﻿Light 
  by 
  Cylinders 
  of 
  Large 
  Radius. 
  81 
  

  

  given 
  by 
  J. 
  J. 
  Thomson 
  *, 
  and 
  for 
  a 
  dielectric 
  cylinder 
  by 
  

   Lord 
  Rayleigh 
  t- 
  These 
  solutions 
  are, 
  however, 
  suitable 
  for 
  

   numerical 
  computation 
  only 
  when 
  the 
  radius 
  of 
  the 
  cylinder 
  

   is 
  comparable 
  with 
  tbe 
  wave-length. 
  A 
  treatment 
  of 
  the 
  

   problem 
  in 
  the 
  case 
  of 
  a 
  cylinder 
  of 
  any 
  radius 
  has 
  been 
  

   recently 
  given 
  by 
  Debye 
  J 
  . 
  He 
  considers 
  the 
  electromagnetic 
  

   field 
  round 
  a 
  perfectly 
  reflecting 
  cylinder, 
  whose 
  axis 
  is 
  taken 
  

   for 
  axis 
  of 
  z, 
  with 
  polar 
  co-ordinates 
  r, 
  <£, 
  and 
  waves 
  in 
  the 
  

   plane 
  xy 
  polarized 
  in 
  the 
  direction 
  of 
  2", 
  the 
  electric 
  component 
  

   in 
  z 
  being 
  e 
  ikx 
  . 
  Expressing 
  the 
  disturbance-field 
  in 
  the 
  form 
  

  

  Z=-2e 
  H 
  Ua) 
  ' 
  H 
  *(* 
  r 
  ) 
  cos 
  n< 
  £ 
  

  

  (in 
  which 
  J 
  n 
  is 
  the 
  usual 
  Bessel 
  function, 
  H 
  n 
  is 
  Hankel's 
  

   second 
  cylindrical 
  function, 
  and 
  K 
  = 
  2ir/X) 
  i 
  Debye 
  transforms 
  

   the 
  solution 
  into 
  the 
  simple 
  form 
  

  

  / 
  aC0S 
  2 
  / 
  *\ 
  

  

  Debye's 
  work 
  is 
  of 
  considerable 
  significance, 
  but 
  his 
  final 
  

   solution 
  is 
  valid 
  only 
  for 
  points 
  at 
  a 
  great 
  distance 
  from 
  the 
  

   surface 
  of 
  the 
  cylinder, 
  whereas 
  the 
  phenomena 
  considered 
  

   in 
  the 
  present 
  paper 
  are 
  those 
  observed 
  in 
  its 
  immediate 
  

   neighbourhood. 
  No 
  complete 
  mathematical 
  treatment 
  of 
  

   the 
  subject 
  now 
  dealt 
  with 
  appears 
  to 
  have 
  been 
  given 
  

   so 
  far. 
  

  

  General 
  Description 
  of 
  the 
  Phenomena. 
  

   1. 
  

  

  4. 
  The 
  experimental 
  arrangements 
  are 
  those 
  shown 
  in 
  the 
  

   diagram 
  (fig. 
  1). 
  Light 
  from 
  a 
  slit 
  S 
  falls 
  on 
  a 
  polished 
  

  

  * 
  ' 
  Recent 
  Researches 
  in 
  Electricity 
  and 
  Magnetism,' 
  p. 
  428. 
  

  

  t 
  Phil. 
  Mag. 
  1881 
  . 
  ' 
  Scientific 
  Works,' 
  vol. 
  i. 
  p. 
  534. 
  

  

  \ 
  P. 
  Debye, 
  " 
  On 
  the 
  Electromagnetic 
  Field 
  surrounding 
  a 
  Cylinder 
  

   and 
  the 
  Theory 
  of 
  the 
  Rainbow," 
  Phys. 
  Zeitschr. 
  ix. 
  pp. 
  775-778, 
  Nov. 
  

   1908. 
  Also 
  Deutsch. 
  Phys. 
  Gesell. 
  Verh. 
  10, 
  20, 
  pp. 
  741-749, 
  Oct. 
  1908 
  ; 
  

   and 
  ' 
  Science 
  Abstracts,' 
  No. 
  258 
  (1909). 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  205. 
  Jan. 
  1918. 
  G 
  

  

  