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  Kinetic 
  Energy 
  of 
  Negative 
  Electrons 
  emitted 
  by 
  Hot 
  Bodies. 
  

  

  the 
  emitted 
  particles 
  is 
  that 
  which 
  has 
  been 
  deduced 
  from 
  

   these 
  experiments. 
  

  

  This 
  method 
  does 
  not 
  enable 
  ns 
  to 
  determine 
  by 
  experiment 
  

   the 
  distribution 
  of 
  velocity 
  among 
  the 
  electrons 
  in 
  a 
  closed 
  

   space 
  including 
  a 
  piece 
  of 
  hot 
  metal 
  when 
  the 
  final 
  state 
  

   of 
  statistical 
  equilibrium 
  has 
  been 
  reached. 
  All 
  that 
  we 
  are 
  

   able 
  to 
  do 
  is 
  to 
  examine 
  the 
  distribution 
  of 
  velocity 
  among 
  the 
  

   particles 
  emitted 
  from 
  the 
  hot 
  metal 
  at 
  any 
  instant, 
  and 
  to 
  

   show 
  that 
  in 
  the 
  case 
  of 
  platinum 
  at 
  least 
  the 
  results 
  are 
  con- 
  

   sistent 
  with 
  what 
  would 
  be 
  required 
  if 
  in 
  the 
  state 
  of 
  statistical 
  

   equilibrium 
  the 
  distribution 
  of 
  velocity 
  among 
  the 
  electrons 
  

   outside 
  the 
  metal 
  were 
  determined 
  by 
  Maxwell's 
  law. 
  This 
  

   leads 
  to 
  a 
  strong 
  presumption 
  that 
  the 
  distribution 
  of 
  velocity 
  

   among 
  the 
  external 
  electrons 
  in 
  the 
  steady 
  state 
  would 
  be 
  

   given 
  by 
  Maxwell's 
  law, 
  with 
  the 
  mean 
  translational 
  kinetic 
  

   energy 
  identical 
  with 
  that 
  of 
  the 
  molecules 
  of 
  a 
  gas 
  at 
  the 
  

   temperature 
  of 
  the 
  metal. 
  This 
  involves 
  the 
  further 
  conclusion 
  

   that 
  the 
  distribution 
  of 
  velocity 
  among 
  the 
  free 
  electrons 
  

   inside 
  the 
  metal 
  is 
  also 
  determined 
  by 
  Maxwell's 
  law. 
  

   For 
  if 
  the 
  free 
  electrons 
  inside 
  the 
  metal 
  are 
  free 
  in 
  the 
  

   sense 
  of 
  the 
  kinetic 
  theory 
  of 
  gases, 
  the 
  only 
  difference 
  

   between 
  those 
  inside 
  and 
  those 
  outside 
  the 
  metal 
  will 
  be 
  due 
  

   to 
  the 
  difference 
  of 
  their 
  potential 
  energy. 
  There 
  is 
  a 
  well- 
  

   known 
  theorem 
  in 
  the 
  kinetic 
  theory 
  of 
  gases 
  which 
  proves 
  

   that 
  when 
  two 
  regions 
  of 
  the 
  same 
  gas 
  at 
  the 
  same 
  temperature 
  

   are 
  compared, 
  the 
  regions 
  being 
  such 
  that 
  the 
  mean 
  potential 
  

   energy 
  of 
  the 
  molecules 
  is 
  different 
  in 
  the 
  two 
  regions, 
  the 
  

   mean 
  translational 
  kinetic 
  energy 
  is 
  the 
  same 
  in 
  both, 
  and 
  is 
  

   distributed 
  according 
  to 
  the 
  same 
  law. 
  The 
  only 
  effect 
  of 
  

   the 
  difference 
  of 
  potential 
  energy 
  is 
  to 
  make 
  the 
  concentration 
  

   of 
  the 
  molecules 
  different 
  in 
  the 
  two 
  regions. 
  Applying 
  this 
  

   theorem 
  to 
  the 
  case 
  of 
  the 
  electrons 
  inside 
  and 
  outside 
  a 
  

   piece 
  of 
  hot 
  metal, 
  it 
  follows 
  that 
  the 
  mean 
  translational 
  

   energy 
  and 
  the 
  way 
  in 
  which 
  it 
  is 
  distributed 
  among 
  the 
  

   electrons 
  will 
  be 
  the 
  same 
  both 
  inside 
  and 
  outside 
  the 
  metal. 
  

   The 
  conclusion 
  that 
  the 
  average 
  translational 
  kinetic 
  energy 
  

   and 
  the 
  law 
  of 
  distribution 
  of 
  velocity 
  of 
  the 
  electrons 
  inside 
  

   a 
  metal 
  are 
  identical 
  with 
  those 
  among 
  the 
  molecules 
  of 
  a 
  

   gas 
  at 
  the 
  same 
  temperature 
  as 
  that 
  of 
  the 
  metal 
  is 
  of 
  great 
  

   importance 
  in 
  the 
  electron 
  theory 
  of 
  metallic 
  conduction 
  and 
  

   thermal 
  radiation. 
  

  

  Princeton, 
  N. 
  J., 
  June 
  5, 
  1908. 
  

  

  