610 ON LEAF-ARRANGEMENT [ch. 



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 this "theory, if correct, would be fundamental for 

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

 plant construction than in animals." The parallel 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, eithei' 

 with Mr Church's theories, or my own objections to themf. 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 



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

 with the line of cui'rent-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. 



■\ 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 ceU-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 Chiuch makes the following 

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

 than that of the j)araboloid 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." 



