﻿358 
  Prof. 
  Richardson 
  and 
  Mr. 
  Brown 
  on 
  the 
  Kinetic 
  

  

  pressure, 
  since 
  hydrogen 
  is 
  a 
  monovalent 
  element 
  having 
  a 
  

   diatomic 
  molecule 
  in 
  the 
  gaseous 
  state. 
  Thus 
  on 
  this 
  view 
  

   both 
  ve 
  and 
  R 
  are 
  well 
  known 
  physical 
  constants. 
  

  

  The 
  preceding 
  relations 
  may 
  be 
  used 
  to 
  determine 
  the 
  way 
  

   in 
  which 
  the 
  potential 
  of 
  the 
  upper 
  plate 
  varies 
  with 
  the 
  

   time 
  t, 
  during 
  which 
  the 
  current 
  from 
  the 
  hot 
  body 
  has 
  been 
  

   flowing. 
  If 
  C 
  is 
  the 
  capacity 
  of 
  the 
  upper 
  plate 
  and 
  its 
  

   connexions 
  we 
  have 
  

  

  dt 
  

   so 
  that 
  

  

  dV 
  - 
  -v 
  

  

  

  ve 
  

  

  6 
  B0 
  V 
  dV=^dt; 
  

  

  integrating 
  this, 
  

   £=0, 
  we 
  have 
  

  

  subject 
  to 
  the 
  condii 
  

  

  

  ve 
  

  

  or 
  ^ 
  T 
  R0, 
  t\ 
  ve 
  

  

  V= 
  — 
  W 
  

  

  (l 
  + 
  S-fcl) 
  .... 
  (12) 
  

  

  ve 
  

   and 
  . 
  r^dV 
  . 
  //., 
  ve 
  i. 
  \ 
  _ 
  rtX 
  

  

  i 
  = 
  C 
  7«=V( 
  1+ 
  Ktf-60- 
  • 
  ' 
  • 
  (13) 
  

  

  The 
  current, 
  therefore, 
  is 
  always 
  finite 
  and 
  vanishes 
  when 
  

   t=co. 
  Nevertheless 
  the 
  potential 
  is 
  infinite 
  when 
  t 
  is 
  in- 
  

   finite. 
  This 
  approach 
  to 
  an 
  infinite 
  value 
  of 
  the 
  potential 
  is 
  

   not 
  observed 
  in 
  practice. 
  This 
  is 
  probably 
  due 
  to 
  the 
  fact 
  

   that 
  the 
  current 
  falls 
  off' 
  with 
  the 
  time 
  so 
  rapidly 
  that 
  it 
  soon 
  

   becomes 
  comparable 
  with 
  the 
  small 
  leaks 
  inherent 
  in 
  the 
  

   apparatus, 
  and 
  with 
  the 
  discharging 
  current 
  carried 
  by 
  ions 
  

   of 
  the 
  opposite 
  sign. 
  For 
  these 
  reasons 
  a 
  limit 
  is 
  soon 
  fcund 
  

   to 
  the 
  potential 
  to 
  which 
  the 
  upper 
  plate 
  can 
  be 
  charged 
  in 
  

   this 
  way. 
  

  

  The 
  two 
  formula? 
  (11) 
  and 
  (12), 
  which 
  give 
  the 
  current 
  

   as 
  a 
  function 
  of 
  the 
  potential-difference 
  and 
  the 
  potential- 
  

   difference 
  as 
  a 
  function 
  of 
  the 
  time 
  respectively, 
  are 
  not 
  

   independent 
  of 
  one 
  another, 
  since 
  the 
  former 
  can 
  be 
  obtained 
  

   from 
  the 
  latter 
  by 
  differentiation 
  with 
  respect 
  to 
  the 
  time. 
  

   To 
  test 
  the 
  theory, 
  therefore, 
  it 
  is 
  only 
  necessary 
  to 
  examine 
  

   the 
  truth 
  of 
  one 
  of 
  the 
  two 
  fo¥inula5. 
  This 
  has 
  been 
  done 
  

  

  i 
  ve 
  

  

  for 
  the 
  formula 
  log 
  e 
  ~ 
  = 
  — 
  p^V 
  ni 
  a 
  manner 
  which 
  will 
  

  

  now 
  be 
  described. 
  *° 
  v 
  

  

  