﻿Flow 
  of 
  Energy 
  in 
  a 
  System 
  of 
  Interference 
  Fringes. 
  251 
  

  

  large 
  flow 
  across 
  unit 
  section 
  taken 
  perpendicular 
  to 
  the 
  

   sheets. 
  

  

  We 
  may, 
  however, 
  have 
  a 
  fringe 
  which 
  is 
  absolutely 
  

   black, 
  for 
  there 
  is 
  nothing 
  to 
  prevent 
  us 
  from 
  considering 
  

   the 
  sources 
  as 
  vibrating 
  with 
  a 
  difference 
  of 
  phase 
  of 
  180°. 
  

   This 
  makes 
  the 
  centre 
  of 
  the 
  system 
  dark, 
  and 
  equal 
  to 
  zero, 
  

   and 
  it 
  must 
  act 
  as 
  a 
  barrier 
  to 
  the 
  flow 
  of 
  energy 
  from 
  both 
  

   sources. 
  In 
  other 
  words, 
  the 
  central 
  fringe 
  can 
  be 
  considered 
  

   as 
  acting 
  as 
  a 
  perfect 
  mirror, 
  and 
  we 
  can 
  regard 
  the 
  fringes 
  

   as 
  formed 
  by 
  the 
  interference 
  of 
  these 
  reflected 
  waves 
  with 
  

   the 
  direct. 
  If 
  the 
  flow 
  of 
  energy 
  is 
  along 
  the 
  hyperboloids, 
  

   it 
  is 
  evident 
  that 
  in 
  the 
  region 
  between 
  the 
  sources 
  the 
  flow 
  

   is 
  in 
  a 
  direction 
  nearly 
  perpendicular 
  to 
  the 
  rays. 
  We 
  can 
  

   watch 
  this 
  flow 
  with 
  the 
  mercnry 
  ripples 
  and 
  tuning-forks. 
  

   (I 
  find 
  that 
  a 
  ring 
  of 
  castor-oil 
  or 
  glycerine 
  poured 
  around 
  

   the 
  edge 
  of 
  the 
  mercury 
  surface 
  prevents 
  disturbing 
  reflexion 
  

   from 
  the 
  walls, 
  and 
  to 
  a 
  large 
  extent 
  waves 
  due 
  to 
  jars 
  from 
  

   the 
  table.) 
  The 
  bars 
  of 
  light 
  perpendicular 
  to 
  the 
  line 
  joining 
  

   the 
  vibrating 
  sources 
  slide 
  out 
  sideways, 
  each 
  one 
  of 
  them 
  

   forming 
  one 
  of 
  the 
  waves 
  which 
  travel 
  along 
  the 
  hyperboloid. 
  

   We 
  can 
  perhaps 
  get 
  a 
  better 
  idea 
  of 
  what 
  happens 
  if 
  we 
  con- 
  

   sider 
  what 
  is 
  going 
  on 
  in 
  a 
  bright 
  fringe 
  outside 
  of 
  the 
  region 
  

   between 
  the 
  sources. 
  What 
  is 
  the 
  type 
  of 
  wave, 
  and 
  is 
  it 
  

   capable 
  of 
  showing 
  us 
  both 
  of 
  the 
  sources 
  if 
  it 
  alone 
  is 
  allowed 
  

   to 
  enter 
  the 
  eye 
  ? 
  If 
  we 
  regard 
  the 
  dark 
  fringes 
  as 
  absolutely 
  

   dark, 
  that 
  is 
  as 
  perfect 
  reflectors, 
  we 
  must 
  regard 
  the 
  waves 
  

   as 
  travelling 
  between 
  them 
  as 
  between 
  two 
  silver 
  walls. 
  The 
  

   incidence 
  is 
  very 
  oblique, 
  i. 
  e. 
  the 
  wave 
  is 
  nearly 
  perpen- 
  

   dicular 
  to 
  the 
  reflecting 
  plane 
  ; 
  and 
  if 
  we 
  consider 
  the 
  wave 
  

   as 
  a 
  portion 
  of 
  a 
  sphere 
  with 
  its 
  centre 
  at 
  one 
  of 
  the 
  sources, 
  

   the 
  w^ave 
  after 
  reflexion 
  from 
  the 
  interference 
  plane 
  will 
  be 
  a 
  

   portion 
  of 
  a 
  sphere 
  with 
  its 
  centre 
  of 
  curvature 
  at 
  the 
  other 
  

   source. 
  This 
  process 
  will 
  repeat 
  itself 
  over 
  and 
  over 
  again, 
  

   a 
  given 
  portion 
  of 
  the 
  wave-front 
  appearing 
  to 
  come 
  first 
  

   from 
  one 
  source 
  and 
  then 
  from 
  the 
  other. 
  The 
  bright 
  fringe 
  

   w^ill 
  then 
  contain 
  two 
  groups 
  of 
  wave-fronts 
  inclined 
  to 
  each 
  

   other 
  at 
  a 
  small 
  angle. 
  These 
  can 
  be 
  seen 
  with 
  the 
  tuning- 
  

   fork 
  waves, 
  and 
  on 
  looking 
  over 
  some 
  of 
  Mr. 
  Vincent's 
  

   photographs, 
  published 
  in 
  this 
  Journal 
  some 
  time 
  ago, 
  I 
  found 
  

   one 
  which 
  showed 
  the 
  phenomenon 
  very 
  clearly. 
  An 
  enlarge- 
  

   ment 
  of 
  a 
  portion 
  of 
  this 
  photograph 
  is 
  reproduced 
  on 
  

   Plate 
  VIII. 
  fig. 
  3, 
  the 
  inclined 
  wave- 
  fronts 
  showing 
  especially 
  

   well 
  above 
  the 
  point 
  marked 
  X. 
  

  

  Though 
  each 
  bright 
  fringe 
  contains 
  two 
  wave-fronts, 
  we 
  

   cannot 
  " 
  resolve 
  ^^ 
  the 
  sources 
  with 
  them, 
  for 
  calculation 
  

   shows 
  that 
  their 
  width 
  will 
  be 
  insufficient. 
  In 
  other 
  words, 
  

  

  