﻿200 
  Mr. 
  F. 
  E. 
  Wood 
  : 
  A 
  Criticism 
  of 
  

  

  temperature 
  be 
  raised 
  to 
  2 
  an( 
  i 
  that 
  the 
  corresponding 
  curve 
  

   be 
  plotted. 
  From 
  the 
  above 
  theorems 
  and 
  the 
  relation 
  

   X0 
  = 
  const., 
  it 
  follows 
  that 
  the 
  molecules 
  which 
  produced 
  

  

  waves 
  of 
  length 
  \ 
  x 
  will 
  now 
  produce 
  waves 
  of 
  length 
  ~ 
  X 
  l5 
  

  

  and 
  those 
  which 
  produeed 
  waves 
  of 
  length 
  X 
  1 
  -^-8k 
  1 
  will 
  now 
  

  

  produce 
  waves 
  of 
  length 
  ~ 
  (X 
  a 
  + 
  h\ 
  x 
  ). 
  Therefore 
  the 
  number 
  

  

  of 
  molecules 
  producing 
  waves 
  with 
  lengths 
  in 
  an 
  interval 
  

  

  with 
  width 
  S\ 
  x 
  about 
  A 
  : 
  in 
  a 
  gas 
  at 
  a 
  temperature 
  6 
  1 
  is 
  equal 
  

  

  to 
  the 
  number 
  producing 
  waves 
  with 
  lengths 
  in 
  an 
  interval 
  

  

  

  

  with 
  width 
  -^h\i 
  about 
  ^Xr 
  when 
  the 
  temperature 
  is 
  2 
  . 
  

  

  Now 
  <£(X 
  1? 
  ^ 
  1 
  )8\ 
  1 
  is 
  the 
  intensity 
  of 
  radiation 
  carried 
  by 
  

  

  waves 
  with 
  lengths 
  in 
  the 
  interval 
  X^X;^;^ 
  + 
  S\j 
  for 
  — 
  Xi 
  

  

  1 
  \ 
  

  

  and 
  <j)l 
  TpXi, 
  #2)^^i 
  is 
  the 
  intensity 
  of 
  radiation 
  carried 
  by 
  

   \a 
  2 
  J 
  u 
  2 
  q 
  q 
  

  

  the 
  waves 
  with 
  lengths 
  in 
  the 
  interval 
  t^X 
  1 
  <X^^(X 
  1 
  + 
  h\^)-~ 
  . 
  

  

  2 
  / 
  \6 
  

  

  When 
  1 
  and 
  2 
  are 
  given, 
  (b(k^ 
  0i)&\i 
  and 
  $( 
  7r-^i, 
  ^2/^^i 
  

  

  will 
  be 
  called 
  corresponding 
  radiation 
  elements. 
  In 
  general, 
  

   two 
  corresponding 
  radiation 
  elements 
  are 
  not 
  equal, 
  since 
  

   the 
  total 
  radiation 
  increases 
  when 
  the 
  temperature 
  is 
  increased 
  

   (Stefan-Boltzmann 
  law). 
  

  

  The 
  intensity 
  of 
  radiation 
  produced 
  by 
  a 
  molecule 
  is 
  a 
  

   function 
  of 
  the 
  velocity 
  of 
  that 
  molecule 
  ; 
  then 
  

  

  e=9(J), 
  (29) 
  

  

  where 
  e 
  is 
  the 
  intensity 
  of 
  radiation 
  produced 
  by 
  a 
  molecule 
  

   with 
  velocity 
  v 
  and 
  g 
  is 
  an 
  unknown 
  function 
  of 
  v 
  2 
  alone. 
  

   Therefore, 
  using 
  Wien's 
  second 
  hypothesis, 
  

  

  where 
  N 
  is 
  the 
  number 
  of 
  molecuJes 
  producing 
  waves 
  with 
  

   lengths 
  in 
  the 
  interval 
  X 
  1 
  <X<X 
  1 
  + 
  ^X 
  1 
  , 
  and 
  uj 
  and 
  v 
  2 
  are 
  the 
  

   velocities 
  of 
  these 
  molecules 
  when 
  the 
  temperature 
  is 
  L 
  and 
  

   # 
  2 
  respectively. 
  

  

  It 
  follows 
  from 
  (30) 
  and 
  Theorem 
  III. 
  that 
  

  

  </)(X!, 
  e^sXj 
  __g(fc0i) 
  „ 
  n 
  

  

  