XIV] OR PHYLLOTAXIS 919 



cone approximating to a cylinder. This mathematical conception is 

 translated, in botany, into actual fact. The fir-cone may be looked 

 upon as a cylindrical axis coiltracted at both ends, until it becomes 

 approximately an ellipsoidal solid of revolution, generated about 

 the long axis of the ellipse ; and the semi-ellipsoidal capitulum of the 

 teasel, the more or less hemispherical one of the thistle, and the 

 flattened but still convex one of the sunflower, are all beautiful and 

 successive deformations of what is typically a long, conical, and all 

 but cylindrical stem. On the other hand, every stem as it grows 

 out into its long cylindrical shape is but a deformation of the little 

 spheroidal or ellipsoidal or conical surface which was its forerunner 

 in the bud. 



This identity of the helical spirals around the stem with spirals 

 projected on a plane was clearly recognised by Hofmeister, who was 

 accustomed to represent his diagrams of leaf-arrangement either in 

 one way or the other, though not in a strictly geometrical projection*. 



According to Mr A. H. Church f, who has dealt carefully and 

 elaborately with the whole question of phyllotaxis, the spirals such 

 as we see in the disc of the sunflower have a far greater importance 

 and a far deeper meaning than this brief treatment of mine would 

 accord to them : and Sir Theodore Cook, in his book on the Curves 

 of Life, adopted and helped to expound and popularise Mr Church's 

 investigations. 



Mr Church, regarding the problem as one of "uniform growth," 

 easily arrives at the conclusion that, if this growth can be conceived 

 as taking place sjnnmetrically about a central point or "pole," the 

 uniform growth would then manifest itself in logarithmic spirals, 

 including df course the limiting cases of the circle and straight line. 

 With this statement I have Httle fault to find; it is in essence 

 identical with much that I have said in a previous chapter. But 

 other statements of Mr Church's, and many theories woven about 

 them by Sir T. Cook and himself, I am less able to follow. Mr 

 Church tells us that the essential phenomenon in the sunflower disc 

 is a series of orthogonally intersecting logarithmic spirals. Unless 

 I wholly misapprehend Mr Church's meaning, I should say that this 



* Allgemeine Morphologie der Gewdchse, 1868, p. 442, etc. 



t Relation of Phyllotaxis to Mechanical Laws, Oxford, 1901-1903; cf. Ann. Bot, 

 XV, p. 481, 1901. 



