550 Morphologie und Teratologie. 



CHURCH, A. H., On the Relation of Phyllotaxis to 

 Mechanical Laws. Part I. Construction by 

 Orthogonal Trajectories. 80 pp. 10 plates. 3 sh. 6 d. 

 September 1901. — Part II. Asymmetry and 

 Symmetry. 120 pp. 16 plates. 5 sh. January 1902. 

 London and Oxford (Williams and Norgate). 



The author devotes himself to the mechanical nature of the 

 constructions observed in the phenomena of the arrangement 

 of the lateral members of higher plants. With perfect justice 

 he points out that these cannot necessarily be determined by 

 the study of adult structures which have ceased growing, but 

 must be traced as far as possible in the growing region of the 

 shoot-apex; and that all phyllotaxis relations are essentially 

 phenomena of growth. Since the study of growing and 

 expanding Systems is capable of mathematical treatment, the 

 author postulates, to commence with, the condition of uniform 

 growth around a gro wth -ce nt r e, in which all asymmetrical 

 construction curves must necessarily become orthogonally 

 interseding logarithmic spirals. He points ont that phyllotaxis 

 spirals must therefore be regarded as derivatives of equiangular 

 or logarithmic spirals; and thus not only does the initial error 

 underlying the formulae of Schimper and Braun become 

 apparent, since these involved construction by helices and 

 spirals of Archimedes; but it is also clear that all theories based 

 on the secondary correction of these formulae by torsion or 

 secondary displacements, as put forward by Schwenden er, 

 are equally unnecessary and wide of the mark. The so-called 

 „orthostichies" of spiral phyllotaxis are non-existent as straight 

 lines, although the error may be so small that it may be 

 inappreciable to the eye; while on adult shoots the appearance 

 of helices of Schimper and Braun are only secondarily 

 produced as the members and internodes attain constant 

 volume. 



The „genetic-spiral" is again shown to be preferably regarded 

 as a secondary effect, and all phyllotaxis appearances are to 

 be rather regarded as Systems of interseding curves, — the 

 expression of a rhythmic production of new growth 

 impulses, — the properties of such Systems can readily be 

 observed by drawing similar geometrical constructions: The 

 general appearance of a Single „ontogenetic" line of production 

 being due to the fact that the number of contact parastichies 

 in either direction is only divisible by unity, just as equality 

 in the number of interseding curves gives the appearance of 

 whorls when the System is subsequently pulled ont. 



The subject matter of the present communication is in 

 many parts highly mathematical, and hence the author gives a 

 preliminary discussion in which the mathematics are presented 

 in geometrical form. The diagrams and illustrations are very 

 numerous (over 80) and clear and are extremely welcome as 

 an aid to the digestion of the somewhat abtruse text. 



