﻿908 
  Prof. 
  0. 
  W. 
  Richardson 
  on 
  the 
  Kinetic 
  

  

  negative 
  ions, 
  which 
  depends 
  on 
  their 
  velocity 
  component 
  

   perpendicular 
  to 
  the 
  surface, 
  is 
  greatly 
  increased 
  by 
  previous 
  

   exposure 
  of 
  the 
  hot 
  metal 
  to 
  high 
  positive 
  potentials. 
  So 
  far 
  

   as 
  they 
  go, 
  these 
  experiments 
  seem 
  to 
  show 
  that 
  the 
  sideways 
  

   kinetic 
  energy 
  of 
  the 
  ions 
  is 
  not 
  affected 
  by 
  similar 
  treat- 
  

   ment, 
  but 
  this 
  question 
  has 
  not 
  yet 
  been 
  examined 
  at 
  all 
  

   thoroughly. 
  

  

  The 
  magnitude 
  of 
  the 
  potential-difference 
  V 
  through 
  

   which 
  the 
  ions 
  would 
  have 
  had 
  to 
  fall 
  in 
  order 
  to 
  gain 
  the 
  

   mean 
  sideways 
  kinetic 
  energy 
  assigned 
  to 
  them 
  by 
  the 
  

   preceding 
  measurements 
  is 
  given 
  by 
  V'n*=JR0. 
  Leaving 
  

   the 
  results 
  obtained 
  by 
  the 
  third 
  method 
  out 
  of 
  account, 
  the 
  

   values 
  are 
  : 
  — 
  

  

  For 
  the 
  negative 
  ions 
  : 
  0=1500° 
  abs.. 
  mean 
  R 
  = 
  4*55 
  X 
  10 
  3 
  

  

  V'= 
  -083 
  volt. 
  

  

  For 
  the 
  positive 
  ions: 
  d- 
  1100° 
  abs., 
  mean 
  R 
  = 
  3'G7xl0 
  3 
  , 
  

   V'=-050volt. 
  

  

  So 
  Par 
  we 
  have 
  only 
  considered 
  the 
  case 
  in 
  which 
  hmv 
  2 
  is 
  

   small 
  compared 
  with 
  Ve. 
  There 
  is 
  one 
  other 
  case 
  in 
  which 
  

   the 
  formulas 
  assume 
  a 
  very 
  simple 
  form, 
  and 
  that 
  is 
  when 
  

   Y 
  = 
  (>. 
  If 
  V 
  = 
  n. 
  .,,-(), 
  and 
  fand 
  f 
  are 
  infinitesimal, 
  the 
  

   integral 
  (4) 
  reduces 
  to 
  

  

  1= 
  

  

  "Jo 
  

  

  »',,- 
  

  

  -s£ 
  

  

  -•J 
  

  

  2 
  (*»+#*)*/*' 
  * 
  

  

  If 
  I 
  is 
  the 
  value 
  of 
  I 
  when 
  ,v 
  = 
  0, 
  

  

  (12) 
  

  

  Io=^ 
  03) 
  

  

  So 
  that 
  

  

  / 
  .2 
  \ 
  3 
  2 
  

  

  I/r 
  °=(?T?) 
  (14 
  > 
  

  

  Calling 
  I/I 
  , 
  7? 
  and 
  #/z, 
  g 
  we 
  have 
  

  

  p=l/(l+fP* 
  (15) 
  

  

  This 
  curve 
  is 
  shown 
  with 
  q 
  drawn 
  to 
  two 
  different 
  scales 
  

   in 
  fig. 
  6. 
  The 
  general 
  appearance 
  of 
  the 
  curve 
  is 
  similar 
  to 
  

   that 
  which 
  obtains 
  with 
  high 
  voltages 
  except 
  that 
  it 
  is 
  spread 
  

   out 
  much 
  more 
  along 
  the 
  axis 
  of 
  q 
  or 
  x. 
  When 
  V 
  = 
  the 
  

   value 
  of 
  I/I 
  is 
  determined 
  solely 
  by 
  the 
  ratio 
  xjz 
  and 
  is 
  

   independent 
  of 
  the 
  temperature 
  of 
  the 
  strip 
  and 
  the 
  charge 
  

   on 
  the 
  ions. 
  The 
  same 
  is 
  true 
  of 
  I 
  and 
  I 
  separately 
  except 
  

  

  