﻿84 
  Mr. 
  Nalinimohan 
  Basu 
  on 
  the 
  Diffraction 
  of 
  

  

  present 
  paper. 
  With 
  a 
  sharp 
  edge, 
  the 
  fringes 
  of 
  the 
  Fresnel 
  

   type 
  disappear 
  when 
  the 
  focal 
  plane 
  coincides 
  with 
  it, 
  and 
  

   reappear 
  without 
  alteration 
  of 
  type 
  when 
  the 
  focal 
  plane 
  is 
  

   between 
  the 
  edge 
  and 
  the 
  source 
  of 
  light. 
  As 
  mentioned 
  

   above 
  and 
  shown 
  in 
  figs. 
  VII. 
  and 
  VIII. 
  of 
  the 
  Plate, 
  fringes 
  

   of 
  this 
  type 
  may 
  also 
  be 
  observed 
  with 
  the 
  cylinder 
  when 
  the 
  

   focal 
  plane 
  is 
  in 
  this 
  position, 
  and 
  in 
  addition 
  we 
  have, 
  

   inside 
  the 
  shadow, 
  an 
  entirely 
  separate 
  system 
  of 
  fringes 
  

   characterized 
  by 
  perfectly 
  black 
  minima 
  and 
  a 
  series 
  of 
  

   maxima 
  with 
  intensities 
  converging 
  to 
  zero. 
  This 
  latter 
  

   system 
  has 
  nothing 
  in 
  common 
  with 
  the 
  diffraction 
  phe- 
  

   nomena 
  of 
  the 
  Fresnel 
  class, 
  and 
  has 
  obviously 
  an 
  entirely 
  

   different 
  origin. 
  That 
  it 
  is 
  formed 
  exclusively 
  by 
  the 
  light 
  

   reflected 
  from 
  the 
  surface 
  of 
  the 
  cylinder 
  is 
  proved 
  by 
  the 
  

   fact 
  that 
  it 
  may 
  be 
  cut 
  off 
  without 
  affecting 
  the 
  rest 
  of 
  the 
  

   field 
  by 
  screening 
  the 
  surface. 
  It 
  is 
  accordingly 
  clear 
  that 
  

   the 
  light 
  reflected 
  from 
  the 
  surface 
  of 
  the 
  cylinder 
  plays 
  a 
  

   most 
  important 
  part 
  in 
  the 
  explanation 
  of 
  the 
  phenomena, 
  

   and 
  that 
  the 
  edge 
  of 
  the 
  cylinder 
  grazed 
  by 
  the 
  incident 
  rays 
  

   alone 
  acts 
  as 
  a 
  diffracting 
  edge 
  in 
  the 
  usual 
  way, 
  and 
  not 
  all 
  

   the 
  elements 
  of 
  the 
  surface 
  as 
  supposed 
  by 
  Brush. 
  We 
  shall 
  

   accordingly 
  proceed 
  on 
  this 
  basis 
  to 
  consider 
  the 
  theory 
  of 
  

   the 
  fringes 
  observed 
  in 
  various 
  positions 
  of 
  the 
  focal 
  plane 
  

   of 
  the 
  objective. 
  

  

  Theory 
  of 
  the 
  Fringes 
  at 
  the 
  edge 
  of 
  the 
  cylinder. 
  

  

  9. 
  When 
  the 
  focal 
  plane 
  coincides 
  with 
  the 
  edge 
  at 
  which 
  

   the 
  incident 
  light 
  grazes 
  the 
  cylinder, 
  it 
  is 
  permissible 
  to 
  

   regard 
  the 
  fringes 
  seen 
  as 
  formed 
  by 
  T 
  simple 
  interference 
  

   between 
  the 
  light 
  that 
  passes 
  the 
  cylinder 
  unobstructed 
  and 
  

   the 
  light 
  that 
  suffers 
  reflexion 
  at 
  the 
  surface 
  of 
  the 
  cylinder 
  

   at 
  various 
  incidences 
  ; 
  for, 
  if 
  a 
  sharp 
  diffracting 
  edge 
  be 
  put 
  

   in 
  the 
  focal 
  plane 
  in 
  the 
  same 
  position, 
  no 
  diffraction-fringes 
  

   would 
  be 
  visible. 
  The 
  positions 
  of 
  the 
  minima 
  of 
  illumination 
  

   in 
  the 
  field 
  may 
  be 
  readily 
  calculated. 
  

  

  In 
  fig. 
  2, 
  let 
  be 
  the 
  centre 
  of 
  the 
  cross-section 
  of 
  

   the 
  cylinder 
  in 
  the 
  plane 
  of 
  incidence, 
  and 
  let 
  C 
  be 
  the 
  

   point 
  at 
  which 
  the 
  light 
  grazes 
  the 
  cylinder. 
  It 
  is 
  sufficient 
  

   for 
  practical 
  purposes 
  to 
  consider 
  the 
  incident 
  beam 
  as 
  a 
  

   parallel 
  pencil 
  of 
  rays. 
  The 
  ray 
  meeting 
  the 
  cylinder 
  at 
  the 
  

   point 
  Q 
  is 
  reflected 
  in 
  the 
  direction 
  QP. 
  Let 
  L 
  QOA 
  = 
  #, 
  so 
  

  

  that 
  Z0QP= 
  \ 
  + 
  0> 
  and 
  ZOPQ 
  = 
  ^-2<9. 
  Let 
  a 
  be 
  the 
  

  

  radius 
  of 
  the 
  cylinder 
  and 
  CP=#. 
  The 
  difference 
  of 
  path, 
  8, 
  

   between 
  the 
  direct 
  ray 
  and 
  the 
  reflected 
  ray 
  reaching 
  the 
  

  

  