Symmetry 165 



sate (opposite-leaved) phyllotaxy. In the latter type the two primordia 

 at a node are as far apart as they can be, and the position of each suc- 

 cessive pair is at right angles to the pairs above and below. This more 

 nearly fulfills the requirements for efficient spacing and maximum 

 divergence than does the spiral arrangement. One therefore wonders 

 why the latter is so much more common, particularly since the cotyledons 

 and sometimes the first foliage leaves are opposite. The transformation 

 of an opposite to a spiral phyllotaxy involves a radical rearrangement of 

 the meristematic region. This seems to be an expression of an inherent 

 tendency toward spirality which is evident in so many places in the 

 structure and activity of plants and their parts. This inherent spirality, 

 imposed on systems of different sizes and forms may, from the mere 

 geometrical necessities of the case, result in the various systems of 

 spiral phyllotaxy that we have been discussing. Physiological factors 

 doubtless have an important role here— auxin, mechanical pressure, 

 genetic determination of growth, and others— but the underlying spirality 

 seems to be a phenomenon fundamental to all organisms. This may 

 appear to be an oversimplification of a problem that has involved more 

 diverse hypotheses than almost any other in plant morphology. If it proves 

 possible, however, thus to get at the heart of this mass of facts and 

 pick out one that underlies them all, we shall have come closer to an 

 understanding of one aspect, at least, of the phenomenon of organic 

 symmetry. 



Spirality seems to be deeply seated in living stuff. It is evident in the 

 spiral movements (nutations) seen in the growth of roots and shoots, 

 particularly when this is speeded up by time-lapse photography. Tendrils 

 coil spirally. Protoplasm streams in a spiral course. Molecules of DNA 

 are spiral. Spiral threads (cytonemata) occur in cytoplasm (Strugger, 

 1957). Spiral grain has been found almost invariably in tree trunks 

 (Northcott, 1957). In protoxylem the wall markings are in spirals, save 

 in the earliest cells, and there are spiral markings in many other xylem 

 cells. Whether these are all due to the same basic cause may perhaps be 

 doubted, but one can find spirality almost everywhere in the plant 

 body. 



The simplest place to study it is in the cell itself and especially in 

 the ceil wall. Much now is known about the submicroscopic structure of 

 this wall and of the system of microfibrils that compose it (Preston, 

 1952; Frey-Wyssling, 1953). The sporangiophore of the fungus Phycomy- 

 ces is favorable material for this sort of work since, as it elongates, it 

 twists spirally, as can be shown by following the course of marks placed 

 on the cell surface (Castle, 1942). Spirality here seems to have its basis 

 in the minute structure of the wall. Heyn (1939) believes that it is due 

 to the fact that the chitin molecules which form the framework of the 



