
  

   consider 
  how 
  the 
  quantity 
  which 
  the 
  electrometer 
  measures 
  

   is 
  related 
  to 
  the 
  quantity 
  v 
  referred 
  to 
  above. 
  

  

  Suppose, 
  for 
  example, 
  that 
  the 
  plate 
  A 
  is 
  connected 
  to 
  the 
  

   electrometer. 
  Let 
  8TJ 
  a 
  be 
  the 
  alteration 
  of 
  potential 
  and 
  8q 
  

   the 
  quantity 
  of 
  electricity 
  going 
  into 
  the 
  electrometer 
  in 
  the 
  

   time 
  8t. 
  The 
  alteration 
  of 
  potential 
  of 
  the 
  plate 
  A 
  is 
  also 
  8Jl 
  a 
  , 
  

  

  and 
  is 
  composed 
  of 
  two 
  parts, 
  the 
  part 
  — 
  \ 
  af 
  ( 
  — 
  \ 
  — 
  hf( 
  j- 
  ) 
  [ 
  St 
  

   referred 
  to 
  above, 
  and 
  a 
  part 
  — 
  ^r, 
  where 
  C 
  a 
  is 
  the 
  capacity 
  

  

  of 
  the 
  plate 
  A 
  modified 
  as 
  it 
  is 
  by 
  the 
  presence 
  of 
  the 
  plates 
  

   B 
  and 
  C. 
  There 
  is 
  a 
  third 
  part 
  which 
  we 
  shall 
  call 
  p 
  arising 
  

   from 
  the 
  induced 
  displacements 
  on 
  the 
  plates 
  and 
  B, 
  and 
  

   resulting 
  from 
  the 
  edge 
  effects. 
  We 
  shall 
  not 
  introduce 
  this 
  

   part 
  into 
  the 
  formula, 
  as 
  it 
  will 
  rather 
  complicate 
  the 
  ex- 
  

   pressions, 
  and 
  its 
  effect 
  can 
  sufficiently 
  well 
  be 
  discussed 
  

   afterwards. 
  

  

  