﻿EQUILIBRIUM 
  OF 
  ELASTIC 
  SOLIDS. 
  117 
  

  

  and 
  if 
  the 
  retardation 
  at 
  o 
  be 
  taken 
  for 
  unity, 
  the 
  isochromatic 
  curves 
  2, 
  4, 
  sur- 
  

   round 
  A 
  2 
  and 
  A 
  2 
  ; 
  that 
  in 
  which 
  the 
  retardation 
  is 
  unity 
  has 
  two 
  loops, 
  and 
  

  

  passes 
  through 
  ; 
  the 
  curves 
  ~> 
  i 
  are 
  continuous, 
  and 
  have 
  points 
  of 
  contrary 
  

  

  flexure; 
  the 
  curve 
  g 
  has 
  multiple 
  points 
  at 
  C 
  t 
  and 
  C 
  2 
  , 
  where 
  k 
  x 
  C 
  1 
  = 
  A 
  l 
  A 
  2 
  , 
  and 
  

  

  two 
  loops 
  surrounding 
  B 
  x 
  and 
  B 
  2 
  ; 
  the 
  other 
  curves, 
  for 
  which 
  I—jfl 
  g^, 
  &c, 
  con- 
  

   sists 
  each 
  of 
  two 
  ovals 
  surrounding 
  B 
  x 
  and 
  B 
  2 
  , 
  and 
  an 
  exterior 
  portion 
  surround- 
  

   ing 
  all 
  the 
  former 
  curves. 
  

  

  I 
  have 
  produced 
  these 
  curves 
  in 
  the 
  jelly 
  of 
  isinglass 
  described 
  in 
  Case 
  I. 
  

   They 
  are 
  best 
  seen 
  by 
  using 
  circularly 
  polarized 
  light, 
  as 
  the 
  curves 
  are 
  then 
  

   seen 
  without 
  interruption, 
  and 
  their 
  resemblance 
  to 
  the 
  calculated 
  curves 
  is 
  more 
  

   apparent. 
  To 
  avoid 
  crowding 
  the 
  curves 
  toward 
  the 
  centre 
  of 
  the 
  figure, 
  I 
  have 
  

   taken 
  the 
  values 
  of 
  I 
  for 
  the 
  different 
  curves, 
  not 
  in 
  an 
  arithmetical, 
  but 
  in 
  a 
  geo- 
  

   metrical 
  progression, 
  ascending 
  by 
  powers 
  of 
  2. 
  

  

  Case 
  XIV. 
  

  

  On 
  the 
  determination 
  of 
  the 
  pressures 
  which 
  act 
  in 
  the 
  interior 
  of 
  transpa- 
  

   rent 
  solids, 
  from 
  observations 
  of 
  the 
  action 
  of 
  the 
  solid 
  on 
  polarized 
  light. 
  

  

  Sir 
  David 
  Brewster 
  has 
  pointed 
  out 
  the 
  method 
  by 
  which 
  polarized 
  light 
  

   might 
  be 
  made 
  to 
  indicate 
  the 
  strains 
  in 
  elastic 
  solids 
  ; 
  and 
  his 
  experiments 
  on 
  

   bent 
  glass 
  confirm 
  the 
  theories 
  of 
  the 
  bending 
  of 
  beams. 
  

  

  The 
  phenomena 
  of 
  heated 
  and 
  unannealed 
  glass 
  are 
  of 
  a 
  much 
  more 
  complex 
  

   nature, 
  and 
  they 
  cannot 
  be 
  predicted 
  and 
  explained 
  without 
  a 
  knowledge 
  of 
  the 
  

   laws 
  of 
  cooling 
  and 
  solidification, 
  combined 
  with 
  those 
  of 
  elastic 
  equilibrium. 
  

  

  In 
  Case 
  X. 
  I 
  have 
  given 
  an 
  example 
  of 
  the 
  inverse 
  problem, 
  in 
  the 
  case 
  of 
  a 
  

   cylinder 
  in 
  which 
  the 
  action 
  on 
  light 
  followed 
  a 
  simple 
  law 
  ; 
  and 
  I 
  now 
  go 
  on 
  to 
  

   describe 
  the 
  method 
  of 
  determining 
  the 
  pressures 
  in 
  a 
  general 
  case, 
  applyiDg 
  it 
  to 
  

   the 
  case 
  of 
  a 
  triangle 
  of 
  unannealed 
  plate-glass. 
  

  

  The 
  lines 
  of 
  equal 
  intensity 
  of 
  the 
  action 
  on 
  light 
  are 
  seen 
  without 
  interrup- 
  

   tion, 
  by 
  using 
  circularly 
  polarized 
  light. 
  They 
  are 
  represented 
  in 
  fig. 
  2, 
  where 
  

   A, 
  BBB, 
  DDD 
  are 
  the 
  neutral 
  points, 
  or 
  points 
  of 
  no 
  action 
  on 
  light, 
  and 
  CCC, 
  EEE 
  

   are 
  the 
  points 
  where 
  that 
  action 
  is 
  greatest; 
  and 
  the 
  intensity 
  of 
  the 
  action 
  at 
  

   any 
  other 
  point 
  is 
  determined 
  by 
  its 
  position 
  with 
  respect 
  to 
  the 
  isochromatic 
  

   curves. 
  

  

  The 
  direction 
  of 
  the 
  principal 
  axes 
  of 
  pressure 
  at 
  any 
  point 
  is 
  found 
  by 
  trans- 
  

   mitting 
  plane 
  polarized 
  light, 
  and 
  analysing 
  it 
  in 
  the 
  plane 
  perpendicular 
  to 
  that 
  

   of 
  polarization. 
  The 
  light 
  is 
  then 
  restored 
  in 
  every 
  part 
  of 
  the 
  triangle, 
  except 
  

   in 
  those 
  points 
  at 
  which 
  one 
  of 
  the 
  principal 
  axes 
  is 
  parallel 
  to 
  the 
  plane 
  of 
  

   polarization. 
  A 
  dark 
  band 
  formed 
  of 
  all 
  these 
  points 
  is 
  seen, 
  which 
  shifts 
  its 
  

   position 
  as 
  the 
  triangle 
  is 
  turned 
  round 
  in 
  its 
  own 
  plane. 
  Fig. 
  3 
  represents 
  these 
  

  

  