﻿98 
  PROCEEDINGS 
  OP 
  THE 
  CALIFORNIA 
  

  

  On 
  the 
  structure 
  of 
  the 
  Honey-bag 
  in 
  the 
  Honey-making 
  An 
  t 
  

   Myrmecoeystus 
  Mexieanus. 
  

  

  BY 
  JAMES 
  BLAKE, 
  M.D. 
  

  

  Having 
  prepared 
  the 
  two 
  specimens 
  of 
  the 
  honey-making 
  ant 
  that 
  were 
  ex- 
  

   hibited 
  in 
  connection 
  with 
  Mr. 
  Edwards' 
  paper 
  at 
  a 
  previous 
  meeting 
  of 
  the 
  

   Academy, 
  I 
  have 
  been 
  enabled, 
  by 
  preserving 
  them 
  in 
  a 
  solution 
  that 
  renders 
  

   the 
  sack 
  containing 
  the 
  honey 
  perfectly 
  transparent, 
  to 
  ascertain 
  the 
  curious 
  

   fact 
  that 
  the 
  intestine 
  of 
  the 
  insect 
  is 
  not 
  continued 
  beyond 
  the 
  tborax, 
  so 
  that 
  

   there 
  is 
  no 
  way 
  in 
  which 
  the 
  remains 
  of 
  the 
  food 
  can 
  be 
  expelled 
  from 
  the 
  body, 
  

   except 
  by 
  the 
  mouth. 
  The 
  honey-bag 
  is 
  evidently 
  formed 
  by 
  the 
  expansion 
  of 
  

   the 
  abdominal 
  segments, 
  as 
  the 
  remains 
  of 
  the 
  four 
  chitinous 
  rings 
  in 
  which 
  it 
  

   was 
  originally 
  enclosed 
  are 
  still 
  visible. 
  The 
  first 
  ring 
  anteriorly 
  retains 
  its 
  

   connection 
  with 
  the 
  thorax, 
  the 
  posterior 
  part 
  being 
  split 
  so 
  as 
  to 
  expand. 
  The 
  

   remains 
  of 
  the 
  other 
  rings 
  are 
  seen 
  as 
  small 
  scales 
  on 
  the 
  dorsal 
  and 
  ventral 
  

   surfaces 
  of 
  the 
  honey-bag. 
  The 
  expansion 
  of 
  the 
  abdominal 
  cavity 
  has 
  not 
  

   taken 
  place 
  evenly, 
  as 
  the 
  orifice 
  of 
  the 
  cloaca 
  with 
  the 
  ovipositor, 
  which 
  in 
  the 
  

   ant 
  is 
  situated 
  at 
  the 
  end 
  of 
  the 
  abdomen, 
  is 
  now 
  found 
  at 
  some 
  distance 
  from 
  

   the 
  end 
  on 
  the 
  ventral 
  surface, 
  so 
  that 
  the 
  expansion 
  of 
  the 
  abdomen 
  has 
  evi- 
  

   dently 
  been 
  greater 
  on 
  the 
  dorsal 
  than 
  on 
  the 
  ventral 
  surface. 
  One 
  curious 
  fact 
  

   resulting 
  from 
  the 
  want 
  of 
  connection 
  between 
  the 
  intestine 
  and 
  the 
  cloaca 
  is, 
  

   that 
  all 
  the 
  food 
  the 
  animal 
  takes 
  must 
  go 
  to 
  form 
  the 
  honey, 
  with 
  the 
  exception 
  

   of 
  the 
  small 
  quantity 
  consumed 
  in 
  keeping 
  up 
  the 
  functions 
  of 
  the 
  body. 
  This 
  

   is 
  the 
  more 
  singular, 
  when 
  we 
  consider 
  the 
  habits 
  of 
  the 
  insect 
  as 
  described 
  by 
  

   Mr. 
  Edwards, 
  as 
  these 
  would 
  apparently 
  render 
  it 
  almost 
  impossible 
  that 
  they 
  

   should 
  be 
  supplied 
  exclusively 
  with 
  nectar 
  from 
  the 
  flowers. 
  

  

  New 
  Problems 
  in 
  Mensuration.* 
  

  

  BY 
  GEORGE 
  DAVIDSON. 
  

  

  XIII. 
  Having 
  given 
  the 
  sides 
  of 
  a 
  rectangle, 
  determine, 
  in 
  

   terms 
  of 
  those 
  sides, 
  the 
  sides 
  of 
  a 
  required 
  consecutive 
  series 
  of 
  

   interior 
  hollow 
  rectangles 
  and 
  central 
  rectangle, 
  into 
  which 
  it 
  may 
  

   be 
  divided, 
  having 
  equal 
  areas 
  with 
  each 
  other. 
  

  

  To 
  divide 
  it 
  into 
  n 
  hollow 
  rectangles, 
  and 
  the 
  central 
  rectangle 
  ; 
  

   call 
  I 
  the 
  length 
  and 
  b 
  the 
  breadth 
  of 
  the 
  given 
  rectangle 
  ; 
  x, 
  t/, 
  

   etc., 
  the 
  required 
  lengths 
  next 
  interior 
  ; 
  x',7/\ 
  etc., 
  the 
  correspond- 
  

   ing 
  breadths 
  ; 
  (w 
  — 
  1) 
  and 
  w 
  the 
  last 
  two 
  lengths, 
  and 
  {w' 
  — 
  1) 
  

   and 
  zv' 
  the 
  last 
  two 
  breadths 
  ; 
  then 
  

  

  *Iu 
  continuation 
  of 
  former 
  ijroblems 
  in 
  this 
  and 
  in 
  Vol. 
  IV. 
  

  

  