﻿338 
  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  

  

  it 
  always 
  has 
  some 
  width 
  — 
  in 
  other 
  words, 
  it 
  consists 
  of 
  

   light 
  of 
  wave-lengths 
  ranging 
  between 
  limits 
  which 
  may 
  be 
  

   close 
  but 
  cannot 
  be 
  coincident. 
  What 
  happens 
  under 
  these 
  

   circumstances 
  is 
  discussed 
  in 
  the 
  Phil. 
  Mag. 
  for 
  Feb. 
  1903, 
  

   p. 
  275 
  et 
  seg., 
  from 
  which 
  discussion 
  it 
  appears 
  that 
  it 
  is 
  

   permissible 
  to 
  divide 
  the 
  wave-lengths 
  of 
  the 
  light 
  which 
  

   issues 
  from 
  the 
  minute 
  hole 
  ./, 
  into 
  little 
  groups 
  within 
  each 
  

   of 
  which 
  the 
  wave-lengths 
  shall 
  vary 
  between 
  narrow 
  limits 
  ; 
  

   and 
  we 
  may 
  then 
  substitute 
  light 
  of 
  one 
  wave-length 
  for 
  

   each 
  of 
  these. 
  This 
  resultant, 
  however, 
  is 
  not 
  the 
  simple 
  

   kind 
  of 
  uf 
  W 
  of 
  which 
  we 
  have 
  hitherto 
  been 
  thinking, 
  for 
  

   the 
  luminous 
  undulations 
  which 
  occur 
  in 
  nature 
  always 
  have, 
  

   at 
  any 
  given 
  station, 
  fluctuations 
  in 
  intensity 
  of 
  the 
  same 
  

   nature 
  as 
  beats 
  in 
  acoustics, 
  which 
  however 
  need 
  not 
  be 
  so 
  

   simple 
  as 
  to 
  be 
  periodic 
  but 
  will 
  occur 
  in 
  whatever 
  manner 
  

   may 
  be 
  the 
  outcome 
  of 
  the 
  conditions 
  — 
  probably 
  molecular 
  

   conditions 
  — 
  that 
  have 
  prevailed 
  in 
  the 
  parts 
  of 
  the 
  source 
  

   from 
  which 
  the 
  light 
  has 
  come. 
  Abrupt 
  changes 
  of 
  phase 
  may 
  

   also 
  take 
  place, 
  of 
  the 
  same 
  nature 
  but 
  not 
  of 
  the 
  same 
  simple 
  

   kind 
  as 
  the 
  reversals 
  of 
  phase 
  that 
  occur 
  when 
  there 
  are 
  beats 
  

   in 
  music. 
  And 
  also 
  alterations 
  of 
  the 
  state 
  of 
  polarization. 
  

  

  We 
  have 
  referred 
  to 
  these 
  complications'* 
  in 
  order 
  to 
  have 
  

   an 
  opportunity 
  of 
  pointing 
  out 
  that 
  though 
  the 
  result 
  will 
  

   be 
  one 
  of 
  immense 
  complexity 
  which 
  it 
  is 
  impossible 
  to 
  

   simplify 
  in 
  any 
  experiments 
  man 
  can 
  make, 
  it 
  nevertheless 
  

   is 
  of 
  such 
  a 
  character 
  that 
  the 
  fluctuations 
  which 
  take 
  place 
  

   do 
  not 
  prevent 
  portions 
  of 
  light 
  derived 
  from 
  any 
  single 
  one 
  

   of 
  these 
  complex 
  uf 
  Ws 
  from 
  being 
  capable 
  of 
  interfering 
  

   with 
  one 
  another 
  and 
  furnishing 
  that 
  persistent 
  kind 
  of 
  inter- 
  

   ference 
  upon 
  which 
  we 
  shall 
  find 
  that 
  the 
  formation 
  of 
  visible 
  

  

  * 
  A 
  resolution 
  of 
  light 
  into 
  undulations 
  of 
  flat 
  waves 
  of 
  finite 
  intensity 
  

   however 
  small, 
  is 
  only 
  legitimate 
  when 
  dealing 
  with 
  what 
  happens 
  

   within 
  a 
  limited 
  volume 
  of 
  space 
  and 
  a 
  limited 
  duration 
  of 
  time. 
  [See 
  

   Phil 
  Mag. 
  for 
  February 
  1903 
  ; 
  Theorem 
  X. 
  p. 
  274, 
  and 
  Theorem 
  XIII. 
  

   p. 
  279 
  ; 
  see 
  also 
  § 
  4 
  on 
  p. 
  265.] 
  All 
  such 
  undulations 
  are 
  more 
  or 
  less 
  

   affected 
  by 
  the 
  complications 
  referred 
  to 
  in 
  the 
  text 
  — 
  more, 
  if 
  the 
  

   number 
  of 
  the 
  components 
  is 
  moderate 
  and 
  their 
  intensities 
  considerable 
  ; 
  

   less, 
  when 
  the 
  number 
  of 
  components 
  is 
  increased 
  and 
  their 
  separate 
  

   intensities 
  correspondingly 
  lowered. 
  During 
  this 
  process 
  the 
  volume 
  

   within 
  which 
  the 
  resolution 
  is 
  available 
  increases. 
  But, 
  as 
  the 
  mathe- 
  

   matical 
  reader 
  will 
  understand, 
  it 
  is 
  only 
  at 
  the 
  limit, 
  when 
  the 
  number 
  

   of 
  components 
  has 
  been 
  increased 
  indefinitely 
  and 
  their 
  intensities 
  fall 
  

   to 
  being 
  infinitesimal 
  —when 
  in 
  fact 
  wavelets 
  take 
  the 
  place 
  in 
  the 
  

   undulations 
  of 
  waves, 
  and 
  when 
  the 
  range 
  of 
  wave-lengths 
  for 
  which 
  

   each 
  X 
  stands 
  has 
  become 
  an 
  infinitesimal 
  range 
  — 
  it 
  is 
  only 
  at 
  this 
  limit, 
  

   unattainable 
  in 
  practice, 
  that 
  the 
  components 
  are 
  entirely 
  devoid 
  of 
  the 
  

   above-mentioned 
  complications 
  and 
  become 
  undulations 
  of 
  waves 
  that 
  

   are 
  absolutely 
  alike. 
  The 
  resolution 
  would 
  then 
  become 
  what 
  would 
  be 
  

   true 
  of 
  all 
  space 
  and 
  all 
  time, 
  if 
  in 
  a 
  uniform 
  transparent 
  medium 
  of 
  

   infinite 
  extent. 
  

  

  