﻿906 
  Prof. 
  0. 
  W. 
  Richardson 
  on 
  the 
  Kinetic 
  

  

  5*5 
  mms. 
  The 
  density 
  of 
  the 
  ions 
  received 
  by 
  different 
  

   portions 
  of 
  the 
  plates 
  would 
  therefore 
  not 
  be 
  the 
  same 
  

   everywhere 
  along 
  a 
  line 
  parallel 
  to 
  the 
  slit, 
  as 
  the 
  above 
  

   correction 
  assumes, 
  but 
  would 
  fall 
  off 
  towards 
  the 
  edges. 
  

   Neglecting 
  the 
  spreading 
  of 
  the 
  ions 
  parallel 
  to 
  the 
  length 
  of 
  

   the 
  strip 
  and 
  assuming 
  the 
  temperature 
  of 
  the 
  strip 
  to 
  be 
  

   uniform 
  throughout 
  we 
  should 
  thus 
  obtain 
  a 
  new 
  correction 
  

   factor, 
  viz.. 
  5*5/3"7 
  = 
  l"49. 
  Since 
  the 
  strip 
  is 
  much 
  hotter 
  in 
  

   the 
  centre 
  than 
  towards 
  the 
  ends, 
  this 
  will 
  tend 
  to 
  equalise 
  

   the 
  effect 
  of 
  the 
  ions 
  spreading 
  along 
  the 
  length 
  of 
  the 
  strip, 
  

   although 
  this 
  will 
  probably 
  be 
  accentuated 
  by 
  the 
  electric 
  

   held 
  not 
  being 
  uniform. 
  We 
  shall 
  therefore 
  take 
  1*49 
  as 
  

   being 
  the 
  best 
  guess 
  we 
  can 
  make 
  as 
  to 
  the 
  value 
  of 
  this 
  

   correction 
  factor. 
  

  

  [n 
  applying 
  this 
  method 
  it 
  is 
  necessary 
  to 
  have 
  absolute 
  

   values 
  of 
  i 
  , 
  the 
  fraction 
  of 
  the 
  total 
  number 
  of 
  ions 
  which 
  

   pass 
  through 
  the 
  slit. 
  The 
  ratios 
  of 
  the 
  electrometer 
  deflex- 
  

   ions 
  which 
  are 
  given 
  in 
  the 
  various 
  curves 
  have 
  therefore 
  

   to 
  be 
  divided 
  by 
  the 
  ratio 
  of 
  the 
  two 
  capacities, 
  as 
  explained 
  

   on 
  p. 
  897. 
  This 
  ratio 
  was 
  not 
  accurately 
  determined 
  but 
  was 
  

   known 
  to 
  be 
  about 
  12. 
  The 
  uncertainty 
  in 
  this 
  factor 
  is, 
  

   however, 
  a 
  small 
  matter 
  compared 
  with 
  the 
  uncertainty 
  

   arising 
  out 
  of 
  the 
  correction 
  discussed 
  in 
  the 
  previous 
  

   paragraph. 
  

  

  In 
  all 
  the 
  experiments 
  described 
  in 
  this 
  paper 
  the 
  width 
  of 
  

   the 
  slit 
  was 
  0302 
  cm. 
  and 
  that 
  of 
  the 
  strip 
  "026 
  cm. 
  

  

  Equation 
  (6) 
  may 
  be 
  written 
  in 
  the 
  form 
  

  

  M=J^ 
  K 
  (11) 
  

  

  l7r:- 
  *„- 
  v 
  y 
  

  

  With 
  the 
  negative 
  ions, 
  in 
  the 
  neighbourhood 
  of 
  V 
  = 
  10 
  

   volts, 
  the 
  relation 
  Y/e 
  2 
  = 
  constant 
  when 
  the 
  other 
  variables 
  

   are 
  kept 
  constant, 
  was 
  approximately 
  fulfilled 
  ; 
  though 
  this 
  

   was 
  not 
  the 
  case 
  at 
  high 
  voltages, 
  as 
  we 
  have 
  already 
  

   explained. 
  For 
  the 
  data 
  given 
  in 
  fig. 
  3 
  the 
  corrected 
  value 
  

   of 
  f 
  was 
  found 
  to 
  lie 
  "171. 
  Substituting 
  the 
  values 
  of 
  the 
  

   other 
  quantities 
  which 
  have 
  already 
  been 
  given 
  we 
  find 
  

   R=2"52xl0 
  3 
  . 
  

  

  This 
  value 
  shows 
  that 
  the 
  third 
  method 
  gives 
  results 
  which 
  

   are 
  consistent 
  with 
  the 
  first 
  two. 
  It 
  is 
  probable 
  that 
  the 
  

   correction 
  is 
  somewhat 
  overdone 
  in 
  the 
  case 
  of 
  the 
  negative 
  

   ions. 
  

  

  (b) 
  Positive 
  Ions. 
  — 
  In 
  the 
  case 
  of 
  the 
  positive 
  ions 
  we 
  

   have 
  seen 
  that 
  the 
  relation 
  i 
  2 
  /V 
  = 
  constant 
  was 
  fulfilled 
  

   throughout 
  the 
  whole 
  range 
  of 
  potential-differences 
  em- 
  

   ployed. 
  The 
  method 
  was 
  therefore 
  consistent 
  over 
  a 
  greater 
  

  

  