﻿156 
  Prof. 
  D. 
  N. 
  Mallik 
  on 
  Fermat's 
  Law. 
  

  

  Moreover, 
  it' 
  we 
  take 
  the 
  kinetic 
  energy 
  

  

  we 
  have 
  the 
  momentum 
  of 
  the 
  tubes, 
  or 
  the 
  momentum 
  of 
  

   the 
  medium 
  in 
  the 
  direction 
  of 
  a, 
  

  

  OU 
  4//,\ 
  0% 
  J 
  

  

  = 
  (gc-hb) 
  

  

  where 
  a, 
  b, 
  c 
  are 
  the 
  components 
  of 
  the 
  magnetic 
  induction. 
  

  

  This 
  system 
  of 
  momenta 
  in 
  the 
  field 
  is 
  found 
  to 
  be 
  " 
  pro- 
  

   portional 
  to 
  amounts 
  of 
  energy 
  transferred 
  in 
  unit 
  time 
  

   across 
  unit 
  plane 
  at 
  right 
  angles 
  to 
  the 
  axes 
  of 
  w, 
  y, 
  z 
  in 
  

   Poynting's 
  theory 
  of 
  the 
  transfer 
  of 
  energy 
  in 
  the 
  electro- 
  

   magnetic 
  field. 
  " 
  Hence 
  the 
  direction 
  of 
  momentum 
  coincides 
  

   with 
  the 
  direction 
  of 
  flow 
  of 
  energy, 
  on 
  this 
  theory. 
  

  

  Again, 
  on 
  the 
  assumption 
  that 
  T 
  may 
  also 
  t 
  be 
  taken 
  to 
  be 
  

   equal 
  to 
  

  

  we 
  have 
  

  

  4-7T/ 
  _ 
  _ 
  . 
  

  

  — 
  -r~= 
  wb 
  — 
  vc 
  = 
  X) 
  &c. 
  

  

  (i. 
  e. 
  electromotive 
  intensity 
  (X, 
  Y, 
  Z) 
  is 
  due 
  to 
  the 
  motion 
  

   of 
  Faraday 
  tubes 
  only). 
  

   And 
  since 
  

  

  l> 
  = 
  4z7T/jU 
  ( 
  fw 
  — 
  h 
  u) 
  , 
  

  

  c 
  = 
  4:7rp(gu—fv), 
  

   we 
  have 
  

  

  f=:fik{f(u 
  2 
  + 
  v 
  2 
  + 
  w 
  2 
  ) 
  — 
  u{ 
  fu 
  + 
  gv 
  + 
  hiv)}, 
  &c. 
  

  

  .*. 
  multiplying 
  in 
  order 
  by 
  u, 
  v, 
  w, 
  we 
  have 
  

  

  fu 
  + 
  gv 
  + 
  hw 
  = 
  0, 
  

  

  and 
  .*. 
  

  

  u 
  2 
  + 
  v 
  2 
  + 
  w 
  2 
  = 
  ~ 
  =V 
  2 
  , 
  

  

  fjLrC 
  

  

  where 
  V 
  is 
  the 
  velocity 
  of 
  light 
  in 
  the 
  medium. 
  

  

  That 
  is, 
  the 
  tubes 
  move 
  with 
  the 
  velocity 
  of 
  light 
  at 
  right 
  

   angles 
  to 
  the 
  direction 
  of 
  polarization 
  and 
  also 
  at 
  right 
  

   angles 
  to 
  the 
  direction 
  of 
  the 
  magnetic 
  force. 
  The 
  energy 
  of 
  

   the 
  electromagnetic 
  field 
  is 
  seen, 
  therefore, 
  on 
  this 
  view 
  to 
  

   be 
  entirely 
  kinetic. 
  [Art. 
  26.] 
  

  

  