﻿Corpuscular 
  Radiation. 
  583 
  

  

  § 
  5. 
  Now 
  let 
  Q, 
  A, 
  A 
  be 
  points 
  on 
  a 
  unit 
  sphere 
  whose 
  

   coordinates 
  are 
  (#, 
  /3, 
  7), 
  (A,, 
  /j, 
  v), 
  (\ 
  , 
  p#, 
  v 
  ) 
  respectively. 
  

   Let 
  II 
  be 
  the 
  tangent 
  plane 
  at 
  the 
  point 
  T 
  diametrically 
  

   opposite 
  to 
  Q 
  and 
  let 
  QA, 
  QA 
  meet 
  IT 
  in 
  the 
  points 
  B, 
  B 
  

   respectively. 
  Let 
  C 
  be 
  the 
  middle 
  point 
  of 
  BB 
  , 
  then 
  if 
  V 
  

   denote 
  the 
  vector 
  CQ 
  we 
  have 
  

  

  E 
  = 
  

  

  J^aT 
  

   2Mdr' 
  

  

  The 
  changes 
  in 
  the 
  positions 
  o£ 
  A 
  and 
  A 
  in 
  time 
  dr 
  must 
  

   now 
  be 
  marked 
  on 
  the 
  sphere 
  and 
  dY 
  is 
  then 
  represented 
  by 
  

   the 
  change 
  in 
  the 
  position 
  of 
  C 
  (fig. 
  2). 
  

  

  Fig. 
  2. 
  

  

  Again, 
  if 
  A 
  represents 
  a 
  vector 
  in 
  the 
  plane 
  IT 
  at 
  right 
  

   angles 
  to 
  TC 
  and 
  equal 
  in 
  magnitude 
  to 
  TC, 
  we 
  have 
  

  

  2M 
  dr' 
  

  

  H 
  = 
  ;r=r^= 
  

  

  If 
  dA 
  is 
  rotated 
  through 
  a 
  right 
  angle 
  in 
  a 
  suitable 
  

   direction, 
  it 
  is 
  also 
  represented 
  in 
  magnitude 
  and 
  direction 
  

   by 
  the 
  displacement 
  of 
  C. 
  This 
  result 
  proves 
  at 
  once 
  that 
  E 
  

   and 
  H 
  are 
  perpendicular 
  and 
  equal 
  in 
  magnitude. 
  

  

  Since 
  the 
  factor 
  ^-= 
  is 
  always 
  negative, 
  the 
  directions 
  of 
  

  

  the 
  electric 
  and 
  magnetic 
  vectors 
  are 
  indicated 
  at 
  once 
  by 
  

   our 
  geometrical 
  construction. 
  It 
  is 
  evident 
  that 
  they 
  are 
  

   both 
  perpendicular 
  to 
  the 
  radius 
  from 
  the 
  effective 
  position 
  

   of 
  the 
  gun. 
  

  

  § 
  6. 
  This 
  last 
  fact 
  makes 
  it 
  possible 
  for 
  us 
  to 
  draw 
  lines 
  of 
  

   electric 
  and 
  magnetic 
  force 
  on 
  a 
  sphere 
  whose 
  centre 
  is 
  G. 
  

   It 
  will 
  be 
  sufficient 
  to 
  take 
  this 
  as 
  our 
  unit 
  sphere, 
  for 
  the 
  

   lines 
  of 
  force 
  on 
  a 
  larger 
  sphere 
  may 
  be 
  obtained 
  by 
  a 
  simple 
  

   magnification 
  round 
  G. 
  

  

  2R2 
  

  

  