292 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



greatest mutual pressures can only press them into close rhom- 

 boidal contact and convert their section into the form of quasi- 

 squares. 



The appearance presented by a typical foliage-bud, however, is 

 very different from any such theoretical construction ; and it is 

 clear that the assumption of the considerable amount of flattening 

 included under the conventional use of the term " dorsiventrality," 

 which is much greater than that of the original primordium, must 

 entail correlated alterations in the rates of growth. The secondary 

 flattening of the member is most simply regarded as the effect of 

 a diminution in the rate of radial growth of the whole system 

 (fig. 100) ; and as soon as the members diminish in radial growth 

 at a greater rate than the axis does, the bud loosens its contacts 

 and begins to open out. Such diminution of radial growth may 

 also produce the effect of a tangential extension where this does 

 not really exist, or again it might be associated with such an 

 increased tangential rate of growth. The several cases may thus 

 be considered from the standpoint of differences in the rates of 

 growth-expansion in two directions, the radial and the tangential, 

 these being represented in any given system by the diagonals of 

 the rhomboid meshes, which in the case of spiral systems are 

 both spiral lines. 



In a typical bud, again, this " flattening " is also always associated 

 in spiral systems with a phenomenon of " sliding-growth," which is 

 one of the most remarkable properties of a leafy shoot, in that 

 the method adopted is perfectly definite. The leaf-members 

 exhibit a certain amount of slipping at their edges, and the 

 arrangement is carried out with the gi'eatest precision, so long as 

 the construction is asymmetrical and spiral. It must be noted, 

 however, that the corresponding phenomena in the case of whorled 

 symmetrical constructions is either wanting {cf. vahate preflora- 

 tion), wholly irregular, or very rarely according to a definite 

 scheme (cf. convolute prefloration). In fact, it appears possible 

 even at this point to make the generalisation that a certain 

 primary sliding-growth must be a mathematical necessity of 

 assymmetrical construction in phyllotaxis systems.* 

 * Gf. Mathematical Notes. 



