324 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



more, the scale areas remaining the same; the angle subtended 

 by each scale thus falls to 25° or 30°, with the necessary result 

 that the parastichy system now observed is that of (8 + 13). 

 Similarly, in Pinus Pinea the closed cone 75 mm. in diameter 

 presents scale-facets 23-24 mm. across, subtending an angle of 

 36° to 38°. When correction is made for overlapping, it is clear 

 that the system observed will be (8 + 13); but when the cone 

 expands to a diameter of 110 mm., the angle subtended by a 

 scale falls to 20° or 25°, which approaches the 19'8° of the 

 (13 + 21) system. 



The apparent contact-curves of the Pine-cone therefore present 

 in themselves no reliable evidence whatever of the actual system 

 with which the carpels were laid down at the apex, beyond the 

 fact that ratios of the Fibonacci series were utilised; the fact 

 that they are the ones really employed is only to be proved by 

 an examination of the curves of the developing shoot-apex ; and 

 similarly, it is impossible to say from the mere examination of 

 the free tips of any cluster of leaf-members what the true 

 phyllotaxis system might have been {cf. Sempervivum spinulosum, 

 fig. 4, and cones of Arauearia). No satisfactory generalisations 

 concerning phyllotaxis can be made for any given asymmetrically 

 constructed plant until the curve-system, or the contact-relations 

 of the members at their insertion on the actual growing-point, 

 has been determined. The system is not necessarily obvious on 

 the adult shoot, and the appearances seen in the case of adult 

 structures need bear no direct relation to the true construction 

 system ; the number of parastichies only helps in that it affords 

 a guide to the ratio-series concerned (cf. fruiting heads of 

 Helianthus, Scahiosa, and Bipsacus, in which the assumption of a 

 uniform type of fruit may cause the construction as judged in 

 terms of contact-parastichies to vary one stage in the ratio-series). 



The primary curve-system of the growing-point thus tends to 

 be more or less destroyed by the action of the following factors, 

 all of which may be present to a greater or less extent in the 

 production of a typical foliage leaf-bud : — 



(1) Diminution in the tangential rate of growth, resulting in 

 the lowering of the angle subtended by the member. 



