﻿196 
  Mr. 
  F. 
  E. 
  Wood 
  : 
  A 
  Criticism 
  of 
  

  

  Therefore, 
  Drude 
  has 
  not 
  proved 
  the 
  displacement 
  law; 
  

   if, 
  however, 
  (17) 
  be 
  regarded 
  as 
  proved, 
  then 
  the 
  remainder 
  

   of 
  Drude' 
  s 
  argument 
  for 
  proving 
  the 
  distribution 
  law 
  can 
  be 
  

   made 
  rigorous 
  *. 
  

  

  L6t 
  ^^W*)., 
  .... 
  (20) 
  

  

  where 
  F(X),/(\), 
  and 
  <E>(\#) 
  are 
  unknown 
  functions. 
  Put 
  

   then 
  (20) 
  becomes 
  

  

  FW=^,/(X) 
  = 
  - 
  B 
  f) 
  ; 
  

  

  BW 
  i 
  

  

  A(A>" 
  s^*(X0) 
  (21) 
  

  

  Now 
  if 
  X 
  be 
  replaced 
  by 
  kX 
  and 
  ^by 
  7, 
  the 
  right-hand 
  

   member 
  of 
  (21) 
  is 
  unchanged, 
  and 
  therefore 
  

  

  B(\) 
  B(A-A) 
  

  

  A{X)e 
  A 
  * 
  ==A(kX)e 
  he 
  (22) 
  

  

  B(A) 
  B(AA) 
  

  

  If 
  the 
  expressions 
  e 
  A<? 
  , 
  e 
  Afl 
  be 
  expanded, 
  (22) 
  becomes 
  

  

  or 
  

  

  [A(\) 
  -A(#X)] 
  + 
  ^[A(\)B(X)-A(ife\)B(*X)] 
  + 
  ... 
  = 
  0. 
  (23) 
  

  

  Since 
  (23) 
  is 
  an 
  identity 
  in 
  0, 
  

  

  A{X) 
  = 
  A{kX); 
  (24) 
  

  

  and 
  since 
  (24) 
  is 
  an 
  identity 
  in 
  k, 
  A(A.) 
  = 
  C 
  where 
  C 
  is 
  a 
  

   constant. 
  Also 
  from 
  (23) 
  

  

  A(X)B(\) 
  -A(kX)B(kX) 
  = 
  0, 
  

  

  from 
  which 
  B(\) 
  = 
  c, 
  where 
  c 
  is 
  a 
  constant; 
  so 
  

  

  I'M- 
  51, 
  /W=J- 
  

  

  * 
  This 
  derivation 
  of 
  the 
  form 
  of 
  F(A) 
  and 
  /(X) 
  is 
  due 
  to 
  Professor 
  

   Moulton, 
  of 
  Northwestern 
  University. 
  

  

  