﻿the 
  Reflexion 
  of 
  the 
  X-rays. 
  229 
  

  

  Discussion 
  of 
  the 
  General 
  Reflexion. 
  

  

  We 
  have 
  seen 
  that 
  monochromatic 
  radiation 
  is 
  reflected 
  

   only 
  at 
  certain 
  special 
  angles, 
  but 
  that 
  reflexion 
  of 
  the 
  general 
  

   radiation 
  from 
  an 
  X-ray 
  tube 
  occurs 
  for 
  all 
  angles 
  of 
  incidence. 
  

   This 
  shows 
  that 
  the 
  general 
  X-rays 
  resemble 
  white 
  light. 
  

   The 
  primary 
  radiation 
  may 
  therefore, 
  for 
  convenience, 
  be 
  

   imagined 
  to 
  contain 
  constituents 
  with 
  wave-lengths 
  varying 
  

   continuously 
  over 
  a 
  finite 
  range, 
  though, 
  as 
  a 
  matter 
  of 
  fact, 
  

   these 
  constituents 
  are 
  produced 
  by 
  the 
  analysing 
  property 
  of 
  

   the 
  crystal. 
  These 
  rays 
  are 
  sorted 
  out 
  into 
  a 
  continuous 
  

   spectrum 
  of 
  monochromatic 
  waves, 
  and 
  only 
  those 
  constituents 
  

   are 
  reflected 
  at 
  a 
  glancing 
  angle 
  6 
  of 
  which 
  the 
  wave-lengths 
  

   satisfy 
  the 
  condition 
  n\ 
  = 
  2d 
  sin 
  6. 
  "With 
  the 
  help 
  of 
  this 
  

   condition 
  the 
  § 
  variation 
  of 
  the 
  reflexion 
  with 
  angle 
  can 
  be 
  

   predicted 
  in 
  general 
  terms. 
  

  

  Suppose 
  that 
  the 
  energy 
  in 
  the 
  spectrum 
  is 
  largely 
  con- 
  

   centrated 
  into 
  a 
  limited 
  range 
  of 
  wave-lengths. 
  For 
  very 
  

   small 
  values 
  of 
  6 
  the 
  intensity 
  of 
  reflexion 
  will 
  be 
  small, 
  as 
  

   only 
  the 
  constituents 
  with 
  the 
  shortest 
  wave-lengths 
  will 
  be 
  

   present 
  even 
  in 
  the 
  first 
  order. 
  The 
  radiation 
  will 
  here 
  be 
  

   exceptionally 
  penetrating, 
  since 
  the 
  absorption 
  coefficient 
  in 
  

   aluminium 
  increases 
  very 
  rapidly 
  with 
  the 
  wave-length. 
  As 
  

   6 
  is 
  increased 
  the 
  intensity 
  reaches 
  a 
  maximum, 
  which 
  

   roughly 
  corresponds 
  with 
  that 
  component 
  which 
  has 
  the 
  

   greatest 
  intensity 
  in 
  the 
  spectrum. 
  At 
  greater 
  angles 
  the 
  

   intensity 
  falls 
  otf, 
  and 
  the 
  radiation 
  becomes 
  continuously 
  

   softer. 
  Here 
  the 
  effect 
  of 
  the 
  short 
  wave-lengths 
  reflected 
  

   in 
  the 
  second 
  and 
  higher 
  orders 
  begins 
  to 
  become 
  noticeable. 
  

   Under 
  the 
  conditions 
  of 
  these 
  experiments 
  but 
  few 
  of 
  the 
  

   softer 
  types 
  of 
  radiation 
  could 
  reach 
  the 
  detector. 
  At 
  large 
  

   angles 
  therefore 
  the 
  effect 
  of 
  the 
  constituents 
  reflected 
  in 
  the 
  

   first 
  order 
  will 
  become 
  small, 
  and 
  the 
  penetrating 
  power 
  of 
  

   the 
  radiation 
  will 
  no 
  longer 
  even 
  approximately 
  correspond 
  

   to 
  it. 
  Eventually 
  the 
  reflected 
  beam 
  will 
  consist 
  of 
  such 
  a 
  

   mixture 
  of 
  constituents 
  reflected 
  in 
  various 
  orders 
  that 
  its 
  

   quality 
  will 
  become 
  approximately 
  constant. 
  A< 
  the 
  X-ray 
  

   tube 
  is 
  softened 
  the 
  angle 
  for 
  which 
  the 
  reflexion 
  is 
  a 
  maxi- 
  

   mum 
  will 
  of 
  course 
  become 
  greater. 
  

  

  The 
  reflexion 
  found 
  for 
  rocksalt 
  is 
  in 
  perfect 
  agreement 
  

   with 
  this 
  theory. 
  In 
  fig. 
  2, 
  curve 
  II., 
  the 
  maximum 
  close 
  to 
  

   4° 
  and 
  tin; 
  very 
  rapid 
  decrease 
  in 
  intensity 
  for 
  -mailer 
  angles 
  

   are 
  conspicuous. 
  For 
  larger 
  angles 
  the 
  curve 
  lulls 
  oil 
  less 
  

   steeply, 
  and 
  at 
  0° 
  the 
  second-order 
  spectrnm 
  is 
  no 
  doubtjusl 
  

   making 
  \\< 
  appearance. 
  We 
  know, 
  however, 
  from 
  the 
  

   experiments 
  with 
  monochromatic 
  rays 
  that 
  the 
  second 
  order 
  

   in 
  rock^alr 
  ha- 
  very 
  little 
  intensity 
  compared 
  with 
  fh<' 
  first, 
  

  

  