﻿ACADEMY 
  OF 
  SCIENCES. 
  135 
  

  

  four-tenths 
  of 
  a 
  second 
  of 
  arc 
  to 
  six-tentlis, 
  and 
  are 
  read 
  to 
  one-tenth 
  of 
  a 
  di- 
  

   vision, 
  or 
  six-hundredths 
  of 
  a 
  second 
  of 
  arc. 
  For 
  work 
  with 
  this 
  instrument 
  

   the 
  micrometer 
  may 
  be 
  divided 
  to 
  seconds 
  of 
  arc, 
  and 
  read 
  to 
  half 
  seconds 
  or 
  

   less. 
  

  

  Figure 
  1 
  exhibits, 
  without 
  details 
  of 
  bars 
  or 
  adjustment, 
  a 
  plan 
  of 
  the 
  tube 
  

   A 
  B, 
  carrying 
  the 
  base 
  bar 
  of 
  six 
  feet, 
  the 
  object 
  glasses 
  O 
  and 
  W 
  of 
  two 
  tel- 
  

   escopes 
  with 
  micrometer 
  ej'e-piece 
  E, 
  common 
  to 
  both, 
  and 
  the 
  prisms 
  L, 
  R, 
  

   and 
  C, 
  1). 
  This 
  tube 
  will 
  be 
  about 
  three 
  inches 
  in 
  diameter 
  ; 
  the 
  object 
  glass 
  

   about 
  two 
  and 
  a 
  half 
  inches, 
  and 
  the 
  powers 
  of 
  the 
  eye 
  glass 
  from 
  twenty 
  to 
  

   fifty. 
  An 
  opening 
  can 
  be 
  made 
  in 
  the 
  center 
  of 
  the 
  tube 
  in 
  front 
  of 
  the 
  prisms 
  

   for 
  illumination 
  at 
  night 
  ; 
  and 
  above 
  the 
  eye 
  tube 
  a 
  short 
  outside 
  director 
  to 
  

   rapidly 
  obtain 
  the 
  direction 
  of 
  the 
  object 
  to 
  be 
  observed 
  upon. 
  

  

  Instead 
  of 
  reflectors, 
  right-angled 
  prisms 
  are 
  prepared 
  and 
  arranged 
  for 
  each 
  

   telescope, 
  with 
  their 
  hypothenusal 
  sides 
  parallel 
  to 
  each 
  other 
  at 
  an 
  angle 
  of 
  

   forty-five 
  degrees 
  with 
  the 
  base. 
  Necessarily 
  the 
  central 
  prisms, 
  C 
  and 
  D, 
  are 
  

   placed 
  one 
  above 
  the 
  other, 
  but 
  touching. 
  With 
  this 
  arrangement 
  a 
  ray 
  of 
  

   light 
  from 
  an 
  infinite 
  distance, 
  or 
  from 
  a 
  star, 
  after 
  entering 
  the 
  object 
  glass, 
  

   O, 
  follows 
  the 
  direction 
  of 
  the 
  line, 
  a, 
  «, 
  a', 
  in 
  the 
  left-hand 
  telescope 
  to 
  the 
  

   point, 
  X, 
  in 
  the 
  focus 
  of 
  the 
  telescope, 
  and 
  also 
  entering 
  0' 
  , 
  follows 
  the 
  line, 
  

   b,b, 
  c', 
  in 
  the 
  right-hand 
  telescope 
  to 
  the 
  same 
  point. 
  If 
  the 
  prisms 
  are 
  in 
  ad- 
  

   justment, 
  the 
  image 
  of 
  a 
  star 
  through 
  each 
  telescope 
  will 
  be 
  seen 
  as 
  a 
  single 
  ob- 
  

   ject 
  at 
  A'. 
  And 
  this 
  last 
  condition 
  is 
  the 
  test 
  of 
  adjustment. 
  In 
  using 
  a 
  star 
  

