﻿736 
  Fluctuations 
  

  

  for 
  this 
  purpose 
  a 
  point 
  is 
  chosen 
  which 
  lies 
  

   exactly 
  half 
  way 
  between 
  the 
  average 
  and 
  the 
  

   extreme. 
  Not 
  however 
  half 
  way 
  with 
  respect 
  to 
  

   the 
  amplitude 
  of 
  the 
  extreme 
  deviation, 
  for 
  on 
  

   this 
  ground 
  it 
  would 
  partake 
  of 
  the 
  uncertainty 
  

   of 
  the 
  extreme 
  itself. 
  It 
  is 
  the 
  point 
  on 
  the 
  

   curve 
  which 
  is 
  surpassed 
  by 
  half 
  the 
  number, 
  

   and 
  not 
  reached 
  by 
  the 
  other 
  half 
  of 
  the 
  num- 
  

   ber 
  of 
  the 
  observations 
  included 
  in 
  the 
  half 
  of 
  

   the 
  curve. 
  This 
  point 
  corresponds 
  to 
  the 
  im- 
  

   portant 
  value 
  called 
  the 
  probable 
  error, 
  and 
  

   was 
  designated 
  by 
  Galton 
  as 
  the 
  quartile. 
  For 
  

   it 
  is 
  evident 
  that 
  the 
  average 
  and 
  the 
  two 
  quar- 
  

   tiles 
  divide 
  the 
  whole 
  of 
  the 
  observations 
  into 
  

   four 
  equal 
  parts. 
  

  

  Choosing 
  the 
  quartiles 
  as 
  the 
  basis 
  for 
  cal- 
  

   culations 
  we 
  are 
  independent 
  of 
  all 
  the 
  second- 
  

   ary 
  causes 
  of 
  error, 
  which 
  necessarily 
  are 
  in- 
  

   herent 
  in 
  the 
  extremes. 
  At 
  a 
  casual 
  examina- 
  

   tion, 
  or 
  for 
  demonstrative 
  purposes, 
  the 
  ex- 
  

   tremes 
  may 
  be 
  prominent, 
  but 
  for 
  all 
  further 
  

   considerations 
  the 
  quartiles 
  are 
  the 
  real 
  values 
  

   upon 
  which 
  to 
  rest 
  calculations. 
  

  

  Moreover 
  if 
  the 
  agreement 
  with 
  the 
  law 
  of 
  

   probability 
  is 
  once 
  conceded, 
  the 
  whole 
  curve 
  is 
  

   defined 
  by 
  the 
  average 
  and 
  the 
  quartiles, 
  and 
  

   the 
  result 
  of 
  hundreds 
  of 
  measurements 
  or 
  

   countings 
  may 
  be 
  summed 
  up 
  in 
  three, 
  or, 
  in 
  

  

  