﻿118 
  Mr. 
  C. 
  A. 
  Sadler 
  on 
  tJw 
  

  

  small 
  subsequent 
  increase 
  in 
  penetrating 
  power 
  of 
  the 
  secon- 
  

   dary 
  beam, 
  values 
  of 
  R 
  30 
  to 
  40 
  times 
  as 
  big 
  as 
  the 
  previous 
  

   steady 
  values 
  are 
  obtained 
  ; 
  this 
  increase 
  corresponding 
  to 
  

   the 
  excitation 
  of 
  the 
  characteristic 
  tertiary 
  radiation. 
  

  

  Let 
  us 
  consider 
  the 
  tertiary 
  radiation 
  emitted 
  normally 
  

   from 
  a 
  given 
  radiator 
  of 
  area 
  S 
  upon 
  which 
  a 
  uniform 
  

   parallel 
  beam 
  of 
  secondary 
  rays 
  is 
  incident 
  normally. 
  

  

  Let 
  us 
  define 
  a 
  quantity 
  k, 
  such 
  that 
  the 
  fraction 
  of 
  the 
  

   energy 
  of 
  the 
  secondary 
  beam 
  passing 
  normally 
  through 
  a 
  

   thin 
  layer 
  Ba; 
  of 
  the 
  tertiary 
  radiator 
  which 
  is 
  transformed 
  

   into 
  tertiary 
  radiation 
  is 
  kBx. 
  Thus, 
  if 
  I 
  be 
  a 
  measure 
  of 
  the 
  

   energy 
  passing 
  normally 
  per 
  second 
  through 
  unit 
  area 
  of 
  the 
  

   tertiary 
  radiator 
  at 
  a 
  depth 
  a' 
  below 
  the 
  surface, 
  the 
  energy 
  

   transformed 
  per 
  second 
  in 
  a 
  layer 
  8a.'=lk8x. 
  

  

  Now 
  Barkla 
  * 
  has 
  shown 
  that 
  when 
  this 
  homogeneous 
  

   type 
  of 
  radiation 
  is 
  excited, 
  it 
  is 
  practically 
  evenly 
  distri- 
  

   buted 
  in 
  all 
  directions 
  : 
  consequently, 
  the 
  energy 
  passing 
  per 
  

   second 
  as 
  tertiary 
  radiation 
  from 
  the 
  layer 
  Sx 
  through 
  the 
  

   tissue-paper-covered 
  window 
  of 
  an 
  electroscope 
  of 
  the 
  Wilson 
  

   type 
  (I 
  being 
  constant 
  over 
  the 
  whole 
  area 
  of 
  the 
  radiator) 
  

  

  = 
  £^^lkB.ve-^^, 
  (1) 
  

  

  where 
  X2 
  is 
  the 
  absorption 
  coefficient 
  of 
  the 
  tertiary 
  radiation 
  

   by 
  the 
  material 
  of 
  which 
  the 
  tertiary 
  radiator 
  is 
  composed, 
  

   and 
  CO 
  is 
  the 
  mean 
  solid 
  angle 
  subtended 
  by 
  the 
  aperture 
  of 
  

   the 
  electroscope 
  at 
  all 
  parts 
  of 
  the 
  radiating 
  area. 
  

  

  But 
  if 
  lo 
  is 
  a 
  measure 
  of 
  the 
  energy 
  incident 
  normally 
  per 
  

   second 
  on 
  unit 
  area 
  of 
  the 
  tertiary 
  radiator 
  at 
  the 
  surface, 
  

  

  I 
  = 
  lo^-^i^ 
  

  

  where 
  Xi 
  is 
  the 
  absorption 
  coefficient 
  of 
  the 
  secondary 
  beam 
  

   by 
  the 
  material 
  of 
  which 
  the 
  tertiary 
  radiator 
  is 
  composed, 
  

   and 
  the 
  whole 
  energy 
  passing 
  into 
  the 
  electroscope 
  per 
  

   second 
  from 
  the 
  tertiary 
  radiator 
  

  

  ^SIo^- 
  \ 
  e-^^^^'^^',d.v 
  .... 
  (2) 
  

  

  Att 
  

  

  t/O 
  

  

  = 
  4^«V^. 
  ....... 
  (3) 
  

  

  If 
  now 
  we 
  remove 
  the 
  tertiary 
  radiator, 
  and 
  place 
  the 
  

  

  electroscope 
  previously 
  used 
  in 
  the 
  path 
  of 
  the 
  secondary 
  

  

  beam, 
  with 
  the 
  centre 
  of 
  its 
  tissue-paper-covered 
  window 
  

  

  occupying 
  the 
  position 
  previously 
  occupied 
  by 
  the 
  centre 
  of 
  

  

  * 
  Barkla, 
  T^liil. 
  Mag. 
  Feb. 
  1908, 
  pp. 
  288-296. 
  

  

  