   the 
  adjustment 
  would 
  necessarily 
  be 
  made 
  at 
  night, 
  but 
  the 
  test 
  could 
  be 
  fre- 
  

   quently 
  made 
  during 
  the 
  day 
  by 
  similar 
  observations 
  upon 
  the 
  border 
  of 
  the 
  

   sun, 
  or 
  upon 
  some 
  well 
  marked 
  spot 
  on 
  its 
  disc. 
  If 
  it 
  is 
  desired 
  to 
  test 
  the 
  ad- 
  

   justment 
  upon 
  a 
  near 
  object, 
  say 
  at 
  one 
  hundred 
  yards, 
  then 
  after 
  the 
  adjust- 
  

   ment 
  upon 
  a 
  star 
  or 
  the 
  sun, 
  the 
  micrometer 
  difference 
  of 
  the 
  two 
  images 
  of 
  an 
  

   object 
  at 
  that 
  distance 
  must 
  be 
  determined 
  (or 
  may 
  be 
  computed) 
  and 
  used 
  

   thereafter 
  as 
  a 
  constant 
  from 
  which 
  to 
  make 
  the 
  necessary 
  adjustment 
  for 
  infin- 
  

   ite 
  distance. 
  But 
  this 
  method 
  would 
  require 
  the 
  change 
  of 
  focus 
  of 
  the 
  tel- 
  

   escope, 
  whence 
  would 
  arise 
  change 
  of 
  the 
  arc 
  value 
  of 
  the 
  micrometer 
  divisions. 
  

  

  If 
  the 
  prisms 
  are 
  in 
  adjustment 
  and 
  the 
  object 
  observed 
  upon 
  is 
  not 
  at 
  an 
  in- 
  

   finite 
  distance, 
  the 
  rays 
  of 
  light 
  from 
  it 
  will 
  not 
  enter 
  the 
  two 
  object 
  glasses 
  in 
  

   parallel 
  lines, 
  but 
  at 
  angles 
  varying 
  with 
  a 
  function 
  of 
  the 
  distance, 
  and 
  will 
  

   follow 
  the 
  lines, 
  cc 
  c 
  and 
  d 
  d 
  d', 
  so 
  that 
  the 
  images, 
  P 
  and 
  P', 
  of 
  the 
  same 
  ob- 
  

   ject 
  will 
  be 
  formed 
  at 
  the 
  common 
  focus 
  of 
  the 
  two 
  telescopes. 
  The 
  horizontal 
  

   distance 
  apart 
  of 
  these 
  images 
  is 
  measured 
  by 
  the 
  micrometer, 
  and 
  the 
  dis- 
  

   tance 
  of 
  the 
  object 
  deduced 
  therefrom. 
  

  

  With 
  the 
  ordinary 
  micrometer 
  this 
  separation 
  of 
  the 
  images 
  can 
  be 
  measured 
  

   by 
  single 
  readings 
  only, 
  but 
  with 
  the 
  proposed 
  micrometer 
  the 
  measure 
  may 
  be 
  

   repeated 
  any 
  number 
  of 
  times, 
  thereby 
  virtually 
  increasing 
  the 
  length 
  of 
  base 
  

   used, 
  by 
  each 
  repetition. 
  Thus, 
  by 
  repeating 
  the 
  measure 
  ten 
  times, 
  we 
  have, 
  

   as 
  it 
  were, 
  increased 
  the 
  case 
  from 
  six 
  to 
  sixty 
  feet 
  ; 
  whilst 
  a 
  second 
  set 
  of 
  ten 
  

   repetitions 
  serve 
  not 
  only 
  as 
  a 
  test 
  of 
  the 
  first 
  set, 
  but 
  give 
  an 
  accuracy 
  ap- 
  

   proximating 
  that 
  obtainable 
  with 
  a 
  base 
  of 
  one 
  hundred 
  and 
  twenty 
  feet. 
  

  

  