﻿Motion 
  of 
  Electrons 
  la 
  Solids. 
  211 
  

  

  ^^•l>«^« 
  .,,= 
  ^\ 
  CO. 
  ptdt, 
  (51) 
  

  

  

  

  a'5^= 
  i 
  A^sinptdt 
  (52) 
  

  

  The 
  value 
  of 
  Bg 
  can 
  be 
  similarly 
  resolved 
  into 
  harmonic 
  

   terms, 
  with 
  typical 
  coefficients 
  /3gp, 
  ^^^p. 
  The 
  whole 
  motion 
  

   is 
  now 
  resolved 
  into 
  regular 
  waves. 
  There 
  are 
  waves 
  o£ 
  all 
  

   possible 
  frequencies, 
  and 
  the 
  waves 
  of 
  any 
  single 
  frequency 
  

   iire 
  of 
  all 
  possible 
  wave-lengths. 
  Consequently 
  these 
  waves 
  

   travel 
  with 
  all 
  possible 
  velocities. 
  

  

  27. 
  The 
  magnetic 
  force 
  at 
  time 
  t 
  produced 
  at 
  a 
  sufficiently 
  

   distant 
  point 
  .v\ 
  y\ 
  z 
  in 
  direction 
  l\ 
  ??i', 
  n' 
  by 
  the 
  x 
  com- 
  

   ponents 
  of 
  velocity 
  of 
  the 
  electrons 
  inside 
  the 
  prism, 
  is, 
  by 
  

   •expression 
  (47), 
  ^^i 
  

  

  (0, 
  -«',m')|-,(Jj7.'^4 
  • 
  • 
  • 
  ^^^^ 
  

  

  X=-l 
  

  

  in 
  which 
  ^x 
  is 
  evaluated 
  at 
  time 
  t 
  — 
  r/Y. 
  

  

  From 
  equation 
  (50) 
  the 
  value 
  of 
  A,^ 
  at 
  time 
  t 
  — 
  r/Y 
  is 
  

  

  A, 
  = 
  -J 
  ^cc^pcosp[t-to- 
  ^ 
  j 
  +cc\p 
  sin 
  2:)(t- 
  to- 
  y^yip, 
  

  

  ^"? 
  . 
  

  

  where 
  ^o 
  is 
  the 
  time 
  required 
  for 
  radiation 
  to 
  travel 
  from 
  the 
  

  

  middle 
  point 
  of 
  the 
  prism 
  (.v 
  = 
  0) 
  to 
  x\i/\ 
  z. 
  

  

  This 
  gives, 
  as 
  the 
  value 
  of 
  the 
  integral 
  in 
  expression 
  (53), 
  

  

  x=l 
  x-=l 
  p=Xi 
  q=:X) 
  

  

  I 
  jxdx= 
  "2 
  I 
  ^-^ 
  1 
  1 
  a9;jCOs<yci'cosp( 
  f 
  — 
  ^0 
  s^Yp 
  ^^9. 
  

  

  j:--1 
  X— 
  — 
  1 
  p=0 
  q=0 
  

  

  + 
  similar 
  terms 
  in 
  a'^p, 
  ^qp, 
  ^\p^ 
  

  

  ry 
  + 
  fyV 
  -■ 
  

  

  H- 
  . 
  . 
  . 
  ~ 
  a 
  similar 
  function 
  of 
  — 
  Z, 
  

  

  = 
  -^\ 
  («9p)?=i>;vcos;<f-fo) 
  <-h^ 
  + 
  

  

  p=0 
  

  

  = 
  -r[(«./^+/S',p)cosX^-g 
  

  

  + 
  («V-/e,p)sinX<-g].Zy>, 
  . 
  (54) 
  

   P2 
  

  

  