XIV] OR PHYLLOTAXIS 639 



it becomes approximately an ellipsoidal solid of revolution, 

 generated about the long axis of the ellipse ; and the semi- ellip- 

 soidal capitulum of the teasel, the more or less hemispherical one 

 of the thistle, and the flattened but still convex one of the sun- 

 flower, 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 

 surface, or cone, 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. Churchf, who has dealt very carefully 

 and elaborately with the whole question of phyllotaxis, the 

 logarithmic 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, has adopted and has 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, i/this growth can be conceived 

 as taking place symmetrically about a central point or "pole," 

 the uniform growth would then manifest itself in logarithmic 

 spirals, including of course the limiting cases of the circle and 

 straight line. With this statement I have little 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 w^holly misapprehend Mr Church's meaning, I 

 should say that this is very far from essential. The spirals 



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

 f Relation of Phyllotaxis to Mechanical Laivs, Oxford, 1901-1903; cf. Ann. 

 of Botany, xv, p. 481, 1901. 



