﻿228 
  Messrs. 
  H. 
  G. 
  J. 
  Moseley 
  and 
  C. 
  Gr. 
  Darwin 
  on 
  

  

  this 
  it 
  may 
  be 
  concluded 
  that 
  these 
  characteristic 
  radiations 
  

   are 
  very 
  nearly 
  monochromatic. 
  A 
  mathematical 
  treatment 
  

   of 
  this 
  question 
  shows 
  that 
  if 
  these 
  radiations 
  are 
  damped 
  

   waves, 
  the 
  damping 
  cannot 
  reduce 
  the 
  amplitude 
  to 
  half 
  

   value 
  in 
  less 
  than 
  50 
  vibrations. 
  

  

  Probably 
  the 
  number 
  of 
  vibrations 
  is 
  really 
  much 
  greater 
  

   than 
  this. 
  If 
  it 
  is 
  assumed 
  that 
  the 
  system 
  which 
  emits 
  the 
  

   characteristic 
  radiation 
  is 
  a 
  freely 
  vibrating 
  electron, 
  

   the 
  vibrator 
  will, 
  owing 
  to 
  its 
  very 
  high 
  frequency, 
  be 
  

   appreciably 
  damped 
  by 
  radiation. 
  The 
  equation 
  of 
  motion 
  

   of 
  such 
  an 
  electron 
  is 
  according 
  to 
  the 
  ordinary 
  electro- 
  

   magnetic 
  theory 
  

  

  

  d 
  

  

  f?™\ 
  2 
  _ 
  2 
  - 
  — 
  = 
  

  

  ct 
  

  

  The 
  displacement 
  is 
  therefore 
  e 
  cos27r. 
  — 
  where 
  

   4tj-2 
  e 
  2 
  \ 
  A 
  

  

  <r 
  = 
  — 
  r 
  ' 
  — 
  ^ 
  (e 
  is 
  the 
  charge, 
  m 
  the 
  mass 
  of 
  the 
  electron, 
  

  

  and 
  c 
  the 
  velocity 
  of 
  light). 
  This 
  gives 
  rise 
  in 
  the 
  case 
  of 
  a 
  

   radiator 
  with 
  the 
  frequency 
  of 
  the 
  characteristic 
  ft 
  to 
  a 
  wave, 
  

   of 
  which 
  the 
  amplitude 
  is 
  damped 
  to 
  half 
  value 
  in 
  2680 
  Ki 
  

   wave-lengths. 
  A 
  wave 
  damped 
  to 
  this 
  extent 
  will 
  be 
  

   reflected 
  over 
  a 
  range 
  of 
  angles 
  of 
  incidence 
  large 
  enough 
  

   to 
  be 
  capable 
  of 
  being 
  detected 
  experimentally. 
  An 
  attempt 
  

   will 
  be 
  made 
  to 
  measure 
  this 
  range, 
  as 
  the 
  matter 
  is 
  of 
  great 
  

   theoretical 
  interest. 
  

  

  The 
  same 
  experimental 
  arrangements 
  were 
  used 
  to 
  test 
  

   how 
  precisely 
  the 
  laws 
  of 
  reflexion 
  are 
  obeyed. 
  The 
  slits 
  

   Avere 
  far 
  too 
  broad 
  to 
  introduce 
  diffraction 
  in 
  the 
  case 
  of 
  

   radiation 
  of 
  such 
  short 
  wave-length. 
  Attempts 
  are, 
  however, 
  

   sometimes 
  made 
  to 
  explain 
  the 
  corpuscular 
  properties 
  of 
  

   X-rays 
  by 
  endowing 
  them 
  with 
  a 
  very 
  restricted 
  wave-front. 
  

   If 
  such 
  a 
  beam 
  struck 
  a 
  crystal 
  the 
  scattering 
  from 
  the 
  

   atoms 
  would 
  give 
  a 
  system 
  of 
  waves, 
  of 
  which 
  the 
  inter- 
  

   ference 
  would 
  show 
  the 
  same 
  arrangement 
  as 
  the 
  diffraction 
  

   pattern 
  round 
  a 
  small 
  hole. 
  The 
  crystal 
  was 
  set 
  permanently 
  

   at 
  the 
  special 
  angle 
  /3 
  3 
  , 
  so 
  that 
  unless 
  diffraction 
  occurred, 
  

   the 
  reflected 
  radiation 
  would 
  consist 
  almost 
  entirely 
  of 
  

   characteristic 
  rays 
  proceeding 
  in 
  a 
  parallel 
  beam 
  0°5 
  mm. 
  

   wide. 
  The 
  opening 
  of 
  the 
  detector, 
  0*5 
  mm. 
  wide, 
  was 
  

   moved 
  across 
  this 
  beam. 
  The 
  result 
  showed 
  no 
  trace 
  of 
  

   diffraction. 
  It 
  was 
  calculated 
  that 
  in 
  each 
  reflecting 
  plane 
  

   an 
  area 
  containing 
  at 
  least 
  a 
  million 
  atoms 
  must 
  have 
  been 
  

   concern 
  r 
  d 
  in 
  producing 
  so 
  perfect 
  a 
  reflexion. 
  

  

  