﻿412 
  On 
  Wood's 
  Criticism 
  of 
  Wien's 
  Distribution 
  Law. 
  

   Hence 
  we 
  must 
  have, 
  by 
  (5), 
  

  

  bPF(\) 
  i 
  r,_ 
  i 
  ,, 
  .i 
  1 
  

  

  ^aV 
  eXP 
  "^V 
  (X) 
  "^ 
  /(aX) 
  H 
  L 
  * 
  (?) 
  

  

  Now 
  k, 
  a, 
  b 
  and 
  X 
  are 
  perfectly 
  independent 
  of 
  a, 
  and 
  

   therefore 
  this 
  transformation 
  cannot 
  be 
  possible 
  for 
  other 
  

   values 
  of 
  the 
  temperature 
  unless 
  

  

  /( 
  a 
  \)=F/(X) 
  (8) 
  

  

  for 
  all 
  values 
  of 
  \. 
  

  

  Hence 
  f{aa'X) 
  = 
  k\a')f(a\) 
  = 
  k\a')k\a)f^\), 
  

  

  and 
  also 
  =k\aa 
  / 
  )f(X). 
  

  

  Therefore 
  k(aa 
  f 
  ) 
  = 
  k(a)k(a'), 
  and 
  thence 
  it 
  is 
  easily 
  shown 
  

   that 
  k(a) 
  must 
  be 
  equal 
  to 
  a 
  log 
  k(e), 
  where 
  e 
  is 
  the 
  base 
  of 
  

   the 
  Napierian 
  logarithms, 
  and 
  k(e) 
  is 
  an 
  unknown 
  constant. 
  

   Iuogk(e) 
  may 
  therefore 
  be 
  put 
  equal 
  to 
  a 
  further 
  constant 
  h. 
  

  

  Therefore 
  f(a\)=a* 
  h 
  f(\), 
  ...'.. 
  (9) 
  

  

  (10) 
  

  

  and 
  f(a\) 
  _/(X) 
  

  

  {a\) 
  A, 
  

  

  whatever 
  a 
  may 
  be, 
  showing 
  that 
  

  

  /(\)/X 
  2A 
  is 
  an 
  absolute 
  constant. 
  

   Hence 
  v 
  is 
  proportional 
  to 
  X 
  , 
  . 
  . 
  . 
  . 
  (11) 
  

  

  making 
  

  

  -3 
  

  

  647T 
  ^^ 
  ' 
  dl> 
  

  

  = 
  N0-%A, 
  m 
  -\ 
  (12) 
  

  

  where 
  a 
  is 
  another 
  absolute 
  constant. 
  

   Altogether 
  

  

  *(X,tf) 
  = 
  N^-l\ 
  lu 
  - 
  I 
  «- 
  tt 
  */', 
  . 
  . 
  . 
  (13) 
  

  

  where 
  g, 
  h, 
  and 
  Z 
  are 
  unknown 
  constants. 
  

  

  Wien 
  introduces 
  the 
  further 
  assumption 
  that 
  the 
  number 
  

   a 
  is 
  equal 
  to 
  k~ 
  2 
  , 
  making 
  

  

  h=-i, 
  (U) 
  

  

  and 
  v 
  2 
  proportional 
  to 
  l/\. 
  In 
  this 
  case 
  the 
  distribution 
  

   law 
  reduces 
  to 
  Wood's 
  form 
  as 
  modified 
  in 
  the 
  first 
  paragraph 
  

   of 
  this 
  paper, 
  namely 
  

  

  4>(\0)=Xge-*\-%e- 
  l/k9 
  (15) 
  

  

  