﻿G90 
  Dr. 
  W. 
  F. 
  G. 
  Swann 
  on 
  a 
  Case 
  oj 
  

  

  ourselves 
  with 
  the 
  second 
  kind 
  of 
  strain, 
  viz., 
  that 
  kind 
  

   of 
  strain 
  which 
  releases 
  itself 
  on 
  removal 
  of 
  the 
  electric 
  

   force. 
  

  

  When 
  the 
  centre 
  plate 
  is 
  charged 
  ; 
  there 
  is 
  a 
  displacement 
  

   of 
  electricity 
  in 
  each 
  volume 
  element 
  of 
  the 
  wax. 
  If 
  E 
  is 
  

   the 
  total 
  charge 
  per 
  cubic 
  centimetre 
  taking 
  part 
  in 
  the 
  

   displacement, 
  and 
  x 
  and 
  y 
  the 
  average 
  separation 
  of 
  the 
  

   corresponding 
  positive 
  and 
  negative 
  constituents 
  of 
  the 
  

   volume 
  elements 
  between 
  C 
  and 
  A 
  and 
  between 
  C 
  and 
  B 
  

   respectively, 
  the 
  lowering 
  of 
  the 
  potential 
  difference 
  between 
  

   C 
  and 
  A 
  due 
  to 
  the 
  displacement 
  is 
  2tt¥jx. 
  Similarly, 
  the 
  

   displacement 
  in 
  the 
  wax 
  between 
  C 
  and 
  B 
  results 
  in 
  a 
  

   lowering 
  of 
  the 
  potential 
  difference 
  between 
  these 
  plates, 
  

   of 
  27rE?/. 
  A 
  portion 
  of 
  the 
  displacements 
  x 
  and 
  y 
  follow 
  

   the 
  field 
  immediately, 
  and 
  are 
  responsible 
  for 
  the 
  ordinary 
  

   phenomenon 
  of 
  the 
  existence 
  of 
  a 
  specific 
  inductive 
  capacity 
  

   greater 
  than 
  unity. 
  In 
  most 
  dielectrics 
  a 
  portion 
  occurs 
  

   only 
  after 
  an 
  interval 
  after 
  the 
  change 
  of 
  field. 
  Let 
  us 
  

   consider 
  the 
  first 
  portion. 
  As 
  the 
  potential 
  of 
  C 
  falls, 
  owing 
  

   to 
  conduction 
  of 
  electricity 
  across 
  the 
  wax, 
  these 
  displace- 
  

   ments 
  diminish. 
  If 
  Bx 
  and 
  By 
  are 
  the 
  diminutions 
  for 
  a 
  fall 
  

   BY 
  in 
  the 
  potential 
  of 
  C, 
  the 
  fall 
  of 
  A 
  (supposed 
  insulated), 
  

   due 
  to 
  this 
  cause 
  is 
  

  

  A 
  V 
  = 
  2ttE 
  a 
  Bx 
  - 
  2ttE 
  b 
  By. 
  

  

  If 
  the 
  strain 
  is 
  proportional 
  to 
  the 
  potential 
  gradient 
  

   aSx 
  = 
  bSij 
  and 
  AV 
  is 
  zero. 
  Any 
  departure 
  from 
  a 
  linear 
  

   relationship 
  between 
  the 
  strain 
  and 
  the 
  potential 
  gradient 
  

   would 
  be 
  expected 
  to 
  be 
  such 
  as 
  to 
  make 
  the 
  strain 
  increase 
  

   more 
  rapidly 
  with 
  the 
  field 
  than 
  would 
  be 
  accounted 
  for 
  by 
  

   a 
  first 
  power 
  law, 
  which 
  would 
  result 
  in 
  AY 
  being 
  the 
  

   negative 
  instead 
  of 
  positive 
  as 
  was 
  found. 
  

  

  Considering 
  the 
  possibility 
  of 
  the 
  existence 
  of 
  a 
  portion 
  

   of 
  the 
  strain 
  showing 
  a 
  hysteresis 
  effect*, 
  we 
  may 
  remark 
  

   that 
  the 
  probability 
  of 
  the 
  effect 
  being 
  of 
  importance 
  in 
  the 
  

   present 
  experiments 
  is 
  small, 
  since 
  the 
  curves 
  of 
  fig. 
  2 
  fit 
  

   those 
  of 
  fig. 
  3 
  almost 
  exactly 
  when 
  superposed 
  (although 
  

   the 
  plate 
  C 
  started 
  at 
  entirely 
  different 
  potentials 
  in 
  the 
  two 
  

   experiments), 
  which 
  is 
  a 
  fact 
  difficult 
  to 
  explain 
  on 
  the 
  

   assumption 
  that 
  the 
  results 
  are 
  due 
  to 
  hysteresis, 
  unless 
  one 
  

   makes 
  certain 
  special 
  assumptions 
  with 
  regard 
  to 
  the 
  lag. 
  

  

  * 
  It 
  may 
  be 
  remarked 
  that 
  H. 
  A. 
  Wilson 
  (Proc. 
  Roy. 
  Soc. 
  vol. 
  lxxxii. 
  

   1909) 
  finds 
  that 
  paraffin-wax 
  shows 
  no 
  hysteresis 
  effect, 
  though 
  of 
  

   course 
  his 
  results 
  apply 
  to 
  much 
  smaller 
  potential 
  gradients 
  than 
  those 
  

   here 
  used. 
  

  

  