﻿894 
  Prof. 
  0. 
  W. 
  Richardson 
  on 
  the 
  Kinetic 
  

  

  The 
  experiments 
  of 
  Richardson 
  and 
  Brown 
  (loc. 
  cit.) 
  have 
  

   shown 
  that 
  in 
  the 
  case 
  of 
  hot 
  platinum 
  under 
  certain 
  condi- 
  

   tions 
  the 
  normal 
  velocity 
  component 
  w 
  Q 
  is 
  distributed 
  among 
  

   the 
  emitted 
  ions 
  according 
  to 
  Maxwell's 
  law, 
  and 
  the 
  value 
  

   of 
  the 
  constant 
  which 
  determines 
  the 
  mean 
  kinetic 
  energy 
  is 
  

   the 
  same 
  as 
  that 
  for 
  a 
  molecule 
  of 
  a 
  gas 
  at 
  the 
  temperature 
  

   of 
  the 
  metal. 
  Under 
  these 
  conditions 
  it 
  seems 
  likely 
  that 
  

   the 
  same 
  law 
  will 
  hold 
  for 
  the 
  component 
  of 
  velocity 
  parallel 
  

   to 
  the 
  surface, 
  and 
  it 
  is 
  interesting 
  to 
  examine 
  the 
  conse- 
  

   quences 
  of 
  this 
  hypothesis. 
  If 
  Maxwell's 
  law 
  holds 
  we 
  have 
  

  

  where 
  

  

  and 
  

  

  ,y 
  v 
  /k)ll\ 
  

  

  £ 
  mx 
  i-fonuo 
  a 
  

  

  e 
  

  

  -/. 
  

  

  1,1 
  ir. 
  

  

  where 
  m 
  IS 
  the 
  mass 
  of 
  the 
  ions 
  and 
  ; 
  , 
  ; 
  /' 
  their 
  mean 
  trans- 
  

   lational 
  kinetic 
  energy. 
  ( 
  >n 
  this 
  view 
  the 
  number 
  which 
  

   pass 
  through 
  fche 
  -lit 
  of 
  width 
  f 
  is 
  therefore 
  

  

  ■afe) 
  1 
  aA***" 
  \ 
  , 
  llt 
  ;: 
  : 
  

  

  We 
  can 
  test 
  the 
  correctness 
  of 
  the 
  substitutions 
  which 
  

   have 
  been 
  made 
  by 
  calculating 
  the 
  total 
  number 
  of 
  ions 
  

   which 
  reach 
  the 
  lower 
  plate. 
  This 
  will 
  evidently 
  be 
  

  

  H-f/2 
  

  

  9 
  n, 
  (km)H 
  ( 
  

  

  J 
  -51' 
  J,, 
  J- 
  

  

  —hmu, 
  t 
  

  

  du 
  Q 
  e 
  

  

  This, 
  as 
  it 
  should 
  be, 
  is 
  equal 
  to 
  riy 
  the 
  number 
  of 
  ions 
  emitted 
  

   by 
  the 
  strip. 
  

  

  The 
  integral 
  (I) 
  cannot 
  be 
  evaluated 
  in 
  finite 
  terms, 
  and 
  

   there 
  is 
  no 
  single 
  method 
  of 
  approximation 
  which 
  can 
  be 
  

   made 
  to 
  cover 
  the 
  whole 
  range 
  of 
  experimental 
  conditions. 
  

   There 
  are, 
  however, 
  two 
  special 
  cases 
  in 
  which 
  the 
  expression 
  

   assumes 
  a 
  very 
  simple 
  form. 
  In 
  both 
  of 
  these 
  f 
  and 
  f 
  are 
  

   regarded 
  as 
  very 
  small 
  quantities. 
  In 
  addition, 
  Ye 
  is 
  large 
  

   compared 
  with 
  ^mw 
  Q 
  2 
  in 
  the 
  first 
  case 
  and 
  is 
  equal 
  to 
  zero 
  in 
  

   the 
  second. 
  AVe 
  shall 
  consider 
  first 
  the 
  case 
  in 
  which 
  Ve 
  is 
  

   great 
  compared 
  with 
  ^mw 
  2 
  . 
  

  

  It 
  will 
  be 
  observed 
  that 
  Ve 
  can 
  never 
  be 
  great 
  compared 
  

  

  