﻿ry-Hai/s 
  of 
  Uranium 
  and 
  Kadium. 
  641 
  

  

  equally 
  thick 
  electroscope 
  o£ 
  another 
  metal 
  had 
  been 
  em- 
  

   ployed. 
  The 
  work 
  o£ 
  Eve 
  just 
  published 
  (Phil. 
  Mag. 
  1909, 
  

   x^dii. 
  p. 
  175), 
  taken 
  into 
  conjunction 
  with 
  that 
  of 
  Kleeman, 
  

   Bragg 
  and 
  Madsen, 
  led 
  him 
  to 
  the 
  view 
  that 
  lead 
  is 
  peculiar 
  

   in 
  that 
  it 
  absorbs 
  secondary 
  y-radiation 
  and 
  generates 
  little 
  

   or 
  none 
  (compare 
  concluding 
  paragraph 
  of 
  section 
  10).] 
  

  

  9. 
  The 
  Effect 
  of 
  Secondary 
  Penetrating 
  Radiation. 
  

  

  The 
  absorption 
  of 
  7-rays 
  by 
  matter 
  may 
  be 
  conveniently 
  

   expressed 
  with 
  fair 
  accuracy 
  by 
  an 
  exponential 
  law 
  though 
  

   small 
  departures 
  from 
  this 
  law 
  are 
  probably 
  always 
  present. 
  

   We 
  think 
  that 
  in 
  an 
  unsuitable 
  form 
  of 
  apparatus 
  secondary 
  

   penetrating 
  rays 
  play 
  a 
  large 
  part 
  in 
  causing 
  these 
  deviations. 
  

   We 
  have 
  not 
  been 
  able 
  by 
  any 
  theory 
  of 
  secondary 
  radiation 
  

   to 
  predict 
  beforehand 
  what 
  variation 
  is 
  likely 
  to 
  be 
  obtained 
  

   in 
  any 
  ordinary 
  case. 
  It 
  sujfices 
  in 
  the 
  first 
  instance 
  to 
  

   suppose 
  that 
  the 
  y-rays 
  generate 
  at 
  each 
  point 
  in 
  passage 
  

   through 
  matter 
  a 
  secondary 
  radiation 
  proportional 
  in 
  intensity 
  

   to 
  the 
  primary, 
  but 
  with 
  a 
  different 
  coefficient 
  of 
  absorption. 
  

   If 
  we 
  assume 
  that 
  the 
  rays, 
  both 
  primary 
  and 
  secondary, 
  

   traverse 
  the 
  plate 
  normally, 
  the 
  mathematical 
  proposition 
  is, 
  

   reading 
  thickness 
  instead 
  of 
  time, 
  formally 
  identical 
  to 
  that 
  of 
  

   the 
  theory 
  of 
  successive 
  chemical 
  changes, 
  such, 
  for 
  example, 
  

   as 
  has 
  been 
  thoroughly 
  worked 
  out 
  by 
  Rutherford 
  for 
  suc- 
  

   cessive 
  radioactive 
  changes. 
  If 
  Qo 
  indicates 
  the 
  initial 
  energy 
  

   of 
  the 
  primary 
  beam, 
  Q^ 
  the 
  energy 
  of 
  the 
  combined 
  primary 
  

   and 
  secondary 
  em_erging 
  from 
  a 
  plate 
  of 
  thickness 
  /, 
  Xi 
  and 
  

   Xo 
  the 
  absorption 
  coefficients 
  of 
  the 
  primary 
  and 
  secondary 
  

   respectively, 
  and 
  /c 
  is 
  a 
  coefficient 
  of 
  transformation, 
  repre- 
  

   senting 
  the 
  fraction 
  of 
  the 
  absorbed 
  primary 
  transformed 
  

   into 
  secondary, 
  it 
  can 
  be 
  at 
  once 
  shown 
  that 
  

  

  ^=(l 
  + 
  A)€-^i^-A(6-^-3^), 
  

  

  where 
  * 
  _ 
  kX^ 
  

  

  A2 
  — 
  f^\ 
  

  

  As 
  the 
  ionizations, 
  not 
  the 
  energies, 
  are 
  measured, 
  and 
  

   these 
  are 
  directly 
  proportional 
  to 
  the 
  absorption 
  coefficients, 
  

   this 
  must 
  be 
  allowed 
  for, 
  and 
  we 
  obtain 
  

  

  ^^=(l 
  + 
  B)€-^i^-B(€-^^0> 
  

   where 
  t) 
  _ 
  /cXq 
  

  

  A<2 
  — 
  A<i 
  

  

  and 
  It, 
  Iq 
  refer 
  to 
  the 
  ionizations. 
  

  

  