202 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



may be again said to be lost, and the system may be explained as in 

 Araucaria (7 + 11), and the bijugate (6 + 10) system, from the stand- 

 point of a change in the bulk-ratio ; but the question is only 

 removed one degree farther on, seeing that the reason is now 

 required as to why in such plants the bulk-ratio becomes 

 modified. 



One of the most beautiful examples of such variation is afiforded 

 by Lycopodium Selago. The leafy apices are easy to cut, the leaf 

 members are all uniform and very little modified, and branching of 

 the main axis takes place by dichotomy of the apex, and not by the 

 reduced axUlary shoots. 



Parastichy systems are exhibited in the forms — 

 (5 + 6), (4+5), (3 + 3), 



(5 + 5), (4 + 4), (2 + 2), (the last being found in the axillary 

 shoots), and transitional stages may be observed. 



Thus out of 20 apices, 7 were (5 + 5), 

 5 „ (5 + 6), 

 5 „ (4+5), 

 2 „ (4+4), 

 1 was (3 + 3). 



Comparison of a series of such apices, drawn under the same power, 

 shows at once that the round leaf-primordia are constant through- 

 out, but the diameter of the apex varies, and becomes gradually 

 smaller in correlation with the lowering of the bulk-ratio (figs. 78, 

 79, 80). 



The special point of interest, however, is the close approximation 

 to symmetry, and the large proportion of symmetrical cases found. 

 Thus 10 out of 20 apices were symmetrical, while the small lateral 

 bulbils appear to be constantly (2 + 2). , 



In such cases, where, as theoretical diagrams indicate, the primor- 

 dia subtend an angle of between 50° and 60°, small changes in the 

 bulk-ratio cannot explain the whole of the phenomena. As already 

 shown, the bulk-ratio for (4+4) is practically identical with that of 

 (3 + 5), and the bulk-ratio in such constructions cannot therefore 

 be regarded as the sole determining factor ; but behind these pheno- 

 mena there appears a controlling power which is aiming at a 



