﻿Light 
  Distribution 
  round 
  the 
  Focus 
  of 
  a 
  Lens. 
  31 
  

  

  which 
  are 
  developed 
  into 
  power 
  series 
  of 
  the 
  upper 
  limit 
  or 
  of 
  

   its 
  reciprocal. 
  LommePs 
  results 
  have 
  been 
  adapted, 
  in 
  1891, 
  

   to 
  the 
  problem 
  of 
  pin-hole 
  photography 
  by 
  Lord 
  Rayleigh*, 
  

   whose 
  paper, 
  besides 
  a 
  theoretical 
  and 
  experimental 
  discussion 
  

   of 
  the 
  subject, 
  gives 
  also 
  five 
  curves 
  exhibiting 
  the 
  distri- 
  

   bution 
  of 
  light 
  round 
  the 
  centre 
  of 
  the 
  image 
  corresponding 
  

   to 
  different 
  apertures. 
  As 
  will 
  be 
  seen 
  later 
  on, 
  the 
  typical 
  

   phase 
  aberrations 
  of 
  wave-surfaces 
  emerging 
  from 
  lenses 
  

   differ 
  in 
  kind 
  from 
  those 
  involved 
  in 
  the 
  pin-hole 
  problem. 
  

   Investigations 
  laiming 
  directly 
  at 
  a 
  diffractional 
  treatment 
  of 
  

   the 
  images 
  produced 
  by 
  lenses 
  were 
  undertaken, 
  in 
  1893, 
  by 
  

   R. 
  Straubel, 
  whose 
  papers 
  are 
  quoted 
  in 
  Winkelmann's 
  

   * 
  Handbuch 
  ' 
  (1906, 
  vol. 
  vi. 
  p. 
  106), 
  but 
  unfortunately 
  are 
  

   not 
  accessible 
  to 
  the 
  writer, 
  and 
  a 
  little 
  later 
  by 
  K. 
  Strehl 
  in 
  

   a 
  very 
  attractive 
  book 
  entitled 
  ' 
  Theorie 
  des 
  Fernrohrs 
  auf 
  

   Grund 
  der 
  Beugung 
  des 
  Lichts' 
  (Barth: 
  Leipzig, 
  1894) 
  f. 
  

   The 
  earlier 
  part 
  of 
  the 
  work 
  being 
  dedicated 
  to 
  preparatory 
  

   matter, 
  Strehl 
  investigates 
  in 
  Chap. 
  V. 
  and 
  VI. 
  the 
  intensity 
  

   along 
  the 
  optical 
  axis 
  aud 
  in 
  the 
  focal 
  plane 
  of 
  an 
  aplanatic 
  

   object-glass, 
  and 
  since 
  this 
  is 
  materially 
  the 
  same 
  problem 
  as 
  

   that 
  of 
  a 
  circular 
  aperture 
  treated 
  by 
  Lommel 
  (loc. 
  cit.), 
  

   Strehl 
  bases 
  himself 
  upon 
  Lommel's 
  results, 
  as 
  had 
  already 
  

   been 
  done 
  by 
  Lord 
  Rayleigh, 
  and 
  enunciates 
  a 
  number 
  of 
  

   theorems 
  on 
  the 
  general 
  features 
  of 
  the 
  light 
  distribution 
  for 
  

   the 
  case 
  in 
  question. 
  The 
  effects 
  of 
  " 
  spherical 
  aberration" 
  

   are 
  treated 
  in 
  Chap. 
  VII., 
  where 
  the 
  intensity 
  formula 
  is 
  

   developed 
  for 
  the 
  case 
  in 
  which 
  the 
  emergent 
  wave 
  is 
  an 
  

   ellipsoid 
  of 
  revolution 
  ; 
  the 
  series 
  developments 
  (pp. 
  62-63) 
  

   are 
  very 
  complicated, 
  and 
  it 
  does 
  not 
  appear 
  that 
  they 
  could 
  

   conveniently 
  be 
  applied 
  to 
  concrete 
  numerical 
  calculations. 
  

   They 
  enable 
  Strehl, 
  however, 
  to 
  enunciate 
  some 
  general 
  

   theorems 
  about 
  the 
  symmetry 
  relations 
  of 
  the 
  diffraction 
  

   effects 
  associated 
  with 
  spherical 
  aberration 
  of 
  the 
  said 
  kind, 
  

   and 
  an 
  important 
  conclusion 
  on 
  the 
  true 
  measure 
  of 
  the 
  mis- 
  

   chievous 
  effect 
  of 
  spherical 
  aberration 
  (p. 
  65). 
  In 
  a 
  sense, 
  

   Strehl 
  is 
  right 
  in 
  declaring 
  that 
  by 
  his 
  investigation 
  "the 
  

   problem 
  of 
  spherical 
  aberration 
  is 
  completely 
  solved." 
  So 
  

  

  * 
  Phil. 
  Mag. 
  vol. 
  xxxi. 
  (1891) 
  pp. 
  87-99. 
  

  

  f 
  After 
  that 
  Strehl 
  has 
  published 
  several 
  papers 
  in 
  Zeitschr. 
  f. 
  

   Instrument 
  enkunde 
  for 
  1895-98 
  which 
  I 
  have 
  not 
  been 
  able 
  to 
  consult. 
  

   However, 
  to 
  judge 
  from 
  Winkelmann's 
  quotation, 
  the 
  ground 
  covered 
  

   "by 
  these 
  papers 
  is 
  essentially 
  that 
  of 
  Strehl's 
  book. 
  Winkelmann 
  {loc. 
  

   cit. 
  p. 
  403) 
  quotes 
  also, 
  in 
  connexion 
  with 
  the 
  diffractional 
  theory 
  of 
  

   the 
  telescope, 
  Ch. 
  Andrews 
  " 
  Etude 
  de 
  la 
  diffraction 
  dans 
  les 
  instruments 
  

   d'optique 
  " 
  (Paris, 
  1876J, 
  without, 
  however, 
  describing 
  the 
  contents 
  of 
  

   this 
  paper, 
  which 
  was 
  published 
  in 
  Ann. 
  sc. 
  de 
  l^cole 
  norm, 
  super 
  ieure, 
  

   vol. 
  v. 
  

  

  