﻿Lord 
  Rayleigh 
  on 
  the 
  Pressure 
  of 
  Radiation. 
  523 
  

  

  consideration 
  the 
  magnetic 
  force 
  reduces 
  itself 
  to 
  the 
  com- 
  

   ponent 
  (ft) 
  parallel 
  to 
  y, 
  and 
  the 
  current 
  to 
  the 
  component 
  

   (to) 
  parallel 
  to 
  z. 
  The 
  waves 
  which 
  penetrate 
  the 
  conducting 
  

   mass 
  die 
  out 
  more 
  or 
  less 
  quickly 
  according 
  to 
  the 
  conductivity. 
  

   If 
  the 
  conductivity 
  is 
  great, 
  most 
  of 
  the 
  energy 
  is 
  reflected, 
  

   and 
  such 
  part 
  as 
  is 
  propagated 
  into 
  the 
  conductor 
  is 
  limited 
  

   to 
  a 
  thin 
  skin 
  at 
  # 
  = 
  0. 
  According 
  to 
  the 
  usual 
  equations 
  the 
  

   mechanical 
  force 
  exercised 
  upon 
  unit 
  of 
  area 
  of 
  the 
  slice 
  dx 
  of 
  

   the 
  conductor 
  is 
  —wbdx, 
  or 
  altogether 
  

  

  wbdx. 
  . 
  (2) 
  

  

  Here 
  b 
  denotes 
  the 
  magnetic 
  induction, 
  and 
  is 
  equal 
  to 
  fift, 
  if 
  

   fj, 
  be 
  the 
  permeability 
  and 
  ft 
  the 
  magnetic 
  force. 
  Now 
  

  

  4:7TW=dl3/dx, 
  

  

  so 
  that 
  the 
  integral 
  becomes 
  

  

  &{&-£}, 
  ...... 
  (3) 
  

  

  where 
  ft 
  is 
  the 
  value 
  of 
  ft 
  within 
  the 
  conductor 
  at 
  a? 
  = 
  0, 
  and 
  

   ft 
  oo 
  =0, 
  if 
  the 
  conducting 
  slab 
  be 
  sufficiently 
  thick. 
  Since 
  

   there 
  is 
  no 
  discontinuity 
  of 
  magnetic 
  force 
  at 
  x 
  = 
  0, 
  ft 
  maybe 
  

   taken 
  also 
  to 
  refer 
  to 
  the 
  value 
  at 
  x 
  = 
  just 
  outside 
  the 
  metallic 
  

   surface. 
  

  

  The 
  expression 
  (3) 
  gives 
  the 
  force 
  at 
  any 
  moment 
  ; 
  but 
  we 
  

   are 
  concerned 
  only 
  with 
  the 
  mean 
  value. 
  Since 
  the 
  mean 
  

   value 
  of 
  ft 
  is 
  one-half 
  the 
  maximum 
  value, 
  we 
  have 
  for 
  the 
  

   pressure 
  

  

  P=& 
  r 
  0L* 
  W 
  

  

  It 
  only 
  remains 
  to 
  compare 
  with 
  the 
  density 
  of 
  the 
  energy 
  

   outside 
  the 
  metal, 
  and 
  we 
  may 
  limit 
  ourselves 
  to 
  the 
  case 
  of 
  

   complete 
  reflexion. 
  The 
  constant 
  energy 
  of 
  the 
  stationary 
  

   waves 
  passes 
  alternately 
  between 
  the 
  electric 
  and 
  magnetic 
  

   forms. 
  If 
  we 
  estimate 
  it 
  at 
  the 
  moment 
  of 
  maximum 
  mag- 
  

   netic 
  force, 
  we 
  have 
  

  

  energy 
  = 
  ^- 
  \\\ft 
  2 
  dx 
  dy 
  dz. 
  . 
  . 
  . 
  # 
  . 
  (5) 
  

  

  In 
  (5) 
  ft 
  is 
  variable 
  with 
  x. 
  If 
  /3 
  max 
  . 
  denote 
  the 
  maximum 
  

   value 
  which 
  occurs 
  at 
  x 
  = 
  0, 
  the 
  mean 
  of 
  ft 
  2 
  = 
  j>ftm 
  & 
  x. 
  Thus 
  

  

  energy 
  1 
  

  

  density 
  of 
  energy 
  = 
  — 
  , 
  "• 
  = 
  — 
  — 
  R* 
  , 
  . 
  . 
  ($\ 
  

  

  J 
  oj 
  volume 
  lb7T 
  Mmax 
  - 
  W 
  

  

  