12 THE STRUCTURE OF FLOWERS. 



distichous or ^ type, every other arrangement always has 

 three leaves in every projected circle. 



It may be noticed that No. 4 not only does not occur in 

 the row 1, 6, 9, etc., — a fact which corresponds with the rarity 

 of a ternary arrangement occurring amongst flowers of 

 Dicotyledons, — but in order to fall over No. 1 it would have 

 to pass through 270°, that is from right to left, practically 

 an impossibility; so that when "threes" are met with in 

 Dicotyledons we must look for some other interpretation 

 than to refer them to the J- type. 



The numbers 7 and 11, as stated, are extremely rare in 

 flowers, and this is in accordance with the fact that they 

 belong to another series, viz. j, I, f, tVi t5> etc , which is rarely 

 represented in nature. Examples, however, will be found in 

 the leaves of Sedum reflexum, on some branches of Araucaria 

 imhricata, and sometimes in the Jerusalem Artichoke. In 

 the last case, it will be discovered that the heptastichous or 

 y type arises out of verticils of threes, in precisely the same 

 way as the pentastichous or f type does from an opposite and 

 decussate an-angement ; and as there are always four leaves 

 in every projected circle, for every type of this series, except- 

 ing the first or ^, it can only occur where the leaves are 

 narrow or are short, or do not occupy too much space so as 

 to overshadow one another. 



Variations in the Tloral Symmetry. — Besides the fact 

 that certain numbers are often characteristic of certain 

 species, genera, or even orders, great variations in the sym- 

 metry exist, iiot only in different genera of the same order, 

 but in different species of the same genus.* 



Now, with reference to this latter fact, it mnst be borne 

 in mind that flowers are so highly differentiated from the 



* See note by the author, On the Causes of the 'Numerical Increase of 

 Paris of Plants, Joam. Lin. Soc. Bot., xvi. p. 1. 



