﻿Motion 
  of 
  Electrons 
  in 
  Solids. 
  213 
  

  

  From 
  the 
  law 
  of 
  distribution 
  of 
  velocities 
  there 
  is 
  known 
  

   to 
  be 
  no 
  correlation 
  between 
  the 
  velocity-components 
  of 
  two 
  

   different 
  electrons, 
  either 
  at 
  the 
  same 
  or 
  at 
  different 
  instants. 
  

   Hence 
  in 
  equation 
  (56), 
  the 
  whole 
  value 
  of 
  7/ 
  must 
  arise 
  

   from 
  terms 
  in 
  which 
  the 
  two 
  electrons 
  concerned 
  are 
  iden- 
  

   tical 
  : 
  we 
  must 
  haA^e 
  

  

  29. 
  In 
  dealing 
  with 
  radiation 
  of 
  great 
  w^ave-length 
  we 
  

  

  neglect 
  jt?/y, 
  and 
  therefore 
  replace 
  pit^-^t^-^^-^^^^^^) 
  

   hjpih^to), 
  \ 
  V 
  / 
  

  

  The 
  value 
  of 
  7/ 
  now 
  becomes 
  

  

  7/ 
  — 
  i 
  j 
  X 
  e^UiU2 
  cos 
  p(^i-- 
  ^2) 
  ^h 
  ^^25 
  

  

  Jo 
  Jo 
  

  

  (58) 
  

  

  and 
  this 
  is 
  readily 
  seen 
  to 
  be 
  identical 
  with 
  the 
  value 
  obtained 
  

   in 
  our 
  previous 
  analysis 
  for 
  the 
  corresponding 
  quantity 
  *, 
  as 
  

   of 
  course 
  it 
  ought 
  to 
  be. 
  

  

  Formula 
  (58), 
  in 
  which 
  pJY 
  is 
  neglected, 
  may 
  also 
  be 
  

   interpreted 
  in 
  another 
  way 
  : 
  it 
  is 
  a 
  formula 
  for 
  radiation 
  of 
  

   all 
  wave-lengths, 
  in 
  which 
  the 
  finiteness 
  of 
  the 
  velocity 
  of 
  

   propagation 
  is 
  neglected. 
  It 
  is 
  of 
  interest 
  to 
  notice 
  that 
  

   from 
  formula 
  (58) 
  which 
  had 
  already 
  been 
  obtained, 
  we 
  

   could 
  have 
  deduced 
  the 
  more 
  general 
  formula 
  (57) 
  by 
  an 
  

   appeal 
  to 
  the 
  principle 
  of 
  relativity. 
  

  

  Still 
  another 
  meaning 
  can 
  be 
  given 
  to 
  formula 
  (58) 
  : 
  it 
  is 
  

   a 
  general 
  formula 
  for 
  radiation 
  of 
  all 
  wave-lengths, 
  in 
  which 
  

   the 
  Doppler-effect 
  is 
  neglected. 
  In 
  all 
  observed 
  radiation 
  

   the 
  influence 
  of 
  the 
  Doppler-effect 
  on 
  the 
  partition 
  of 
  energy 
  

   in 
  the 
  spectrum 
  is 
  insignificant 
  t, 
  so 
  that 
  w^e 
  may 
  take 
  (58) 
  

   to 
  be 
  a 
  formula 
  for 
  radiation 
  of 
  all 
  wave-lengths 
  under 
  

   natural 
  conditions. 
  

  

  Formula 
  (58) 
  is 
  independent 
  of 
  the 
  direction 
  V, 
  m\ 
  n' 
  . 
  

   Adding 
  to 
  it 
  the 
  corresponding 
  quantities 
  which 
  originate 
  in 
  

   the 
  velocities 
  of 
  the 
  electrons 
  parallel 
  to 
  0^ 
  and 
  0-2', 
  we 
  obtain, 
  

   as 
  in 
  Part 
  I., 
  for 
  the 
  total 
  emission 
  per 
  unit 
  volume 
  in 
  time 
  f 
  , 
  

  

  ;3=0 
  

  

  = 
  00 
  t 
  t 
  

  

  j 
  ?M 
  \ 
  \ 
  Xe'^(uiU2 
  + 
  ViV2-\-iOiW2) 
  cosp(ti 
  — 
  t2)dtidt2\dp* 
  (59) 
  

  

  * 
  The 
  present 
  ;?^yp2 
  is 
  identical 
  with 
  the 
  previous 
  Ap^-\-'Bp'^. 
  

  

  t 
  At 
  0^ 
  C. 
  it/\= 
  ^^'^0 
  ; 
  in 
  the 
  sun, 
  at 
  6000- 
  C, 
  m/V= 
  ^ 
  Ao- 
  It 
  is 
  

   easily 
  .shown 
  that 
  the 
  error 
  introduced 
  by 
  neglecting 
  the 
  Doppler-effect 
  

   is 
  of 
  the 
  order 
  of 
  w^V^ 
  

  

  