﻿366 
  REPORT 
  UNITED 
  STATES 
  GEOLOGICAL 
  SURVEY. 
  

  

  joined 
  in 
  tlie 
  same 
  way, 
  we 
  will 
  bave 
  three 
  chords 
  of 
  three 
  required 
  

   great 
  circles, 
  which 
  will 
  closely 
  correspond 
  to 
  the 
  circles 
  themselves. 
  

   These 
  chords 
  will 
  join 
  in 
  the 
  required 
  point. 
  Or 
  if 
  the 
  triangles 
  are 
  too 
  

   large 
  compared 
  with 
  the 
  great 
  triangle, 
  slight 
  allowance 
  may 
  be 
  made 
  

   for 
  the 
  curvature 
  or 
  a 
  third, 
  triangle 
  of 
  error 
  be 
  formed, 
  and 
  the 
  re- 
  

   quired 
  point 
  be 
  determined 
  with 
  the 
  greatest 
  exactness. 
  

  

  To 
  locate 
  by 
  this 
  method, 
  then, 
  orient 
  the 
  table 
  as 
  nearly 
  as 
  possible 
  

   and 
  form 
  a 
  triangle 
  of 
  error, 
  shift 
  then 
  slightly 
  the 
  position 
  of 
  the 
  

   table, 
  and, 
  forming 
  a 
  second 
  triangle 
  of 
  error, 
  join 
  the 
  similar 
  angles 
  

   of 
  the 
  two 
  triangles. 
  The 
  required 
  point 
  will 
  be 
  at 
  the 
  intersection 
  of 
  

   these 
  lines. 
  

  

  The 
  live 
  cases 
  are 
  represented 
  graphically 
  on 
  Plate 
  LY, 
  and 
  the 
  

   details 
  of 
  the 
  third 
  case 
  are 
  shown 
  in 
  construction, 
  while 
  in 
  the 
  follow- 
  

   ing 
  figures 
  are 
  shown 
  the 
  relations 
  of 
  the 
  triangles 
  of 
  error 
  under 
  the 
  

   different 
  conditions. 
  

  

  In 
  regard 
  to 
  the 
  accuracy 
  of 
  the 
  locations 
  under 
  the 
  different 
  cases, 
  it 
  

   may 
  be 
  said 
  in 
  general 
  when 
  the 
  arcs 
  of 
  the 
  great 
  circles 
  intersect 
  at 
  large 
  

   angles 
  with 
  each 
  other, 
  the 
  location 
  may 
  be 
  considered 
  good, 
  and 
  also 
  

   where 
  the 
  intersections 
  of 
  the 
  lines 
  of 
  the 
  outside 
  points 
  intersect 
  

   acutely 
  and 
  the 
  middle 
  point 
  is 
  near, 
  the 
  location 
  will 
  be 
  good. 
  But 
  

   when 
  the 
  lines 
  from 
  the 
  outside 
  points 
  intersect 
  acutely 
  and 
  the 
  middle 
  

   point 
  is 
  far 
  off, 
  accuracy 
  decreases, 
  and 
  directly 
  in 
  proportion 
  as 
  the 
  

   middle 
  point 
  is 
  more 
  distant 
  than 
  the 
  other 
  two. 
  The 
  reason 
  of 
  this 
  

   fact 
  may 
  be 
  readily 
  seen 
  by 
  a 
  construction 
  of 
  the 
  circles 
  of 
  location. 
  

  

  Case 
  5 
  being 
  on 
  the 
  great 
  circle 
  of 
  the 
  three 
  points, 
  will 
  be 
  indeter- 
  

   minate, 
  for 
  the 
  circles 
  of 
  location 
  must 
  necessarily 
  coincide. 
  

  

  As 
  I 
  said 
  earlier, 
  I 
  often 
  found 
  this 
  simple 
  device 
  of 
  great 
  aid 
  in 
  

   quickly 
  determining 
  my 
  location, 
  especially 
  when 
  my 
  points 
  were 
  

   badly 
  conditioned, 
  and 
  have 
  little 
  doubt 
  but 
  that 
  under 
  certain 
  circum- 
  

   stances 
  it 
  would 
  be 
  found 
  useful 
  by 
  most 
  any 
  plane-table 
  worker. 
  

