﻿Laws 
  of 
  Fluctuations 
  739 
  

  

  heads 
  in 
  our 
  particular 
  case. 
  It 
  is 
  the 
  

   series 
  to 
  which 
  we 
  have 
  already 
  alluded 
  

   when 
  dealing 
  with 
  the 
  arrangement 
  of 
  the 
  leaves 
  

   on 
  the 
  twisted 
  teasels. 
  It 
  commences 
  with 
  

   1 
  and 
  2 
  and 
  each 
  following 
  figure 
  is 
  equal 
  to 
  

   the 
  sum 
  of 
  its 
  two 
  precedents. 
  The 
  most 
  com- 
  

   mon 
  figures 
  are 
  3, 
  5, 
  8, 
  13, 
  18, 
  21, 
  higher 
  cases 
  

   seldom 
  coming 
  under 
  observation. 
  Now 
  the 
  

   secondary 
  summits 
  of 
  the 
  ray-curves 
  of 
  the 
  

   composites 
  are 
  seen 
  to 
  agree, 
  as 
  a 
  rule, 
  with 
  

   these 
  figures. 
  Other 
  instances 
  could 
  readily 
  be 
  

   given. 
  

  

  Our 
  second 
  heading 
  includes 
  those 
  cases 
  

   which 
  exhibit 
  two 
  summits 
  of 
  equal 
  or 
  nearly 
  

   equal 
  height. 
  Such 
  cases 
  occur 
  when 
  dif- 
  

   ferent 
  races 
  are 
  mixed, 
  each 
  retaining 
  its 
  own 
  

   average 
  and 
  its 
  own 
  curve-summit. 
  We 
  have 
  al- 
  

   ready 
  demonstrated 
  such 
  a 
  case 
  when 
  dealing 
  

   with 
  the 
  origin 
  of 
  our 
  double 
  corn-chrysanthe- 
  

   mum. 
  The 
  wild 
  species 
  culminates 
  with 
  13 
  rays, 
  

   and 
  the 
  grandiflorum 
  variety 
  with 
  21. 
  Often 
  

   the 
  latter 
  is 
  found 
  to 
  be 
  impure, 
  being 
  mixed 
  

   with 
  the 
  typical 
  species 
  to 
  a 
  varying 
  extent. 
  

   This 
  is 
  not 
  easily 
  ascertained 
  by 
  a 
  casual 
  in- 
  

   spection 
  of 
  the 
  cultures, 
  but 
  the 
  true 
  condition 
  

   will 
  promptly 
  betray 
  itself, 
  if 
  curves 
  are 
  con- 
  

   structed. 
  In 
  this 
  way 
  curves 
  may 
  in 
  many 
  in- 
  

   stances 
  be 
  made 
  use 
  of 
  to 
  discover 
  mixed 
  races. 
  

  

  Double 
  curves 
  may 
  also 
  result 
  from 
  the 
  inves- 
  

  

  