﻿Light 
  by 
  Cylinders 
  of 
  Large 
  Radius. 
  85 
  

  

  point 
  P 
  is 
  evidently 
  equal 
  to 
  QP 
  — 
  RP, 
  which 
  can 
  be 
  easily 
  

   shown 
  to 
  be 
  given 
  by 
  

  

  8=a 
  sin 
  0(sec 
  20-1). 
  

  

  Fig. 
  2. 
  

  

  Similarly, 
  we 
  shall 
  have 
  

  

  x 
  — 
  a 
  sec 
  2<9(cos 
  0— 
  cos 
  29). 
  

   Therefore, 
  neglecting 
  4th 
  and 
  higher 
  powers 
  of 
  6 
  t 
  we 
  have 
  

  

  8 
  = 
  '2a0\ 
  and 
  x 
  = 
  3ad 
  2 
  /2, 
  

   so 
  that 
  S=2a(|) 
  1 
  . 
  

  

  Since 
  by 
  reflexion 
  the 
  rays 
  suffer 
  a 
  phase 
  change 
  of 
  half 
  a 
  

   wave-length, 
  the 
  edge 
  will 
  form 
  the 
  centre 
  of 
  a 
  dark 
  band, 
  

   and 
  the 
  successive 
  minima 
  are 
  therefore 
  given 
  by 
  

  

  where 
  n~l, 
  2, 
  3, 
  &c. 
  The 
  results 
  calculated 
  according 
  to 
  

   the 
  above 
  theory 
  and 
  those 
  found 
  in 
  experiment 
  are 
  given 
  in 
  

   Table 
  I. 
  

  

  