ANOMALOUS SERIES. 



205 



soon as equality is reached, the symmetrical construction follows as a 

 mathematical consequence. How small the change may be is shown, 

 for example, by comparing the structural diagram for a (6 + 7) with 

 a (6 + 6). The result, however, is very striking in that an accu- 

 rately simultaneous formation of a whole cycle of members is 

 substituted for a serial formation ; but it serves to bring out the 

 fact that the actual appearance of the members, in time, has possibly 

 little to do with the mechanism which produces them within the 

 protoplasmic mass of the apex. It is important to note that the 



Kg. 



-Lycopodium Selago, (3 + 3) and (3 + 3), changing to (4 + 4). 



simultaneous formation is a mathematical fact dependent on the 

 manner in which the construction is directly changed from a pre- 

 sentation in terms of a spiral-vortex to that of a circular one. 



In many Cactaceae, such an assumption of symmetry appears to 

 be entirely accidental {of. special section), and asymmetry may be 

 again produced. In the case of specialised decussate assimilating 

 shoots, the fact that reversion to asymmetry may take place in the 

 sporophylls (Galycanthus) has been held to support the view that 

 the decussate condition is of biological utility. An example, again 

 taken from Lycopodium Selago (fig. 80), shows that symmetry is 



