REFUTATION OF THE SPIRAL THEORY. 



495 



of the so-called doctrine of phyllotaxis founded by Schimper and Alexander Braun, 

 and the spiral theory lying at the foundation of it, and which has dominated Botany 

 for more than forty years. This theory was derived from the consideration of the 

 upright radially-constructed shoots of the vascular plants, in which the above- 

 named spiral arrangement of the leaves commonly occurs. On imagining the 

 leaves of such a shoot-axis connected together by a line in the order of their age, 

 this line took the form of a spiral line continually winding round the shoot-axis, and 

 this was designated the genetic spiral; in it the fundamental law of growth of the 

 vegetable kingdom was supposed to be perceived. It was therefore sought, even in 

 cases where the leaves stand in two straight rows on the shoot-axis, and further, 

 where they are distributed in decussate pairs or in alternating whorls (Fig. 331), and 

 even in such cases where they appear on one side only of the shoot-axis, to carry 

 out the spiral arrangement as the fundamental law of growth, whereby it was 

 necessary to employ the aid of a series of the most arbitrary assumptions. 



An unprejudiced observation of the processes at the growing-point, taking into 



FIG. ^sa—Diagram of a shoot, the leaves of which 

 are scattered with a divergence of z-sths. 



FIG. 331. — Diagram of the flowering stem of 

 Paris quadrifotia. /^ whorl of large foliage leaves 

 beneath the flower ; ap outer, ip inner perianth ; 

 a a outer, ia inner stamens. In the centre is the 

 young fruit consisting of four carpels. 



account at the same time the physiological relations of growth, demonstrates, however, 

 as Goebel has abeady expressly shown, that the spiral theory is not transferable to 

 dorsi-ventral shoots, because it directly contradicts the facts; the above-mentioned 

 relations of growth of Caulerpa, Lygodium, the Rhizocarpeae, Liverworts, etc., show 

 that not only the places of origin of the leaves but also those of the lateral shoots, 

 roots, and sexual organs, are to a certain extent determined by tlie dorsi-ventral or 

 radial structure of the mother-shoot. There is not the smallest ground for regarding 

 the single rectilinear series of leaves on the dorsal line of the stem of Lygodium in 

 any way as an expression of spiral arrangement, and just as little is this possible with 

 the phyllotaxis and branching of the Rhizocarps, and even the very numerous cases 

 of two-rowed phyllotaxis, especially for example in the Grasses, and likewise the 



I, for my part, in the establishment of the idea of dorsi-ventrality by no means had in view exclusively 

 the anatomical structure, but just as much, on the one hand, the molecular structure, and, on the other 

 hand, the capacity to produce different organs in different directions. Only there was no necessity 

 for me to go more in detail into the latter point, Goebel having done it so well. 



