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  Fluctuations 
  

  

  win, 
  and 
  exercised 
  much 
  influence 
  upon 
  his 
  

   views 
  at 
  various 
  times. 
  

  

  Quetelet's 
  famous 
  discovery 
  of 
  the 
  law 
  of 
  

   fluctuating 
  variability 
  changed 
  the 
  entire 
  situa- 
  

   tion 
  and 
  cleared 
  up 
  many 
  difficulties. 
  While 
  a 
  

   clear 
  conception 
  of 
  fluctuations 
  was 
  thus 
  gained, 
  

   mutations 
  were 
  excluded 
  from 
  consideration, 
  

   being 
  considered 
  as 
  very 
  rare, 
  or 
  non-existent. 
  

   They 
  seemed 
  wholly 
  superfluous 
  for 
  the 
  theory 
  

   of 
  descent, 
  and 
  very 
  little 
  importance 
  was 
  atr 
  

   tached 
  to 
  their 
  study. 
  Current 
  scientific 
  belief 
  

   in 
  the 
  matter 
  has 
  changed 
  only 
  in 
  recent 
  

   years. 
  Mendel's 
  law 
  of 
  varietal 
  hybrids 
  is 
  

   based 
  upon 
  the 
  principle 
  of 
  unit-characters, 
  and 
  

   the 
  validity 
  of 
  this 
  conception 
  has 
  thus 
  been 
  

   brought 
  home 
  to 
  many 
  investigators. 
  

  

  A 
  study 
  of 
  fluctuating 
  or 
  individual 
  variabil- 
  

   ity, 
  as 
  it 
  was 
  formerly 
  called, 
  is 
  now 
  carried 
  on 
  

   chiefly 
  by 
  mathematical 
  methods. 
  It 
  is 
  not 
  my 
  

   purpose 
  to 
  go 
  into 
  details, 
  as 
  it 
  would 
  re- 
  

   quire 
  a 
  separate 
  course 
  of 
  lectures. 
  I 
  shall 
  con- 
  

   sider 
  the 
  limits 
  between 
  fluctuation 
  and 
  muta- 
  

   tion 
  only, 
  and 
  attempt 
  to 
  set 
  forth 
  an 
  adequate 
  

   idea 
  of 
  the 
  principles 
  of 
  the 
  first 
  as 
  far 
  as 
  they 
  

   touch 
  these 
  limits. 
  The 
  mathematical 
  treat- 
  

   ment 
  of 
  the 
  facts 
  is 
  no 
  doubt 
  of 
  very 
  great 
  value, 
  

   but 
  the 
  violent 
  discussions 
  now 
  going 
  on 
  be- 
  

   tween 
  mathematicians 
  such 
  as 
  Pearson, 
  Kap- 
  

   teyn 
  and 
  others 
  should 
  warn 
  biologists 
  to 
  ab- 
  

  

  