﻿Harhiess 
  — 
  Achromatic 
  Objectives 
  of 
  Telescopes. 
  287 
  

  

  Art. 
  XXIX. 
  — 
  On 
  the 
  Best 
  Form 
  for 
  the 
  Double 
  Achromatic 
  

   Objectives 
  of 
  Telescopes 
  /* 
  by 
  Wi. 
  Harkness. 
  

  

  When 
  the 
  thicknesses 
  and 
  distances 
  apart 
  of 
  the 
  two 
  com- 
  

   ponent 
  lenses 
  are 
  so 
  small 
  that 
  they 
  can 
  be 
  neglected, 
  the 
  

   curvatures 
  of 
  the 
  surfaces 
  of 
  these 
  lenses 
  are 
  the 
  only 
  disposable 
  

   constants 
  for 
  satisfying 
  the 
  equations 
  which 
  determine 
  the 
  

   properties 
  of 
  a 
  double 
  achromatic 
  objective. 
  As 
  there 
  are 
  

   four 
  of 
  these 
  surfaces, 
  four 
  conditions 
  can 
  be 
  satisfied. 
  Three 
  

   of 
  them 
  are 
  always 
  employed 
  in 
  determining 
  the 
  focal 
  length 
  

   of 
  the 
  objective, 
  its 
  color 
  correction, 
  and 
  the 
  correction 
  for 
  

   spherical 
  aberration 
  of 
  rays 
  proceeding 
  from 
  an 
  infinitely 
  dis- 
  

   tant 
  point 
  lying 
  in 
  the 
  optical 
  axis 
  of 
  the 
  telescope. 
  For 
  the 
  

   disposition 
  of 
  the 
  remaining 
  constant 
  various 
  conditions 
  have 
  

   been 
  proposed, 
  among 
  which 
  the 
  following 
  may 
  be 
  mentioned 
  

   because 
  they 
  have 
  secured 
  a 
  prominent 
  place 
  in 
  optical 
  practice 
  : 
  

  

  In 
  1756 
  Clairautf 
  suggested 
  that 
  the 
  interior 
  surfaces 
  of 
  the 
  

   crown 
  and 
  flint 
  lenses 
  should 
  have 
  the 
  same 
  curvature, 
  in 
  order 
  

   that 
  they 
  might 
  be 
  cemented 
  together, 
  and 
  that 
  plan 
  has 
  since 
  

   been 
  almost 
  universally 
  adopted 
  in 
  all 
  spy 
  and 
  binocular 
  glasses. 
  

   In 
  1778 
  Kliigel 
  proposed 
  that 
  the 
  crown 
  lens 
  should 
  be 
  made 
  

   equi-convex, 
  in 
  order 
  to 
  secure 
  with 
  a 
  given 
  thickness 
  of 
  glass 
  

   the 
  shortest 
  possible 
  focal 
  distance, 
  or, 
  in 
  other 
  words, 
  the 
  

   greatest 
  possible 
  angular 
  aperture 
  ; 
  and 
  in 
  1810;}; 
  he 
  proposed 
  

   that 
  the 
  radii 
  of 
  the 
  outer 
  and 
  inner 
  surfaces 
  of 
  the 
  crown 
  lens 
  

   should 
  be 
  to 
  each 
  other 
  as 
  1 
  : 
  3, 
  or 
  more 
  exactly 
  as 
  (2 
  — 
  n) 
  :n, 
  

   where 
  n 
  is 
  the 
  refractive 
  index 
  of 
  the 
  glass. 
  The 
  method 
  of 
  

   determining 
  the 
  curves 
  of 
  the 
  objective 
  when 
  the 
  crown 
  is 
  

   equi-convex 
  was 
  greatly 
  improved 
  by 
  Littrow 
  in 
  1827§ 
  and 
  

   since 
  then 
  that 
  construction 
  has 
  been 
  much 
  employed 
  under 
  

   the 
  name 
  of 
  Littrow's 
  objective. 
  In 
  1816 
  Bohnenberger 
  wrote 
  

   a 
  paper 
  to 
  show 
  that 
  the 
  spherical 
  and 
  achromatic 
  aberrations 
  

   were 
  best 
  corrected 
  by 
  making 
  the 
  radii 
  of 
  the 
  outer 
  and 
  inner 
  

   surfaces 
  of 
  the 
  crown 
  lens 
  in 
  the 
  ratio 
  of 
  2:3, 
  and 
  that 
  con- 
  

   struction 
  has 
  also 
  found 
  much 
  favor. 
  Finally, 
  about 
  1824 
  or 
  

   1825 
  Fraunhofer 
  introduced 
  a 
  form 
  of 
  objective 
  which 
  is 
  cer- 
  

   tainly 
  superior 
  to 
  any 
  previously 
  known, 
  but 
  he 
  never 
  gave 
  its 
  

   theory, 
  and 
  because 
  it 
  is 
  rather 
  more 
  difficult 
  to 
  make 
  and 
  

   adjust 
  than 
  the 
  forms 
  advocated 
  by 
  Clairaut, 
  Kliigel, 
  Littrow 
  

   and 
  Bohnenberger, 
  it 
  has 
  never 
  been 
  popular 
  with 
  practical 
  

   opticians. 
  

  

  * 
  This 
  paper, 
  in 
  a 
  slightly 
  different 
  form, 
  was 
  read 
  before 
  the 
  Philosophical 
  

   Society 
  of 
  Washington 
  on 
  October 
  23, 
  1893. 
  

   t 
  Mem. 
  Paris 
  Acad., 
  1756, 
  p. 
  431. 
  

   % 
  Gilbert's 
  Annalen. 
  1810, 
  xxxiv, 
  280. 
  

   §Mem. 
  Roy. 
  Ast. 
  Soc, 
  1827, 
  vol. 
  iii, 
  pp. 
  235-255. 
  

  

  