RELATIVE POSITIONS OF LATERAL MEMBERS, I97 



members is preceded by circumstances connected with their development which assist 

 in determining their place of origin. 0-f this nature, for instance, is the connexion 

 between the points of origin of lateral roots and the fibro-vascular bundles, the 

 course of which determines the arrangement of the roots in rows; and this in 

 turn determines the lateral roots being arranged spirally or in whorls. Here 

 the arrangement in longitudinal rows is clearly the general and primary one; the 

 divergences and longitudinal distances are a secondary effect determined by special 

 accessory circumstances. The point of origin of a lateral shoot is, on the other 

 hand, in general primarily determined by its relation to the nearest leaf, since it must 

 be formed beneath, beside, or above its median plane ; forces of secondary import- 

 ance then determine whether lateral shoots are formed in connexion with each leaf 

 or only with particular leaves of an axis, and so forth. The phyllotaxis of the lateral 

 shoot may differ from that of its primary shoot, because the growth^ of the latter 

 assists in influencing it ; as, for instance, in theccase of lateral shoots with a distichous 

 phyllotaxis on primary shoots with an arrangement in. several rows. Under this 

 heading falls also the bilateral branching of leaves, whether -the stem itself be bilateral 

 or multilateral. The dimensions of the growing point; and the thickness of the axial 

 structure derived from it may also determine the number of the rows of lateral 

 structures; thus thick mother- roots usually produce three or more rows of seconc^ary 

 roots, while more slender primary roots produce only two rows or at all events a 

 smaller number. Thus, for instance, the roots of Cryptogams (according to Nageli 

 and Leitgeb), the thick primary roots of the-, maize, oak, pea, scarlet-runner, &c., 

 form three, fourj five, six, or more orthostichies of lateral roots, which, on their part, 

 are much slenderer and produce fewer* orthostichies. The same is not unfrequently 

 the case with the phyllotaxis of stems. When the size of the grov/ing point increases, 

 the leaves are arranged in a larger number of rows, as in the vigorous seedlings of 

 many Dicotyledons, in Palms, Nephrodium Filix-mas, &g. This is most strikingly 

 exhibited in the many-rowed flower-heads of the sunflower on the four-rowed foliage- 

 stem, the size of the growing point undergoing a sudden and great increase at the 

 period when the flower-head is being formed (Fig. 126, p. 171). But, vice versS^ 

 the number of the rows of leaves diminishes when the size of the growing end of the 

 stem decreases in consequence of vigorous growth in lengthy this is seen, for 

 instance, in the few-rowed long and slender peduncles which proceed from the 

 many-rayed leaf-rosettes of s^QCiQS-^'Oi Alo€\ Echeverm, &c. If the insertion of the 

 leaves or shoots takes up, at an early stage, a large part of the periphery at the 

 -growing point, only a few rows of leaves are formed; if the insertion-planes are 

 relatively small, the number of rows- on the axis increases. This is- illustrated by the 

 many rows of small flowers in "the spadicesof Aroideae or the racemes of Trifolium, 

 while the leaves of' the same plants are in few rows, their insertions embracing the 

 stem or being-even broaden Hofmeister \ to whom we owe the introduction of this 

 point of view in the theory of phyllotaxis, states the general rule in' the following 



B' Allgemeine Morphologic, § 11, where particular cases are discussed in detail. This treatise is 

 ond question the most important that has hitherto been written on phyllotaxis; nevertheless, in 

 my account, which necessary limits have confined almost to a mere sketch, I differ from Hofmeister's 

 views even in some points of primary importance. 



