﻿Trausfoi'mations 
  of 
  X-Bai/s. 
  119 
  

  

  the 
  radiator, 
  and 
  with 
  its 
  plane 
  perpendicular 
  to 
  the 
  axis 
  of 
  

   the 
  secondary 
  beam, 
  the 
  energy 
  passing 
  per 
  second 
  through 
  

   the 
  window, 
  if 
  its 
  area 
  is 
  A, 
  is 
  IqA. 
  

  

  Therefore 
  the 
  ratio 
  of 
  the 
  energy 
  in 
  the 
  tertiary 
  beam 
  

   passing 
  per 
  second 
  into 
  the 
  electroscope 
  in 
  the 
  first 
  position 
  

   to 
  the 
  energy 
  of 
  the 
  secondary 
  beam 
  passing 
  per 
  second 
  into 
  

   the 
  electroscope 
  ia 
  its 
  second 
  position 
  

  

  = 
  ^^ 
  __A_ 
  . 
  . 
  a^ 
  

  

  47rA 
  \i 
  + 
  X2 
  ^ 
  

  

  There 
  is 
  considerable 
  evidence 
  that 
  the 
  ionization 
  produced 
  

   in 
  a 
  given 
  volume 
  of 
  air 
  by 
  a 
  beam 
  of 
  Rontgen 
  radiation 
  is 
  

   approximately 
  proportional 
  to 
  the 
  absorption 
  of 
  that 
  radiation 
  

   by 
  the 
  air. 
  It 
  has 
  been 
  found 
  * 
  also 
  that 
  the 
  ratio 
  of 
  the 
  

   absorption 
  coefficients 
  of 
  homogeneous 
  beams 
  of 
  different 
  

   penetrating 
  powers 
  by 
  any 
  two 
  substances, 
  e. 
  g. 
  carbon 
  and 
  

   aluminium, 
  in 
  which 
  no 
  radiation 
  of 
  the 
  homogeneous 
  type 
  

   is 
  excited 
  by 
  the 
  beam 
  under 
  consideration, 
  is 
  a 
  constant. 
  

   Also 
  it 
  has 
  been 
  found 
  that 
  the 
  absorption 
  of 
  a 
  beam 
  of 
  

   Rontgpn 
  rays 
  by 
  any 
  substance 
  depends 
  only 
  upon 
  the 
  

   quantity 
  of 
  matter 
  present 
  and 
  not 
  upon 
  its 
  state 
  of 
  

   aggregation. 
  

  

  It 
  is 
  assumed 
  on 
  the 
  basis 
  of 
  these 
  results, 
  that 
  the 
  ioniza- 
  

   tions 
  produced 
  in 
  a 
  given 
  volume 
  of 
  air 
  by 
  homogeneous 
  

   beams 
  of 
  different 
  penetrating 
  powers 
  are 
  proportional 
  to 
  the 
  

   absorption 
  coefficients 
  of 
  these 
  beams 
  by 
  carbon 
  or 
  aluminium. 
  

  

  Making 
  this 
  assumption, 
  we 
  have 
  the 
  ratio 
  of 
  the 
  ioniza- 
  

   tions 
  produced 
  in 
  the 
  electroscope 
  by 
  the 
  tertiary 
  and 
  

   secondary 
  beams 
  

  

  Q) 
  S 
  k 
  ^ 
  ^ 
  

  

  where 
  a 
  and 
  /5 
  are 
  the 
  absorption 
  coefficients 
  by 
  aluminium 
  

   of 
  the 
  secondary 
  and 
  tertiary 
  beams 
  respectively. 
  From 
  (5) 
  

   we 
  find 
  that 
  k 
  

  

  _^ 
  « 
  A 
  477 
  

  

  In 
  the 
  above 
  calculations 
  we 
  have 
  considered 
  the 
  special 
  

   case 
  of 
  normal 
  incidence 
  and 
  emergence, 
  but, 
  since 
  we 
  are 
  

   dealing 
  with 
  radiators 
  sufficiently 
  thick 
  to 
  absorb 
  the 
  whole 
  

   of 
  the 
  incident 
  radiation, 
  it 
  is 
  easy 
  to 
  show 
  that 
  the 
  results 
  

   (4), 
  (5), 
  (6) 
  are 
  quite 
  general 
  for 
  oblique 
  incidence 
  and 
  

   emergencp, 
  where 
  the 
  incident 
  and 
  emergent 
  beams 
  make 
  

   equal 
  angles 
  with 
  the 
  normal 
  to 
  the 
  radiating 
  surface. 
  

  

  * 
  Barkla 
  & 
  Sadler, 
  Phil. 
  Mag. 
  May 
  1909. 
  

  

  