ANOMALOrrs SERIES. 197 



rare. Similarly (4 + 5), (5 + 6) may be found in Zycopodium and 

 Cadi as constants, but not the rest of the series ; although their 

 occurrence as transitional stages is not impossible (Cacti), the 

 general rule which may be formulated at this stage of the con- 

 sideration of anomalous series being, that any anomalous system 

 represents an equal or a nearer approach to equality in the ratios 

 than those of the normal series, and that their occurrence may be 

 taken as a sign of a nearer approximation to symmetry. 

 The following cases may be considered separately : — 



1. High ratios approximating equality and associated with 



symmetry. 



2. High ratios produced as expansion systems. 



3. Low ratios as specific or individual variations. 



4. Production of anomalous systems by irregular introduction or 



loss of curves. 



5. Acquisition of symmetry. 



I. High nunibers the ratio of which is considerably nearer equality 

 tlian the normal 1 : 1'62. 



That these represent variations on all but perfect attainment of 

 the symmetrical condition is shown by the fact that they occur side 

 by side with true whorled specimens. 



For example : — Acorus Galmnus commonly presents parastichies of the form 

 (15 + 15), but almost eciually (14 + 15) may be comited. EcMnops 

 dahuricus, often described as whorled in its inflorescence, shows paras- 

 tichies very clearly on the almost spherical receptacle after the fall of 

 flowers and fruit in autumn : Ave primary heads gave (16 + 16), (16 + 13), 

 (16 + 16), (15 + 12), and (15 + 13), while smaller lateral inflorescences only 

 (12 + 13) and (13 + 13). 



It is difficult to avoid the conclusion that these numbers represent slight 

 deviations from a symmetrical construction based on an asymmetrical 

 system (10 + 16) or (8 + 13). 



The scales on the fruits of Baphia Buffia, again, vary between (6 + 6), (6 + 7), 

 (7 + 7) and (6 + 8) on the same inflorescence, fig. 72, (6 + 6). 



It is of interest to note that in these cases the question of normal 

 phyllotaxis is entirely put on one side. In the two first, the prim- 

 ary members are, so far as is visible, ontogeneticaUy absent, and the 

 secondary radial floral axes cannot be expected to necessarily follow 

 identical laws; while in the last, the lateral members are emer- 



