﻿382 
  Dr. 
  H. 
  Sfcansfield 
  on 
  

  

  it 
  may 
  be 
  shown 
  that 
  

  

  and 
  the 
  values 
  calculated 
  from 
  these 
  formulae 
  show 
  that, 
  

   when 
  this 
  echelon 
  is 
  in 
  the 
  direct 
  position, 
  '^o^'^u 
  ^^ 
  *'^ 
  P^^ 
  

   cent, 
  of 
  i/tj^ 
  for 
  an 
  order 
  one 
  place 
  from 
  the 
  position 
  of 
  

   greatest 
  brightness, 
  1*4 
  per 
  cent, 
  of 
  -i/r^j 
  for 
  an 
  order 
  two 
  

   places 
  away, 
  and 
  so 
  on. 
  The 
  corresponding 
  values 
  for 
  the 
  

   reversed 
  position 
  are 
  '^ 
  per 
  cent, 
  and 
  '9 
  per 
  cent. 
  

  

  Effects 
  produced 
  hy 
  Temperature 
  Changes, 
  

  

  The 
  position 
  of 
  the 
  various 
  orders 
  in 
  the 
  field 
  of 
  view 
  when 
  

   the 
  echelon 
  is 
  in 
  a 
  definite 
  position, 
  such 
  as 
  the 
  normal 
  

   position, 
  depends 
  on 
  the 
  temperature 
  of 
  the 
  echelon 
  and 
  on 
  

   the 
  refractive 
  index 
  of 
  the 
  surrounding 
  air. 
  Records 
  of 
  the 
  

   temperature 
  of 
  the 
  echelon 
  and 
  micrometer 
  readings 
  of 
  the 
  

   position 
  of 
  the 
  orders 
  in 
  the 
  field 
  of 
  view, 
  taken 
  from 
  day 
  to 
  

   day, 
  show 
  that 
  a 
  rise 
  of 
  temperature 
  of 
  ^'^^ 
  C. 
  moves 
  the 
  

   spectrum 
  through 
  a 
  distance 
  equal 
  to 
  the 
  interval 
  between 
  

   neighbouring 
  orders, 
  indicating 
  an 
  increase 
  of 
  one 
  wave- 
  

   length 
  in 
  the 
  retardation, 
  R, 
  for 
  this 
  rise 
  of 
  temperature. 
  

  

  Curving 
  of 
  the 
  Spectrum 
  Lines. 
  

  

  The 
  echelon 
  spectrum 
  lines, 
  like 
  those 
  of 
  a 
  prism 
  spectrum, 
  

   are 
  curved 
  with 
  the 
  concave 
  side 
  toward 
  the 
  violet 
  end. 
  The 
  

   curving 
  is 
  due 
  to 
  the 
  variation 
  in 
  the 
  angle 
  of 
  incidence, 
  and 
  

   therefore 
  in 
  the 
  retardation, 
  R, 
  of 
  light 
  from 
  different 
  points 
  

   along 
  the 
  length 
  of 
  the 
  slit. 
  The 
  theory 
  has 
  been 
  given 
  

   by 
  Laue 
  *. 
  

  

  Consider 
  the 
  simplest 
  case, 
  in 
  which 
  the 
  slit 
  is 
  vertical 
  and 
  

   the 
  plates 
  are 
  normal 
  to 
  the 
  axis 
  of 
  the 
  collimator 
  : 
  then 
  light 
  

   from 
  points 
  above 
  and 
  below 
  the 
  centre 
  of 
  the 
  slit 
  will 
  have 
  

   a 
  vertical 
  plane 
  of 
  incidence 
  on 
  the 
  plates. 
  Writing 
  i 
  instead 
  

   of 
  6 
  for 
  the 
  angle 
  of 
  incidence 
  in 
  equation 
  (3), 
  

  

  Z 
  [Jb 
  

   but 
  from 
  equation 
  (1), 
  

  

  R-R„ 
  = 
  <t-fo); 
  

  

  * 
  Phtjsikalische 
  ZeitscJirift, 
  vi. 
  pp. 
  283-285 
  (1905). 
  

  

  