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  ( 
  7 
  ) 
  

  

  290 
  Mr. 
  McClung 
  on 
  the 
  Rate 
  of 
  lie 
  combination 
  of 
  

   and 
  Q 
  and 
  N 
  determined. 
  This 
  equation 
  may 
  be 
  written 
  

  

  Q 
  

  

  where 
  K 
  is 
  equal 
  to 
  the 
  constant 
  ZAj 
  11+ 
  —^ 
  \ 
  _, 
  which 
  de- 
  

   pends 
  entirely 
  upon 
  the 
  dimensions 
  and 
  position 
  of 
  the 
  

   apparatus. 
  

  

  The 
  value 
  obtained 
  for 
  a. 
  will 
  be 
  discussed 
  later 
  in 
  the 
  

   paper. 
  

  

  The 
  theory 
  of 
  recombination 
  may 
  be 
  considered 
  also 
  in 
  

   regard 
  to 
  the 
  time 
  taken 
  by 
  the 
  maximum 
  number 
  o£ 
  ions 
  to 
  

   fall 
  to 
  half 
  their 
  value. 
  

  

  Let 
  n 
  = 
  maximum 
  number 
  of 
  ions 
  per 
  c.c. 
  at 
  a 
  point 
  

   distant 
  x 
  from 
  (fig. 
  3) 
  . 
  

  

  Let 
  n 
  t 
  = 
  number 
  per 
  c.c. 
  at 
  the 
  end 
  of 
  a 
  time 
  t 
  after 
  the 
  

   rays 
  have 
  ceased. 
  

  

  Then 
  by 
  equation 
  (2) 
  

  

  1 
  1 
  

   -— 
  - 
  =oct. 
  

   n 
  t 
  n 
  

  

  The 
  decrease 
  in 
  time 
  t 
  per 
  c.c. 
  = 
  ?2 
  — 
  n 
  t 
  . 
  

   The 
  decrease 
  in 
  a 
  thin 
  cross-sectional 
  area 
  A, 
  of 
  a 
  thick- 
  

   ness 
  dx, 
  would 
  be 
  A(n 
  Q 
  — 
  n 
  t 
  )dx. 
  

  

  

  

  l 
  _ 
  

  

  n 
  t 
  

  

  -+at; 
  

  

  n 
  

  

  

  

  

  •'• 
  

  

  n 
  - 
  

  

  n 
  2 
  at 
  

  

  -nt— 
  — 
  - 
  . 
  

  

  14- 
  n 
  at 
  

  

  

  

  Also 
  

  

  

  an 
  2 
  

  

  - 
  q 
  ~ 
  x 
  2 
  ' 
  

  

  

  

  

  •*• 
  

  

  n 
  2 
  = 
  

  

  a. 
  ' 
  x 
  2 
  

  

  

  

  Therefore 
  the 
  decrease 
  in 
  the 
  cross-sectional 
  area 
  

  

  A 
  in 
  

  

  time 
  

  

  t 
  is 
  equal 
  to 
  

  

  

  

  

  

  

  

  A^ 
  2 
  

  

  /god 
  2 
  

  

  I 
  ux 
  2 
  

  

  ■ 
  1 
  /-)* 
  

  

  .d 
  /a 
  n 
  l 
  

  

  

  

  Atfotx 
  

  

  dx 
  

  

  x 
  + 
  td 
  V^a 
  

  

  