﻿ACADEMY 
  OF 
  SCIENCES. 
  263 
  

  

  A 
  modification 
  of 
  this 
  form 
  is 
  given, 
  by 
  making 
  each 
  index 
  glass 
  half 
  the 
  

   width 
  of 
  the 
  ordinary 
  form, 
  their 
  inner 
  edges 
  meeting, 
  as 
  it 
  were, 
  over 
  the 
  'cen- 
  

   ter 
  of 
  the 
  instrument, 
  and 
  thus 
  allowing 
  them 
  to 
  move 
  in 
  the 
  same 
  horizontal 
  

   plane. 
  

  

  Figure 
  3 
  exhibits 
  the 
  next 
  solution 
  of 
  this 
  problem, 
  and 
  affords 
  a 
  much 
  

   more 
  stable 
  instrument, 
  suited 
  to 
  the 
  rough 
  usage 
  of 
  boat 
  duty. 
  This 
  form 
  is 
  

   unique. 
  There 
  are 
  two 
  index 
  and 
  one 
  horizon 
  glasses, 
  whose 
  center 
  of 
  motion 
  

   are 
  in 
  the 
  same 
  straight 
  line 
  and 
  in 
  the 
  same 
  horizontal 
  plane 
  ; 
  but 
  the 
  index 
  

   glasses 
  have 
  independent 
  centers 
  of 
  motion, 
  so 
  that 
  the 
  arcs 
  of 
  graduation, 
  

   although 
  of 
  one 
  piece 
  and 
  in 
  the 
  same 
  plane, 
  have 
  different 
  radii. 
  The 
  gradua- 
  

   tion 
  is 
  from 
  degrees 
  to 
  120 
  degrees 
  from 
  each 
  end 
  to 
  the 
  theoretical 
  junction 
  

   of 
  the 
  arcs. 
  The 
  index 
  glass 
  nearest 
  the 
  horizon 
  glass, 
  is 
  one-half 
  the 
  height 
  

   of 
  the 
  other 
  one. 
  

  

  The 
  fourth 
  solution 
  gives 
  to 
  the 
  ordinary 
  sextant 
  an 
  extra 
  index 
  glass, 
  which 
  

   may 
  either 
  move 
  in 
  the 
  same 
  or 
  a 
  parallel 
  plane 
  to 
  that 
  of 
  the 
  other 
  index 
  glass 
  

   — 
  and 
  this 
  extra 
  inde.x; 
  glass 
  has 
  an 
  arm 
  which 
  moves 
  on 
  the 
  under 
  face 
  of 
  

   sextant, 
  but 
  its 
  extremity 
  is 
  curved 
  so 
  as 
  to 
  bring 
  its 
  vernier 
  upon 
  the 
  same 
  

   graduation 
  as 
  the 
  upper 
  index 
  arm. 
  

  

  Problem 
  III. 
  To 
  make 
  the 
  sextant 
  capable 
  of 
  measuring 
  two 
  angles, 
  one 
  

   to 
  the 
  right 
  aud 
  the 
  other 
  to 
  the 
  left 
  of 
  the 
  central 
  object, 
  in 
  quick 
  succession, 
  

   without 
  previously 
  estimating 
  their 
  relative 
  magnitudes 
  or 
  inverting 
  the 
  sextant 
  

   or 
  lengthening 
  its 
  arc. 
  This 
  is 
  done 
  by 
  using 
  the 
  ordinswy 
  sextant 
  with 
  the 
  

   addition 
  of 
  a 
  second 
  index 
  glass 
  secured 
  upon 
  the 
  usual 
  index 
  glass, 
  and 
  at 
  an 
  

   angle 
  of 
  60 
  degrees 
  therewith. 
  It 
  is 
  thus 
  evident 
  that 
  when 
  one 
  index 
  glass 
  

   measures 
  an 
  angle 
  of 
  120 
  degrees, 
  the 
  other 
  is 
  at 
  the 
  zero 
  of 
  the 
  first. 
  The 
  

   index 
  glasses 
  may 
  be 
  placed 
  one 
  abc^ve 
  the 
  other, 
  or 
  in 
  the 
  same 
  horizontal 
  

   plane. 
  With 
  this, 
  there 
  is 
  also 
  added 
  a 
  detachable 
  stop, 
  with 
  vernier 
  at 
  the 
  ex- 
  

   tremity 
  of 
  the 
  index 
  arm 
  bearing 
  its 
  usual 
  vernier 
  : 
  this 
  stop 
  to 
  be 
  so 
  adjusted 
  

   that, 
  when 
  clamped, 
  it 
  will 
  allow 
  the- 
  index 
  arm 
  to 
  move 
  freely 
  for 
  the 
  next 
  

   angle. 
  

  

  The 
  ordinary 
  sextant 
  may 
  be 
  made 
  to 
  measure 
  an 
  angle, 
  and 
  give 
  an 
  inter- 
  

   range, 
  at 
  the 
  same 
  instant, 
  by 
  placing 
  a 
  low 
  mirror 
  upon 
  the 
  frame, 
  and 
  in 
  a 
  - 
  

   line 
  joining 
  the 
  centers 
  of 
  motion 
  of 
  the 
  index 
  and 
  horizon 
  glasses, 
  and 
  at 
  such 
  

   an 
  angle 
  as 
  to 
  reflect 
  the 
  rays, 
  parallel 
  to 
  the 
  line 
  of 
  sight, 
  from 
  the 
  back 
  object, 
  

   into 
  the 
  horizon 
  glass. 
  This 
  is 
  a 
  modification* 
  of 
  Daussy's 
  improvement, 
  but 
  

   fulfills 
  many 
  conditions 
  which 
  his 
  will 
  not. 
  

  

  