﻿446 
  Lord 
  Rayleigh 
  on 
  Reflexion 
  from 
  

  

  substantially 
  the 
  same 
  as 
  in 
  the 
  former 
  observations 
  upon 
  

   water, 
  and 
  can 
  only 
  be 
  sketched 
  briefly 
  here. 
  Sunlight 
  

   reflected 
  horizontally 
  from 
  a 
  heliostat 
  was 
  caused 
  to 
  traverse 
  

   the 
  polarizing 
  nicol 
  mounted 
  in 
  a 
  circle 
  which 
  allowed 
  the 
  

   rotation 
  to 
  be 
  read 
  to 
  a 
  minute 
  of 
  angle. 
  After 
  reflexion 
  

   from 
  the 
  plate 
  under 
  examination 
  the 
  light 
  traversed 
  in 
  

   succession 
  a 
  quarter-wave-plate 
  of 
  mica 
  and 
  the 
  analysing 
  

   nicol 
  and 
  was 
  then 
  received 
  into 
  the 
  eye, 
  either 
  directly, 
  or 
  

   with 
  the 
  intervention 
  of 
  a 
  small 
  telescope 
  magnifying 
  about 
  

   twice. 
  A 
  green 
  glass 
  was 
  also 
  often 
  introduced 
  in 
  order 
  to 
  

   mitigate 
  chromatic 
  effects. 
  Both 
  the 
  mica 
  and 
  the 
  analysing 
  

   nicol 
  were 
  mounted 
  so 
  as 
  to 
  be 
  capable 
  of 
  rotation 
  about 
  the 
  

   direction 
  of 
  the 
  reflected 
  ray. 
  

  

  The 
  theory 
  of 
  the 
  method 
  is 
  as 
  follows. 
  FresnePs 
  expres- 
  

   sions 
  S 
  and 
  T 
  (sine-formula 
  and 
  tangent-ioYmv\&) 
  give 
  the 
  

   ratios 
  of 
  the 
  reflected 
  to 
  the 
  incident 
  vibrations, 
  for 
  the 
  two 
  

   principal 
  planes 
  ; 
  and 
  their 
  reality 
  indicates 
  that 
  there 
  is 
  no 
  

   change 
  of 
  phase 
  in 
  reflexion 
  (other 
  than 
  180°). 
  The 
  ellip- 
  

   ticity 
  is 
  represented 
  by 
  the 
  addition 
  to 
  T 
  of 
  iM, 
  where 
  M 
  is 
  

   small 
  and 
  z 
  = 
  ^/( 
  — 
  1). 
  Thus 
  if 
  the 
  incident 
  light 
  be 
  polarized 
  

   in 
  the 
  plane 
  making 
  an 
  angle 
  u 
  with 
  the 
  principal 
  plane, 
  the 
  

   reflected 
  vibrations 
  may 
  be 
  represented 
  by 
  

  

  (T 
  + 
  i 
  M) 
  cos 
  a., 
  S 
  sin 
  a. 
  

  

  By 
  the 
  action 
  of 
  the 
  mica, 
  suitably 
  adjusted, 
  a 
  relative 
  

   change 
  of 
  phase 
  \ir 
  is 
  introduced. 
  This 
  is 
  represented 
  by 
  

   writing 
  for 
  S 
  sin 
  a, 
  i 
  S 
  sin 
  a. 
  The 
  vibration 
  transmitted 
  by 
  

   the 
  analyser, 
  set 
  at 
  angle 
  ft, 
  is 
  then 
  

  

  cos 
  a 
  cos 
  ft(T 
  + 
  i 
  M) 
  + 
  i 
  S 
  sin 
  a 
  sin 
  ft 
  ; 
  

  

  and 
  the 
  intensity 
  of 
  this 
  is 
  

  

  T 
  2 
  cos 
  2 
  a 
  cos 
  2 
  ft 
  + 
  (M 
  cos 
  a 
  cos 
  ft 
  + 
  S 
  sin 
  a 
  sin 
  ft) 
  2 
  . 
  

  

  In 
  order 
  that 
  the 
  light 
  may 
  vanish, 
  we 
  must 
  have 
  both 
  

   T 
  = 
  and 
  

  

  M 
  + 
  Stanatan/3 
  = 
  0, 
  

  

  the 
  first 
  of 
  which 
  shows 
  that 
  the 
  dark 
  spot 
  occurs 
  at 
  the 
  

   Brewsterian 
  angle, 
  while 
  tan 
  a. 
  tan 
  ft 
  gives 
  the 
  value 
  of 
  M/S, 
  

   viz. 
  the 
  k 
  of 
  Jamin. 
  Accordingly 
  if 
  ft 
  be 
  set 
  to 
  any 
  con- 
  

   venient 
  angle 
  (such 
  as 
  45°) 
  and 
  a 
  be 
  then 
  adjusted 
  so 
  as 
  to 
  

   bring 
  the 
  dark 
  spot 
  to 
  the 
  central 
  position, 
  the 
  product 
  of 
  

   the 
  tangents 
  of 
  a 
  and 
  ft, 
  each 
  measured 
  from 
  the 
  proper 
  

   zeros, 
  gives 
  k. 
  

  

  In 
  practice 
  it 
  is 
  not 
  necessary 
  to 
  use 
  the 
  zeros. 
  Set 
  ft, 
  

   e. 
  g. 
  to 
  +45°, 
  and 
  find 
  a 
  ; 
  then 
  reset 
  ft 
  to 
  —45°. 
  The 
  new 
  

  

  