  

  In 
  constructing 
  the 
  drainage 
  of 
  this 
  district 
  so 
  that 
  the 
  rivers 
  and 
  

   main 
  water 
  courses 
  might 
  be 
  of 
  greater 
  accuracy, 
  I 
  have 
  run 
  time- 
  

   meanders 
  of 
  them 
  all, 
  swinging 
  in 
  by 
  very 
  numerous 
  locations 
  along 
  the 
  

   route. 
  In 
  this 
  way 
  I 
  have 
  run 
  out 
  the 
  La 
  Plata, 
  Mancos, 
  San 
  Juan, 
  

   McElmo, 
  Montezuma, 
  Hovenweep, 
  and 
  greater 
  part 
  of 
  the 
  Dolores, 
  and 
  

   from 
  the 
  closeness 
  of 
  the 
  checks 
  am 
  very 
  well 
  satisfied 
  with 
  the 
  results 
  

   of 
  such 
  time-meandering. 
  

  

  By 
  continuous 
  riding 
  of 
  the 
  same 
  animal, 
  and 
  careful 
  watching 
  of 
  his 
  

   gait 
  under 
  differing 
  circumstances, 
  a, 
  very 
  even 
  pace 
  can 
  be 
  obtained, 
  

   which, 
  when 
  checked 
  at 
  every 
  six 
  or 
  ten 
  miles 
  by 
  absolute 
  location, 
  

   will 
  not 
  bring 
  in 
  appreciable 
  errors 
  on 
  a 
  scale 
  of 
  4 
  miles 
  to 
  1 
  inch. 
  

   The 
  topographer 
  is 
  furnished 
  with 
  a 
  system 
  of 
  primary 
  triangulation 
  

   on 
  which 
  to 
  base 
  his 
  work. 
  This 
  system 
  has 
  sides 
  of 
  length 
  varying 
  

   from 
  15 
  to 
  perhaps 
  50 
  or 
  60 
  miles 
  in 
  length. 
  Within 
  this 
  main 
  system, 
  

   which 
  is 
  developed 
  with 
  great 
  care, 
  the 
  topograj)her 
  carries 
  on 
  his 
  

   own 
  secondary 
  with 
  side 
  of 
  much 
  shorter 
  extent, 
  connecting, 
  as 
  far 
  

   as 
  possible, 
  his 
  stations 
  with 
  a 
  continuous 
  chain 
  of 
  closed 
  triangles. 
  

   The 
  angles 
  of 
  those 
  triangles, 
  as 
  well 
  as 
  all 
  those 
  used 
  in 
  topographical 
  

   locations, 
  are 
  read 
  with 
  the 
  gradienter 
  — 
  a 
  single-minute 
  instrument 
  of 
  

   compact 
  form, 
  rather 
  large 
  circle 
  and 
  extremely 
  powerful 
  glass. 
  This 
  

   instrument 
  was 
  first 
  made 
  for 
  the 
  Coast 
  Survey, 
  but 
  is 
  exceedingly 
  well 
  

   adapted 
  to 
  our 
  purposes, 
  and 
  is 
  readily 
  carried 
  for 
  a 
  whole 
  season 
  with 
  but 
  

   slight 
  danger 
  of 
  derangement. 
  It 
  has 
  but 
  one 
  horizontal 
  movement, 
  that 
  

   of 
  the 
  limb, 
  and 
  will 
  not 
  reverse 
  ; 
  it 
  has, 
  however, 
  a 
  segment 
  of 
  a 
  vertical 
  

   arc 
  which 
  will 
  read 
  to 
  20° 
  of 
  elevation 
  or 
  depression,enough 
  for 
  all 
  ordi- 
  

   nary 
  topographical 
  purposes. 
  I 
  append 
  a 
  drawing 
  (Plate 
  LVI) 
  of 
  this 
  

  

  