﻿Wiens 
  Distribution 
  Law. 
  195 
  

  

  of 
  the 
  absolute 
  temperature. 
  Another 
  form 
  of 
  the 
  Stefan- 
  

   Boltzmann 
  law 
  is 
  that 
  yfr(0) 
  = 
  C6 
  4: 
  , 
  where 
  ty(d) 
  is 
  the 
  total 
  

   radiation, 
  and 
  C 
  is 
  a 
  constant. 
  

  

  Drude 
  * 
  attempts 
  to 
  prove 
  a 
  statement 
  that 
  is 
  equivalent 
  

   to 
  (5), 
  namely 
  that 
  

  

  ^=/(^x 
  (I?) 
  

  

  where 
  / 
  is 
  an 
  unknown 
  function 
  of 
  \6 
  alone. 
  He 
  states 
  

   that 
  (17) 
  follows 
  from 
  

  

  ^=j;^ 
  ( 
  x*), 
  .... 
  (is) 
  

  

  an 
  equation 
  which 
  is 
  an 
  immediate 
  consequence 
  of 
  the 
  

   definition 
  of 
  TJr{0), 
  viz. 
  

  

  ^(<9)=t 
  <j>{\,0)d\. 
  

  

  j; 
  

  

  Jo 
  

   Now 
  (17) 
  cannot 
  follow 
  from 
  (18) 
  unless 
  ■ 
  JL 
  ' 
  = 
  a 
  const. 
  ; 
  

  

  since 
  this 
  is 
  true, 
  by 
  the 
  Stefan-Boltzmann 
  law, 
  Drude's 
  

   conclusion 
  is 
  not 
  impossible. 
  Suppose 
  then 
  that 
  

  

  ^^(\0) 
  = 
  aconst. 
  . 
  . 
  . 
  (19) 
  

  

  Now 
  (17) 
  does 
  not 
  follow 
  from 
  (19) 
  alone, 
  as 
  the 
  following 
  

   example 
  will 
  show. 
  Let 
  <j>(\, 
  6) 
  = 
  1 
  2 
  ; 
  then 
  n 
  b 
  

   is 
  not 
  a 
  function 
  of 
  \6 
  alone 
  ; 
  however, 
  

  

  _/(X) 
  

  

  Even 
  if 
  we 
  put 
  <p(\ 
  6) 
  =Y(\)e 
  d 
  , 
  it 
  is 
  still 
  possible 
  to 
  

   choose 
  F(\) 
  and 
  /(A) 
  so 
  that 
  (19) 
  is 
  satisfied, 
  while 
  (17) 
  is 
  

   not. 
  

  

  For 
  if 
  F(A) 
  =X 
  3 
  , 
  /(\)=X, 
  then 
  ^ 
  ^ 
  is 
  not 
  a 
  function 
  

   of 
  \0 
  while 
  u 
  

  

  i 
  

  

  p*-id(X0) 
  = 
  6L 
  

  

  * 
  Lehrbuch 
  dei' 
  Optik, 
  p. 
  480 
  (1900). 
  This 
  treatment 
  is 
  repeated 
  in 
  

   the 
  second 
  edition. 
  

  

  t 
  Pierce, 
  * 
  A 
  Short 
  Table 
  of 
  Integrals,' 
  formulas 
  480 
  and 
  493. 
  

  

  