﻿194 
  Mr. 
  F. 
  E. 
  Wood 
  : 
  A 
  Criticism 
  of 
  

  

  Suppose 
  first 
  \k\ 
  <1 
  ; 
  then 
  the 
  A 
  function 
  has 
  the 
  same 
  

  

  value 
  at 
  the 
  points 
  as, 
  kx, 
  k 
  n 
  x, 
  . 
  . 
  . 
  This 
  set 
  of 
  points 
  

  

  converges 
  to 
  the 
  point 
  # 
  = 
  0, 
  and 
  therefore 
  A(#) 
  =lim 
  A(#) 
  ; 
  

   but 
  since 
  A(x) 
  is 
  continuous 
  x=0 
  

  

  lira 
  A(x) 
  = 
  A(0), 
  and 
  A(x) 
  = 
  A(0). 
  

  

  x=0 
  

  

  This 
  is 
  true 
  for 
  every 
  value 
  of 
  a?, 
  and 
  therefore 
  A(x) 
  is 
  a 
  

   constant. 
  

  

  Now 
  suppose 
  \k\ 
  > 
  1 
  ; 
  make 
  the 
  transformation 
  kx=y 
  in 
  

  

  (14), 
  then 
  (14) 
  becomes 
  A(y) 
  = 
  A\jr\ 
  and 
  therefore 
  the 
  

  

  function 
  has 
  the 
  same 
  value 
  at 
  the 
  set 
  of 
  points 
  y, 
  j, 
  . 
  . 
  . 
  . 
  

  

  ~, 
  . 
  . 
  . 
  which 
  converges 
  to 
  the 
  point 
  # 
  = 
  0, 
  and 
  therefore, 
  by 
  

  

  the 
  same 
  reasoning 
  as 
  for 
  \k\ 
  < 
  1, 
  A(x) 
  is 
  a 
  constant. 
  ~ 
  

  

  Therefore 
  A(#) 
  = 
  C 
  in 
  every 
  case, 
  and 
  by 
  (13) 
  #(o?) 
  = 
  — 
  , 
  

  

  which 
  proves 
  the 
  lemma. 
  

  

  Equations 
  (10) 
  and 
  (11) 
  are 
  of 
  the 
  form 
  (12), 
  where 
  

  

  #= 
  ~ 
  and 
  therefore 
  

  

  fw=t> 
  < 
  15 
  > 
  

  

  FW 
  = 
  § 
  (15') 
  

  

  These 
  values, 
  substituted 
  in 
  (3), 
  give 
  Wien's 
  distribution 
  

   law. 
  

  

  3. 
  A 
  criticism 
  of 
  Drude* 
  s 
  proof 
  of 
  the 
  Wien 
  Displacement* 
  

   and 
  Distribution 
  Laws. 
  

  

  Equation 
  (5) 
  is 
  the 
  Wien 
  displacement 
  law 
  and 
  is 
  

   generally 
  derived 
  from 
  the 
  Stefan-Boltzmnnn 
  law, 
  which 
  

   states 
  that 
  

  

  .[ 
  

  

  d\=a 
  const., 
  .... 
  (16) 
  

  

  or 
  that 
  the 
  total 
  radiation 
  varies 
  directly 
  as 
  the 
  fourth 
  power 
  

  

  * 
  The 
  relation 
  X0 
  = 
  a 
  const, 
  is 
  sometimes 
  known 
  as 
  the 
  Wien 
  dis- 
  

   placement 
  law, 
  and 
  sometimes 
  as 
  a 
  part 
  of 
  that 
  law, 
  but 
  in 
  this 
  paper 
  

   will 
  be 
  regarded 
  as 
  a 
  distinct 
  law. 
  The 
  equation 
  X#=a 
  const, 
  of 
  itself 
  

   means 
  nothing, 
  since 
  X 
  and 
  i) 
  are 
  independent. 
  The 
  equation 
  is 
  a 
  short- 
  

   hand 
  way 
  of 
  stating 
  that 
  the 
  radiation 
  for 
  X=X 
  2 
  , 
  8 
  — 
  6 
  l 
  will 
  become 
  the 
  

   radiation 
  for 
  X 
  = 
  X 
  2 
  when 
  6=6 
  2 
  , 
  where 
  X 
  1 
  1 
  = 
  X 
  2 
  #2. 
  Wien 
  obtains 
  this 
  

   relation 
  by 
  actually 
  determining 
  the 
  change 
  of 
  wave-length, 
  the 
  tem- 
  

   perature 
  being 
  increased 
  by 
  an 
  adiabatic 
  compression 
  of 
  the 
  gas. 
  No 
  

   criticism 
  of 
  the 
  derivation 
  of 
  this 
  relation 
  is 
  intended 
  in 
  this 
  article. 
  

  

  