﻿Primary 
  and 
  Secondary 
  Rontgen 
  Radiation. 
  127 
  

  

  energy 
  of 
  the 
  radiation, 
  we 
  shall 
  obtain 
  a 
  measure 
  of 
  the 
  

   ratio 
  of 
  the 
  energies 
  in 
  the 
  two 
  kinds 
  of 
  radiation. 
  

  

  The 
  experimental 
  work 
  involves 
  two 
  separate 
  deter- 
  

   minations. 
  In 
  the 
  first 
  place, 
  the 
  ratio 
  of 
  the 
  total 
  ionization 
  

   caused 
  by 
  the 
  secondary 
  rays 
  to 
  that 
  produced 
  within 
  a 
  

   known 
  space 
  by 
  the 
  primary; 
  and, 
  secondly, 
  the 
  absorption 
  

   experienced 
  by 
  the 
  primary 
  rays 
  in 
  traversing 
  a 
  known 
  

   distance. 
  

  

  With 
  the 
  assumption 
  just 
  stated, 
  the 
  absorption 
  of 
  energy 
  

   in 
  a 
  parallel 
  beam 
  of 
  rays 
  in 
  traversing 
  a 
  thin 
  layer 
  of 
  gas 
  of 
  

   thickness 
  dl 
  at 
  a 
  point 
  where 
  the 
  intensity 
  is 
  I 
  is 
  equal 
  to 
  

   Xldl, 
  where 
  X 
  is 
  the 
  coefficient 
  of 
  absorption 
  of 
  the 
  gas. 
  

  

  For 
  simplicity 
  we 
  may 
  consider 
  the 
  radiation 
  contained 
  in 
  

   a 
  cone 
  of 
  small 
  solid 
  angle 
  dco, 
  with 
  its 
  vertex 
  at 
  the 
  anti- 
  

   cathode. 
  If 
  I 
  denote 
  the 
  intensity 
  of 
  radiation 
  at 
  a 
  distance 
  r 
  

   from 
  the 
  vertex, 
  we 
  obtain 
  the 
  following 
  differential 
  equation 
  

   for 
  determining 
  I 
  in 
  terms 
  of 
  r 
  : 
  

  

  ( 
  I 
  + 
  ~ 
  dr\ 
  (r 
  + 
  dr) 
  2 
  day 
  - 
  Ir*d<o 
  = 
  \Ir*drda>, 
  

  

  ... 
  ^-(Ir 
  2 
  )=Xlr 
  2 
  . 
  

  

  dr 
  ' 
  

  

  The 
  solution 
  of 
  this 
  equation 
  is 
  

  

  Ir 
  2 
  =V 
  2 
  r^-'-o). 
  

  

  The 
  ionization 
  produced 
  by 
  the 
  rays 
  in 
  the 
  element 
  of 
  

   volume 
  may 
  be 
  expressed 
  as 
  k!r 
  2 
  drdco, 
  where 
  k 
  is 
  a 
  constant. 
  

  

  Hence 
  the 
  total 
  ionization 
  produced 
  within 
  the 
  boundary 
  

   of 
  the 
  cone 
  between 
  r 
  and 
  infinity 
  is 
  

  

  

  The 
  ionization 
  actually 
  measured 
  is 
  that 
  produced 
  in 
  the 
  

   same 
  cone 
  between 
  r 
  and 
  r 
  + 
  dr 
  , 
  and, 
  using 
  the 
  same 
  

   notation, 
  may 
  be 
  written 
  

  

  kI 
  Q 
  r 
  Q 
  2 
  dr 
  Q 
  da). 
  

  

  Thus 
  the 
  total 
  ionization 
  may 
  be 
  obtained 
  by 
  dividing 
  this, 
  

   the 
  observed 
  quantity, 
  by 
  \dr 
  . 
  

  

  The 
  method 
  employed 
  in 
  the 
  first 
  determination, 
  that 
  of 
  

   the 
  ionization 
  produced 
  by 
  the 
  secondary 
  rays, 
  was 
  similar 
  to 
  

   that 
  used 
  by 
  Perrin 
  (loc. 
  cit.) 
  ) 
  and 
  consisted 
  in 
  the 
  com- 
  

   parison 
  of 
  the 
  rates 
  of 
  leak 
  from 
  two 
  condensers, 
  the 
  leak 
  in 
  

  

  