920 ON LEAF-ARRANGEMENT [ch. 



is very far from essential. The spirals intersect isogonally, but 

 orthogonal intersection would be only one particular case, and in all 

 probability a very infrequent one, in the intersection of logarithmic 

 spirals developed about a common pole. Again on the analogy of 

 the hydrodynamic lines of force in certain vortex movements, and of 

 similar lines of force in certain magnetic phenomena, Mr Church 

 proceeds to argue that the energies of life follow lines comparable 

 to those of electric energy, and that the logarithmic spirals of the 

 sunflower are, so to speak, lines of equipotential*. And Sir T. Cook 

 remarks that thife "theory, if correct, would be fundamental for all 

 forms of growth, though it would be more easily observed in plant 

 construction than in animals." But the physical analogies are remote, 

 and the deductions I am not able to follow. 



Mr Church sees in phyllotaxis an organic mystery, a something 

 for which we are unable to suggest any precise cause : a phenomenon 

 which is to be referred, somehow, to waves of growth emanating 

 from a centre, but on the other hand not to be explained by the 

 division of an apical cell, or any other histological factor. As Sir 

 T. Cook puts it, "at the growing point of a plant where the new 

 members are being formed, there is simply nothing to see.'' 



But it is impossible to deal satisfactorily, in brief space, either 

 with Mr Church's theories, or my own objections to themj*. Let 

 it suffice to say that I, for my part, see no subtle mystery in the 

 matter, other than what lies in the steady production of similar 

 growing parts, similarly situated, at similar successive intervals of 

 time. If such be the case, then we are bound to have in consequence 



* "The proposition is that the genetic spiral is a logarithmic spiral, homologous 

 with the line of current-flow in a spiral vortex ; and that in such a system the 

 action of orthogonal forces will be mapped out by other orthogonally intersecting 

 logarithmic spirals— the ' parastichies ' " ; Church, op. cit. i, p. 42. 



t Mr Church's whole theory, if it be not based upon, is interwoven with, Sachs's 

 theory of the orthogonal intersection of cell- walls, and the elaborate theories of 

 the symmetry of a growing point or apical cell which are connected therewith. 

 According to Mr Church, "the law of the orthogonal intersection of cell- walls at 

 a growing apex may be taken as generally accepted" (p. 32); but I have taken 

 a very different view of Sachs's law, in the eighth chapter of the present book. 

 With regard to his own and Sachs's hypotheses, Mr Church .makes the following 

 curious remark (p. 42) : "Nor are the hypotheses here put forward more imaginative 

 than that of the paraboloid apex of Sachs which remains incapable of proof, or his 

 construction for the apical cell of Pteris which does not satisfy the evidence of his 

 own drawings." 



