﻿606 
  Prof. 
  L. 
  V. 
  King 
  on 
  the 
  Gradient 
  of 
  the 
  

  

  of 
  1 
  cm. 
  from 
  1 
  curie 
  of 
  radium 
  supposed 
  concentrated 
  at 
  a 
  

   point 
  (absorption 
  of 
  7- 
  rays 
  by 
  air 
  and 
  by 
  the 
  substance 
  of 
  

   the 
  radium 
  salt 
  neglected). 
  

  

  Eve 
  * 
  obtains 
  for 
  the 
  value 
  of 
  n 
  the 
  number 
  ?i 
  = 
  3'74 
  x 
  10 
  9 
  , 
  

   while 
  a 
  more 
  recent 
  determination 
  by 
  Moseley 
  and 
  Robinson 
  t 
  

   gave 
  the 
  value 
  n 
  — 
  6 
  X 
  10 
  9 
  . 
  

  

  Q 
  represents 
  the 
  mean 
  radium 
  content 
  for 
  sedimentary 
  

   rocks. 
  A 
  table 
  of 
  value 
  for 
  various 
  rocks 
  as 
  determined 
  by 
  

   Strutt 
  is 
  quoted 
  by 
  Rutherford 
  J 
  : 
  a 
  value 
  of 
  the 
  order 
  of 
  

   Q 
  = 
  3'0xl0 
  -12 
  gram 
  per 
  c.c. 
  of 
  sedimentary 
  rock 
  may 
  be 
  

   taken 
  to 
  represent 
  a 
  rough 
  value. 
  

  

  If 
  the 
  radium 
  content 
  is 
  distributed 
  uniformly 
  throughout 
  

   a 
  semi-infinite 
  solid 
  bounded 
  by 
  a 
  plane, 
  the 
  value 
  of 
  n 
  at 
  a 
  

   height 
  z 
  above 
  the 
  surface 
  is 
  given 
  by 
  

  

  »=^M 
  (2) 
  

  

  f(jiiZi) 
  being 
  the 
  function 
  defined 
  by 
  equation 
  (1). 
  This 
  

   function 
  has 
  very 
  simple 
  properties, 
  which 
  often 
  enable 
  us 
  to 
  

   write 
  down 
  without 
  calculation 
  the 
  intensity 
  of 
  radiation 
  in 
  

   more 
  complicated 
  cases 
  of 
  distribution 
  : 
  thus 
  if 
  we 
  draw 
  a 
  

   horizontal 
  plane 
  at 
  a 
  depth 
  z 
  2 
  below 
  the 
  surface 
  it 
  is 
  easily 
  

   shown 
  that 
  the 
  contribution 
  to 
  n 
  arising 
  from 
  the 
  distri- 
  

   bution 
  of 
  radium 
  below 
  this 
  plane 
  is 
  given 
  by 
  

  

  fJ<2 
  

  

  Hence 
  by 
  subtraction 
  we 
  obtain 
  the 
  intensity 
  due 
  to 
  a 
  

   plate 
  of 
  thickness 
  z 
  2 
  in 
  the 
  form 
  

  

  n' 
  = 
  (27rQ 
  ) 
  n 
  lfi 
  2 
  ){f(/M 
  l 
  z 
  l 
  )^f(fi 
  1 
  z 
  1 
  + 
  /i 
  2 
  z 
  2 
  )}, 
  . 
  . 
  (3) 
  

  

  agreeing 
  with 
  the 
  value 
  obtained 
  in 
  the 
  previous 
  paper, 
  

   where 
  a 
  numerical 
  table 
  of 
  the 
  function 
  f(js) 
  is 
  given, 
  

   enabling 
  (2) 
  and 
  (3) 
  to 
  be 
  evaluated. 
  It 
  is 
  shown 
  that 
  n 
  

   and 
  n 
  are 
  practically 
  identical 
  if 
  z 
  2 
  exceeds 
  11 
  cm., 
  so 
  that 
  

   the 
  entire 
  contribution 
  to 
  the 
  penetrating 
  radiation 
  is 
  limited 
  

   to 
  that 
  coming 
  from 
  a 
  few 
  centimetres' 
  depth 
  of 
  radium- 
  

   bearing 
  rock 
  or 
  soil 
  at 
  the 
  earth's 
  surface. 
  

  

  The 
  number 
  of 
  ions 
  produced 
  in 
  a 
  small 
  cavity 
  at 
  a 
  depth 
  

   z 
  2 
  below 
  the 
  surface 
  is 
  easily 
  obtained 
  by 
  writing 
  down 
  the 
  

   contribution 
  at 
  the 
  surface 
  of 
  a 
  slab 
  of 
  thickness 
  z 
  2 
  lying 
  

  

  * 
  Eve, 
  Phil. 
  Mag. 
  Oct. 
  1911, 
  p. 
  551. 
  

  

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

  

  X 
  Rutherford, 
  ' 
  Radio-activity,' 
  1913, 
  p. 
  645. 
  

  

  