﻿310 
  PROCEEDINGS 
  OF 
  THE 
  CALIFORNIA 
  

  

  which 
  the 
  eye 
  cannot 
  dhcern 
  no?' 
  the 
  touch 
  perceive, 
  are 
  we 
  enabled 
  to 
  sift 
  them 
  

   from 
  our 
  observations. 
  Still, 
  the 
  observer 
  should 
  use 
  the 
  most 
  powerful 
  telescope 
  

   available. 
  The 
  improvement 
  which 
  I 
  now 
  propose, 
  (besides 
  a 
  few 
  other 
  mat- 
  

   ters 
  of 
  detail) 
  in 
  the 
  ordinary 
  reflecting 
  angular 
  instruments, 
  is 
  a 
  device 
  for 
  

   duplicating 
  the 
  image 
  of 
  an 
  object 
  by 
  optical 
  means. 
  

  

  This 
  I 
  accomplish 
  by 
  fixing 
  an 
  extra 
  index-glass 
  directly 
  above, 
  or 
  in 
  the 
  

   same 
  plane 
  with 
  that 
  of 
  the 
  ordinary 
  one 
  of 
  the 
  reflecting 
  repealing 
  circle, 
  and 
  

   at 
  an 
  angle 
  therewith 
  equal 
  to 
  the 
  apparent 
  semi-diameter 
  of 
  the 
  sun 
  ; 
  or 
  per- 
  

   haps, 
  a 
  more 
  complete 
  solution 
  of 
  the 
  problem, 
  is 
  to 
  fix 
  a 
  small 
  sphere 
  of 
  Iceland 
  

   spar 
  on 
  the 
  direct 
  line 
  between 
  the 
  index 
  and 
  horizon 
  glasses, 
  (see 
  Fig. 
  No. 
  1) 
  

   and 
  thus 
  obtain 
  two 
  images 
  of 
  the 
  sun 
  equally 
  distinct 
  (see 
  s 
  s', 
  Fig. 
  No. 
  4). 
  

   This 
  sphere 
  to 
  be 
  mounted 
  in 
  a 
  light 
  metallic 
  frame, 
  so 
  connected 
  with 
  a 
  micro- 
  

   meter 
  that 
  its 
  most 
  delicate 
  movements 
  can 
  be 
  read 
  oS". 
  In 
  Fig. 
  No. 
  2, 
  a 
  is 
  the 
  

   sun, 
  and 
  b 
  its 
  duplicated 
  image, 
  as 
  seen 
  in 
  the 
  horizon 
  glass 
  ; 
  and 
  b 
  is 
  this 
  

   same 
  duplicated 
  image 
  brought 
  in 
  contact 
  with 
  the 
  horizon 
  ; 
  c 
  is 
  the 
  position 
  of 
  

   the 
  observer. 
  Now, 
  in 
  observing, 
  it 
  makes 
  but 
  little 
  difference 
  whether 
  these 
  

   duplicated 
  images 
  are 
  exactly 
  tangent, 
  slightly 
  overlapping, 
  or 
  slightly 
  separ- 
  

   ated, 
  (as 
  shown 
  atd,/, 
  and 
  e, 
  in 
  Fig. 
  No. 
  4) 
  for 
  in 
  the 
  first 
  case 
  we 
  have 
  but 
  to 
  

   bring 
  the 
  horizon 
  to 
  the 
  point 
  of 
  tangency 
  ; 
  in 
  the 
  second, 
  to 
  bisect 
  the 
  two 
  ex- 
  

   terior 
  angles 
  ; 
  or 
  in 
  the 
  third, 
  to 
  bisect 
  the 
  space 
  between 
  the 
  adjacent 
  limbs 
  of 
  

   the 
  sun. 
  It 
  is 
  obvious 
  that 
  this 
  method 
  of 
  observing 
  the 
  contacts 
  of 
  both 
  limbs 
  

