﻿288 
  

  

  Mr. 
  McClung 
  on 
  the 
  Rate 
  of 
  Recombination 
  of 
  

  

  taking 
  a 
  series 
  of 
  observations, 
  the 
  bulb 
  was 
  run 
  at 
  regular 
  

   intervals 
  as 
  far 
  as 
  possible, 
  Besides 
  that, 
  instead 
  of 
  depending 
  

   on 
  a 
  single 
  observation 
  in 
  any 
  one 
  ease, 
  several 
  observations 
  

   were 
  made, 
  and 
  then 
  the 
  mean 
  of 
  these 
  taken. 
  All 
  through 
  

   the 
  investigation 
  this 
  system 
  of 
  averages 
  has 
  been 
  adopted. 
  

  

  Theoretical 
  Considerations. 
  

  

  Before 
  proceeding 
  to 
  the 
  actual 
  results 
  obtained 
  by 
  expe- 
  

   riment, 
  some 
  theoretical 
  questions 
  must 
  be 
  considered. 
  

  

  Suppose 
  that 
  the 
  number 
  of 
  ions 
  per 
  c.c. 
  which 
  are 
  being 
  

   produced 
  at 
  any 
  given 
  point 
  in 
  the 
  gas 
  per 
  second 
  is 
  q, 
  and 
  

   suppose 
  n 
  equals 
  the 
  actual 
  number 
  per 
  c.c. 
  in 
  the 
  gas 
  at 
  the 
  

   same 
  point, 
  then 
  it 
  has 
  been 
  shown 
  (J. 
  J. 
  Thomson 
  and 
  E. 
  

   Butherford, 
  Phil. 
  Mag. 
  Nov. 
  1896) 
  that 
  when 
  a 
  steady 
  state 
  

   has 
  been 
  reached, 
  that 
  is, 
  when 
  the 
  rate 
  of 
  production 
  is 
  equal 
  

   -to 
  the 
  rate 
  of 
  recombination, 
  

  

  (3) 
  

  

  q 
  = 
  an 
  2 
  . 
  

  

  In 
  fig. 
  3 
  let 
  represent 
  the 
  source 
  of 
  the 
  rays, 
  and 
  let 
  C 
  Ci 
  

   represent 
  the 
  cone 
  of 
  rays 
  passing 
  through 
  the 
  rectangular 
  

   orifice 
  H 
  (fig. 
  1) 
  and 
  thence 
  into 
  the 
  cylinder. 
  Let 
  bb 
  l 
  c 
  1 
  c 
  

   represent 
  the 
  part 
  of 
  the 
  cone 
  included 
  between 
  the 
  two 
  

   extreme 
  plates 
  within 
  the 
  cylinder. 
  Suppose 
  H, 
  A 
  l5 
  and 
  A 
  2 
  

   to 
  represent 
  the 
  cross-sectional 
  areas 
  of 
  the 
  cone 
  at 
  the 
  orifice 
  

   and 
  the 
  two 
  plates, 
  respectively. 
  Let 
  h 
  and 
  d 
  represent 
  the 
  

   distances 
  of 
  a 
  a 
  x 
  and 
  b 
  b 
  x 
  respectively 
  from 
  0, 
  while 
  I 
  is 
  the 
  

   distance 
  between 
  the 
  plates 
  b 
  b 
  x 
  and 
  c 
  c 
  v 
  

  

  Let 
  </ 
  = 
  the 
  number 
  of 
  ions 
  per 
  c.c. 
  produced 
  per 
  second 
  

   at 
  the 
  plate 
  b 
  \. 
  

  

  Let 
  Q 
  = 
  total 
  number 
  produced 
  per 
  second 
  in 
  the 
  volume 
  

   between 
  b 
  b 
  x 
  and 
  c 
  c 
  x 
  ; 
  

  

  ... 
  Q=j^V, 
  

  

  where 
  q 
  = 
  the 
  number 
  of 
  ions 
  per 
  c.c. 
  at 
  a 
  distance 
  x 
  from 
  0, 
  

  

  and 
  dV 
  = 
  Adrt 
  } 
  the 
  cross-sectional 
  area 
  at 
  the 
  distance 
  x 
  

  

  being- 
  A. 
  

  

  _x 
  2 
  

   A=^A 
  i; 
  

  

  and 
  since 
  the 
  number 
  of 
  ions 
  per 
  c.c. 
  varies 
  inversely 
  as 
  the 
  

  

  