ORGANS AND SYSTEMS OF ORGANS. 171 



organs may develop from the same horizontal plane of the mother- 

 organ. Example : the two-leaved whorl of the Labiatce, the three- 

 leaved whorls of Juniper us. 



IV. The organs are arranged in spiral lines. The so-called 

 "spiral" position of leaves and branches will be more fully dis- 

 cussed in the following chapter. 



A. SPIRAL ARRANGEMENT OF LEAVES. THEORIES OF PHYLLOTAXY. 



A line continuing around the stem in the same direction and 

 cutting the various lateral organs by the shortest path is called the 

 ground-spiral. 



This ground-spiral, according to more recent investigators, is not 

 necessarily a genetic line (genetic spiral) ; that is, the leaves need not 

 follow this line in the order of their development, although they 

 may follow a spiral line subsequently. We shall base our state- 

 ments upon the studies of ScnwENDENER. 1 



As indicated above, there are only a very few cases in which the 

 genetic line corresponds to the ground-spiral, as in the leaf-form- 

 ing segments of the apical cell of mosses (Fig. 100). In other 

 plant-groups the spiral arrangement is different, even among those 

 in which an apical cell cuts off segments in succession along a 

 spiral line. It has been observed (Schwendener) that in the fern 

 the course of the leaf-spiral is independent of the segmentation- 

 spiral of the apical cell. Also in Equisetum scirpoides there seems 

 to be no fixed relation between the \e&i-whorl and the spirally pro- 

 duced segments of the apical cell. The flowers on the disk of 

 IleliantTius are evidently not always developed acropetally corre- 

 sponding to the ground-spiral. The fact that apical cell-growth in 

 the stem of dicotyledons is not well known in all cases adds to the 

 difficulty of finding the relation of the leaf-spiral to the spiral of the 

 apical cell-segments. Therefore it cannot be maintained that the 

 spiral arrangement of the leaves in the ferns, dicotyledons and 

 monocotyledons, corresponds to a definite spiral position of foliar 

 protuberances near the apex of the stem. With Schwendener we 

 must consider the following of importance in giving a clearer 

 knowledge of the subject. The young lateral organs or leaf -begin- 

 nings, which appear as small protuberances, touch each other; they 



1 Mechanische Theorie der Blattstellung, 1878. HOFMEISTER is recognized as 

 having done the preliminary work in this line. 



