﻿riiOCEEDIJNGS 
  OF 
  THE 
  FOUKTII 
  ENTOMOLOGICAL 
  MEETING 
  283 
  

  

  covered 
  by 
  tlie 
  body 
  in 
  its 
  movement, 
  and 
  not 
  merely 
  to 
  the 
  distance 
  

   between 
  its 
  initial 
  and 
  final 
  positions. 
  

  

  Now 
  according 
  to 
  the 
  mosaic 
  theory 
  of 
  insect-vision 
  originally 
  

   advanced 
  by 
  MuUer, 
  each 
  facet 
  of 
  the 
  fly's 
  eye 
  commands 
  a 
  certain 
  

   definite 
  area 
  of 
  the 
  field 
  of 
  view, 
  and 
  by 
  the 
  juxtaposition 
  of 
  these 
  

   elements 
  a 
  composite 
  image 
  is 
  built 
  up, 
  as 
  we 
  might 
  piece 
  together 
  a 
  

   mosaic 
  out 
  of 
  little 
  bricks. 
  Exner 
  has 
  shown, 
  however, 
  that 
  in 
  many 
  

   cases 
  a 
  certain 
  amount 
  of 
  superposition 
  of 
  image-elements 
  also 
  occurs, 
  

   in 
  the 
  sense 
  that 
  light 
  from 
  a 
  single 
  point 
  may 
  be 
  registered 
  by 
  more 
  

   than 
  a 
  single 
  facet, 
  and 
  that 
  while 
  this 
  will 
  tend 
  to 
  decrease 
  the 
  accuracy 
  

   with 
  which 
  forms 
  are 
  perceived 
  it 
  will 
  enhance 
  the 
  acuteness 
  of 
  percep- 
  

   tion 
  of 
  motion, 
  since 
  motion 
  of 
  a 
  single 
  point 
  will 
  effect 
  more 
  than 
  a 
  

   single 
  facet. 
  I 
  am 
  unable 
  to 
  refer 
  to 
  Exner's 
  classic 
  work 
  on 
  this 
  subject, 
  

   or 
  to 
  treat 
  the 
  present 
  example 
  in 
  anything 
  but 
  crude 
  fashion. 
  How- 
  

   ever, 
  the 
  data 
  given 
  may 
  perhaps 
  furnish 
  a 
  basis 
  for 
  a 
  more 
  accurate 
  

   analysis. 
  

  

  Taking 
  the 
  radius 
  of 
  curvature 
  of 
  the 
  eye 
  as 
  5 
  mm., 
  and 
  the 
  dia- 
  

   meter 
  of 
  a 
  single 
  facet 
  as 
  -04 
  nun., 
  then, 
  multiplying 
  together 
  the 
  number 
  

   of 
  facets 
  covered 
  in 
  a 
  vertical 
  direction 
  by 
  the 
  height 
  of 
  the 
  object, 
  and 
  

   the 
  number 
  covered 
  horizontally 
  by 
  the 
  lateral 
  movement 
  of 
  the 
  object, 
  

   we 
  get 
  the 
  following 
  figures 
  as 
  to 
  facets 
  afiected 
  : 
  — 
  

  

  6 
  2x12-1- 
  —25 
  

  

  9 
  4x8 
  —32 
  

  

  U 
  7x51 
  —36 
  

  

  17 
  9|x4i 
  —40 
  

  

  Now 
  if 
  the 
  disturbing 
  effect 
  of 
  the 
  moving 
  object 
  were 
  exactly 
  pro- 
  

   portional 
  to 
  the 
  square 
  of 
  the 
  distance, 
  there 
  would 
  be 
  identical 
  numbers 
  

   of 
  facets 
  {i.e., 
  areas), 
  and 
  we 
  could 
  say 
  that 
  there 
  was 
  a 
  constant 
  minimum 
  

   stimulus 
  (the 
  excitation 
  of 
  a 
  certain 
  number 
  of 
  facets) 
  which 
  would 
  

   make 
  a 
  fly 
  dodge. 
  It 
  is 
  evident 
  that 
  they 
  are 
  not 
  identical, 
  and 
  the 
  

   discrepancy 
  is 
  beyond 
  the 
  probable 
  limits 
  of 
  error. 
  

  

  These 
  numbers 
  when 
  pFotted 
  give 
  an 
  indication 
  that 
  the 
  minimum 
  

   number 
  of 
  facets 
  to 
  be 
  stimulated 
  at 
  close 
  range 
  in 
  order 
  to 
  make 
  the 
  

   fly 
  dodge 
  might 
  be 
  expected 
  to 
  be 
  about 
  16, 
  and 
  that 
  the 
  formula 
  N 
  = 
  

   (16-|-1*5 
  D), 
  where 
  D 
  is 
  distance 
  in 
  feet, 
  will 
  give 
  us 
  the 
  approximate 
  

   number 
  of 
  facets 
  to 
  be 
  stimulated 
  for 
  various 
  distances. 
  

  

  Assuming 
  this 
  formula 
  to 
  hold, 
  a 
  man 
  6 
  feet 
  high 
  at 
  a 
  distance 
  of 
  

   30 
  feet 
  would 
  have 
  to 
  move 
  rapidly 
  over 
  a 
  sufficient 
  distance 
  to 
  stimu- 
  

   late 
  61 
  facets. 
  His 
  height 
  of 
  6 
  feet 
  subtends 
  an 
  angle 
  embracing 
  2^- 
  

   facets, 
  so 
  that 
  his 
  lateral 
  movement 
  must 
  cover 
  24 
  facets 
  (24x2|=60), 
  

   or 
  approximately 
  1 
  mm. 
  (0-04x24) 
  on 
  the 
  surface 
  of 
  the 
  eye. 
  To 
  do 
  

   this 
  it 
  would 
  be 
  necessary 
  for 
  him 
  to 
  move 
  a 
  distance 
  of 
  about 
  20 
  yards 
  

  

  