﻿524 
  Lord 
  Rayleigh 
  on 
  the 
  Pressure 
  of 
  Radiation. 
  

  

  Thus, 
  if 
  the 
  permeability 
  /x 
  of 
  the 
  metal 
  be 
  unity, 
  (4) 
  and 
  

   (6) 
  coincide; 
  and 
  we 
  conclude 
  that 
  in 
  this 
  case 
  the 
  pressure 
  

   is 
  equal 
  to 
  the 
  density 
  of 
  the 
  energy 
  in 
  the 
  neighbourhood 
  of 
  

   the 
  metal. 
  This 
  is 
  Maxwell's 
  result. 
  When 
  we 
  consider 
  

   radiation 
  in 
  all 
  directions, 
  the 
  pressure 
  is 
  expressed 
  as 
  one- 
  

   third 
  of 
  the 
  density 
  of 
  energy. 
  

  

  The 
  difficulty 
  that 
  I 
  have 
  to 
  raise 
  relates 
  to 
  the 
  case 
  where 
  

   fju 
  is 
  not 
  equal 
  to 
  unity. 
  The 
  conclusion 
  in 
  (4) 
  that 
  the 
  pres- 
  

   sure 
  is 
  proportional 
  to 
  /i 
  would 
  make 
  havoc 
  of 
  the 
  theory 
  of 
  

   Boltzmann 
  and 
  Wien 
  and 
  must, 
  I 
  think, 
  be 
  rejected. 
  So 
  

   long 
  as 
  the 
  reflexion 
  is 
  complete 
  — 
  and 
  it 
  may 
  be 
  complete 
  

   independently 
  of 
  /jl 
  — 
  the 
  radiation 
  is 
  similarly 
  influenced, 
  and 
  

   (one 
  would 
  suppose) 
  must 
  exercise 
  a 
  similar 
  force 
  upon 
  the 
  

   reflector. 
  But 
  if 
  the 
  conclusion 
  is 
  impossible, 
  where 
  is 
  the 
  

   flaw 
  in 
  the 
  process 
  by 
  which 
  it 
  is 
  arrived 
  at 
  ? 
  Being 
  unable 
  

   to 
  find 
  any 
  fault 
  with 
  the 
  deduction 
  above 
  given 
  (after 
  Prof. 
  

   J. 
  J. 
  Thomson), 
  I 
  was 
  led 
  to 
  scrutinize 
  more 
  closely 
  the 
  funda- 
  

   mental 
  equation 
  itself; 
  and 
  I 
  will 
  now 
  explain 
  why 
  it 
  appears 
  

   to 
  me 
  to 
  be 
  incorrect. 
  

  

  For 
  this 
  purpose 
  let 
  us 
  apply 
  it 
  to 
  the 
  very 
  simple 
  case 
  of 
  

   a 
  wire 
  of 
  circular 
  section, 
  parallel 
  to 
  z 
  y 
  moving 
  in 
  the 
  direction 
  

   of 
  a? 
  across 
  an 
  originally 
  uniform 
  magnetic 
  field 
  (/3). 
  The 
  uni- 
  

   formity 
  of 
  the 
  field 
  is 
  disturbed 
  in 
  two 
  ways 
  : 
  (i.) 
  by 
  the 
  

   operation 
  of 
  the 
  current 
  (w 
  ) 
  flowing 
  in 
  the 
  various 
  filaments 
  

   of 
  the 
  wire, 
  and 
  (ii 
  ) 
  independently 
  of 
  a 
  current, 
  by 
  the 
  mag- 
  

   netic 
  effect 
  of 
  the 
  material 
  composing 
  the 
  wire 
  whose 
  permea- 
  

   bility 
  {/jl) 
  is 
  supposed 
  to 
  be 
  great. 
  In 
  estimating 
  as 
  in 
  (2) 
  

   the 
  mechanical 
  force 
  parallel 
  to 
  x 
  operative 
  upon 
  the 
  wire, 
  we 
  

   should 
  have 
  to 
  integrate 
  wb 
  over 
  the 
  cross-section. 
  In 
  this 
  w 
  

   is 
  supposed 
  to 
  be 
  constant, 
  and 
  the 
  local 
  value 
  is 
  every 
  whe/'e 
  

   to 
  be 
  attributed 
  to 
  b. 
  We 
  may 
  indeed, 
  if 
  we 
  please, 
  omit 
  

   from 
  b 
  the 
  part 
  due 
  to 
  the 
  currents 
  in 
  the 
  wire, 
  which 
  will 
  

   in 
  the 
  end 
  contribute 
  nothing 
  to 
  the 
  result 
  ; 
  but 
  we 
  are 
  directed 
  

   to 
  use 
  the 
  actual 
  value 
  of 
  b 
  as 
  disturbed 
  by 
  the 
  presence 
  of 
  

   the 
  magnetic 
  material. 
  In 
  the 
  particular 
  case 
  supposed, 
  where 
  

   /x 
  is 
  great, 
  the 
  value 
  of 
  b 
  within 
  the 
  wire 
  is 
  uniform, 
  and 
  just 
  

   twice 
  as 
  great 
  as 
  at 
  a 
  distance. 
  It 
  follows, 
  when 
  the 
  inte- 
  

   gration 
  is 
  effected, 
  that 
  the 
  force 
  parallel 
  to 
  x 
  acting 
  upon 
  the 
  

   wire 
  is 
  greater 
  (in 
  the 
  particular 
  case 
  doubly 
  greater) 
  than 
  it 
  

   w 
  7 
  ould 
  be 
  if 
  the 
  value 
  of 
  /jl 
  were 
  unity. 
  

  

  But 
  this 
  conclusion 
  cannot 
  be 
  accepted. 
  The 
  force 
  depends 
  

   upon 
  the 
  number 
  of 
  lines 
  of 
  force 
  to 
  be 
  crossed 
  when 
  the 
  wire 
  

   makes 
  a 
  movement 
  parallel 
  to 
  x. 
  And 
  it 
  is 
  clear 
  that 
  the 
  

   lines 
  effectively 
  crossed 
  in 
  such 
  a 
  movement 
  are 
  not 
  the 
  con- 
  

   densed 
  lines 
  due 
  to 
  the 
  magnetic 
  quality 
  of 
  the 
  wire, 
  but 
  are 
  

   to 
  be 
  reckoned 
  from 
  the 
  intensity 
  of 
  the 
  undisturbed 
  field. 
  

  

  