﻿Motion 
  of 
  Electrons 
  in 
  Solids, 
  215 
  

  

  The 
  formulae 
  which 
  have 
  now 
  been 
  obtained 
  not 
  only 
  

   enable 
  us 
  to 
  verify 
  this 
  last 
  conclusion, 
  but 
  also 
  give 
  us 
  an 
  

   insight 
  into 
  the 
  mechanism 
  by 
  which 
  equipartition 
  is 
  arrived 
  

   at 
  and 
  maintained. 
  

  

  31. 
  In 
  §§ 
  2-7 
  of 
  Part 
  I. 
  an 
  expression 
  was 
  obtained 
  for 
  c, 
  

   the 
  conductivity, 
  on 
  the 
  supposition 
  that 
  the 
  motion 
  of 
  the 
  

   electrons 
  was 
  checked 
  or 
  modified 
  only 
  by 
  the 
  forces 
  acting 
  

   upon 
  the 
  electrons 
  from 
  the 
  matter. 
  We 
  must 
  now 
  con- 
  

   sider 
  nlso 
  the 
  possibility 
  of 
  the 
  motion 
  of 
  the 
  electron 
  being- 
  

   modified 
  by 
  the 
  pulses 
  and 
  waves 
  of 
  radiation 
  through 
  which 
  

   it 
  passes 
  on 
  its 
  path. 
  If, 
  as 
  will 
  be 
  found 
  to 
  be 
  the 
  case^ 
  

   the 
  partition 
  of 
  radiation 
  is 
  that 
  given 
  by 
  formula 
  (61), 
  the 
  

   expectation 
  of 
  electric 
  force 
  arising 
  from 
  the 
  radiation 
  at 
  

   any 
  point 
  is 
  infinite, 
  or, 
  more 
  strictly, 
  is 
  limited 
  only 
  by 
  the 
  

   imperfections 
  in 
  the 
  reflecting 
  powers 
  of 
  the 
  walls 
  or 
  by 
  the 
  

   imperfect 
  homogeneity 
  (coarse-grainedness) 
  of 
  the 
  aether, 
  

   both 
  of 
  which 
  disturbino- 
  factors 
  we 
  have 
  agreed 
  to 
  neg-lect*. 
  

   Thus 
  the 
  forces 
  produced 
  by 
  the 
  radiation 
  preponderate 
  over 
  

   those 
  originating 
  in 
  the 
  matter. 
  We 
  must 
  still 
  picture 
  the 
  

   electrons 
  as 
  checked 
  in 
  their 
  motion 
  by 
  the 
  molecules 
  of 
  

   matter, 
  but 
  must 
  also 
  regard 
  them 
  as 
  being 
  continually 
  

   buffeted 
  by 
  waves 
  and 
  pulses 
  of 
  free 
  radiation. 
  

  

  32. 
  Whatever 
  forces 
  act, 
  it 
  is 
  clear 
  that 
  the 
  general 
  argu- 
  

   ment 
  of 
  §§ 
  2-7 
  may 
  still 
  be 
  used, 
  provided 
  we 
  take 
  account 
  

   of 
  encounters 
  with 
  pulses 
  and 
  waves 
  of 
  radiation 
  as 
  well 
  as 
  

   with 
  molecules. 
  The 
  value 
  of 
  k 
  will 
  then 
  depend 
  on 
  the 
  

   partition 
  of 
  energy 
  in 
  the 
  aether, 
  but, 
  whatever 
  its 
  value, 
  

   the 
  relation 
  expressed 
  by 
  equation 
  (10) 
  will 
  still 
  be 
  true,. 
  

   namely, 
  

  

  c= 
  %~^. 
  {62} 
  

  

  Kyjnn- 
  

  

  Also, 
  provided 
  this 
  same 
  value 
  of 
  k 
  is 
  still 
  used, 
  equation 
  

   (38) 
  is 
  also 
  true, 
  namely 
  

  

  i, 
  = 
  i,e-<*^-'-^\ 
  (63) 
  

  

  where 
  e^^e-lniK. 
  

  

  These 
  equations 
  are 
  still 
  subject 
  to 
  the 
  limitation 
  that 
  they 
  

   are 
  true 
  only 
  if 
  the 
  time 
  intervals 
  27r/p 
  and 
  ^1 
  — 
  ^2 
  are 
  great 
  

  

  * 
  Let 
  Aq 
  be, 
  roughly 
  speaking, 
  the 
  jrliortest 
  wave-lengtli 
  which 
  can 
  

   exist 
  in, 
  and 
  be 
  retained 
  by, 
  the 
  enclosure. 
  The 
  radiant 
  energy 
  per 
  

   unit 
  voiume 
  obtained 
  by 
  integration 
  of 
  (61) 
  is 
  SttRT/SAq^ 
  Half 
  of 
  

   this 
  must 
  be 
  the 
  mean 
  value 
  of 
  E^Stt, 
  where 
  E 
  is 
  the 
  electric 
  force 
  

   resulting 
  from 
  the 
  presence 
  of 
  the 
  radiation. 
  Thus 
  the 
  values 
  of 
  E 
  

   are 
  arranged 
  (and 
  it 
  can 
  be 
  shq-wn 
  that 
  thev 
  are 
  arranged 
  according 
  to 
  

   Maxwell's 
  law) 
  about 
  the 
  mean 
  square 
  value 
  E'- 
  = 
  327i2RT/3Xo^ 
  

  

  