﻿Corpuscular 
  Radiation. 
  585 
  

  

  <j> 
  = 
  constant, 
  yfr= 
  constant 
  are 
  evidently 
  the 
  level 
  curves 
  and 
  

   stream-lines 
  due 
  to 
  the 
  two 
  doublets 
  AA', 
  A 
  A 
  ', 
  where 
  the 
  

   flow 
  takes 
  place 
  in 
  two 
  dimensions. 
  

  

  To 
  find 
  the 
  points 
  on 
  the 
  sphere 
  for 
  which 
  the 
  electric 
  and 
  

   magnetic 
  vectors 
  are 
  zero 
  we 
  must 
  find 
  when 
  R 
  and 
  S 
  

   coincide. 
  The 
  line 
  QR 
  is 
  then 
  a 
  common 
  tractor 
  of 
  two 
  

   pairs 
  of 
  polar 
  lines 
  *. 
  

  

  Putting 
  r=s, 
  we 
  have 
  two 
  equations, 
  

  

  <2 
  r 
  — 
  i{q 
  + 
  r)(a 
  + 
  a 
  )+aa 
  = 
  0, 
  

   qr-i(q 
  + 
  r)(a' 
  + 
  a 
  ') 
  + 
  a'a 
  ' 
  = 
  0, 
  

  

  which 
  determine 
  the 
  values 
  of 
  q 
  and 
  r 
  corresponding 
  to 
  the 
  

   two 
  real 
  points 
  cut 
  out 
  on 
  the 
  sphere 
  by 
  one 
  of 
  the 
  tractors 
  

   of 
  the 
  two 
  pairs 
  of 
  polar 
  lines. 
  The 
  other 
  tractor 
  is 
  the 
  

   polar 
  line 
  of 
  the 
  first 
  with 
  regard 
  to 
  the 
  sphere 
  and 
  does 
  not 
  

   (generally) 
  meet 
  the 
  sphere 
  in 
  real 
  points. 
  

  

  Hence 
  there 
  are 
  two 
  real 
  points 
  on 
  the 
  sphere 
  at 
  which 
  the 
  

   electric 
  and 
  magnetic 
  forces 
  vanish. 
  There 
  are 
  also 
  two 
  points 
  

   at 
  which 
  the 
  forces 
  are 
  infinite, 
  viz. 
  the 
  points 
  A 
  and 
  A 
  in 
  

   which 
  the 
  sphere 
  is 
  pierced 
  by 
  bullets. 
  

  

  It 
  should 
  be 
  noticed 
  that 
  we 
  have 
  proved 
  incidentally 
  that 
  

   two 
  pairs 
  of 
  real 
  polar 
  lines 
  with 
  regard 
  to 
  a 
  sphere 
  always 
  

   have 
  two 
  real 
  tractors. 
  

  

  § 
  7. 
  Let 
  us 
  now 
  consider 
  the 
  reflexion 
  of 
  an 
  electro- 
  

   magnetic 
  disturbance 
  of 
  the 
  type 
  we 
  have 
  been 
  studying 
  

   when 
  the 
  mirror 
  is 
  an 
  infinite 
  plane 
  and 
  a 
  perfect 
  reflector. 
  

   Let 
  x=0 
  be 
  the 
  plane 
  of 
  the 
  mirror, 
  then 
  we 
  can 
  satisfy 
  the 
  

   boundary 
  condition 
  at 
  its 
  surface 
  by 
  subtracting 
  irom 
  the 
  

   original 
  electromagnetic 
  field 
  another 
  one 
  of 
  a 
  similar 
  type 
  

   in 
  which 
  the 
  motion 
  of 
  the 
  gun 
  is 
  given 
  by 
  the 
  equations 
  

  

  and 
  the 
  direction-cosines 
  of 
  its 
  barrels 
  are 
  — 
  \(o), 
  fi(o), 
  v(o); 
  

   — 
  \ 
  {o), 
  1*0(0-), 
  v 
  (o) 
  respectively^ 
  

  

  When 
  (#, 
  y, 
  z, 
  t) 
  is 
  on 
  the 
  mirror, 
  x=0 
  and 
  ar=r 
  ; 
  the 
  

   values 
  of 
  E 
  , 
  E 
  z 
  , 
  H 
  z 
  are 
  the 
  same 
  in 
  both 
  fields, 
  and 
  so 
  when 
  

   we 
  subtract, 
  the 
  resultant 
  electric 
  force 
  is 
  normal 
  to 
  the 
  

   mirror 
  and 
  the 
  magnetic 
  force 
  tangential. 
  

  

  If 
  this 
  theory 
  is 
  correct 
  the 
  bullets 
  strike 
  the 
  mirror 
  and 
  

   rebound 
  in 
  such 
  a 
  way 
  that 
  the 
  angle 
  of 
  incidence 
  is 
  equal 
  

   to 
  the 
  angle 
  of 
  reflexion, 
  i. 
  e. 
  they 
  are 
  reflected 
  like 
  rays 
  of 
  

   light. 
  

  

  * 
  JT. 
  e., 
  a 
  straight 
  line 
  which 
  meets 
  all 
  four. 
  The 
  term 
  is 
  due 
  to 
  

   Cayley. 
  

  

  