﻿1875.] 
  

  

  Power 
  of 
  the 
  Eye 
  and 
  the 
  Microscope. 
  

  

  527 
  

  

  lines. 
  On 
  the 
  other 
  hand, 
  the 
  tint 
  may 
  be 
  made 
  so 
  faint 
  as 
  to 
  be 
  imper- 
  

   ceptible 
  at 
  6 
  inches 
  (the 
  distance 
  for 
  a 
  young 
  eye 
  of 
  faint 
  or 
  small 
  objects). 
  

   The 
  preceding 
  observations 
  are 
  represented 
  nearly 
  by 
  the 
  following 
  

   formula 
  : 
  — 
  

  

  •-^rSb 
  <*> 
  

  

  where 
  a 
  is 
  the 
  smallest 
  angle 
  (in 
  seconds) 
  at 
  which 
  the 
  separation 
  of 
  the 
  

   lines 
  was 
  visible, 
  and 
  t 
  is 
  the 
  tint 
  or 
  number 
  of 
  the 
  coats 
  of 
  watered 
  ink. 
  

   The 
  calculated 
  values 
  are 
  given 
  in 
  the 
  Table. 
  

  

  When 
  t=^ 
  (of 
  the 
  first 
  tint) 
  the 
  lines, 
  according 
  to 
  the 
  formula, 
  

   should 
  have 
  been 
  just 
  visible 
  at 
  8 
  inches 
  from 
  the 
  eye, 
  or 
  a 
  weaker 
  shade 
  

   on 
  white 
  paper 
  than 
  that 
  made 
  by 
  one 
  drop 
  of 
  the 
  first 
  tint 
  with 
  forty-six 
  

   drops 
  of 
  water 
  could 
  not 
  have 
  been 
  seen. 
  On 
  the 
  other 
  hand, 
  when 
  

   t=12, 
  the 
  difference 
  of 
  the 
  angle 
  of 
  visibility 
  from 
  that 
  for 
  absolute 
  black- 
  

   ness 
  is 
  only 
  0"*1. 
  The 
  constants 
  in 
  this 
  and 
  the 
  other 
  formulas 
  wdll 
  

   depend 
  of 
  course 
  on 
  various 
  circumstances 
  of 
  illumination, 
  the 
  state 
  of 
  

   the 
  individual 
  eye, 
  &c. 
  

  

  Mayer 
  made 
  a 
  series 
  of 
  observations 
  with 
  several 
  parallel 
  lines 
  drawn 
  

   with 
  China 
  ink 
  on 
  white 
  paper 
  (well 
  stretched), 
  the 
  width 
  of 
  the 
  lines 
  and 
  

   intervals 
  in 
  one 
  case 
  being 
  0*032 
  of 
  an 
  English 
  inch 
  (0-36 
  de 
  ligne). 
  

   These 
  lines 
  he 
  could 
  perceive 
  to 
  be 
  several 
  at 
  11 
  feet 
  (jpieds 
  de 
  Boi) 
  dis- 
  

   tance 
  with 
  the 
  light 
  from 
  an 
  open 
  window 
  to 
  north, 
  or 
  when 
  the 
  angle 
  

   subtended 
  by 
  the 
  interval 
  was 
  47". 
  He 
  then 
  made 
  observations 
  with 
  the 
  

   same 
  lines 
  lighted 
  by 
  a 
  wax 
  candle 
  placed 
  at 
  different 
  distances 
  from 
  

   them. 
  

  

  I 
  give 
  Mayer's 
  observations 
  for 
  this 
  set 
  of 
  lines 
  here 
  for 
  comparison 
  

   with 
  the 
  preceding 
  results 
  for 
  different 
  tints. 
  

  

  D. 
  

  

  d. 
  

  

  a. 
  

  

  Observed. 
  

  

  Angle 
  a, 
  calculated 
  by 
  

  

  (3). 
  

  

  Error. 
  

  

  (5). 
  

  

  Error. 
  

  

  (6). 
  

  

  Error. 
  

  

  feet. 
  

  

  feet. 
  

  

  

  

  

  

  

  

  

  7-47 
  

  

  0-5 
  

  

  69 
  

  

  63 
  

  

  - 
  6 
  

  

  66 
  

  

  -3 
  

  

  69 
  

  

  

  

  6-53 
  

  

  10 
  

  

  79 
  

  

  79 
  

  

  

  

  78 
  

  

  

  

  79 
  

  

  

  

  5-73 
  

  

  20 
  

  

  90 
  

  

  99 
  

  

  + 
  9 
  

  

  96 
  

  

  +6 
  

  

  92 
  

  

  +2 
  

  

  4-73 
  

  

  30 
  

  

  109 
  

  

  114 
  

  

  + 
  5 
  

  

  108 
  

  

  -1 
  

  

  103 
  

  

  -6 
  

  

  4-48 
  

  

  4-0 
  

  

  115 
  

  

  125 
  

  

  + 
  10 
  

  

  118 
  

  

  +3 
  

  

  112 
  

  

  -3 
  

  

  3-51 
  

  

  8-0 
  

  

  147 
  

  

  158 
  

  

  + 
  11 
  

  

  146 
  

  

  -1 
  

  

  141 
  

  

  -6 
  

  

  300 
  

  

  130 
  

  

  172 
  

  

  185 
  

  

  + 
  1.5 
  

  

  172 
  

  

  

  

  172 
  

  

  

  

  Mayer 
  considered 
  that 
  he 
  explained 
  his 
  result 
  by 
  supposing 
  the 
  limit- 
  

   ing 
  angle 
  (a) 
  of 
  distinct 
  vision 
  to 
  be 
  as 
  the 
  cube 
  root 
  of 
  the 
  distance 
  of 
  

   the 
  candle 
  from 
  the 
  paper, 
  or 
  

  

  a 
  =79 
  tyd, 
  (3) 
  

  

  where 
  a 
  is 
  in 
  seconds 
  and 
  d 
  is 
  mpieds 
  de 
  Hoi. 
  He 
  also 
  arrived 
  at 
  the 
  

   following 
  curious 
  conclusion. 
  Since 
  the 
  limiting 
  value 
  of 
  a 
  for 
  the 
  

   vol. 
  xxiii. 
  2 
  s 
  

  

  