﻿230 
  Mr. 
  S. 
  H. 
  Burbury 
  on 
  Irreversible 
  

  

  in 
  which 
  I 
  v 
  is 
  the 
  intensity 
  pf 
  the 
  vibrations 
  of 
  the 
  surroupol- 
  

   ing 
  aether 
  whose 
  period 
  is 
  the 
  same 
  as 
  that 
  of 
  the 
  resonator. 
  

   And 
  2av\] 
  is 
  the 
  whole 
  energy 
  emitted 
  per 
  unit 
  of 
  time 
  

   by 
  the 
  resonator 
  having 
  mean 
  energy 
  U. 
  This 
  equation, 
  (22) 
  

   in 
  Planck's 
  notation, 
  is 
  the 
  fundamental 
  equation. 
  

  

  9. 
  Now 
  suppose 
  such 
  a 
  resonator 
  fixed 
  in 
  space, 
  and 
  

   electromagnetic 
  waves 
  to 
  fall 
  upon 
  it, 
  coming 
  from 
  all 
  

   directions, 
  and 
  consider 
  these 
  waves 
  at 
  the 
  small 
  distan 
  -e 
  r 
  

   from 
  the 
  centre 
  of 
  the 
  resonator. 
  Taking 
  the 
  axis 
  of 
  the 
  

   resonator 
  for 
  polar 
  axis, 
  let 
  0, 
  <f> 
  be 
  the 
  usua] 
  angular 
  coordi- 
  

   nates, 
  so 
  that 
  sin 
  0ddd<j> 
  defines 
  the 
  solid 
  angle 
  d£l 
  at 
  in 
  

   direction 
  6 
  <j>. 
  

  

  Let 
  us 
  consider 
  these 
  waves 
  divided 
  into 
  separate 
  waves, 
  

   each 
  having 
  front 
  r^dfl. 
  Let 
  K 
  denote 
  the 
  intensity 
  of 
  the 
  

   vibrations 
  of 
  the 
  wave. 
  Consider 
  an 
  element 
  of 
  area 
  ds 
  = 
  r 
  2 
  d£l 
  

   on 
  the 
  surface 
  of 
  the 
  r 
  sphere, 
  and 
  an 
  element 
  da- 
  at 
  the 
  

   centre 
  perpendicular 
  to 
  the 
  radius 
  to 
  ds. 
  Then 
  the 
  energy 
  

  

  which 
  in 
  time 
  dt 
  passes 
  from 
  ds 
  to 
  da 
  is 
  dt 
  — 
  ^ 
  — 
  K 
  (p. 
  456), 
  

  

  that 
  is 
  dt 
  dcr. 
  dCl 
  K. 
  It 
  follows 
  that 
  the 
  energy 
  per 
  unit 
  of 
  

   volume 
  at 
  the 
  centre 
  due 
  to 
  the 
  wave 
  is 
  the 
  last 
  expression 
  

  

  divided 
  bycdt 
  d<r 
  y 
  that 
  is 
  - 
  d£l, 
  and 
  thewhole 
  energy 
  per 
  unit 
  

  

  G 
  

  

  of 
  volume 
  at 
  the 
  centre 
  is, 
  if 
  & 
  is 
  constant 
  for 
  all 
  positions 
  of 
  

  

  c 
  

  

  10. 
  The 
  vibrations 
  are 
  in 
  the 
  plane 
  of 
  the 
  wave. 
  But 
  the 
  

   polarization 
  may 
  have 
  any 
  direction 
  in 
  that 
  plane. 
  There 
  are 
  

   then, 
  continues 
  Planck, 
  in 
  that 
  plane 
  two 
  mutually 
  perpen- 
  

   dicular 
  directions 
  in 
  which 
  the 
  vibrations 
  have 
  intensity 
  

   respectively 
  greater 
  and 
  less 
  than 
  in 
  any 
  other. 
  These 
  are 
  

   called 
  the 
  principal 
  directions, 
  and 
  the 
  intensities 
  of 
  vibration 
  

   in 
  them, 
  which 
  shall 
  be 
  denoted 
  by 
  K, 
  K', 
  are 
  the 
  principal 
  

   intensities. 
  

  

  We 
  might, 
  however, 
  resolve 
  the 
  vibrations 
  in 
  any 
  other 
  two 
  

   mutually 
  perpendicular 
  directions 
  in 
  the 
  plane 
  of 
  the 
  wave, 
  

  

  making 
  with 
  the 
  principal 
  directions 
  the 
  angles 
  o> 
  and 
  - 
  +co 
  

  

  respectively. 
  If 
  Kj, 
  K 
  2 
  denote 
  the 
  intensities 
  of 
  these 
  re- 
  

   solved 
  vibrations 
  respectively, 
  

  

  K 
  1 
  =Ksin 
  2 
  o) 
  + 
  K 
  / 
  cos 
  2 
  fi), 
  

   K 
  2 
  = 
  K 
  cos' 
  2 
  w 
  + 
  K' 
  sin 
  2 
  e», 
  

  

  and 
  K 
  x 
  + 
  K 
  2 
  = 
  K 
  + 
  K' 
  whatever 
  to 
  may 
  be 
  ; 
  also 
  K 
  x 
  and 
  K 
  2 
  lie 
  

   between 
  K 
  and 
  K 
  ; 
  . 
  

  

  