﻿Ions 
  in 
  Gases 
  under 
  Different 
  Pressures. 
  289 
  

  

  square 
  of 
  the 
  distance 
  from 
  the 
  source, 
  neglecting 
  the 
  ab- 
  

   sorption 
  of 
  the 
  rays 
  by 
  the 
  air, 
  

  

  2?0- 
  

  

  

  This 
  absorption 
  of 
  the 
  air 
  may 
  be 
  neglected 
  without 
  causing 
  

   any 
  serious 
  error; 
  for 
  it 
  has 
  been 
  found 
  (E. 
  Rutherford 
  and 
  

   R. 
  K. 
  McClung, 
  Phil. 
  Trans. 
  Roy. 
  Soc. 
  vol. 
  cxcvi. 
  1901) 
  that 
  

   only 
  about 
  3 
  per 
  cent, 
  of 
  strong 
  radiation 
  was 
  absorbed 
  in 
  

   passing 
  through 
  a 
  metre 
  of 
  air 
  at 
  atmospheric 
  pressure. 
  The 
  

   absorption 
  was 
  shown, 
  by 
  the 
  same 
  authors, 
  to 
  be 
  proportional 
  

   to 
  the 
  pressure 
  of 
  the 
  gas. 
  In 
  the 
  present 
  case, 
  the 
  distance 
  

   between 
  the 
  two 
  plates 
  b 
  \ 
  and 
  c 
  c 
  x 
  was 
  only 
  20 
  centimetres; 
  

   so 
  the 
  absorption 
  would 
  be 
  very 
  small, 
  and 
  therefore 
  

   negligible. 
  

  

  Therefore, 
  supplying 
  these 
  values 
  in 
  the 
  above 
  equation, 
  we 
  

   get 
  

  

  id 
  + 
  lrfZ 
  

  

  = 
  ?oV 
  (4) 
  

  

  Again, 
  let 
  N 
  = 
  total 
  number 
  of 
  ions 
  in 
  the 
  same 
  volume 
  at 
  

   the 
  cessation 
  of 
  the 
  rays 
  ; 
  

  

  where 
  n 
  = 
  residual 
  number 
  per 
  c.c. 
  at 
  the 
  distance 
  x 
  from 
  0. 
  

   N= 
  \\/9-dY, 
  since 
  q=oin' 
  

  

  -if*"' 
  /d 
  

  

  ' 
  V 
  a 
  ) 
  d 
  V 
  £ 
  

  

  = 
  /A 
  VH 
  1+ 
  i> 
  • 
  • 
  • 
  • 
  (5) 
  

  

  But 
  q 
  = 
  j^-j 
  from 
  equation 
  (4) 
  ; 
  

  

  1 
  ••• 
  *= 
  l 
  M 
  1+ 
  iifw 
  ( 
  6 
  > 
  

  

  This 
  equation 
  gives 
  the 
  value 
  of 
  the 
  constant 
  a 
  in 
  absolute 
  

   measure, 
  since 
  the 
  quantities 
  A 
  l5 
  I, 
  and 
  d 
  can 
  be 
  measured 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Yol. 
  3. 
  No. 
  15. 
  March 
  1902. 
  U 
  

  

  ,2 
  

  

  q^.j^dx 
  

  

  