﻿Multiplication 
  of 
  Extremes 
  767 
  

  

  After 
  this 
  hasty 
  survey 
  of 
  the 
  more 
  reliable 
  

   facts 
  of 
  the 
  practice 
  of 
  an 
  asexual 
  multiplica- 
  

   tion 
  of 
  the 
  extremes 
  of 
  fluctuating 
  variability, 
  

   we 
  may 
  now 
  return 
  to 
  the 
  previously 
  mentioned 
  

   theoretical 
  considerations. 
  These 
  are 
  con- 
  

   cerned 
  with 
  an 
  estimation 
  of 
  the 
  chances 
  of 
  the 
  

   occurrence 
  of 
  deviations, 
  large 
  enough 
  to 
  ex- 
  

   hibit 
  commercial 
  value. 
  This 
  chance 
  may 
  be 
  

   calculated 
  on 
  the 
  basis 
  of 
  Quetelet's 
  law, 
  

   whenever 
  the 
  agreement 
  of 
  the 
  fluctuation 
  of 
  the 
  

   quality 
  under 
  consideration 
  has 
  been 
  empiric- 
  

   ally 
  determined. 
  In 
  the 
  discussion 
  of 
  the 
  meth- 
  

   ods 
  of 
  comparing 
  two 
  curves, 
  we 
  have 
  pointed 
  

   to 
  the 
  quartiles 
  as 
  the 
  decisive 
  points, 
  and 
  to 
  

   the 
  necessity 
  of 
  drawing 
  the 
  curves 
  so 
  that 
  these 
  

   points 
  are 
  made 
  to 
  overlie 
  one 
  another, 
  on 
  

   each 
  side 
  of 
  the 
  average. 
  If 
  now 
  we 
  calculate 
  

   the 
  binomium 
  of 
  Newton 
  for 
  different 
  values 
  of 
  

   the 
  exponent, 
  the 
  sum 
  of 
  the 
  coefficients 
  is 
  

   doubled 
  for 
  each 
  higher 
  unit 
  of 
  the 
  exponent, 
  

   and 
  at 
  the 
  same 
  time 
  the 
  extreme 
  limit 
  of 
  the 
  

   curve 
  is 
  extended 
  one 
  step 
  farther. 
  Hence 
  it 
  is 
  

   possible 
  to 
  calculate 
  a 
  relation 
  between 
  the 
  

   value 
  of 
  the 
  extreme 
  and 
  the 
  number 
  of 
  cases 
  

   required. 
  It 
  would 
  take 
  us 
  too 
  long 
  to 
  give 
  this 
  

   calculation 
  in 
  detail, 
  but 
  it 
  is 
  easily 
  seen 
  that 
  

   for 
  each 
  succeeding 
  step 
  the 
  number 
  of 
  individ- 
  

   uals 
  must 
  be 
  doubled, 
  though 
  the 
  length 
  of 
  the 
  

   steps, 
  or 
  the 
  amount 
  of 
  increase 
  of 
  the 
  quality 
  

  

  