﻿Energy 
  of 
  Negative 
  Electrons 
  emitted 
  by 
  Hot 
  Bodies. 
  373 
  

  

  of 
  this 
  curve 
  is 
  that 
  the 
  current 
  Cv 
  corresponding 
  to 
  any 
  

   potential 
  Y 
  is 
  equal 
  to 
  e 
  the 
  charge 
  on 
  an 
  ion 
  multiplied 
  by 
  

   the 
  number 
  of 
  ions 
  shot 
  off 
  in 
  unit 
  time 
  for 
  which 
  \mv? 
  is 
  

   greater 
  than 
  eV. 
  Calling 
  this 
  number 
  N 
  ( 
  v) 
  we 
  have 
  then 
  

   Cy 
  = 
  eN 
  ( 
  v). 
  But 
  if 
  the 
  number 
  of 
  ions 
  emitted 
  per 
  second 
  

   for 
  which 
  the 
  normal 
  component 
  of 
  the 
  energy 
  lies 
  between 
  

   eV 
  and 
  <?(V 
  + 
  <rZY), 
  (i. 
  e. 
  between 
  j^mii 
  2 
  and 
  \ 
  mu 
  2 
  + 
  mudu) 
  is 
  

   denoted 
  by 
  <?N'( 
  e 
  v)^V 
  we 
  shall 
  have 
  

  

  JQO 
  

   W 
  (eY 
  )dY. 
  

   eV 
  

  

  So 
  that 
  

  

  To 
  obtain 
  the 
  number 
  which 
  have 
  velocity 
  components 
  per- 
  

   pendicular 
  to 
  the 
  emitting 
  surface 
  lying 
  between 
  u 
  and 
  u 
  + 
  du 
  

   we 
  have 
  simply 
  to 
  replace 
  eV 
  by 
  its 
  kinetic 
  equivalent 
  ^mu 
  2 
  . 
  

   We 
  thus 
  get 
  

  

  muN'(^mu 
  2 
  )du= 
  -?==■ 
  dY. 
  

  

  The 
  number 
  of 
  particles 
  whose 
  normal 
  velocity 
  or 
  energy 
  

   lies 
  between 
  given 
  limits 
  can 
  thus 
  always 
  be 
  calculated 
  from 
  

   the 
  tangent 
  to 
  the 
  CV 
  curve. 
  

  

  If 
  we 
  apply 
  this 
  method 
  to 
  the 
  experimental 
  numbers 
  

  

  obtained 
  for 
  platinum 
  in 
  what 
  we 
  have 
  called 
  the 
  normal 
  

  

  condition, 
  the 
  function 
  giving 
  the 
  number 
  having 
  energy 
  

  

  between 
  assigned 
  limits 
  is 
  that 
  required 
  by 
  Maxwell's 
  law. 
  

  

  This 
  is 
  sufficiently 
  obvious, 
  since 
  otherwise 
  the 
  equations 
  

  

  obtained 
  previously 
  would 
  not 
  have 
  been 
  satisfied. 
  In 
  the 
  

  

  case 
  where 
  the 
  electrons 
  were 
  emitted 
  from 
  platinum 
  covered 
  

  

  with 
  lime 
  the 
  CY 
  curve 
  lost 
  its 
  exponential 
  character 
  and 
  

  

  became 
  a 
  straight 
  line 
  at 
  high 
  temperatures. 
  In 
  this 
  case 
  

  

  dC 
  ' 
  

  

  -jyr 
  is 
  constant, 
  so 
  that 
  the 
  number 
  of 
  particles 
  whose 
  

  

  energy 
  lies 
  between 
  x 
  and 
  x 
  + 
  dx 
  is 
  proportional 
  to 
  dx 
  and 
  

   independent 
  of 
  x, 
  or, 
  in 
  other 
  words, 
  the 
  number 
  of 
  particles 
  

   having 
  an 
  amount 
  of 
  \mu 
  2 
  lying 
  within 
  a 
  given 
  range 
  is 
  

   independent 
  of 
  the 
  amount 
  itself. 
  This 
  is 
  only 
  true 
  within 
  

   certain 
  limits 
  ; 
  in 
  the 
  case 
  referred 
  to 
  the 
  number 
  of 
  particles 
  

   which 
  had 
  an 
  amount 
  of 
  energy 
  greater 
  than 
  that 
  which 
  

   corresponds 
  to 
  1*22 
  volts 
  was 
  too 
  small 
  to 
  be 
  detected. 
  

  

  The 
  measurements 
  that 
  we 
  have 
  made 
  in 
  the 
  cases 
  in 
  

   which 
  the 
  distribution 
  of 
  energy 
  is 
  abnormal 
  are 
  too 
  meagre 
  

  

  