﻿192 
  Mr. 
  F. 
  E. 
  Wood 
  : 
  A 
  Criticism 
  of 
  

  

  He 
  then 
  states 
  : 
  " 
  Now 
  the 
  variation 
  of 
  the 
  radiation 
  with 
  

   the 
  temperature 
  according 
  to 
  the 
  law 
  given 
  by 
  Boltzmann 
  

   and 
  myself 
  consists 
  of 
  an 
  increase 
  of 
  the 
  total 
  energy 
  in 
  

   proportion 
  to 
  the 
  fourth 
  power 
  of 
  the 
  absolute 
  temperature, 
  

   and 
  a 
  variation 
  of 
  the 
  length 
  of 
  the 
  waves 
  associated 
  with 
  an 
  

   energy 
  quantum 
  and 
  lying 
  between 
  X 
  and 
  X 
  + 
  dX 
  in 
  such 
  a 
  

   way 
  that 
  the 
  corresponding 
  wave-lengths 
  are 
  inversely 
  pro- 
  

   portional 
  to 
  the 
  temperature. 
  So 
  if 
  one 
  plots 
  for 
  any 
  one 
  

   temperature 
  the 
  energy 
  as 
  a 
  function 
  of 
  the 
  wave-length, 
  

   then 
  for 
  any 
  other 
  temperature 
  this 
  curve 
  will 
  be 
  the 
  same 
  

   if 
  the 
  scale 
  units 
  of 
  the 
  graph 
  are 
  so 
  varied 
  that 
  the 
  ordinates 
  

  

  are 
  made 
  smaller 
  in 
  the 
  ratio 
  -^ 
  * 
  and 
  the 
  abscissae 
  are 
  made 
  

  

  larger 
  in- 
  the 
  ratio 
  6. 
  This 
  latter 
  is 
  possible 
  for 
  our 
  value 
  of 
  

   </>(A, 
  6) 
  only 
  when 
  A, 
  and 
  appear 
  in 
  the 
  exponentinl 
  as 
  a 
  

   product 
  XO. 
  Then 
  

  

  o 
  xo> 
  w 
  

  

  where 
  c 
  denotes 
  a 
  constant." 
  

  

  Since 
  I 
  have 
  found 
  no 
  simple 
  proof 
  of 
  (4) 
  from 
  the 
  above 
  

   statements, 
  I 
  propose 
  the 
  following 
  derivation 
  of 
  the 
  form 
  

   of 
  F(\) 
  and 
  J(X) 
  based 
  entirely 
  upon 
  Wien's 
  statements. 
  

   Let 
  Ci 
  be 
  the 
  curve 
  obtained 
  by 
  plotting 
  X 
  as 
  abscissa 
  and 
  

   y 
  = 
  cf>(X, 
  0) 
  as 
  ordinate 
  for 
  an 
  arbitrary 
  temperature 
  1 
  ; 
  then 
  

   the 
  equation 
  of 
  Ci 
  will 
  be 
  

  

  _^> 
  

   y=F(X> 
  "i 
  . 
  

  

  Let 
  C 
  2 
  be 
  a 
  corresponding 
  curve 
  for 
  a 
  temperature 
  6 
  2 
  ; 
  

   then 
  the 
  equation 
  of 
  C 
  2 
  will 
  be 
  

  

  y 
  = 
  F(X)e 
  e 
  * 
  . 
  

   Now 
  Wien's 
  statement, 
  as 
  corrected, 
  is 
  that 
  the 
  trans- 
  

   formation 
  

  

  HI)V, 
  « 
  

  

  *=i 
  x 
  '> 
  ^ 
  

  

  will 
  transform 
  C 
  2 
  into 
  a 
  curve 
  congruent 
  to 
  d. 
  This 
  trans- 
  

   formation 
  gives 
  as 
  the 
  equation 
  of 
  the 
  transform 
  of 
  C 
  2 
  

  

  * 
  This 
  ratio 
  should 
  be 
  -~ 
  ; 
  see 
  Wien, 
  Berlin 
  Sitzungsberichte, 
  vi. 
  p. 
  55 
  

   1893) 
  ; 
  Lorentz, 
  i 
  The 
  Theory 
  of 
  Electrons,' 
  p. 
  74. 
  

  

  