RELATIVE POSITIONS OF LATERAL MEMBERS. 
geometrical rules, by means of which the genetic spiral can be easily deduced 
from the parastichies ^. 
It is evident that the constructions hitherto mentioned can only be more or 
less convenient aids to an understanding of the actual principles of the arrangement 
of leaves. But in order to obtain, with their assistance, a deeper insight into the 
processes of growth themselves of which these principles are the result, it is 
necessary to follow the development, and in every single case to ask the question, 
what circumstances are the cause of a new member being formed just in this place 
and nowhere else. It may be well, therefore, to bring forward here some of the 
points which must be considered in reference to this view. 
(i) The first point is always to determine with certainty the order of succession 
in which the lateral members are formed. 
{2) Attention must be paid not only to the lateral divergence, but also to the 
longitudinal distance at which a new member is formed at the growing point above 
the members last preceding it. The longitudinal distances of the youngest 
lateral structures of a growing point from one another are usually very small ; 
there is often no space to be distinguished between them, i. e. between the 
planes of insertion of the youngest members. This circumstance may, on the 
one hand, assist in the determination of the place where the next member must be 
produced ; but, on the other hand, may give occasion, as the development of the 
axis proceeds with its crowded lateral members, to compression and distortion, by 
which the original arrangement is altered. 
(3) By the increase in length of the common axis, members which were at 
first closely crowded become placed at a considerable distance from one anothi^r, 
while others, in consequence of slower growth, remain closely packed; so that a 
different distribution occurs in different parts of the stem, as in the leaf-rosettes and 
flower- stalks of Crassulaceae, Agave, Aloe, &c. In the same manner the angle of 
divergence frequently becomes changed by the more rapid increase in thickness of 
the axial structure on one side than on the other; and still more commonly by 
torsion round its own axis of growth. By such torsions lateral members, arranged 
at first exactly in straight rows, become displaced so that the orthostichies appear as 
if wound spirally round the axis. This occurs, for instance, according to Nageli 
and Leitgeb, in the root-systems of Ferns, Equisetaceae, and Rhizocarpeae, as well as 
in the three-rowed phyllotaxis of the Moss Fontinalis antipyretica, according to 
Leitgeb. But the most striking example is furnished by the stem of the screw-pine, 
Pandanus uHlis, In the bud, the numerous leaves, already strongly developed, 
stand, as is shown by the transverse section, in three perfectly straight lines with 
the phyllotaxis -J ; but, as the development of the stem advances, it undergoes so 
severe a torsion that the three orthostichies are transformed into three strongly 
curved spiral lines running round the stem (see Fig. 154). In these and similar 
cases the change in the relative positions caused by the torsion of the actual 
structure can be easily and certainly determined. But when the structures are so 
arranged at the apex of the axial structure that the angle of divergence cannot 
^ As the treatment of the subject is only of value to those who are practically concerned with 
phyllotaxis, I must refer to the detailed description in Hofmeister's Allgemeine Morphologie, § 9. 
O 2 
