﻿400 
  Mr. 
  H. 
  P. 
  Walmsley 
  on 
  the 
  Distribution 
  of 
  the 
  

  

  obtain 
  fig. 
  12. 
  The 
  cathode 
  activity 
  decreases 
  roughly 
  ex- 
  

   ponentially 
  with 
  time, 
  and 
  the 
  anode 
  activity 
  rises 
  as 
  the 
  

  

  Fig. 
  12. 
  

  

  

  

  

  

  

  

  

  \ 
  

  

  

  

  ^^—4 
  

  

  I 
  

  

  h 
  1 
  

  

  <►— 
  

  

  \< 
  

  

  ) 
  

  

  

  

  l/fATHODf 
  /tCTIWT 
  

   \ANODE 
  flCT/V/TV. 
  

  

  W£og. 
  Kathode 
  Act 
  

  

  Y. 
  

   'V/TK 
  

  

  

  x/ 
  

  

  

  

  

  

  

  

  

  

  

  

  

  ' 
  

  

  

  

  

  

  

  

  

  

  

  

  nF 
  

  

  ^T 
  

  

  

  

  1-2 
  

  

  1-0 
  

  

  •6S 
  

  

  1-0 
  

  

  1-5 
  2^0 
  

  

  Time 
  in 
  minutes 
  

  

  Z-5 
  

  

  3-0 
  

  

  complementary 
  curve 
  to 
  a 
  maximum 
  which 
  is 
  nearly 
  equal 
  

   to 
  the 
  initial 
  amount 
  o£ 
  deposit 
  present. 
  This 
  result 
  is 
  in 
  

   agreement 
  with 
  the 
  ordinary 
  law 
  of 
  recombination. 
  It 
  N^ 
  be 
  

   the 
  number 
  of 
  positively 
  charged 
  active 
  deposit 
  atoms 
  present 
  

   at 
  time 
  t 
  and 
  n 
  is 
  the 
  number 
  of 
  negative 
  charges 
  present 
  

   either 
  as 
  ions 
  or 
  on 
  dust, 
  the 
  law 
  of 
  recombination 
  is 
  given 
  

  

  dm 
  „ 
  

  

  where 
  a 
  is 
  the 
  constant 
  of 
  recombination. 
  If 
  n 
  is 
  sufficiently 
  

   large 
  compared 
  with 
  N^ 
  over 
  the 
  time 
  necessary 
  for 
  the 
  

   complete 
  recombination 
  of 
  the 
  active 
  deposit, 
  we 
  may 
  treat 
  

   un 
  as 
  a 
  constant 
  (equal 
  to 
  k 
  say), 
  whence 
  

  

  If 
  recombination 
  occurs 
  with 
  negatively 
  charged 
  dust 
  par- 
  

   ticles, 
  the 
  number 
  of 
  atoms 
  apparently 
  acquiring 
  a 
  negative 
  

   charge 
  is 
  proportional 
  to 
  the 
  number 
  recombing. 
  Let 
  M 
  be 
  

   the 
  number 
  settling 
  on 
  negatively 
  electrified 
  dust-nuclei, 
  

  

  then 
  

  

  i. 
  e. 
  

  

  sm,x 
  m 
  t 
  , 
  

  

  dM 
  

  

  dt 
  

  

  

  dt 
  

  

  where 
  k' 
  is 
  the 
  new 
  constant 
  of 
  proportionality. 
  

  

  