Symmetry 157 



are various complexities in the shoot meristem, there is little good evi- 

 dence from this source in support of Plantefol's theory. 



Although this theory has received strong support from a number of 

 French botanists, objections have been raised against it in other quarters. 

 What are chosen as foliar helices are evidently one of the parastichies or 

 spiral rows of leaf traces to be seen along the axis, but which of these is 

 the true helix in any instance seems difficult to determine. The leaves 

 on a helix must have some vascular connection with each other, accord- 

 ing to the theory, but in most stems at least two different parastichies 

 could be chosen which would fulfill this requirement. A figure in one 



Fig. 7-4. Two foliar helices, the members of one connected 

 by dots and of the other by dashes, seen as though 

 the surface of the stem were removed and spread out. 

 (From Plantefol.) 



en 

 i 



Fig. 7-5. Diagram of shoot apex according to Plantefol's 

 hypothesis, showing the generative center and the ab- 

 sence of divisions at the very tip. Dots indicate mitoses. 

 ( From Plantefol. ) 



of Dr. Esau's papers (1943, Fig. 1), though it was not drawn to clarify 

 the problems of phyllotaxy, makes these relationships evident (Fig. 

 7-6). This is a diagram of the primary vascular system of Linum. The 

 genetic spiral is shown, with the leaves numbered along it. In the series 

 25-33-41, the bundle is continuous with a branch that passes laterally to 

 the next in the series, and there are eight of these helices around the 

 stem. In the series 28-33-38, the right-hand lateral of one is continu- 

 ous with the left-hand lateral of the next, and there are five helices. 

 Members of the series 30-33-36 have no direct vascular connection with 

 one another but are in a definite row. Which of these spirals should be 

 chosen as the foliar helix? One might determine the true one, perhaps, 



