﻿532 
  On 
  the 
  Power 
  of 
  the 
  Eye 
  and 
  the 
  Microscope. 
  [June 
  17/ 
  

  

  of 
  an 
  inch 
  wide 
  should 
  be 
  seen 
  with 
  a 
  power 
  of 
  125, 
  and 
  counted 
  with 
  a 
  

   power 
  of 
  160 
  (the 
  distance 
  for 
  the 
  unaided 
  eye 
  being 
  considered 
  8 
  inches). 
  

   We 
  have, 
  however, 
  obviously 
  in 
  the 
  high 
  bands 
  to 
  include 
  the 
  case 
  of 
  ob- 
  

   servation 
  7, 
  the 
  lines 
  on 
  the 
  photographs 
  being 
  excessively 
  faint. 
  "When 
  

   we 
  add 
  to 
  this 
  fact 
  (a 
  most 
  important 
  one 
  when 
  such 
  lines 
  are 
  supposed 
  

   to 
  give 
  some 
  measure 
  of 
  the 
  power 
  of 
  the 
  microscope) 
  that 
  it 
  appears 
  that 
  

   separate 
  lines 
  cannot 
  be 
  drawn 
  of 
  a 
  less 
  width 
  than 
  about 
  180> 
  1 
  000 
  of 
  an 
  

   inch 
  under 
  the 
  diminished 
  pressure 
  of 
  Mr. 
  Robert's 
  machine 
  without 
  

   the 
  graving-point 
  sliding 
  into 
  previous 
  grooves, 
  we 
  have 
  a 
  sufficient 
  ex- 
  

   planation 
  why 
  the 
  power 
  of 
  the 
  microscope 
  cannot 
  be 
  measured 
  by 
  these 
  

   lines. 
  

  

  The 
  following 
  are 
  the 
  conclusions 
  of 
  this 
  note 
  : 
  — 
  

  

  1st. 
  That 
  lines 
  can 
  be 
  seen 
  by 
  the 
  naked 
  eye 
  with 
  transmitted 
  light 
  

   the 
  width 
  of 
  which 
  subtends 
  an 
  angle 
  of 
  about 
  1" 
  (2nd 
  observation). 
  

  

  2nd. 
  That 
  the 
  visibility 
  of 
  a 
  line, 
  or 
  the 
  distance 
  at 
  which 
  it 
  can 
  be 
  seen, 
  

   depends 
  on 
  the 
  logarithm 
  of 
  its 
  length, 
  the 
  product 
  of 
  the 
  angle 
  subtended 
  

   by 
  the 
  width 
  and 
  the 
  cube 
  root 
  of 
  that 
  subtended 
  by 
  the 
  length 
  being 
  nearly 
  

   constant 
  (4th 
  observation). 
  

  

  3rd. 
  Short 
  parallel 
  lines 
  could 
  be 
  seen 
  by 
  transmitted 
  light 
  when 
  the 
  

   angle 
  formed 
  by 
  the 
  width 
  of 
  the 
  spaces 
  and 
  intervals 
  was 
  20" 
  (5th 
  ob- 
  

   servation). 
  . 
  •' 
  

  

  4th. 
  The 
  visibility 
  of 
  lines 
  of 
  the 
  same 
  width 
  increases 
  as 
  the 
  distance 
  

   between 
  them 
  decreases 
  (6th 
  observation). 
  

  

  5th. 
  The 
  visibility 
  of 
  parallel 
  hues 
  depends 
  on 
  the 
  darkness 
  of 
  the 
  

   shade 
  or 
  tint 
  of 
  the 
  lines 
  up 
  to 
  a 
  certain 
  feeble 
  tint, 
  after 
  which 
  no 
  black- 
  

   ing 
  of 
  the 
  lines 
  increases 
  the 
  visibility 
  ; 
  the 
  distance 
  to 
  which 
  the 
  lines 
  can 
  

   be 
  seen 
  depends 
  on 
  c*, 
  where 
  c 
  is 
  a 
  constant 
  and 
  t 
  is 
  the 
  number 
  of 
  the 
  

   tint 
  or 
  shade 
  (the 
  number 
  of 
  coats 
  of 
  a 
  weak 
  tint) 
  (7th 
  observation). 
  

  

  6th. 
  The 
  visibility 
  of 
  dark 
  parallel 
  lines 
  lighted 
  with 
  a 
  candle 
  depends 
  

   on 
  the 
  logarithm 
  of 
  the 
  distance 
  of 
  the 
  candle 
  from 
  the 
  lines 
  ; 
  and 
  they 
  

   can 
  be 
  seen 
  as 
  well 
  with 
  a 
  candle 
  placed 
  quite 
  near 
  as 
  with 
  the 
  strongest 
  

   daylight. 
  This 
  results 
  from 
  Tobias 
  Mayer's 
  observations. 
  

  

  7th. 
  The 
  visibility 
  of 
  parallel 
  lines 
  depends 
  on 
  the 
  logarithm 
  of 
  their 
  

   length, 
  as 
  in 
  the 
  case 
  of 
  single 
  lines, 
  the 
  variation 
  being 
  much 
  greater 
  for 
  

   short 
  parallel 
  lines 
  than 
  for 
  long 
  ones. 
  Also 
  for 
  short 
  parallel 
  lines 
  the 
  

   product 
  a 
  \/j3 
  is 
  nearly 
  constant, 
  as 
  for 
  single 
  lines 
  (see 
  second 
  conclusion). 
  

  

  8th. 
  Parallel 
  lines 
  are 
  least 
  visible 
  when 
  there 
  are 
  only 
  two, 
  and 
  in- 
  

   crease 
  in 
  visibility 
  with 
  their 
  number. 
  

  

  9th. 
  Robert's 
  test-lines 
  fail 
  as 
  a 
  test 
  for 
  the 
  microscope, 
  especially 
  in 
  

   the 
  highest 
  bands, 
  from 
  the 
  incapacity 
  of 
  the 
  machine 
  to 
  make 
  separate 
  

   lines 
  at 
  less 
  intervals 
  and 
  of 
  less 
  width 
  than 
  1 
  6Q 
  * 
  00Q 
  of 
  an 
  inch 
  ; 
  they 
  also 
  

   fail, 
  in 
  all 
  probability, 
  on 
  account 
  of 
  the 
  faintness 
  of 
  the 
  tint 
  or 
  shade 
  of 
  the 
  

   lines 
  made 
  on 
  the 
  retina. 
  

  

  