﻿136 
  PROCEEDINGS 
  OF 
  THE 
  CALIFORNIA 
  

  

  Figure 
  II 
  exhibits 
  the 
  repeating 
  micrometer, 
  which 
  essentially 
  consists 
  of 
  

   three 
  frames. 
  The 
  first, 
  F, 
  is 
  attached 
  by 
  screws 
  to 
  the 
  eye 
  tube 
  of 
  the 
  teles- 
  

   cope. 
  At 
  the 
  left-hand 
  end 
  it 
  carries 
  a 
  moderately 
  fine 
  micrometer 
  screw, 
  

   G, 
  which 
  moves 
  the 
  two 
  frames, 
  H 
  and 
  /, 
  which 
  are 
  themselves 
  attached 
  to 
  each 
  

   other 
  by 
  the 
  fine 
  micrometer 
  screw, 
  /, 
  bearing 
  the 
  micrometer 
  head, 
  K, 
  and 
  

   carrying 
  the 
  micrometer 
  thread, 
  N. 
  The 
  springs, 
  S 
  and 
  S' 
  , 
  between 
  F 
  and 
  H, 
  

   are 
  for 
  keeping 
  a 
  constant 
  strain 
  between 
  the 
  two 
  frames 
  ; 
  and 
  the 
  springs, 
  L 
  

   and 
  L' 
  , 
  between 
  H 
  and 
  J, 
  are 
  for 
  a 
  similar 
  purpose. 
  The 
  frame, 
  i/, 
  carries 
  the 
  

   micrometer 
  rack, 
  M, 
  by 
  which 
  the 
  whole 
  turns 
  or 
  revolutions 
  of 
  the 
  micrometer 
  

   head 
  of 
  / 
  are 
  noted. 
  

  

  The 
  action 
  of 
  the 
  micrometer 
  is 
  therefore 
  readily 
  seen, 
  and 
  the 
  operation 
  of 
  

   observing 
  is 
  as 
  follows 
  : 
  

  

  P 
  and 
  P' 
  (in 
  both 
  figures) 
  are 
  the 
  two 
  images 
  of 
  the 
  object 
  to 
  be 
  observed 
  upon. 
  

   The 
  micrometer 
  /may 
  be 
  turned 
  until 
  the 
  zero 
  of 
  the 
  head 
  is 
  opposite 
  the 
  pointer 
  

   R, 
  then 
  the 
  micrometer 
  G 
  is 
  turned 
  (moving 
  frames 
  H 
  and 
  I) 
  until 
  the 
  thread 
  

   N 
  bisects 
  the 
  left-hand 
  image 
  P 
  ; 
  the 
  micrometer 
  / 
  is 
  then 
  turned, 
  moving 
  the 
  

   rack 
  /only, 
  until 
  the 
  thread 
  N 
  bisects 
  the 
  right-hand 
  object 
  P', 
  and 
  the 
  mi- 
  

   crometer 
  read 
  off 
  for 
  the 
  divisions 
  less 
  than 
  one 
  hundred, 
  whilst 
  the 
  whole 
  turns 
  

   are 
  noted 
  on 
  the 
  rack, 
  which 
  has 
  a 
  notch 
  for 
  each 
  turn 
  of 
  the 
  micrometer 
  ; 
  this 
  

   difference 
  of 
  the 
  two 
  readings 
  gives 
  the 
  distance 
  apart 
  of 
  the 
  two 
  images 
  of 
  the 
  

   object 
  in 
  terms 
  of 
  the 
  micrometer, 
  and 
  constitutes 
  one 
  measure. 
  The 
  mi- 
  

   crometer 
  G 
  is 
  now 
  turned, 
  and 
  carries 
  both 
  frames 
  H 
  and 
  I 
  until 
  the 
  thread 
  N 
  

   is 
  brought 
  back 
  to 
  bisect 
  the 
  image 
  P 
  ; 
  then 
  the 
  micrometer 
  / 
  is 
  turned 
  until 
  

   the 
  thread 
  iV 
  bisects 
  P' 
  , 
  and 
  read 
  off, 
  as 
  before, 
  for 
  a 
  second 
  measurement 
  ; 
  

   and 
  so 
  for 
  subsequent 
  measures. 
  The 
  measures 
  can 
  be 
  read 
  off 
  after 
  each 
  rep- 
  

   etition 
  ; 
  or, 
  in 
  rapid 
  work, 
  only 
  the 
  readings 
  of 
  the 
  first 
  bisection 
  and 
  the 
  last 
  

   in 
  a 
  set, 
  and 
  the 
  micrometer 
  divisions 
  passed 
  over, 
  divided 
  by 
  the 
  number 
  of 
  rep- 
  

   etitions. 
  And 
  any 
  number 
  of 
  sets 
  may 
  be 
  made 
  to 
  test 
  or 
  increase 
  the 
  accu- 
  

   racy 
  of 
  the 
  work. 
  

  

  If 
  the 
  images 
  of 
  the 
  object 
  to 
  be 
  observed 
  upon 
  are 
  small, 
  clear, 
  and 
  sharply 
  

   defined, 
  the 
  probable 
  error 
  of 
  the 
  individual 
  micrometer 
  measures 
  should 
  not 
  ex- 
  

   ceed 
  half 
  a 
  second 
  of 
  arc, 
  but, 
  on 
  account 
  of 
  the 
  lack 
  of 
  definiteness 
  and 
  

   sharpness 
  of 
  most 
  terrestrial 
  objects, 
  this 
  probable 
  error 
  will 
  be 
  larger 
  ; 
  neverthe- 
  

   less, 
  it 
  is 
  perhaps 
  a 
  large 
  allowance 
  to 
  assume 
  that 
  a 
  probable 
  error 
  of 
  one 
  second 
  

   of 
  arc 
  may 
  exist 
  in 
  the 
  mean 
  of 
  ten 
  repetitions. 
  At 
  the 
  distance 
  of 
  one 
  mile 
  

   this 
  would 
  involve 
  an 
  error 
  of 
  little 
  more 
  than 
  two 
  feet; 
  and 
  at 
  five 
  miles, 
  of 
  

   only 
  fifty-five 
  feet. 
  

  

  Of 
  course, 
  another 
  function 
  of 
  the 
  accuracy 
  of 
  the 
  distance 
  is 
  the 
  accuracy 
  of 
  

   the 
  base-bar 
  itself 
  in 
  the 
  instrument; 
  but 
  this 
  can 
  be 
  obtained 
  with 
  great 
  pre- 
  

   cision. 
  And 
  as 
  the 
  base 
  changes 
  its 
  length 
  by 
  changes 
  of 
  temperature, 
  tables 
  

   of 
  distances 
  for 
  a 
  series 
  of 
  micrometer 
  differences, 
  with 
  the 
  base-bar 
  at 
  different 
  

   temperatures, 
  can 
  be 
  readily 
  constructed. 
  

  

  Upon 
  the 
  upper 
  and 
  middle 
  part 
  of 
  the 
  bar-tube 
  a 
  small 
  prismatic 
  compass 
  

   was 
  placed 
  by 
  General 
  Clerk, 
  to 
  obtain 
  the 
  magnetic 
  bearing 
  of 
  the 
  object. 
  In 
  

  

  