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  Fluctuations 
  

  

  quiry 
  into 
  the 
  phenomenon 
  of 
  regression, 
  or 
  of 
  

   the 
  relation 
  of 
  the 
  degree 
  of 
  deviation 
  of 
  the 
  

   progeny 
  to 
  that 
  of 
  their 
  parents, 
  and 
  the 
  selec- 
  

   tion 
  of 
  extreme 
  instances 
  for 
  multiplication 
  are 
  

   obviously 
  independent 
  of 
  mathematical 
  consid- 
  

   erations. 
  On 
  the 
  other 
  hand 
  an 
  important 
  in- 
  

   quiry 
  lies 
  in 
  the 
  statistical 
  treatment 
  of 
  these 
  

   phenomena, 
  and 
  such 
  treatment 
  requires 
  the 
  

   use 
  of 
  mathematical 
  methods. 
  

  

  Statistics 
  however, 
  are 
  not 
  included 
  in 
  the 
  

   object 
  of 
  these 
  lectures, 
  and 
  therefore 
  I 
  shall 
  

   refrain 
  from 
  an 
  explanation 
  of 
  the 
  method 
  of 
  

   their 
  preparation 
  and 
  limit 
  myself 
  to 
  a 
  general 
  

   comparison 
  of 
  the 
  observed 
  lines 
  with 
  the 
  law 
  

   of 
  chance. 
  Before 
  going 
  into 
  the 
  details, 
  it 
  

   should 
  be 
  repeated 
  once 
  more 
  that 
  the 
  empirical 
  

   result 
  is 
  quite 
  the 
  same 
  for 
  individual 
  and 
  for 
  

   partial 
  fluctuations. 
  As 
  a 
  rule, 
  the 
  latter 
  occur 
  

   in 
  far 
  greater 
  number, 
  and 
  are 
  thus 
  more 
  easily 
  

   investigated, 
  but 
  individual 
  or 
  personal 
  aver- 
  

   ages 
  have 
  also 
  been 
  studied. 
  

  

  Newton 
  discovered 
  that 
  the 
  law 
  of 
  chance 
  can 
  

   be 
  expressed 
  by 
  very 
  simple 
  mathematical 
  cal- 
  

   culations. 
  Without 
  going 
  into 
  details, 
  we 
  may 
  

   at 
  once 
  state 
  that 
  these 
  calculations 
  are 
  based 
  

   upon 
  his 
  binomimn. 
  If 
  the 
  form 
  (a 
  + 
  b) 
  n 
  is 
  cal- 
  

   culated 
  for 
  some 
  value 
  of 
  the 
  exponent, 
  and 
  if 
  

   the 
  values 
  of 
  the 
  coefficients 
  after 
  develop- 
  

   ment 
  are 
  alone 
  considered, 
  they 
  yield 
  the 
  basis 
  

  

  