﻿Penetrating 
  Radiation 
  from 
  the 
  Earth. 
  

  

  607 
  

  

  above 
  the 
  canity 
  and 
  that 
  due 
  to 
  the 
  semi-infinite 
  solid 
  below 
  

   it 
  : 
  we 
  thus 
  have 
  

  

  B! 
  =^ 
  {1 
  _ 
  /(/¥!)}+ 
  M% 
  = 
  M»_» 
  {2 
  _ 
  /fe 
  , 
  )} 
  . 
  . 
  

  

  We 
  note 
  that 
  when 
  the 
  cavity 
  is 
  at 
  a 
  considerable 
  depth 
  

  

  47rQ« 
  

  

  f(p2 
  z 
  2) 
  becomes 
  negligible 
  and 
  (?? 
  2 
  ) 
  c 
  

  

  /*2 
  

  

  agreeing 
  

  

  with 
  

  

  the 
  value 
  calculated 
  directly 
  to 
  correspond 
  to 
  this 
  condition 
  *. 
  

   Also 
  if 
  we 
  take 
  2"- 
  2 
  = 
  0, 
  corresponding 
  to 
  the 
  intensity 
  at 
  the 
  

   earth's 
  surface, 
  we 
  have, 
  since 
  /(0) 
  = 
  1, 
  for 
  the 
  corresponding 
  

   ionization 
  the 
  value 
  (n 
  2 
  )o 
  = 
  27rQnJ 
  fi 
  2 
  . 
  In 
  this 
  connexion 
  

   Rutherford 
  f 
  points 
  out 
  that, 
  if 
  we 
  take 
  n 
  = 
  3 
  ions 
  per 
  c.c. 
  

   per 
  sec. 
  to 
  represent 
  the 
  effect 
  of 
  penetrating 
  radiation 
  at 
  

   the 
  earth's 
  surface 
  and 
  make 
  use 
  of 
  the 
  constants 
  cited 
  at 
  the 
  

   beginning 
  of 
  the 
  present 
  section, 
  we 
  obtain 
  a 
  value 
  of 
  Q 
  of 
  

   the 
  correct 
  magnitude, 
  thus 
  affording 
  evidence 
  of 
  the 
  origin 
  

   of 
  the 
  penetrating 
  radiation 
  as 
  due 
  chiefly 
  to 
  the 
  radium 
  

   content 
  of 
  the 
  soil. 
  On 
  the 
  other 
  hand, 
  observations 
  made 
  

   during 
  balloon 
  ascensions 
  have 
  failed 
  to 
  reveal 
  the 
  gradient 
  

   required 
  by 
  theory 
  : 
  these 
  are 
  discussed 
  in 
  the 
  next 
  section. 
  

   The 
  gradient 
  of 
  the 
  penetrating 
  radiation 
  above 
  the 
  earth's 
  

   surface 
  is 
  calculated 
  from 
  (2), 
  and 
  below 
  the 
  surface 
  from 
  

   (4), 
  making 
  use 
  of 
  the 
  numerical 
  tables 
  in 
  the 
  paper 
  pre- 
  

   viously 
  cited 
  : 
  the 
  results 
  are 
  tabulated 
  below 
  and 
  are 
  shown 
  

  

  Table 
  I. 
  

  

  fiz. 
  

  

  Gradient 
  above 
  earth's 
  surface. 
  

   j» 
  1 
  =6-0xl0'^ 
  6 
  om.~ 
  1 
  . 
  

  

  Gradient 
  below 
  earth's 
  surface. 
  

   jK 
  3 
  =-12cin. 
  _1 
  . 
  

  

  z 
  x 
  . 
  

   metres. 
  

  

  Am)- 
  

  

  z 
  2 
  . 
  

   cm. 
  

  

  {2-/fe)}. 
  

  

  000 
  

  

  •05 
  

  

  •1 
  

  

  •2 
  

  

  •3 
  

  

  •5 
  

  

  •7 
  

  

  10 
  

  

  20 
  

  

  

  

  8-3 
  

   167 
  

   33-4 
  

   50 
  

   83 
  

   117 
  

   167 
  

   333 
  

  

  1-000 
  

   •828 
  

   •722 
  

   •574 
  

   •469 
  

   •327 
  

   •235 
  

   •148 
  

   •037 
  

  

  

  

  •42 
  

   •83 
  

   1-67 
  

   2-50 
  

   416 
  

   5-83 
  

   8-33 
  

   16-7 
  

  

  1000 
  

   1-172 
  

   1-278 
  

   1-426 
  

   1-531 
  

   1-673 
  

   1-765 
  

   1-852 
  

   1-963 
  

  

  * 
  King, 
  Phil. 
  Mag. 
  xxiii. 
  Feb. 
  1912, 
  p. 
  247. 
  The 
  writer 
  takes 
  the 
  

   occasion 
  to 
  correct 
  the 
  description 
  of 
  tig. 
  II., 
  which 
  should 
  read 
  : 
  

   Curve 
  I., 
  ^ 
  = 
  '11 
  cm.; 
  Curve 
  II., 
  h 
  = 
  Vl 
  cm.; 
  Curve 
  III., 
  ^ 
  = 
  11 
  cm. 
  ; 
  

   Curve 
  IV., 
  h 
  = 
  cc 
  . 
  

  

  t 
  Rutherford, 
  'Radio-activity,' 
  1913, 
  p. 
  637. 
  

  

  (4) 
  

  

  