260 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



The change of angle observed in the intersection of the para- 

 stichy curves of such inflorescences is thus due to the relative 

 growth of the rapidly enlarging receptacle and its fruits. These 

 changes are therefore tertiary effects in the phyllotaxis appear- 

 ances, and are merely the expression of the mathematical 

 properties of intersecting spiral curves, directly comparable to 

 similar curve changes observed in shoots passing through a 

 secondary zone of growth. Not only will any small amount of 

 slipping of the angles of such ovaries, in the readjustment of 

 radially elongated growth forms, tend to bring a third set of curves 

 into view,* but the same appearance necessarily follows as soon as 

 any growth change lowers the angle of the intersection of the 

 contact-parastichies to 60° or raises it to 120°. These again are 

 geometrical phenomena due to different rates of growth in a 

 system which was previously considered to be adult, and have no 

 bearing on the formation of the initial curve-systems observed 

 in the first stage of development of the capitulum. 



An identical phenomenon of growth adjustment, or " packing," 

 occurs in the typical Aroid spadix, and is well seen in the case of 

 the dimerous flowers of Anthurium. These inflorescences, like 

 Gynara, possess their bract growth-centres clearly existent and 

 functional, although, save for exceptional cases such as Acorus, 

 they are only traced through the intermediary of their axillary 

 flower-shoots ; and these in many species {cf. fig. 93) present a 

 normal curve-system of (8-1-13). But the dimerous fiowers of 

 Anthurium, (2 + 2) in constrxiction, and orientated in the " median 

 plane," present two outer perianth segments as the first-developed 

 members, and hence in a growing system these will be larger 

 than the others, so that the flower is always slightly elongated 

 in the " median-plane," that is to say, approximately along the 

 long axis of the spadix, and presenting a radial extension of the 



elongates in compensation sufficiently to loosen all contact-pressures, but the 

 curve-systems remain undisturbed ; although, a new set of spirals may appeal 

 to the eye, owing to the large relative size of the involucels. Hence a lateral 

 (8-t-13) capitulum becomes (5-t-8) in the fruiting condition. 



* When the long curves become thus stepped, and so tend to be less con- 

 spicuous, a (34-1-55) system is readily confused with a (55-1-89) in the latter 

 fruiting condition. Cf. Jost, Bot. Zeit., 1902 ; Leisering, Prings. Jahrb., 1902. 



