﻿32 
  Dr. 
  L. 
  Silberstein 
  on 
  Lijht 
  Distribution 
  

  

  fact 
  it 
  is, 
  in 
  its 
  essence. 
  None 
  the 
  less 
  it 
  seems 
  desirable 
  to 
  

   treat 
  problems 
  relating 
  to 
  concrete 
  lenses 
  with 
  all 
  numerical 
  

   (or 
  graphical) 
  details, 
  and 
  to 
  express 
  the 
  results 
  in 
  terms 
  of 
  

   the 
  attributes 
  of 
  the 
  given 
  lens 
  or 
  lens 
  system. 
  

  

  It 
  is 
  precisely 
  the 
  object 
  of 
  the 
  present 
  paper 
  to 
  give 
  

   a 
  fully 
  worked 
  out 
  example 
  of 
  this 
  kind, 
  as 
  a 
  part 
  of 
  investi- 
  

   gations 
  undertaken 
  at 
  the 
  instance 
  of 
  Messrs. 
  Adam 
  Hilger 
  

   in 
  connexion 
  with 
  their 
  Lens 
  Interferometer 
  which 
  exhibits 
  

   ad 
  oculos, 
  through 
  its 
  " 
  contour 
  map/' 
  the 
  phase 
  retardation 
  

   of 
  all 
  the 
  elements 
  of 
  an 
  originally 
  plane 
  wave 
  produced 
  

   by 
  the 
  passage 
  through 
  a 
  given 
  lens. 
  The 
  example 
  selected 
  

   for 
  the 
  present 
  purpose 
  relates 
  to 
  the 
  simplest 
  possible 
  lens, 
  

   viz. 
  the 
  plano-convex 
  lens, 
  traversed 
  by 
  a 
  beam 
  of 
  finite 
  

   circular 
  section 
  along 
  the 
  optical 
  axis. 
  It 
  has 
  seemed 
  that, 
  

   owing 
  to 
  its 
  extreme 
  simplicity, 
  it 
  may 
  be 
  the 
  best 
  to 
  show 
  

   the 
  reader 
  a 
  practicable 
  and 
  easy 
  way 
  of 
  dealing 
  with 
  more 
  

   complicated 
  telescopic 
  objectives. 
  

  

  To 
  complete 
  the 
  above 
  bibliographic 
  sketch 
  we 
  ha\e 
  

   still 
  to 
  mention 
  that 
  the 
  remaining 
  chapters 
  of 
  Strehl's 
  

   work 
  are 
  dedicated 
  to 
  the 
  diffractional 
  aspect 
  of 
  astigmatism 
  

   and 
  coma 
  which 
  are 
  treated 
  on 
  similar 
  lines 
  as 
  spherical 
  

   aberration, 
  to 
  cylindrical 
  waves, 
  etc. 
  These 
  subjects, 
  how- 
  

   ever, 
  are 
  beyond 
  the 
  scope 
  of 
  the 
  present 
  communication. 
  

   Lastly, 
  we 
  have 
  to 
  mention 
  a 
  more 
  recent 
  paper 
  by 
  James 
  

   Walker 
  (Proc. 
  Phys. 
  Soc. 
  London, 
  vol. 
  xxiv. 
  1912, 
  pp. 
  160- 
  

   164) 
  in 
  which 
  the 
  subject 
  of 
  Strehl's 
  Chapter 
  VII., 
  viz. 
  the 
  

   intensity 
  due 
  to 
  a 
  rotationally 
  ellipsoidal 
  wave, 
  is 
  again 
  

   taken 
  up. 
  Here 
  the 
  expression 
  for 
  the 
  intensity 
  is 
  deve- 
  

   loped 
  into 
  a 
  complicated 
  double 
  series 
  (c/. 
  last 
  line 
  of 
  the 
  

   paper 
  quoted) 
  which, 
  although 
  mathematically 
  unobjection- 
  

   able, 
  does 
  not 
  seem 
  convenient 
  for 
  actual 
  calculation 
  *. 
  

  

  It 
  must 
  be 
  kept 
  in 
  mind 
  that 
  for 
  physical 
  applications 
  

   hardly 
  more 
  than 
  two 
  significant 
  figures 
  in 
  the 
  final 
  light 
  

   intensity 
  are 
  required. 
  Under 
  these 
  circumstances 
  the 
  

   method 
  of 
  mechanical 
  quadratures 
  or 
  a 
  graphic 
  method, 
  

   analogous 
  to 
  that 
  of 
  the 
  Cornu 
  spiral, 
  seems 
  by 
  far 
  the 
  

   most 
  convenient. 
  Although 
  laborious 
  for 
  very 
  accurate 
  

   work, 
  it 
  certainly 
  becomes 
  very 
  handy 
  when 
  only 
  the 
  said 
  

   degree 
  of 
  precision 
  is 
  aimed 
  at. 
  It 
  will 
  be 
  explained 
  and 
  

   applied 
  in 
  what 
  follows. 
  

  

  * 
  It 
  has 
  occurred 
  to 
  me 
  that 
  some 
  of 
  Walker's 
  intermediate 
  formulae, 
  

   as 
  for 
  instance 
  that 
  on 
  top 
  of 
  p. 
  163, 
  would 
  easily 
  yield 
  a 
  more 
  

   " 
  commodious 
  " 
  expression 
  than 
  is 
  the 
  final 
  one. 
  

  

  