﻿Relativity 
  and 
  Electrodynamics* 
  335 
  

  

  ,\ 
  approximately 
  m 
  v 
  2 
  = 
  2fAU--fj,u 
  - 
  ~ 
  2 
  (2/juu—fiu 
  ) 
  2 
  , 
  

  

  and 
  . 
  (^2 
  — 
  Pi)/o 
  n 
  2 
  ^ 
  w 
  

  

  (2fiu-fiu 
  ) 
  + 
  m<)C 
  2 
  / 
  {2fiu-fiu 
  ) 
  2 
  = 
  -Wfo, 
  

  

  or 
  putting 
  # 
  = 
  2yu.w 
  — 
  fiu 
  , 
  

  

  and 
  X 
  = 
  (k 
  2 
  ~" 
  2 
  ^1) 
  / 
  m 
  o 
  c2 
  > 
  

  

  ^ 
  + 
  \^ 
  2 
  =— 
  ijt? 
  

  

  dp, 
  

  

  .*. 
  integrating 
  we 
  get 
  

  

  b 
  2 
  /p 
  2 
  = 
  - 
  — 
  -— 
  = 
  #— 
  A# 
  2 
  neglecting 
  squares 
  of 
  A, 
  

  

  where 
  b 
  is 
  a 
  constant 
  of 
  integration. 
  

   1 
  2 
  l 
  /<ftA» 
  

  

  •. 
  h2 
  \ 
  u2+ 
  {~^) 
  | 
  =(2/iM-p 
  )-\(2/iM-/iM 
  ) 
  2 
  , 
  

  

  (J 
  M 
  \2 
  

   ^ 
  \ 
  = 
  (2/416 
  — 
  /4U 
  ) 
  — 
  A 
  (2/U.W 
  — 
  yu,w 
  0y 
  ) 
  2 
  — 
  o 
  2 
  u 
  2 
  , 
  

  

  so 
  that 
  the 
  integral 
  is 
  of 
  the 
  form 
  

  

  Ju 
  = 
  l 
  + 
  «cos[{l+i£jH 
  **-,], 
  

  

  where 
  97 
  is 
  an 
  arbitrary 
  constant 
  and 
  I 
  and 
  e 
  are 
  determinate 
  

   constants 
  in 
  At, 
  a, 
  6, 
  and 
  X. 
  This 
  solution 
  implies 
  an 
  elliptic 
  

   orbit 
  slowly 
  revolving 
  in 
  its 
  own 
  plane. 
  The 
  eccentricity 
  

   does 
  not 
  change, 
  but 
  the 
  apses 
  will 
  advance 
  in 
  the 
  direction 
  

   of 
  description 
  of 
  the 
  orbit 
  by 
  

  

  — 
  2tt 
  for 
  each 
  description 
  of 
  the 
  orbit, 
  

  

  Now 
  

  

  P 
  

  

  'du 
  

  

  or 
  

  

  i. 
  e. 
  since 
  A 
  is 
  small, 
  

   by 
  kn^X 
  

  

  b 
  2 
  ' 
  

  

  or 
  ^ 
  (ih-h)/c 
  2 
  . 
  

  

  