﻿136 
  Transactions. 
  — 
  Miscellaneous. 
  

  

  portionately 
  better 
  results, 
  the 
  longer 
  the 
  distance, 
  as 
  I 
  estimate 
  it 
  as 
  subject 
  

   to 
  an 
  average 
  error 
  of 
  5" 
  or 
  6" 
  which 
  is 
  equivalent 
  to 
  about 
  10 
  chains, 
  and 
  

   this 
  error 
  is 
  the 
  same 
  for 
  all 
  distances. 
  Thus, 
  in 
  finding 
  the 
  distance 
  

   between 
  two 
  hills 
  50 
  miles 
  apart, 
  this 
  Avould 
  only 
  introduce 
  an 
  error 
  of 
  

   2 
  J 
  links 
  per 
  10 
  chains, 
  thus 
  nearly 
  approachiug 
  in 
  accuracy 
  to 
  a 
  chained 
  

   measurement, 
  besides 
  being 
  free 
  from 
  accidental 
  errors 
  and 
  omissions 
  which 
  

   all 
  chained 
  measurements 
  are 
  liable 
  to. 
  

  

  But 
  although 
  the 
  errors 
  of 
  observation 
  do 
  not 
  affect 
  the 
  results 
  in 
  pro- 
  

   portion 
  to 
  the 
  distance, 
  still, 
  any 
  error 
  in 
  the 
  estimated 
  refraction 
  will 
  do 
  so; 
  

   therefore 
  this 
  method 
  is 
  only 
  suitable 
  for 
  hilly 
  country, 
  where 
  other 
  methods 
  

   are 
  not 
  available 
  ; 
  as, 
  wheiiever 
  the 
  line 
  of 
  sight 
  between 
  the 
  two 
  stations 
  

   passes 
  for 
  any 
  considerable 
  distance 
  close 
  to 
  the 
  surface 
  of 
  water 
  or 
  level 
  

   land, 
  the 
  refraction 
  is 
  generally 
  very 
  variable 
  and 
  uncertain, 
  and 
  the 
  results 
  

   obtained 
  by 
  this 
  method 
  will 
  then 
  be 
  unreliable. 
  

  

  In 
  my 
  own 
  practice, 
  using 
  an 
  8-inch 
  transit 
  theodolite, 
  reading 
  to 
  10", 
  

   and 
  noting 
  the 
  level 
  readings 
  at 
  each 
  observation, 
  the 
  distances 
  found 
  by 
  

   this 
  method 
  have 
  an 
  average 
  error 
  of 
  half-a-chaiu 
  to 
  the 
  mile. 
  

  

  For 
  instance, 
  in 
  a 
  circuit 
  of 
  50 
  miles 
  between 
  two 
  known 
  points, 
  

   avernge 
  distance 
  of 
  stations 
  10 
  miles 
  apart, 
  the 
  error 
  was 
  found 
  to 
  be 
  23 
  

   chains, 
  or 
  less 
  than 
  half-a-chain 
  per 
  mile. 
  In 
  another 
  case, 
  there 
  was 
  an 
  

   error 
  of 
  31 
  chains 
  in 
  60 
  miles, 
  or 
  about 
  half-a-chain 
  per 
  mile. 
  

  

  It 
  is 
  requisite, 
  in 
  this 
  method, 
  to 
  use 
  only 
  the 
  corrected 
  vertical 
  angles, 
  

   that 
  is, 
  they 
  must 
  be 
  corrected 
  for 
  the 
  height 
  of 
  the 
  eye 
  and 
  object. 
  

  

  Eules 
  for 
  calculating 
  the 
  correction 
  are 
  given 
  in 
  most 
  books 
  on 
  survey- 
  

   ing, 
  but 
  the 
  following 
  blank 
  form 
  will 
  be 
  convenient 
  when 
  the 
  difference 
  of 
  

   heights 
  of 
  the 
  eye 
  and' 
  object 
  is 
  given 
  in 
  feet 
  and 
  inches, 
  and 
  the 
  distance 
  

   between 
  the 
  stations 
  in 
  links 
  : 
  — 
  

  

  Blank 
  Form. 
  

  

  Difference 
  of 
  height 
  of 
  eye 
  and 
  object 
  in 
  inches 
  log 
  ....... 
  

  

  Diitance 
  between 
  stations 
  in 
  links 
  colog 
  . 
  ■ 
  

  

  Colog 
  tang 
  1"— 
  log 
  7'92 
  i:;: 
  constant 
  log 
  4-41570 
  

  

  Correction 
  in 
  seconds 
  of 
  arc 
  = 
  log 
  . 
  • 
  

  

  Kotc. 
  — 
  "When 
  the 
  height 
  of 
  the 
  eye 
  exceeds 
  the 
  height 
  of 
  the 
  object, 
  the 
  

   correction 
  is 
  to 
  be 
  added 
  to 
  an 
  elevation 
  or 
  subtracted 
  from 
  a 
  depression. 
  

  

  "When 
  the 
  height 
  of 
  the 
  object 
  exceeds 
  the 
  height 
  of 
  the 
  eye, 
  the 
  cor- 
  

   rection 
  is 
  to 
  be 
  added 
  to 
  a 
  depression, 
  or 
  subtracted 
  from 
  an 
  elevation 
  ; 
  

  

  Or 
  the 
  rule 
  for 
  applying 
  the 
  corrections 
  may 
  be 
  simplified 
  thus 
  : 
  

  

  Mark 
  angles 
  of 
  elevation 
  -|- 
  mark 
  angles 
  of 
  depression. 
  

   Mark 
  height 
  of 
  eye 
  -f 
  mark 
  height 
  of 
  object. 
  

  

  Then 
  take 
  the 
  algebraical 
  sum 
  of 
  the 
  heights 
  of 
  the 
  eye 
  and 
  object, 
  to 
  com' 
  

  

  pute 
  the 
  correction, 
  to 
  which 
  prefix 
  the 
  same 
  sign 
  ; 
  then 
  the 
  algebraical 
  

  

  sum 
  of 
  this 
  correction, 
  and 
  the 
  observed 
  vertical 
  angle, 
  will 
  give 
  the 
  true 
  

  

  vertical 
  angle, 
  

  

  