﻿96 
  

  

  Diffraction 
  of 
  Light 
  by 
  Cylinders 
  of 
  Large 
  Radius. 
  

   Table 
  IV. 
  

  

  Widths 
  of 
  Bright 
  Bands 
  in 
  cm.xlO" 
  6 
  . 
  

   a 
  = 
  l'54 
  cm. 
  X=6562xl0" 
  8 
  cm. 
  

  

  Observed 
  

   widths. 
  

  

  Calculated 
  

  

  [Airy's 
  

   Formula]. 
  

  

  Calculated 
  

  

  [Formula 
  

  

  (B)]. 
  

  

  Observed 
  

   widths. 
  

  

  Calculated 
  

  

  [Airy's 
  

   Formula], 
  

  

  Calculated 
  

  

  [Formula 
  

  

  (B)]. 
  

  

  :=-2 
  

  

  d=A 
  

  

  1546 
  

   852 
  

  

  722 
  

   672 
  

   622 
  

   590 
  

  

  1550 
  

  

  

  1555 
  

  

  1550 
  

  

  696 
  

  

  894 
  

  

  777 
  

  

  696 
  

  

  570 
  

  

  777 
  

  

  628 
  

  

  570 
  

  

  504 
  

  

  705 
  

  

  590 
  

  

  504 
  

  

  461 
  

  

  637 
  

  

  566 
  

  

  461 
  

  

  429 
  

  

  602 
  

  

  500 
  

  

  429 
  

  

  754 
  

   674 
  

   636 
  

   594 
  

   543 
  

  

  d 
  = 
  '& 
  mm. 
  

  

  ^='8 
  mm. 
  

  

  1513 
  

  

  1550 
  

  

  

  1466 
  

  

  1550 
  

  

  700 
  

  

  696 
  

  

  

  706 
  

  

  696 
  

  

  626 
  

  

  570 
  

  

  586 
  

  

  563 
  

  

  570 
  

  

  536 
  

  

  504 
  

  

  549 
  

  

  503 
  

  

  504 
  

  

  493 
  

  

  461 
  

  

  520 
  

  

  475 
  

  

  461 
  

  

  446 
  

  

  429 
  

  

  497 
  

  

  448 
  

  

  429 
  

  

  508 
  

   483 
  

   463 
  

  

  been 
  done, 
  and 
  in 
  the 
  course 
  of 
  the 
  investigation 
  various 
  

   features 
  of 
  importance 
  overlooked 
  by 
  Brush 
  have 
  come 
  to 
  

   light. 
  The 
  following 
  are 
  the 
  principal 
  conclusions 
  arrived 
  at 
  : 
  

   (a) 
  The 
  fringes 
  seen 
  in 
  the 
  plane 
  at 
  which 
  the 
  incident 
  light 
  

   grazes 
  the 
  cylinder 
  are 
  due 
  to 
  the 
  simple 
  interference 
  of 
  

   the 
  direct 
  and 
  the 
  reflected 
  rays, 
  the 
  positions 
  of 
  the 
  

   dark 
  bands 
  being 
  given 
  by 
  the 
  formula 
  #=-f 
  . 
  (2a)£. 
  (n\)% 
  ; 
  

   (6) 
  the 
  fringes 
  in 
  a 
  plane 
  further 
  removed 
  from 
  the 
  source 
  

   of 
  light 
  than 
  the 
  cylinder 
  are 
  due 
  to 
  diffraction 
  at 
  the 
  edge 
  

   grazed 
  by 
  the 
  incident 
  rays 
  but 
  modified 
  by 
  interference 
  

   with 
  the 
  light 
  reflected 
  from 
  the 
  surface 
  of 
  the 
  cylinder. 
  

   The 
  positions 
  of 
  the 
  dark 
  bands 
  in 
  these 
  fringes 
  are 
  (to 
  a 
  close 
  

   approximation) 
  given 
  by 
  the 
  formulae* 
  x 
  = 
  2d6 
  + 
  3a# 
  2 
  /2, 
  and 
  

   n\ 
  = 
  2d0 
  2 
  -\-2a6 
  3 
  , 
  from 
  which 
  6 
  is 
  to 
  be 
  eliminated; 
  (c) 
  when 
  

   the 
  focal 
  plane 
  of 
  the 
  observing 
  microscope 
  is 
  on 
  the 
  side 
  of 
  

   the 
  cylinder 
  towards 
  the 
  light, 
  the 
  direct 
  and 
  reflected 
  rays 
  

   do 
  not 
  both 
  cover 
  exactly 
  the 
  same 
  part 
  of 
  the 
  field, 
  and 
  by 
  

   putting 
  the 
  focal 
  plane 
  sufficiently 
  forward 
  towards 
  the 
  light, 
  

  

  * 
  This 
  formula 
  is 
  subject 
  to 
  a 
  small 
  correction 
  which 
  is 
  of 
  importance 
  

   only 
  when 
  d 
  is 
  large. 
  

  

  