﻿1875.] 
  

  

  Power 
  of 
  the 
  Eye 
  and 
  the 
  Microscope. 
  

  

  529 
  

  

  the 
  lines 
  receives 
  no 
  improvement 
  in 
  the 
  first 
  case 
  by 
  any 
  increase 
  of 
  depth 
  

   of 
  tint 
  of 
  the 
  lines 
  beyond 
  a 
  certain 
  feeble 
  shade, 
  nor 
  in 
  the 
  second 
  

   (Mayer's) 
  case 
  by 
  any 
  increase 
  of 
  the 
  illumination 
  of 
  both 
  lines 
  and 
  spaces 
  

   beyond 
  that 
  of 
  a 
  candle 
  held 
  near. 
  

  

  8th 
  observation. 
  — 
  It 
  was 
  sought 
  whether 
  the 
  visibility 
  of 
  parallel 
  lines 
  

   increased 
  with 
  their 
  length, 
  as 
  in 
  the 
  case 
  of 
  single 
  lines. 
  Four 
  long 
  

   parallel 
  lines 
  having 
  been 
  drawn, 
  of 
  the 
  width 
  and 
  at 
  the 
  interval 
  of 
  

   0'048 
  inch, 
  on 
  a 
  sheet 
  of 
  white 
  paper, 
  this 
  was 
  pinned, 
  as 
  before, 
  to 
  a 
  

   smooth 
  plank 
  and 
  placed 
  in 
  the 
  open 
  air 
  in 
  the 
  shade 
  (before 
  sunset) 
  ; 
  

   the 
  lines 
  were 
  covered 
  by 
  a 
  sheet 
  of 
  the 
  same 
  paper 
  so 
  as 
  to 
  show 
  variable 
  

  

  lengths. 
  

  

  The 
  following 
  Table 
  contains 
  the 
  results 
  of 
  the 
  observations 
  :- 
  

  

  I. 
  

  

  P. 
  

  

  a. 
  

  

  (7). 
  

  

  Errors. 
  

  

  (3. 
  

  

  in. 
  

  

  ft. 
  in. 
  

  

  49-5 
  

  

  // 
  

  

  

  413 
  

  

  04 
  

  

  16 
  8 
  

  

  49-5 
  

  

  00 
  

  

  0-8 
  

  

  17 
  4 
  

  

  47-6 
  

  

  474 
  

  

  -0-2 
  

  

  794 
  

  

  1-6 
  

  

  18 
  5 
  

  

  44-8 
  

  

  45-5 
  

  

  +0-7 
  

  

  1490 
  

  

  3-2 
  

  

  18 
  10 
  

  

  43-8 
  

  

  43-8 
  

  

  00 
  

  

  2921 
  

  

  64 
  

  

  19 
  5 
  

  

  42-5 
  

  

  42-1 
  

  

  -04 
  

  

  5664 
  

  

  D 
  is 
  the 
  distance 
  of 
  the 
  observer, 
  I 
  the 
  length 
  of 
  the 
  lines, 
  /3 
  is 
  the 
  

   angle 
  subtended 
  by 
  the 
  length 
  at 
  the 
  eye 
  of 
  the 
  observer 
  ; 
  a, 
  the 
  angle 
  sub- 
  

   tended 
  by 
  the 
  width 
  of 
  the 
  lines, 
  is 
  represented 
  nearly 
  by 
  the 
  following 
  

   formula 
  : 
  — 
  

  

  = 
  352 
  

  

  ° 
  logZ+4•53' 
  ,, 
  ••^' 
  \ 
  

  

  where 
  I, 
  the 
  length 
  of 
  the 
  lines, 
  is 
  expressed 
  in 
  units 
  of 
  0*001 
  inch. 
  The 
  

   variation 
  of 
  the 
  angle 
  is 
  comparatively 
  small 
  in 
  this 
  case. 
  The 
  law 
  of 
  

   variation 
  of 
  a 
  seems 
  to 
  change 
  when 
  the 
  length 
  of 
  the 
  lines 
  becomes 
  less 
  

   than 
  the 
  width 
  of 
  the 
  w 
  7 
  hole. 
  

  

  9th 
  observation. 
  — 
  The 
  following 
  observations 
  were 
  made 
  with 
  short 
  

   parallel 
  lines 
  drawn 
  separately 
  on 
  the 
  same 
  sheet, 
  with 
  the 
  same 
  width 
  of 
  

   intervals 
  and 
  lines 
  as 
  in 
  the 
  last 
  case 
  : 
  — 
  

  

  I 
  

  

  D. 
  

  

  a. 
  

  

  (8). 
  

  

  Errors. 
  

  

  /3. 
  

  

  

  in. 
  

  

  in. 
  

  

  

  480 
  

  

  

  404 
  

  

  

  040 
  

  

  204 
  

  

  48-6 
  

  

  -0-6 
  

  

  359 
  

  

  0-20 
  

  

  186 
  

  

  53-2 
  

  

  53-5 
  

  

  4-0-3 
  

  

  222 
  

  

  322 
  

  

  040 
  

  

  168 
  

  

  58-9 
  

  

  60-6 
  

  

  + 
  1-7 
  

  

  123 
  

  

  293 
  

  

  0-05 
  

  

  144 
  

  

  .68-8 
  

  

  69-9 
  

  

  + 
  14 
  

  

  72 
  

  

  286 
  

  

  0'025 
  

  

  120 
  

  

  '82-5 
  

  

  82-5 
  

  

  00 
  

  

  43 
  

  

  289 
  

  

  0-012 
  

  

  96 
  

  

  103-1 
  

  

  101-0 
  

  

  -2-1 
  

  

  26 
  

  

  306 
  

  

  The 
  observations 
  are 
  represented 
  nearly 
  by 
  the 
  equation 
  

  

  137 
  

  

  It 
  will 
  be 
  seen 
  tha 
  tthe 
  angle 
  a 
  increases 
  rapidly 
  as 
  the 
  length 
  dimi- 
  

  

  2 
  s 
  2 
  

  

  