﻿524 
  

  

  Mr. 
  J. 
  A. 
  Broun 
  on 
  the 
  

  

  [June 
  17 
  } 
  

  

  The 
  hair 
  0*9 
  inch 
  long 
  was 
  one 
  foot 
  further 
  off 
  than 
  that 
  2*5 
  inch 
  long 
  

   on 
  the 
  clay 
  preceding 
  (2nd 
  observation). 
  The 
  difference 
  was 
  due, 
  partly 
  

   at 
  least, 
  to 
  the 
  different 
  light 
  of 
  the 
  sky. 
  

  

  4th 
  observation. 
  — 
  The 
  previous 
  observation 
  shows 
  that 
  the 
  line 
  is 
  seen 
  

   at 
  a 
  greater 
  distance 
  as 
  the 
  length 
  increases 
  till 
  a 
  limiting 
  angle 
  is 
  at- 
  

   tained, 
  after 
  which 
  increase 
  of 
  length 
  has 
  no 
  effect 
  on 
  the 
  visibility. 
  The 
  

   following 
  observations 
  were 
  made 
  to 
  determine 
  approximately 
  the 
  law 
  

   which 
  relates 
  visibility 
  to 
  length. 
  

  

  Lines 
  of 
  different 
  lengths, 
  0*045 
  inch 
  wide, 
  were 
  drawn 
  on 
  different 
  

   slips 
  of 
  white 
  paper 
  (5*8 
  by 
  4*5 
  inches) 
  ; 
  the 
  papers 
  were 
  pinned 
  succes- 
  

   sively 
  to 
  a 
  plank 
  placed 
  vertically 
  in 
  the 
  shade 
  (out 
  of 
  doors) 
  with 
  a 
  clear 
  

   sky 
  (April, 
  6 
  p.m.); 
  the 
  mean 
  distance 
  of 
  disappearance 
  on 
  retiring 
  and 
  

   of 
  appearance 
  on 
  approaching 
  the 
  lines 
  was 
  taken. 
  

  

  Length. 
  Distance. 
  

  

  in. 
  

  

  0-045 
  

   0-125 
  

   0-245 
  

   0470 
  

  

  0- 
  970 
  

  

  1- 
  800 
  

   3-400 
  

  

  feet. 
  

  

  "*53 
  

   68 
  

   84 
  

   100 
  

   114 
  

   129 
  

  

  Angle 
  subtended 
  by 
  

  

  

  Length 
  

  

  Width 
  a. 
  

  

  Observed. 
  

  

  Calculated. 
  

  

  

  u 
  

  

  26-4 
  

  

  

  41 
  

  

  14-6 
  

  

  14-5 
  

  

  50 
  

  

  62 
  

  

  114 
  

  

  11-2 
  

  

  45 
  

  

  96 
  

  

  9-2 
  

  

  9-2 
  

  

  42 
  

  

  167 
  

  

  7-7 
  

  

  7-7 
  

  

  42 
  

  

  272 
  

  

  6-8 
  

  

  6-8 
  

  

  44 
  

  

  453 
  

  

  6-0 
  

  

  6-0 
  

  

  46 
  

  

  It 
  will 
  be 
  seen 
  that 
  as 
  the 
  lengths 
  of 
  the 
  lines 
  increase 
  in 
  a 
  geometrical 
  

   progression 
  (nearly), 
  the 
  distances 
  increase 
  in 
  an 
  arithmetical 
  progression 
  

   (nearly). 
  It 
  has 
  been 
  easy 
  then 
  to 
  represent 
  the 
  observed 
  angles 
  (a) 
  by 
  

   the 
  following 
  equation 
  : 
  — 
  

  

  14 
  ' 
  5 
  (1)* 
  

  

  logZ-1-10' 
  

  

  where 
  a 
  iVexpressed 
  in 
  seconds 
  of 
  arc, 
  and 
  I, 
  the 
  length 
  of 
  the 
  line, 
  is 
  in 
  

   units 
  of 
  0-001 
  inch. 
  The 
  calculated 
  values 
  agree 
  very 
  nearly 
  with 
  

   those 
  observed. 
  The 
  angle 
  for 
  a 
  square 
  of 
  0*045 
  inch 
  calculated 
  is 
  26"*4, 
  

   which 
  is 
  very 
  near 
  to 
  the 
  value 
  observed 
  on 
  a 
  previous 
  occasion, 
  a 
  (or 
  

   tana) 
  becomes 
  infinite 
  for 
  Z=12*6 
  (0*0126 
  inch); 
  but 
  the 
  formula 
  does 
  

   not 
  hold 
  for 
  lines 
  in 
  which 
  the 
  length 
  is 
  less 
  than 
  the 
  width. 
  These 
  belong 
  

   to 
  another 
  case, 
  that 
  in 
  which 
  the 
  lengths 
  of 
  the 
  lines 
  are 
  constant 
  and 
  

   the 
  width 
  variable. 
  

  

  Having 
  examined 
  the 
  power 
  of 
  the 
  eye 
  to 
  see 
  single 
  lines, 
  I 
  now 
  sought 
  

   how 
  this 
  power 
  would 
  be 
  affected 
  when 
  more 
  Hues 
  than 
  one 
  were 
  placed 
  

   parallel 
  to 
  each 
  other, 
  and 
  with 
  intervals 
  equal 
  to 
  their 
  widths. 
  

  

  * 
  This 
  equation 
  may 
  be 
  put 
  under 
  the 
  following 
  form, 
  where 
  D, 
  the 
  distance 
  of 
  the 
  

   observer, 
  and 
  I 
  are 
  in 
  units 
  of 
  one 
  inch 
  : 
  — 
  

  

  D= 
  642 
  log 
  79*4 
  1. 
  

  

  