﻿N0.1134. 
  PHILIPPINE 
  ORNITHOLOGY— 
  WORCESTER 
  AND 
  BOURNS. 
  613 
  

  

  the 
  percentage 
  of 
  exceptions 
  found 
  would 
  at 
  first 
  be 
  very 
  mucli 
  smaller 
  

   than 
  this, 
  from 
  the 
  fact 
  that 
  to 
  afford 
  evidence 
  the 
  species 
  must 
  be 
  col- 
  

   lected 
  at 
  least 
  in 
  ])airs, 
  i. 
  e., 
  two 
  to 
  a 
  genus. 
  

  

  To 
  take 
  a 
  very 
  simple 
  illustration, 
  suppose 
  that 
  three 
  figure 
  ones 
  

   were 
  shaken 
  up 
  in 
  a 
  hat, 
  together 
  with 
  two 
  twos, 
  two 
  threes, 
  and 
  two 
  

   fours, 
  and 
  one 
  were 
  then 
  to 
  draw 
  out 
  the 
  figures 
  at 
  random, 
  placing 
  the 
  

   ones 
  in 
  one 
  pile 
  and 
  the 
  pairs 
  of 
  twos, 
  threes, 
  and 
  fours 
  in 
  another; 
  at 
  

   what 
  rate 
  would 
  the 
  two 
  piles 
  growf 
  

  

  On 
  the 
  first 
  draw 
  there 
  would 
  be 
  three 
  chances 
  in 
  nine 
  of 
  getting 
  a 
  

   one, 
  but 
  only 
  two 
  in 
  nine 
  of 
  getting 
  a 
  two, 
  three, 
  or 
  four, 
  and 
  no 
  chance 
  

   whatever 
  of 
  getting 
  a 
  pair 
  of 
  either 
  of 
  the 
  last 
  three 
  numerals. 
  On 
  the 
  

   second 
  draw 
  there 
  would 
  be 
  three 
  chances 
  in 
  eight 
  of 
  getting 
  a 
  one, 
  

   but 
  only 
  two 
  in 
  nine 
  plus 
  two 
  in 
  eight 
  divided 
  by 
  two 
  (the 
  number 
  in 
  

   a 
  i^air) 
  multiplied 
  by 
  three 
  (tlie 
  number 
  of 
  pairs), 
  or 
  seventeen 
  in 
  two 
  

   hundred 
  and 
  sixteen, 
  of 
  getting 
  a 
  pair. 
  Three 
  in 
  eight 
  are 
  equivalent 
  

   to 
  eighty-one 
  in 
  two 
  hundred 
  and 
  sixteen, 
  and 
  the 
  chances 
  of 
  getting 
  

   a 
  one 
  on 
  the 
  second 
  draw 
  would 
  be 
  to 
  those 
  of 
  getting 
  a 
  pair 
  of 
  

   twos, 
  threes, 
  or 
  fours 
  as 
  eighty 
  one 
  is 
  to 
  seventeen. 
  As 
  the 
  drawing 
  

   continued, 
  the 
  chances 
  of 
  getting 
  a 
  pair 
  would 
  improve 
  each 
  time, 
  

   but 
  would 
  equal 
  those 
  of 
  getting 
  a 
  one 
  only 
  at 
  the 
  very 
  close 
  of 
  the 
  

   drawing. 
  

  

  Keturning 
  now 
  to 
  our 
  birds, 
  the 
  matter 
  may 
  be 
  reduced 
  to 
  a 
  formula. 
  

   We 
  may, 
  for 
  convenience, 
  divide 
  them 
  into 
  genera 
  with 
  one 
  species 
  in 
  

   a 
  place, 
  and 
  those 
  with 
  two 
  species 
  in 
  a 
  jjlace, 
  for 
  in 
  genera 
  with 
  more 
  

   than 
  two 
  species 
  in 
  an 
  island 
  the 
  recording 
  of 
  two 
  is 
  enongh 
  to 
  estab- 
  

   lish 
  an 
  exception, 
  while 
  the 
  increased 
  probability 
  of 
  recording 
  two 
  

   species, 
  arising 
  from 
  the 
  fact 
  that 
  there 
  are 
  more 
  than 
  two 
  to 
  draw 
  

   from, 
  will 
  be 
  counterbalanced 
  by 
  the 
  fact 
  that 
  three 
  or 
  four 
  species 
  

   belonging 
  to 
  but 
  one 
  genus 
  constitute 
  but 
  a 
  single 
  exception. 
  

  

  Let 
  a 
  = 
  number 
  of 
  genera 
  with 
  but 
  one 
  species 
  in 
  an 
  island. 
  

  

  Let 
  /> 
  = 
  number 
  of 
  genera 
  with 
  two 
  species 
  in 
  an 
  island. 
  

  

  Then 
  rt 
  + 
  2& 
  = 
  whole 
  number 
  of 
  species 
  in 
  the 
  island. 
  

  

  Let 
  z 
  = 
  number 
  of 
  species 
  known. 
  

  

  Were 
  a 
  collector 
  to 
  take 
  up 
  the 
  work 
  at 
  this 
  point 
  liis 
  chance 
  of 
  

   making 
  an 
  addition 
  to 
  the 
  list 
  of 
  genera 
  represented 
  by 
  single 
  species 
  

  

  would 
  be 
  , 
  21 
  _ 
  ^ 
  , 
  while 
  his 
  chance 
  of 
  making 
  an 
  addition 
  to 
  the 
  

  

  list 
  of 
  genera 
  with 
  two 
  species 
  each 
  would 
  be 
  but 
  a 
  + 
  2& 
  — 
  z, 
  or 
  

  

  1 
  

  

  Since 
  z 
  is 
  the 
  variable 
  factor 
  here, 
  and 
  increases 
  one 
  

  

  a 
  -j- 
  2¥ 
  - 
  bz- 
  

  

  with 
  every 
  addition 
  of 
  a 
  species, 
  it 
  is 
  evident 
  that 
  as 
  the 
  number 
  of 
  

   species 
  of 
  birds 
  known 
  from 
  ar. 
  island 
  approximates 
  the 
  number 
  actu- 
  

   ally 
  existing 
  there 
  the 
  chances 
  of 
  recording 
  exceptions 
  to 
  Steere's 
  law 
  

   will 
  steadily 
  increase. 
  

  

  