204 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



1. Melocactus comrmmis : semi-globular form, showing 21 ridges, 

 formed by a system (9 + 12); a new short curve added raised the 

 system to (9 + 13) = 22 ridges. 



2. Oereus chUeTisis : specimen forming a cylindrical shaft 6 feet 

 high, ridges at level of ground 14 = (7 + 7). The axis was thus 

 symmetrical and remained unchanged for a height of 5 feet, including 

 about 1200 members. A new ridge was then put in, and the system 

 raised to (7 + 8), and this remained constant for about 75 members. 



A second new ridge was then put in (fig. 396), raising the total 

 to 1 6, and this system was continued to the growing point. 



It becomes, therefore, a point of interest to note whether the sym- 

 metrical condition of the greater portion of the shaft was regained, 

 or whether the change was quite aimless. 



The latter proved to be the case, the new parastichy system 

 being (7 + 9). 



On the other hand, a variation which makes for symmetry is 

 shown in Lycopodium Selago (fig. 79). Twin branches, one of 

 which, as is frequently the case, develops more rapidly than the 

 other, showed at their apices the systems (4 + 5) and (4 + 4), the 

 former being about 1 mm. taller than the latter. The asymmetrical 

 shoot thus shows 9 spiral series of leaves ; the symmetrical one 8 

 theoretically vertical orthostichies. As a matter of fact, small 

 growth movements connected with the assumption of dorsiventrality 

 and unequal development render the lines drawn through the 

 centres of construction slightly distorted (fig. 79, 2, 3). 



On examination of these lines in the (4+5) system, it will be 

 seen that a break is commencing at the member numbered 12. 

 Thus 21 falls too much on one side of 12, so that 26 is still more 

 on one side of 17, and does not make contact with 22, its pre- 

 decessor along the " 4 " line. The visible system is thus preparing 

 for the intercalation of a new long path, which will raise the 

 curves to (5 + 5). In contrast, again, to the case mentioned of the 

 symmetrical Oereus chilensis, a shoot of L. Selago, with the sym- 

 metrical construction (3 + 3), was observed to change directly to 

 (4 + 4) (fig. 80), so that the symmetry was purposely retained. 



V. Finally, just as accidental variation may give a bijugate 

 system, or anomalous systems with very nearly equal ratios, so, as 



