﻿138 
  

  

  Transactions. 
  — 
  Miscellaneous. 
  

  

  Inches. 
  

  

  37 
  

   88330 
  

  

  = 
  log 
  

  

  = 
  colog 
  

  

  constant 
  log 
  

  

  1-56820 
  

   5-06389 
  

   4-41570 
  

  

  Correction 
  

  

  Inches. 
  

  

  21 
  

   88330 
  

  

  10-"9 
  = 
  log. 
  

  

  = 
  log 
  

  

  = 
  colog 
  

  

  constant 
  log 
  

  

  1.-03779 
  

  

  1-32222 
  

  

  5'05389 
  

   4-41570 
  

  

  Oorrecttion 
  6'"2 
  = 
  log 
  0-79181 
  

  

  Corrected 
  A 
  

  

  Elev. 
  1° 
  14' 
  13" 
  + 
  10".9 
  = 
  ] 
  

   Dep. 
  1° 
  22' 
  50" 
  ~ 
  6- 
  2 
  = 
  : 
  

  

  1° 
  14' 
  23''-9 
  

   1 
  22 
  43-8 
  

  

  19-9 
  = 
  

  

  /. 
  Distance 
  from 
  Bryant's 
  Hill 
  to 
  Barker's 
  Hill 
  = 
  

   True 
  distance 
  as 
  found 
  by 
  Triangulation 
  = 
  

  

  499-9 
  

   3771 
  

  

  49990 
  

  

  34993 
  

  

  3499 
  

  

  150 
  

  

  88632 
  links 
  

   89197 
  

  

  565 
  

  

  Difference 
  

   Wliich 
  is 
  about 
  half 
  a 
  chain 
  per 
  mile. 
  

  

  Having 
  found 
  the 
  contained 
  arc, 
  or 
  distance 
  between 
  tlie 
  stations, 
  in 
  

   links, 
  by 
  the 
  rules 
  given 
  above, 
  the 
  difference 
  in 
  altitude 
  may 
  be 
  obtained 
  in 
  

   the 
  usual 
  way, 
  viz., 
  by 
  converting 
  the 
  links 
  into 
  feet 
  and 
  then 
  multiplying 
  

   the 
  distance 
  m 
  feet 
  between 
  the 
  stations 
  by 
  the 
  tangent 
  of 
  the 
  true 
  angle 
  

   of 
  elevation 
  or 
  de^jression. 
  (Note. 
  — 
  The 
  true 
  angle 
  of 
  elevation 
  or 
  

   depression 
  is 
  half 
  the 
  sum 
  of 
  the 
  observed 
  reciprocal 
  angles, 
  when 
  one 
  

   is 
  an 
  elevation 
  ; 
  or 
  half 
  the 
  difference 
  when 
  both 
  are 
  depressions 
  ; 
  or, 
  

   generally, 
  if 
  zenith 
  distances 
  are 
  used, 
  the 
  true 
  vertical 
  angle 
  is 
  equal 
  to 
  

   half 
  the 
  difference 
  of 
  the 
  reciprocal 
  zenith 
  distances 
  ; 
  — 
  of 
  course 
  sup- 
  

   posing 
  the 
  eye 
  and 
  object 
  corrections 
  to 
  have 
  been 
  applied.) 
  

  

  But 
  instead 
  of 
  finding 
  the 
  distance 
  between 
  the 
  stations 
  in 
  links, 
  and 
  

  

  then 
  converting 
  it 
  into 
  feet, 
  it 
  would 
  be 
  more 
  simple 
  to 
  find 
  the 
  distance 
  in 
  

  

  feet 
  at 
  once, 
  by 
  using 
  the 
  factor 
  117 
  instead 
  of 
  177*3, 
  as 
  before 
  explained 
  : 
  — 
  

  

  Example, 
  

  

  Bryant's 
  HiU 
  to 
  Barker's 
  Hill. 
  Corrected 
  Elev. 
  1° 
  14' 
  23''-9 
  

   Barker's 
  Hill 
  to 
  Bryant's 
  Hill. 
  

  

  499-9 
  

  

  Dep. 
  

  

  1° 
  22' 
  43"-8 
  

  

  Diff. 
  

  

  8' 
  19"-9 
  

  

  Sum. 
  

  

  2° 
  37 
  07"-7 
  

  

  i 
  Sum. 
  1° 
  18' 
  SS'-S 
  

  

  499-9 
  =^ 
  log 
  2-698883 
  

  

  117 
  = 
  constant 
  log 
  2-068186 
  

  

  i^-lS'SS'-S 
  = 
  tangent 
  8-369040 
  

  

  1837"0 
  feet 
  

  

  3-126109 
  

  

  