﻿Adams. 
  — 
  To 
  calculate 
  Distances 
  hy 
  Reciprocal 
  Vertical 
  Angles, 
  137 
  

  

  In 
  order 
  to 
  compute 
  this 
  correction 
  by 
  the 
  above 
  rules, 
  the 
  distance 
  

   between 
  the 
  stations 
  is 
  required 
  to 
  be 
  known 
  ; 
  but 
  as 
  in 
  all 
  cases 
  where 
  this 
  

   method 
  is 
  used 
  the 
  distance 
  between 
  the 
  stations 
  is 
  not 
  known, 
  we 
  must 
  

   proceed 
  as 
  follows 
  : 
  — 
  

  

  With 
  the 
  observed 
  vertical 
  angles, 
  as 
  they 
  stand 
  in 
  the 
  field-book, 
  

   compute 
  the 
  distance 
  between 
  the 
  stations 
  ; 
  and 
  with 
  this 
  approximate 
  dis- 
  

   tance, 
  compute 
  the 
  eye 
  and 
  object 
  correction. 
  Then, 
  with 
  the 
  corrected 
  

   angles, 
  again 
  compute 
  the 
  distance, 
  and 
  in 
  most 
  cases 
  no 
  further 
  calcula- 
  

   tion 
  will 
  be 
  required 
  ; 
  but 
  in 
  cases 
  where 
  the 
  second 
  calculation 
  gives 
  a 
  

   result 
  differing 
  greatly 
  from 
  the 
  first 
  aj^proximation, 
  it 
  may 
  be 
  advisable 
  to 
  

   repeat 
  the 
  calculation. 
  

  

  Instead, 
  hoAvever, 
  of 
  neglecting 
  the 
  eye 
  and 
  object 
  correction 
  altogether, 
  

   in 
  calculating 
  the 
  first 
  approximation, 
  it 
  will 
  be 
  sometimes 
  advantageous 
  to 
  

   ascertain 
  the 
  correction 
  roughly, 
  and 
  take 
  it 
  into 
  account. 
  This 
  may 
  be 
  

   done 
  as 
  follows 
  : 
  — 
  

  

  As 
  1 
  inch 
  subtends 
  1" 
  at 
  26044 
  links 
  or 
  Sj 
  miles 
  nearly, 
  we 
  can 
  easily 
  

   ascertain 
  the 
  angle 
  subtended 
  by 
  any 
  number 
  of 
  inches, 
  at 
  any 
  number 
  of 
  

   miles 
  distance, 
  by 
  the 
  following 
  rule 
  : 
  — 
  

  

  Multiply 
  the 
  inches 
  by 
  3 
  J 
  and 
  divide 
  the 
  jDroduct 
  by 
  the 
  number 
  of 
  miles, 
  

   the 
  quotient 
  will 
  be 
  the 
  number 
  of 
  seconds 
  subtended. 
  The 
  distance 
  in 
  

   miles 
  can 
  generally 
  be 
  estimated 
  to 
  within 
  10 
  per 
  cent, 
  or 
  so, 
  and 
  calcu- 
  

   lating 
  the 
  first 
  approximate 
  correction 
  in 
  this 
  way 
  will 
  often 
  save 
  time. 
  

  

  Example. 
  

  

  Bryant's 
  Hill 
  to 
  Barker's 
  Hill. 
  Elev. 
  1° 
  14 
  13" 
  

   Barker's 
  Hill 
  to 
  Bryant's 
  Hill. 
  Dep. 
  1° 
  22' 
  50" 
  

  

  Ft. 
  In. 
  

   Bryant's 
  Hill 
  to 
  Barker's 
  Hill. 
  Height 
  of 
  eye 
  =31 
  

  

  object 
  =: 
  

  

  In. 
  

  

  Eye 
  exceeds 
  object 
  3 
  1= 
  37 
  

  

  H 
  

  

  Distance, 
  say 
  10 
  miles 
  10 
  ) 
  120 
  

  

  Ft. 
  In. 
  

  

  Barker's 
  Hill 
  to 
  Bryant's 
  Hill. 
  Height 
  of 
  eye 
  =24 
  

  

  ,, 
  object 
  = 
  7 
  

  

  In. 
  

  

  Eye 
  exceeds 
  object 
  =19— 
  21 
  

  

  _!i 
  

  

  10) 
  68 
  

  

  12-0" 
  

  

  6-8" 
  

  

  Bryant's 
  Hill 
  to 
  Barker's 
  Hill. 
  Elev., 
  1° 
  14' 
  13" 
  + 
  12" 
  = 
  1° 
  14' 
  25" 
  

   Barker's 
  Hill 
  to 
  Bryant's 
  Hill. 
  Dep., 
  1° 
  22' 
  50" 
  — 
  6-"8 
  = 
  1 
  22 
  43-2 
  

  

  

  eye 
  

  

  8 
  18-2 
  = 
  

  

  and 
  object 
  corrections 
  

   First 
  approximation 
  =: 
  

  

  498"-2 
  

   3771 
  

  

  To 
  compute 
  the 
  

  

  49820 
  

  

  34874 
  

  

  3487 
  

  

  149 
  

  

  

  : 
  88330 
  

  

  