﻿[ 
  250 
  ] 
  

  

  XXX. 
  On 
  the 
  Flow 
  of 
  Energy 
  in 
  a 
  System 
  of 
  Interference 
  

   Fringes, 
  By 
  R. 
  W. 
  Wood, 
  Professor 
  of 
  Experimental 
  

   Physics, 
  Johns 
  Hopkins 
  University 
  *. 
  

  

  [Plate 
  VIII. 
  fig. 
  3.] 
  

  

  THE 
  interference 
  minima 
  formed 
  by 
  two 
  similar 
  sources 
  of 
  

   light 
  form 
  a 
  system 
  of 
  confocal 
  hyperboloids, 
  and 
  the 
  

   question 
  of 
  the 
  flow 
  of 
  energy 
  in 
  this 
  case, 
  or 
  any 
  similar 
  

   case, 
  does 
  not 
  appear 
  to 
  have 
  been 
  discussed. 
  Energy 
  is 
  

   obviously 
  flowing 
  out 
  from 
  both 
  sources 
  at 
  its 
  normal 
  rate, 
  

   but 
  the 
  direction 
  of 
  flow 
  is 
  perhaps 
  not 
  quite 
  obvious. 
  

   Suppose 
  the 
  minima 
  equal 
  to 
  zero, 
  which 
  is 
  nearly 
  correct 
  at 
  

   the 
  centre 
  of 
  the 
  system. 
  Energy 
  evidently 
  cannot 
  cross 
  a 
  

   plane 
  along 
  which 
  there 
  is 
  no 
  disturbance. 
  

  

  In 
  stationary 
  waves, 
  if 
  the 
  nodes 
  are 
  absolutely 
  at 
  rest, 
  

   which 
  is 
  the 
  case 
  if 
  the 
  two 
  wave-trains 
  are 
  of 
  equal 
  ampli- 
  

   tude, 
  we 
  cannot 
  speak 
  of 
  a 
  flow 
  of 
  energy 
  across 
  them. 
  A 
  

   node 
  may 
  be 
  considered 
  as 
  having 
  the 
  properties 
  of 
  a 
  perfect 
  

   reflector, 
  that 
  is 
  to 
  say 
  the 
  point 
  acquires 
  the 
  power 
  of 
  

   reflecting 
  as 
  a 
  result 
  of 
  the 
  arrival 
  of 
  a 
  wave 
  travelling 
  in 
  the 
  

   opposite 
  direction. 
  We 
  are 
  thus 
  forced 
  to 
  the 
  conclusion 
  

   that 
  the 
  flow 
  of 
  energy 
  in 
  the 
  case 
  of 
  the 
  interference-fringes 
  

   must 
  be 
  along 
  the 
  hyperboloids, 
  that 
  is 
  along 
  curved 
  paths. 
  

   We 
  can 
  show 
  this 
  experimentally 
  by 
  means 
  of 
  ripples 
  in 
  

   mercury 
  excited 
  by 
  two 
  needles 
  mounted 
  on 
  the 
  prong 
  of 
  a 
  

   tuning-fork. 
  If 
  we 
  view 
  the 
  mercury 
  surface 
  through 
  a 
  

   narrow 
  slit 
  opened 
  and 
  closed 
  by 
  the 
  vibrations 
  of 
  another 
  

   fork 
  slightly 
  out 
  of 
  tune 
  with 
  the 
  first, 
  we 
  see 
  the 
  waves 
  

   (stroboscopically) 
  creeping 
  slowly 
  along 
  the 
  surface, 
  and 
  

   following 
  the 
  lines 
  of 
  the 
  hyperboloids. 
  Two 
  questions 
  now 
  

   naturally 
  occur 
  to 
  us. 
  How 
  does 
  the 
  energy 
  get 
  into 
  the 
  

   bright 
  fringes, 
  if 
  the 
  dark 
  fringes 
  are 
  supposed 
  to 
  act 
  as 
  

   barriers 
  ? 
  and 
  what 
  is 
  the 
  nature 
  of 
  the 
  wave 
  that 
  is 
  travelling 
  

   along 
  a 
  bright 
  fringe 
  ? 
  In 
  regard 
  to 
  the 
  first 
  question 
  : 
  the 
  

   dark 
  fringes 
  are 
  never 
  absolutely 
  black, 
  as 
  no 
  one 
  of 
  them 
  

   is 
  equidistant 
  from 
  both 
  sources. 
  The 
  amplitudes 
  are 
  there- 
  

   fore 
  slightly 
  different, 
  and 
  there 
  will 
  be 
  a 
  flow 
  of 
  energy 
  in 
  

   the 
  direction 
  of 
  the 
  disturbance 
  having 
  the 
  larger 
  amplitude. 
  

   Though 
  it 
  may 
  be 
  very 
  slight 
  at 
  any 
  given 
  point, 
  it 
  is 
  ample 
  

   to 
  account 
  for 
  the 
  flow 
  along 
  the 
  hyper 
  boloid. 
  We 
  can 
  take 
  

   as 
  an 
  analogous 
  case 
  two 
  parallel 
  sheets 
  of 
  cloth 
  tightly 
  

   stretched, 
  and 
  very 
  close 
  together. 
  Consider 
  water 
  forcing 
  

   its 
  way 
  into 
  the 
  space 
  between 
  the 
  two 
  sheets 
  from 
  both 
  sides. 
  

   A 
  very 
  small 
  flow 
  across 
  unit 
  cross-section 
  will 
  give 
  us 
  a 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  

  

  