﻿the 
  Illumination 
  Curves 
  in 
  Oblique 
  Refraction. 
  117 
  

  

  A 
  series 
  of 
  comparisons 
  of 
  the 
  intensities 
  of 
  corresponding 
  

   bands 
  on 
  the 
  two 
  sides 
  of 
  the 
  pattern 
  has 
  been 
  made 
  for 
  the 
  

   cases 
  in 
  which 
  the 
  reflecting 
  surface 
  consists 
  of 
  one, 
  two, 
  

   and 
  three 
  reflecting 
  elements 
  respectively, 
  for 
  various 
  angles 
  

   of 
  incidence. 
  For 
  this 
  purpose, 
  I 
  have 
  used 
  a 
  rotating- 
  

   sector 
  photometer 
  of 
  the 
  Abney 
  type 
  supplied 
  by 
  Messrs. 
  

   Adam 
  Hilger, 
  in 
  which 
  the 
  free 
  disk, 
  which 
  can 
  be 
  adjusted 
  

   by 
  handle 
  while 
  in 
  rotation, 
  is 
  smaller 
  in 
  radius 
  than 
  the 
  

   fixed 
  disk. 
  The 
  sectors 
  when 
  in 
  rotation 
  thus 
  present 
  two 
  

   annuli 
  of 
  different 
  intensities, 
  the 
  ratio 
  of 
  which 
  can 
  be 
  

   adjusted 
  at 
  pleasure 
  by 
  moving 
  the 
  handle 
  of 
  the 
  instrument. 
  

   The 
  disk 
  of 
  the 
  photometer 
  is 
  placed 
  at 
  the 
  focal 
  plane 
  of 
  

   the 
  observing 
  telescope, 
  so 
  that 
  the 
  diffraction 
  pattern 
  can 
  

   be 
  seen 
  through 
  it 
  with 
  an 
  eyepiece, 
  the 
  fringes 
  on 
  the 
  

   brighter 
  side 
  being 
  observed 
  through 
  the 
  inner 
  annulus 
  of 
  

   the 
  disk, 
  and 
  those 
  on 
  the 
  fainter 
  side 
  through 
  the 
  outer 
  

   annulus. 
  To 
  enable 
  the 
  intensities 
  at 
  corresponding 
  points 
  

   on 
  the 
  two 
  sides 
  of 
  the 
  pattern 
  to 
  be 
  compared, 
  a 
  screen 
  

   with 
  two 
  vertical 
  slits 
  is 
  interposed 
  immediately 
  in 
  front 
  of 
  

   the 
  photometric 
  disk 
  so 
  as 
  to 
  cut 
  off 
  everything 
  except 
  the 
  

   regions 
  under 
  observation, 
  which 
  are 
  then 
  adjusted 
  to 
  equality 
  

   of 
  brightness 
  by 
  moving 
  the 
  handle 
  of 
  the 
  photometer. 
  

   Several 
  readings 
  can 
  be 
  taken 
  in 
  succession 
  and 
  their 
  

   average 
  struck. 
  The 
  diffraction 
  angles 
  6 
  and 
  6' 
  of 
  the 
  two 
  

   bands 
  under 
  comparison 
  may 
  then 
  be 
  measured 
  under 
  a 
  

   micrometer 
  eyepiece. 
  Tables 
  V., 
  VI., 
  and 
  VII. 
  show 
  the 
  

   observed 
  ratios 
  of 
  the 
  illumination 
  and 
  those 
  calculated 
  on 
  

   the 
  assumption 
  that 
  the 
  formula 
  for 
  illumination 
  includes 
  a 
  

   factor 
  proportional 
  to 
  the 
  square 
  of 
  the 
  cosine 
  of 
  the 
  obli- 
  

   quity. 
  It 
  is 
  seen 
  that 
  the 
  agreement 
  is 
  good 
  except 
  when 
  

   the 
  ratio 
  is 
  so 
  large 
  that 
  it 
  cannot 
  be 
  measured 
  accurately, 
  

   owing 
  to 
  the 
  near 
  approach 
  of 
  the 
  fainter 
  band 
  towards 
  the 
  

   direct 
  image 
  of 
  the 
  slit. 
  

  

  Table 
  V. 
  

  

  Single 
  Reflecting 
  Surface, 
  width 
  0*90 
  cm. 
  

  

  Ratio 
  of 
  intensity 
  of 
  the 
  first 
  band 
  on 
  the 
  right 
  and 
  

  

  the 
  first 
  band 
  on 
  the 
  left. 
  

  

  Angle 
  of 
  Incidence. 
  Observed 
  ratio 
  

   or 
  illumination. 
  

  

  Calculated, 
  ratio 
  

   cos 
  2 
  0/cos 
  2 
  9'. 
  

  

  88° 
  42' 
  1-80 
  

   88° 
  53' 
  2-31 
  

   88° 
  56' 
  2-81 
  

   88° 
  4' 
  4-09 
  

  

  1-78 
  

   246 
  

   2-89 
  

   421 
  

  

  