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  VII. 
  The 
  Effect 
  of 
  Errors 
  in 
  Ruling 
  on 
  the 
  Appearance 
  of 
  a 
  

   Diffraction 
  Gloating. 
  By 
  H. 
  S. 
  Allen, 
  M.A., 
  B.Sc* 
  

  

  THE 
  effect 
  produced 
  by 
  errors 
  in 
  ruling 
  a 
  diffraction-grating 
  

   on 
  the 
  lines 
  of 
  the 
  spectrum 
  has 
  received 
  considerable 
  

   attention. 
  But 
  the 
  effect 
  on 
  the 
  appearance 
  of 
  the 
  grating 
  

   itself 
  has 
  not 
  been 
  so 
  carefully 
  studied, 
  although 
  from 
  its 
  

   appearance 
  useful 
  information 
  as 
  to 
  the 
  nature 
  of 
  the 
  errors 
  

   may 
  be 
  derived. 
  

  

  If 
  a 
  spectroscope 
  is 
  adjusted 
  to 
  view 
  a 
  single 
  line 
  of 
  the 
  

   spectrum 
  given 
  by 
  a 
  plane 
  grating, 
  and 
  the 
  eyepiece 
  of 
  the 
  

   observing-telescope 
  is 
  removed, 
  the 
  grating 
  is 
  seen 
  illuminated 
  

   by 
  monochromatic 
  light. 
  In 
  the 
  absence 
  of 
  any 
  errors 
  of 
  

   ruling 
  the 
  illumination 
  would 
  be 
  perfectly 
  uniform 
  ; 
  but 
  in 
  

   general 
  the 
  image 
  is 
  seen 
  to 
  be 
  crossed 
  by 
  a 
  number 
  of 
  bands 
  

   parallel 
  to 
  the 
  lines 
  ruled 
  on 
  the 
  grating. 
  The 
  bands 
  may 
  

   be 
  more 
  conveniently 
  studied 
  by 
  focussing 
  the 
  observing- 
  

   telescope 
  on 
  the 
  surface 
  of 
  the 
  grating 
  instead 
  of 
  on 
  the 
  

   slit 
  of 
  the 
  collimator. 
  The 
  object 
  of 
  the 
  present 
  paper 
  is 
  to 
  

   explain 
  the 
  mode 
  of 
  formation 
  of 
  these 
  bands. 
  

  

  If 
  an 
  absolutely 
  perfect 
  grating 
  were 
  illuminated 
  by 
  a 
  parallel 
  

   beam 
  of 
  monochromatic 
  light, 
  all 
  the 
  light 
  going 
  to 
  form 
  the 
  

   spectral 
  line 
  of 
  any 
  particular 
  order 
  would 
  be 
  brought 
  to 
  a 
  

   single 
  focus 
  by 
  the 
  objective 
  of 
  the 
  telescope. 
  If 
  the 
  grating 
  

   were 
  self-luminous, 
  and 
  at 
  a 
  sufficient 
  distance 
  from 
  the 
  lens, 
  

   a 
  real 
  image 
  of 
  it 
  would 
  be 
  formed 
  beyond 
  this 
  focus. 
  In 
  the 
  

   case 
  we 
  are 
  considering, 
  we 
  can 
  hardly 
  speak 
  of 
  the 
  rays 
  

   forming 
  a 
  real 
  image 
  of 
  the 
  grating 
  since 
  they 
  do 
  not 
  cut 
  one 
  

   another 
  at 
  the 
  position 
  of 
  this 
  image. 
  However, 
  the 
  cone 
  of 
  

   rays 
  emerging 
  from 
  the 
  focus 
  must 
  be 
  bounded 
  by 
  the 
  image, 
  

   and 
  a 
  screen 
  placed 
  here 
  would 
  be 
  uniformly 
  illuminated. 
  

  

  In 
  the 
  case 
  of 
  a 
  grating 
  containing 
  two 
  distinct 
  rulings 
  

   differing 
  by 
  only 
  a 
  small 
  amount, 
  the 
  light 
  from 
  each 
  portion 
  

   will 
  be 
  brought 
  to 
  its 
  own 
  appropriate 
  focus. 
  Two 
  different 
  

   cases 
  arise 
  according 
  to 
  the 
  relative 
  positions 
  of 
  the 
  wide 
  and 
  

   narrow 
  rulings. 
  These 
  are 
  shown 
  in 
  fios. 
  1 
  and 
  2. 
  These 
  

   figures 
  are 
  drawn 
  for 
  an 
  order 
  on 
  the 
  right 
  of 
  the 
  central 
  

   image, 
  the 
  observer 
  being 
  supposed 
  to 
  stand 
  facing 
  the 
  

   grating. 
  In 
  fig. 
  1 
  the 
  wide 
  ruling 
  is 
  on 
  the 
  observer's 
  left, 
  

   the 
  narrow 
  ruling 
  on 
  his 
  right. 
  The 
  light 
  from 
  the 
  wide 
  

   ruling 
  is 
  brought 
  to 
  a 
  focus 
  at 
  F 
  x 
  ; 
  that 
  from 
  the 
  narrow 
  

   ruling, 
  which 
  is 
  diffracted 
  at 
  a 
  greater 
  angle, 
  at 
  F 
  2 
  . 
  The 
  

  

  1901 
  

  

  A 
  paper 
  read 
  before 
  Section 
  A 
  of 
  the 
  British 
  Association, 
  Sept. 
  17, 
  

   . 
  Communicated 
  by 
  the 
  Author. 
  

  

  