144 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



and the approximately equal bulk of the members of one cycle in 

 the higher ratios of spiral phyllotaxis ; as also, in actual ontogeny, 

 by the imperceptible differences of time between their serial for- 

 mation when growth is at all rapid. 



The determination of the number of members composing a whorl 

 remains wholly a -property of the protoplasm, though the marked 

 constancy in the retention of the number 5 in the flowers of 

 Dicotyledons, corresponding to an advance on the asymmetrical 

 system (3 + 5), indicates the influence of phylogeny on subsequent 

 specialisation ; on the other hand, the readiness with which whorled 

 pentamerous flowers vary to 6- and 4-merous, and trimerous to 4- and 

 2-merous, shows an increased plasticity in the system, and that 

 with the assumption of a true symmetrical construction, the causes 

 which led to the adoption of the series of Fibonacci must also have been 

 eliminated. 



The same elimination of this series of numbers is observable in 

 the progressive rise of members in a whorl in correlation with an 

 expanding axis bearing more constant members (JYeomeris), and 

 again in the progressive reduction of members along successive 

 degrees of ramification {Equisetum). 



Special interest attaches to the lower members of the series, i.e., 

 those in which one or two pairs of symmetrical curves plot out the 

 construction. The former gives the symmetrical formation of alter- 

 nating members in two rows at angles of 180°, generally known as 

 the distichous condition. 



The latter, produced by two pairs of curves, on axes at 180°, is 

 that usually known as the Decussate system, giving four vertical 

 orthostichies. This appears to be very constantly correlated with 

 xerophytic specialisations in the assimilating system, and is often 

 quite independent of any dimery in the floral members (OlemMtis, 

 Calycanthus, Labiatae). It is remarkable in that it presents the 

 first doubled system ; and while it could not be produced from two 

 concurrent genetic spirals, it is possible that, given such a doubled 

 curve-system, secondary reversion to the asymmetrical condition 

 might be initiated from either pair, and a doubled spiral system be • 

 the result. 



That the decussate system may be also produced as a variation 



