﻿Danstan, 
  Rice 
  and 
  Kraus 
  — 
  Sodium 
  Lines, 
  etc. 
  473 
  

  

  silvered 
  surface 
  D, 
  where 
  part 
  is 
  reflected 
  to 
  the 
  movable 
  

   mirror 
  E 
  and 
  part 
  transmitted 
  to 
  the 
  fixed 
  mirror 
  F. 
  These 
  

   two 
  beams 
  are 
  reflected 
  and 
  both 
  finally 
  enter 
  the 
  telescope 
  G. 
  

  

  Under 
  these 
  conditions, 
  with 
  a 
  telescope 
  focussed 
  for 
  parallel 
  

   rays 
  or 
  with 
  the 
  im 
  aided 
  eye, 
  the 
  observer 
  will 
  see 
  a 
  series 
  of 
  

   concentric 
  circular 
  fringes. 
  If 
  now 
  the 
  mirror 
  E 
  is 
  moved 
  

   away 
  from 
  the 
  observer 
  by 
  turning 
  the 
  screw 
  H, 
  the 
  difference 
  

   of 
  path 
  of 
  the 
  interfering 
  pencils 
  is 
  increased 
  and 
  the 
  fringes 
  

   become 
  periodically 
  more 
  or 
  less 
  distinct 
  or 
  ; 
  ' 
  visible," 
  passing 
  

   through 
  successive 
  maxima 
  and 
  minima. 
  

  

  The 
  visibility 
  is 
  defined 
  as 
  the 
  ratio 
  between 
  the 
  difference 
  

   of 
  intensities 
  of 
  a 
  bright 
  and 
  a 
  dark 
  ring 
  divided 
  by 
  the 
  sum 
  of 
  

   these 
  intensities, 
  or 
  expressed 
  algebraically, 
  

  

  __I 
  bright— 
  I 
  dark 
  

   — 
  I 
  bright 
  + 
  1 
  dark' 
  

  

  If 
  now 
  the 
  visibilities 
  at 
  the 
  maxima 
  be 
  observed 
  for 
  

   increasing 
  differences 
  of 
  path, 
  then 
  the 
  approximate 
  equation 
  

  

  X 
  2 
  

  

  of 
  this 
  curve 
  is 
  of 
  the 
  form 
  Y 
  — 
  2 
  A 
  \ 
  where 
  x 
  is 
  difference 
  of 
  

   path 
  in 
  mm., 
  Y 
  is 
  visibility 
  as 
  a 
  proper 
  fraction, 
  and 
  A 
  is 
  the 
  

   difference 
  of 
  path 
  at 
  which 
  Y 
  falls 
  to 
  half 
  its 
  initial 
  value. 
  

   Now 
  the 
  half- 
  width 
  of 
  either 
  of 
  the 
  two 
  sodium 
  lines 
  giv- 
  

  

  *22X 
  2 
  10 
  7 
  

   ing 
  such 
  a 
  curve 
  is 
  given 
  by 
  8 
  = 
  — 
  — 
  — 
  , 
  where 
  \, 
  A 
  are 
  in 
  

  

  mm. 
  and 
  8 
  in 
  Ang. 
  units. 
  

  

  It 
  is 
  thus 
  seen 
  that 
  the 
  broadening 
  of 
  the 
  two 
  sodium 
  lines 
  

   would 
  be 
  indicated 
  by 
  a 
  more 
  rapid 
  falling 
  off 
  in 
  this 
  visibility 
  

   curve. 
  

  

  The 
  curves 
  obtained 
  by 
  the 
  writers 
  are 
  shown 
  in 
  fig. 
  2. 
  (I) 
  

  

  is 
  the 
  visibility 
  curve 
  obtained 
  as 
  above 
  from 
  the 
  Bunsen 
  

   flame, 
  the 
  magnet 
  not 
  being 
  excited 
  ; 
  while 
  (IY) 
  is 
  the 
  visibil- 
  

   ity 
  curve 
  when 
  the 
  magnetic 
  field 
  between 
  the 
  pole 
  pieces 
  was 
  

  

  