14 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



bulk of the axis, or with increase in both axis and lateral members 

 definitely correlated, the phyllotaxis would remain ^. If a further 

 rise took place, the five gaps would be filled by the five members of 

 a ^ cycle, and in the same manner in successive cycles, two new 

 members being always added opposite the larger gaps corresponding 

 to the members of the last cycle but one, and thus each new 

 cycle would equal the sum of its two predecessors, and the rise 

 in divergence would be repeated ontogenetically in every in- 

 dividual. 



The members of each cycle would have their appropriate angular 

 divergence (although this is only approximated in the figure), and 

 for a constant type of member such an ascending series would be 

 produced with an increased diameter in the stem ; lateral branches, 

 proceeding from two symmetrically placed prophylls, would take on 

 a spiral construction according to their relative bulk. 



The whole figure is orientated for the f position, so uniformly 

 present in the quincuncial calyx, and the members numbered in 

 this relation, so that No. 2 is median posterior. 



An enormous number of facts may be collected in support of 

 such a construction and incorporated with it without, however, 

 necessarily establishing its accuracy. Thus the orientation of a | 

 cycle with regard to a f is in all cases exactly as shown. For 

 example, in Hellehorus foetidus, the flower possesses a § calyx with 

 normal orientation, and eight nectary petals of a f series, of which 

 most commonly 1-5, 6, 7 are present. The missing ones, 8, 7, 6, 

 as the case may be, always leave gaps in the positions marked by 

 these numbers with absolute constancy. The relation of two 

 cycles having been established, the other cycles may be regarded 

 as following the same plan, and may readily be numbered from 

 the divergence scheme — No. 1 being given by line which 

 zigzags through No. 1 of successive cycles to approach the " ideal 

 angle." 



It may be noted that the J spiral gives the odd member anterior, 

 the typical position in the case of trimerous monocotyledonous 

 flowers, while the J cycle falls transversely, as in the case of the 

 two prophylls. 



Although a multitude of facts may be fitted into such- a scheme, 



