﻿Light 
  by 
  Cylinders 
  of 
  Large 
  Radius, 
  95 
  

  

  should 
  be 
  most 
  marked 
  when 
  the 
  region 
  of 
  the 
  caustic 
  under 
  

   observation 
  is 
  nearest 
  the 
  edge 
  o£ 
  the 
  cylinder, 
  and 
  for 
  the 
  

   fringes 
  which 
  are 
  farthest 
  from 
  the 
  caustic. 
  

  

  20. 
  The 
  foregoing 
  conclusions 
  have 
  been 
  tested 
  by 
  a 
  series 
  

   of 
  measurements 
  made 
  with 
  the 
  focal 
  plane 
  in 
  various 
  

   positions 
  in 
  advance 
  of 
  the 
  edge. 
  To 
  prove 
  that 
  the 
  

   boundary 
  of 
  the 
  field 
  within 
  the 
  shadow 
  is 
  the 
  caustic 
  and 
  

   not 
  the 
  surface 
  of 
  the 
  cylinder, 
  measurements 
  were 
  made 
  of 
  

   the 
  length 
  CP^ 
  the 
  rays 
  incident 
  on 
  the 
  cylinder 
  being 
  a 
  

   parallel 
  pencil. 
  

  

  Observed 
  value 
  of 
  CTi. 
  Calculated 
  value. 
  

  

  d=lmm 
  '00454 
  cm. 
  -00433 
  cm. 
  

  

  ^=1-3 
  mm.... 
  -00750 
  cm. 
  -00733 
  cm. 
  

  

  The 
  following 
  shows 
  the 
  widths 
  of 
  the 
  fringes 
  observed 
  in 
  

   the 
  neighbourhood 
  of 
  the 
  caustic 
  when 
  the 
  focal 
  plane 
  was 
  

   1*6 
  mm. 
  in 
  advance 
  of 
  the 
  edge, 
  and 
  the 
  widths 
  calculated 
  

   from 
  Airy's 
  theory. 
  

  

  Width 
  of 
  fringes 
  in 
  cm. 
  x 
  10 
  ~ 
  5 
  . 
  

  

  Observed 
  ... 
  159, 
  69, 
  56, 
  51, 
  45, 
  43 
  

   Calculated... 
  155, 
  70, 
  57, 
  50, 
  46, 
  43, 
  

   (Airy's 
  theory.) 
  

  

  The 
  agreement 
  in 
  both 
  cases 
  is 
  satisfactory. 
  

  

  21. 
  Table 
  IV. 
  shows 
  the 
  results 
  of 
  measurements 
  made 
  of 
  

   the 
  fringes 
  in 
  the 
  transition-stages 
  when 
  the 
  focal 
  plane 
  was 
  

   only 
  a 
  little 
  in 
  advance 
  of 
  the 
  edge, 
  and 
  Airy's 
  theory 
  is 
  not 
  

   fully 
  applicable. 
  The 
  observed 
  results 
  are 
  in 
  general 
  agree- 
  

   ment 
  with 
  the 
  indications 
  of 
  theory 
  set 
  out 
  in 
  paragraph 
  19. 
  

   It 
  will 
  be 
  seen 
  that 
  the 
  fringes 
  farthest 
  within 
  the 
  region 
  of 
  

   the 
  shadow 
  show 
  a 
  fair 
  agreement 
  with 
  Airy's 
  theory, 
  and 
  the 
  

   others 
  are 
  more 
  nearly 
  in 
  agreement 
  with 
  the 
  widths 
  calcu- 
  

   lated 
  from 
  formula 
  (B). 
  

  

  Summary 
  and 
  Conclusion. 
  

  

  22. 
  C. 
  F. 
  Brush 
  has 
  recently 
  published 
  some 
  observations 
  

   of 
  considerable 
  interest 
  on 
  the 
  diffraction 
  of 
  light 
  by 
  cylin- 
  

   drical 
  edges. 
  The 
  views 
  put 
  forward 
  by 
  him 
  to 
  explain 
  the 
  

   phenomena, 
  however, 
  present 
  serious 
  difficulties 
  and 
  are 
  

   open 
  to 
  objection. 
  My 
  attention 
  was 
  drawn 
  to 
  this 
  subject 
  

   by 
  Prof. 
  C. 
  V. 
  Raman, 
  at 
  whose 
  suggestion 
  the 
  present 
  work 
  

   was 
  undertaken 
  by 
  me 
  in 
  order 
  to 
  find 
  the 
  true 
  explanation 
  

   of 
  the 
  effects, 
  and 
  to 
  develop 
  a 
  mathematical 
  theory 
  which 
  

   would 
  stand 
  a 
  quantitative 
  test 
  in 
  experiment. 
  This 
  has 
  now 
  

  

  