   of 
  the 
  sun 
  at 
  the 
  same 
  instant 
  is 
  equally 
  well 
  adapted 
  for 
  double 
  altitudes 
  ; 
  the 
  

   appearance 
  of 
  the 
  images 
  then 
  is 
  shown 
  at 
  m, 
  in 
  Fig. 
  No. 
  4. 
  Other 
  improve- 
  

   ments 
  which 
  I 
  have 
  devised 
  are 
  : 
  1st. 
  A 
  reversable 
  double 
  reflecting 
  index- 
  

   glass, 
  (see 
  Fig. 
  No. 
  3) 
  which 
  eliminates 
  the 
  error 
  due 
  to 
  its 
  parallax 
  ; 
  and 
  2d, 
  

   making 
  both 
  faces 
  of 
  index-glass 
  reflectors, 
  and 
  fixing 
  a 
  glass 
  prism, 
  with 
  sil- 
  

   vered 
  hypothenuse, 
  on 
  the 
  line 
  of 
  sight 
  behind 
  the 
  index-glass, 
  and 
  at 
  such 
  an 
  

   angle 
  as 
  to 
  reflect 
  the 
  rays 
  first 
  reflected 
  from 
  the 
  back 
  face 
  of 
  index 
  glass 
  par- 
  

   allel 
  to 
  the 
  line 
  of 
  sight. 
  This 
  device 
  enables 
  us 
  to 
  measure 
  any 
  angle 
  (shown 
  

   in 
  Fig. 
  No. 
  1). 
  It 
  is 
  obvious 
  that 
  any 
  two-angle 
  reflecting 
  instrument 
  may 
  

   also 
  be 
  made 
  to 
  give 
  this 
  duplication 
  of 
  images; 
  and 
  also 
  give 
  an 
  altitude 
  and 
  

   its 
  supplement 
  at 
  the 
  same 
  instant, 
  and 
  thus 
  give 
  us 
  the 
  algebraic 
  sum 
  of 
  the 
  

   existing 
  refraction 
  and 
  dip. 
  These 
  improvements 
  are 
  all 
  equally 
  adapted 
  and 
  

   easily 
  applied 
  to 
  any 
  reflecting 
  angular 
  instrument. 
  

  

  By 
  making 
  these 
  attachments 
  to 
  the 
  French 
  reflecting, 
  repeating 
  circle, 
  (see 
  

   Fig. 
  No. 
  1) 
  we 
  have 
  an 
  instrument 
  capable 
  of 
  not 
  only 
  eliminating 
  its 
  own 
  

   errors, 
  but 
  those 
  of 
  observation, 
  as 
  well 
  as 
  those 
  due 
  to 
  sudden 
  atmospheric 
  

   changes, 
  and 
  we 
  have 
  an 
  instrument 
  theoretically 
  almost 
  perfect. 
  

  

  Through 
  the 
  efforts 
  of 
  Laplace, 
  Newton, 
  and 
  Pierce, 
  the 
  theory 
  of 
  nautical 
  

   astronomy 
  has 
  reached 
  a 
  point 
  of 
  perfection 
  that 
  only 
  awaits 
  the 
  determination 
  

   of 
  the 
  true 
  dimensions 
  of 
  the 
  aolar 
  system, 
  (which 
  it 
  is 
  hoped 
  the 
  next 
  transit 
  

   of 
  Venus 
  will 
  give) 
  to 
  make 
  it 
  all 
  that 
  can 
  be 
  desired. 
  The 
  invention 
  of 
  the 
  

   chronometer 
  has 
  practically 
  solved 
  the 
  problem 
  of 
  longitudes. 
  And 
  the 
  needle 
  

   of 
  the 
  mariner's 
  compass 
  has 
  felt 
  the 
  touch 
  of 
  a 
  Ritchie, 
  and 
  trembles 
  no 
  more 
  ; 
  

   whilst 
  Beecher 
  and 
  Davidson 
  have 
  given 
  the 
  navigator 
  artificial 
  horizons 
  that 
  

  

  