﻿494 
  Mutations 
  

  

  duced 
  double 
  varieties. 
  One 
  of 
  them 
  is 
  

   the 
  Japanese 
  marigold, 
  others 
  are 
  the 
  cari- 
  

   natum 
  and 
  the 
  imbricatum 
  species. 
  Nearly 
  

   allied 
  are 
  quite 
  a 
  number 
  of 
  garden-plants 
  with 
  

   double 
  flower-heads, 
  among 
  which 
  are 
  the 
  

   double 
  camomiles. 
  

  

  My 
  attention 
  was 
  first 
  drawn 
  to 
  the 
  structure 
  

   of 
  the 
  heads 
  and 
  especially 
  to 
  the 
  number 
  of 
  the 
  

   ray-florets 
  of 
  the 
  corn-marigold. 
  The 
  species 
  

   appertains 
  to 
  that 
  group 
  of 
  composites 
  which 
  

   have 
  a 
  head 
  of 
  small 
  tubular 
  florets 
  surrounded 
  

   by 
  a 
  broad 
  border 
  of 
  rays. 
  These 
  rays, 
  when 
  

   counted, 
  are 
  observed 
  to 
  occur 
  in 
  definite 
  num- 
  

   bers, 
  which 
  are 
  connected 
  with 
  each 
  other 
  by 
  a 
  

   formula, 
  known 
  as 
  " 
  the 
  series 
  " 
  of 
  Braun 
  and 
  

   Schimper. 
  In 
  this 
  formula, 
  which 
  commences 
  

   with 
  1 
  and 
  2, 
  each 
  number 
  is 
  equal 
  to 
  the 
  sum 
  

   of 
  the 
  two 
  foregoing 
  figures. 
  Thus 
  5, 
  8 
  and 
  13 
  

   are 
  very 
  frequent 
  occurrences, 
  and 
  the 
  following 
  

   number, 
  21, 
  is 
  a 
  most 
  general 
  one 
  for 
  apparent- 
  

   ly 
  full 
  rays, 
  such 
  as 
  in 
  daisies, 
  camomiles, 
  Arnica 
  

   and 
  many 
  other 
  wild 
  and 
  cultivated 
  species. 
  

  

  These 
  numbers 
  are 
  not 
  at 
  all 
  constant. 
  They 
  

   are 
  only 
  the 
  averages, 
  around 
  which 
  the 
  real 
  

   numbers 
  fluctuate. 
  There 
  may 
  even 
  be 
  an 
  over- 
  

   lapping 
  of 
  the 
  extremes, 
  since 
  the 
  fluctuation 
  

   around 
  13 
  may 
  even 
  go 
  beyond 
  8 
  and 
  

   21, 
  and 
  so 
  on. 
  But 
  such 
  extremes 
  are 
  only 
  

   found 
  in 
  stray 
  flowers, 
  occurring 
  on 
  the 
  same 
  

  

  