﻿Achromatic 
  Objectives 
  of 
  Telescopes. 
  291 
  

  

  The 
  equations 
  (9) 
  are 
  of 
  the 
  second 
  degree, 
  and 
  consequently 
  

   give 
  two 
  sets 
  of 
  radii. 
  Herschel 
  preferred 
  that 
  set 
  which 
  gave 
  

   the 
  flattest 
  curves 
  to 
  the 
  lenses, 
  and 
  it 
  is 
  to 
  be 
  remarked 
  that 
  

   the 
  resulting 
  objectives 
  resemble 
  those 
  constructed 
  by 
  Fraun- 
  

   hofer 
  so 
  closely 
  as 
  to 
  be 
  practically 
  undistinguishable 
  from 
  

   them. 
  

  

  In 
  double 
  achromatic 
  objectives 
  of 
  Herschel's 
  form 
  the 
  four 
  

   disposable 
  constants 
  are 
  employed 
  as 
  follows 
  : 
  

  

  1. 
  To 
  determine 
  the 
  focal 
  length 
  of 
  the 
  objective. 
  

  

  2. 
  To 
  correct 
  the 
  chromatic 
  aberration 
  for 
  rays 
  of 
  some 
  defi- 
  

   nite 
  wave 
  length. 
  

  

  3. 
  To 
  correct 
  the 
  spherical 
  aberration 
  of 
  central 
  rays 
  pro- 
  

   ceeding 
  from 
  infinitely 
  distant 
  objects. 
  

  

  ■I. 
  To 
  correct 
  the 
  spherical 
  aberration 
  of 
  central 
  rays, 
  so 
  far 
  

   as 
  the 
  first 
  power 
  of 
  the 
  distance 
  is 
  concerned, 
  for 
  all 
  objects, 
  

   no 
  matter 
  what 
  their 
  distance 
  from 
  the 
  telescope. 
  

  

  From 
  what 
  precedes 
  it 
  is 
  evident 
  that 
  the 
  last 
  condition 
  car- 
  

   ries 
  with 
  it 
  the 
  destruction 
  of 
  the 
  lateral 
  spherical 
  aberration 
  

   up 
  to 
  the 
  locus 
  where 
  the 
  term 
  in 
  D* 
  becomes 
  sensible, 
  and 
  as 
  

   that 
  term 
  is 
  practically 
  indestructible, 
  we 
  conclude 
  that 
  objec- 
  

   tives 
  of 
  the 
  Herschel 
  form 
  excel 
  all 
  others 
  consisting 
  of 
  two 
  

   lenses 
  in 
  contact 
  in 
  being 
  aplanatic 
  throughout 
  the 
  largest 
  pos- 
  

   sible 
  field 
  of 
  view, 
  and 
  for 
  objects 
  over 
  the 
  greatest 
  possible 
  

   range 
  of 
  distance. 
  In 
  meridian 
  circles, 
  transit 
  instruments, 
  

   zenith 
  telescopes, 
  photographic 
  telescopes, 
  and 
  all 
  Other 
  instru- 
  

   ments 
  where 
  good 
  definition 
  is 
  required 
  over 
  an 
  extensive 
  field, 
  

   this 
  is 
  of 
  the 
  utmost 
  importance, 
  but 
  for 
  equatorial 
  telescopes 
  

   it 
  is 
  of 
  less 
  consequence, 
  because 
  their 
  more 
  restricted 
  fields 
  

   scarcely 
  permit 
  the 
  lateral 
  aberration 
  to 
  become 
  sensible. 
  

  

  Washington, 
  D. 
  C, 
  Feb. 
  6, 
  1900. 
  

  

  