﻿Grapliical 
  Methods 
  of 
  collecting 
  Telescopic 
  Objectives. 
  471 
  

  

  Completing 
  the 
  application 
  to 
  a 
  distribution 
  x± 
  we 
  have 
  

   the 
  internal 
  potential 
  

  

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  4ttH 
  2 
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  4 
  , 
  a 
  4 
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  4 
  ] 
  

  

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  r^ 
  a 
  6-/^ 
  

  

  1 
  17 
  6 
  S' 
  

  

  As 
  a 
  verification, 
  the 
  internal 
  and 
  external 
  expansions 
  

   coincide 
  if 
  we 
  write 
  r 
  = 
  a. 
  The 
  external 
  potential 
  satisfies 
  

   Laplace's 
  equation 
  while 
  the 
  other 
  yields 
  47rcc*wheii 
  operated 
  

   on 
  with 
  A, 
  agreeing 
  with 
  Poisson's 
  equation*. 
  

  

  LV. 
  On 
  Grapliical 
  Methods 
  of 
  correcting 
  Telescopic 
  Objectives. 
  

   By 
  A. 
  0. 
  Allen, 
  Lecturer 
  in 
  Optics, 
  The 
  University 
  of 
  

   Leeds 
  f. 
  

  

  HAVING 
  had 
  occasion 
  recently 
  to 
  use 
  the 
  N.P.L. 
  tables 
  

   relating 
  to 
  small 
  objectives, 
  it 
  occurred 
  to 
  me 
  that 
  the 
  

   information 
  there 
  furnished, 
  as 
  well 
  as 
  much 
  more 
  of 
  equal 
  

   or 
  even 
  greater 
  importance, 
  could 
  be 
  given 
  in 
  a 
  very 
  small 
  

   compass 
  by 
  means 
  of 
  a 
  few 
  formulae, 
  in 
  combination 
  with 
  

   graphical 
  methods. 
  It 
  is 
  true 
  that 
  this 
  means 
  substituting 
  

   calculation 
  for 
  a 
  direct 
  extraction 
  of 
  values 
  from 
  tables, 
  but 
  

   a 
  number 
  of 
  considerations 
  may 
  be 
  set 
  off 
  against 
  this. 
  First, 
  

   the 
  calculations 
  I 
  propose 
  are 
  quite 
  simple; 
  most 
  of 
  them 
  are 
  

   also 
  fairly 
  short. 
  Such 
  as 
  they 
  are, 
  they 
  are 
  not 
  likely 
  to 
  act 
  

   as 
  a 
  deterrent 
  ; 
  for 
  it 
  must 
  be 
  remembered 
  that 
  both 
  the 
  

   tables 
  and 
  the 
  equivalent 
  calculations 
  lead 
  to 
  figures 
  such 
  as 
  

   no 
  manufacturer 
  with 
  a 
  reputation 
  to 
  keep 
  up 
  would 
  employ. 
  

   It 
  may 
  safely 
  be 
  assumed 
  that 
  in 
  future 
  all 
  lens-makers 
  will 
  

   use 
  the 
  services 
  of 
  an 
  expert 
  computer, 
  and 
  the 
  labour 
  

   of 
  computing 
  is 
  so 
  great 
  in 
  any 
  case 
  that 
  a 
  little 
  more 
  

   at 
  the 
  outset 
  will 
  not 
  be 
  objected 
  to, 
  especially 
  if 
  that 
  

   little 
  extra 
  work 
  saves 
  a 
  great 
  deal 
  of 
  labour 
  further 
  on. 
  

   Again, 
  the 
  tables 
  are 
  only 
  for 
  a 
  few 
  selected 
  glasses 
  ; 
  no 
  

   tables 
  of 
  reasonable 
  bulk 
  could 
  include 
  all 
  available 
  glasses, 
  

   and 
  even 
  with 
  th^se 
  few 
  it 
  is 
  necessary 
  to 
  apply 
  sundry 
  

   corrections 
  for 
  variations 
  of 
  refractive 
  index 
  and 
  dispersive 
  

  

  * 
  In 
  general 
  the 
  polynomial 
  

  

  rm 
  m 
  HH 
  m 
  . 
  a 
  ^H 
  OT 
  _ 
  4 
  

  

  2(2w+3) 
  "r 
  U2m+1) 
  + 
  6(2w-l) 
  "*"' 
  " 
  

  

  yields 
  the 
  right 
  member 
  of 
  (E) 
  when 
  operated 
  on 
  by 
  A, 
  (proof 
  by 
  (F)). 
  

   + 
  Communicated 
  by 
  the 
  Author. 
  

  

  