576 ãThe 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 spiralsãthe ãparastichiesããã; Church, op. cit. I, p. 42.
577 Mr Churchãs whole theory, if it be not based upon, is interwoven with, Sachsãs 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, ãthe law of the orthogonal intersection of cell-walls at a growing apex may be taken as generally acceptedã (p. 32); but I have taken a very different view of Sachsãs law, in the eighth chapter of the present book. With regard to his own and Sachsãs hypotheses, Mr Church makes the following curious remark (p. 42): ãNor 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.ã
578 Amer. Naturalist, VII, p. 449, 1873.