﻿202 
  A 
  Criticism 
  of 
  Wien's 
  Distribution 
  Law. 
  

  

  6. 
  The 
  inconsistency 
  in 
  the 
  Wien 
  Distribution 
  Law, 
  and 
  

   the 
  revised 
  form. 
  

  

  Let 
  us 
  consider 
  the 
  method 
  by 
  which 
  Wien 
  obtained 
  (3) 
  

   from 
  his 
  two 
  hypotheses. 
  From 
  the 
  first 
  hypothesis 
  one 
  

   can 
  write 
  

  

  v 
  = 
  m(\), 
  (34) 
  

  

  where 
  m 
  is 
  an 
  unknown 
  function 
  of 
  X 
  *. 
  

  

  If 
  e=p{\) 
  . 
  , 
  . 
  . 
  . 
  . 
  (35) 
  

  

  denote 
  the 
  intensity 
  of 
  radiation 
  produced 
  by 
  a 
  molecule 
  

   giving 
  off 
  waves 
  of 
  length 
  X, 
  then 
  by 
  using 
  (34), 
  (35), 
  and 
  

   Wien's 
  second 
  hypothesis 
  

  

  A- 
  2 
  m2(A) 
  

  

  <£(X, 
  0) 
  = 
  k 
  1 
  p{\)m*(\)m'(\)e 
  e 
  , 
  

  

  where 
  k 
  x 
  and 
  k 
  2 
  are 
  constants 
  and 
  m'(X) 
  = 
  -3— 
  m(X). 
  So 
  

   Wien 
  has 
  written 
  for 
  brevity 
  ^ 
  

  

  F(X)=/: 
  1/ 
  o(X)m 
  2 
  (X)m'(X); 
  . 
  . 
  . 
  (36) 
  

  

  f(\) 
  = 
  -k 
  2 
  m\\) 
  (37) 
  

  

  Now, 
  from 
  (37) 
  and 
  (15) 
  

  

  M»«\/g; 
  (38) 
  

  

  and 
  from 
  (28), 
  (29), 
  (33), 
  and 
  (35) 
  

  

  PW 
  = 
  £, 
  (39) 
  

  

  where 
  a 
  is 
  a 
  constant. 
  Substituting 
  (38) 
  and 
  (39) 
  in 
  (36) 
  

   gives 
  

  

  F(X) 
  = 
  — 
  (40) 
  

  

  where 
  A 
  is 
  a 
  constant 
  depending 
  upon 
  the 
  constants 
  a, 
  c, 
  & 
  1? 
  

   and 
  k 
  2 
  . 
  But 
  (40) 
  is 
  inconsistent 
  with 
  (15'). 
  Therefore, 
  

   the 
  Wien 
  formula 
  is 
  inconsistent 
  with 
  other 
  results 
  obtained 
  

   from 
  the 
  same 
  hypotheses. 
  

  

  Now 
  by 
  the 
  Maxwell 
  law 
  t, 
  the 
  number 
  of 
  molecules 
  

   having 
  velocities 
  between 
  v 
  and 
  v 
  + 
  dv 
  is 
  

  

  4 
  ^v 
  2 
  - 
  

  

  ^~e 
  « 
  2 
  dv, 
  (41) 
  

  

  * 
  However, 
  the 
  form 
  of 
  m(\) 
  has 
  already 
  "been 
  obtained 
  in 
  this 
  article 
  

   from 
  the 
  relation 
  A0=a 
  const., 
  and 
  certain 
  theorems 
  in 
  the 
  kinetic 
  theory 
  

   of 
  gases 
  ; 
  see 
  Theorem 
  IV. 
  That 
  this 
  form 
  agrees 
  with 
  the 
  form 
  obtained 
  

   by 
  Wien's 
  method 
  is 
  an 
  agreeable 
  fact. 
  

  

  f 
  Scientific 
  Papers 
  of 
  James 
  Clerk 
  Maxwell, 
  i. 
  p. 
  381. 
  

  

  