﻿528 
  

  

  Mr. 
  J. 
  A. 
  Broun 
  on 
  the 
  

  

  [June 
  17, 
  

  

  same 
  lines 
  in 
  full 
  daylight 
  was 
  47", 
  by 
  substituting 
  this 
  value 
  inequation 
  

   (3), 
  he 
  found 
  d=0'2 
  foot; 
  and 
  "we 
  may 
  conclude," 
  he 
  says, 
  "that 
  the 
  

   light 
  of 
  day 
  is 
  as 
  strong 
  as 
  that 
  of 
  a 
  candle 
  at 
  one 
  fifth 
  of 
  a 
  foot 
  from 
  the 
  

   object. 
  Consequently 
  if 
  we 
  wish 
  to 
  light 
  an 
  object 
  with 
  a 
  candle 
  as 
  

   strongly 
  as 
  it 
  would 
  be 
  by 
  daylight 
  [and 
  even 
  by 
  strong 
  sunlight, 
  as 
  

   Mayer 
  found], 
  we 
  must 
  employ 
  twenty-five 
  lighted 
  candles 
  placed 
  at 
  a 
  

   distance 
  of 
  one 
  foot 
  from 
  the 
  object"* 
  ! 
  

  

  Had 
  Mayer's 
  formula 
  been 
  an 
  exact 
  representation 
  of 
  the 
  observations, 
  

   he 
  might 
  have 
  concluded 
  that 
  the 
  eye 
  could 
  separate 
  parallel 
  lines 
  as 
  well 
  

   with 
  twenty-five 
  candles 
  at 
  one 
  foot 
  distance 
  as 
  with 
  full 
  sunlight 
  ; 
  but 
  it 
  

   will 
  be 
  seen 
  that 
  the 
  errors 
  of 
  the 
  formula 
  increase 
  as 
  d 
  increases 
  and 
  

   diminishes. 
  An 
  equation 
  of 
  the 
  form 
  given 
  by 
  Mayer 
  which 
  best 
  repre- 
  

   sents 
  the 
  observations 
  is 
  found 
  by 
  least 
  squares 
  to 
  be 
  

  

  i 
  

  

  a 
  = 
  77-6cr 
  7 
  ; 
  (4) 
  

  

  but 
  this 
  also 
  fails 
  when 
  d 
  is 
  small. 
  The 
  following 
  equation 
  best 
  repre- 
  

   sents 
  Mayer's 
  observations, 
  including 
  that 
  for 
  daylight: 
  — 
  

  

  a-47=25 
  + 
  log 
  (d 
  + 
  0-9) 
  (5) 
  

  

  When 
  d=0, 
  a 
  = 
  48"*3. 
  The 
  errors 
  of 
  this 
  equation 
  are 
  given 
  in 
  the 
  

   preceding 
  Table. 
  But 
  it 
  will 
  be 
  seen 
  here 
  also, 
  from 
  the 
  distances 
  D 
  of 
  

   the 
  observer 
  (which 
  I 
  have 
  calculated 
  from 
  the 
  angles 
  given 
  by 
  Mayer), 
  

   that 
  when 
  the 
  distances 
  d 
  of 
  the 
  candle 
  increase 
  in 
  a 
  geometrical 
  pro- 
  

   gression, 
  the 
  distances 
  D 
  diminish 
  in 
  an 
  arithmetical 
  progression 
  as 
  nearly 
  

   as 
  the 
  accuracy 
  of 
  the 
  observations 
  admit. 
  This 
  fact 
  I 
  have 
  myself 
  veri- 
  

   fied 
  by 
  repeating 
  Mayer's 
  observations. 
  We 
  may 
  then 
  represent 
  the 
  ob- 
  

   servations 
  by 
  an 
  equation 
  of 
  the 
  same 
  form 
  as 
  the 
  others. 
  The 
  following 
  

   has 
  its 
  computed 
  values 
  and 
  errors 
  given 
  in 
  the 
  Table 
  : 
  — 
  

  

  "" 
  l-O-^SSlogd 
  ^ 
  + 
  

   It 
  follows 
  from 
  this 
  formula 
  that 
  when 
  the 
  candle 
  is 
  140 
  feet 
  from 
  the 
  

   paper, 
  the 
  eye 
  at 
  8 
  inches 
  from 
  it 
  could 
  just 
  see 
  the 
  lines 
  and 
  spaces 
  ; 
  

   when 
  d 
  — 
  -^ 
  foot, 
  a 
  =47", 
  the 
  smallest 
  angle 
  under 
  which 
  the 
  lines 
  and 
  

   spaces 
  can 
  be 
  seen. 
  

  

  It 
  might 
  have 
  been 
  supposed 
  that 
  the 
  distance 
  of 
  the 
  observer 
  from 
  the 
  

   paper 
  would 
  vary 
  inversely 
  as 
  the 
  illumination, 
  or 
  that 
  a 
  should 
  vary 
  as 
  

   d 
  2 
  , 
  which, 
  it 
  will 
  be 
  seen, 
  is 
  very 
  far 
  from 
  being 
  the 
  case. 
  

  

  The 
  7th 
  observation 
  previously 
  given 
  represents 
  more 
  nearly 
  the 
  case 
  

   of 
  the 
  examination 
  of 
  test-lines 
  on 
  glass, 
  the 
  spaces 
  being 
  equally 
  bright, 
  

   or 
  nearly 
  so, 
  in 
  all 
  cases, 
  while 
  the 
  lines 
  have 
  a 
  variable 
  depth 
  of 
  shade. 
  

   In 
  Mayer's 
  observations 
  both 
  spaces 
  and 
  lines 
  receive 
  less 
  light 
  as 
  the 
  

   candle 
  is 
  removed. 
  The 
  impression 
  on 
  the 
  retina 
  for 
  the 
  separation 
  of 
  

  

  * 
  Pezenas, 
  c 
  Cours 
  complet 
  d'Optique,' 
  t. 
  ii. 
  p. 
  415. 
  

   t 
  Or, 
  D 
  = 
  6-53 
  (1-0-485 
  log 
  d). 
  

  

  