246 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



due to a subjective impression which has no real basis. The very 

 existence of bud-pressures requires to be proved in any given case. 

 The influence of the pressure of older members of the same system 

 on younger ones may therefore be completely disregarded ; nor 

 have visible primordia any directive influence on other primordia 

 as they become visible : the relations of adjacent members being 

 established, before the protuberances appear, in the actual substance 

 of the protoplasmic mass. 



II. Eecipkocal Pressures in Older Members. 



Such pressures, as already seen, can only be due to an increased 

 rate of growth in the primordia as compared with that of the axis, 

 or to different rates of growth in different directions, or in different 

 parts of the members. If, as by hypothesis, the members are 

 primarily arranged in orthogonal series (loose-packing), all mutual 

 pressure may be resolved into components along the orthogonal 

 paths of the system : these, if equally distributed, can have no effect 

 on the packing of the members, but if at all marked the shape will 

 be altered, and the " circles " will become " squares." Only when 

 the pressures are unequally distributed will any sliding effect be 

 noticed, culminating possibly in close-packing of the hexagonal 

 type. So long as growth is uniform, and the mathematical con- 

 struction holds, the disturbing effect will be nil ; change of shape 

 may take place, but no change of position. 



In a great many leafy shoots this obtains to a considerable 

 degree, and the leaf-primordia assume a rhomboidal form, as seen 

 in transverse section, approaching that of a " square " of the log. 

 spiral meshwork ; and this holds so long as growth proceeds uni- 

 formly throughout the whole shoot. The fundamental section- 

 form of all leaves developed in closely packed systems is therefore 

 that of a quasi-square with more or less rounded angles, the median 

 line of orientation passing along one diagonal. Beautiful examples 

 of such undifferentiated members persist especially among some 

 Coniferae, in which bilaterality is small or wanting, and the leaf 

 elongates to a " needle " type (Oedrus atlanticus, Arav^aria excelsa ; 

 cf. also Mamillaria and the Pine-cone). 



