﻿Corpuscular 
  Radiation. 
  581 
  

  

  The 
  functions 
  I, 
  m, 
  n 
  are 
  always 
  complex 
  quantities, 
  but 
  we 
  

   may 
  obtain 
  a 
  real 
  set 
  o£ 
  solutions 
  of 
  Maxwell's 
  equations 
  

  

  curlE=-f 
  , 
  eurlH=f 
  , 
  

  

  by 
  writing 
  

  

  v 
  - 
  - 
  <* 
  A? 
  B 
  $ 
  tt 
  _ 
  3A, 
  3Ay 
  

  

  where 
  the 
  potentials 
  A*, 
  A 
  y 
  , 
  A 
  $ 
  are 
  defined 
  by 
  tho 
  

   equations 
  

  

  Ax=R-, 
  A 
  y 
  =R-, 
  A,= 
  R-, 
  <D 
  = 
  R-; 
  

  

  w 
  io 
  zy 
  io 
  

  

  the 
  symbol 
  R 
  being 
  used 
  to 
  denote 
  the 
  real 
  part 
  of 
  the 
  

   quantity 
  following 
  it. 
  These 
  four 
  potentials 
  are 
  solutions 
  of 
  

   the 
  wave 
  equation 
  and 
  satisfy 
  the 
  relation 
  

  

  dA 
  g 
  dA 
  y 
  dA, 
  d<S> 
  

  

  3* 
  + 
  "by 
  + 
  a* 
  + 
  a< 
  " 
  

  

  The 
  components 
  of 
  the 
  electric 
  and 
  magnetic 
  vectors 
  are 
  

   found 
  to 
  be 
  

  

  E^Rfrfp-K^+K^-A}, 
  

  

  (. 
  Ot\w 
  vrj 
  qx 
  w 
  2 
  J 
  

  

  Hl 
  =R 
  fptVL 
  _K4)_ 
  |- 
  t 
  (^ 
  -K»U 
  , 
  

   where 
  

  

  We 
  easily 
  see 
  that 
  

  

  |lE 
  x 
  +|lE,+ 
  |^E 
  2 
  =0, 
  

   B.k 
  ay 
  d2 
  * 
  

  

  ..-f^M^, 
  y-^M^, 
  ^-r=M| 
  T 
  . 
  *- 
  T 
  =-M^ 
  

  

  where 
  

  

  M=f(«-©+V(y-fl)+r(«-0-(«-T); 
  

  

  hence 
  it 
  follows 
  that 
  Pointing's 
  vector 
  at 
  any 
  point 
  is 
  along 
  

   the 
  radius 
  from 
  the 
  effective 
  position 
  of 
  the 
  gun. 
  The 
  directions 
  

   of 
  the 
  electric 
  and 
  magnetic 
  vectors 
  are 
  the 
  same 
  for 
  all 
  

   space 
  time 
  points 
  which 
  correspond 
  to 
  a 
  given 
  effective 
  

   Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  154. 
  Oct. 
  1913. 
  2 
  R 
  

  

  