178 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



Further discussion of these effects and the anomalies of a large 

 series of such capitula would be beyond the range of the present 

 paper, which only seeks to trace out the general lines of phyllotaxis 

 as indicated by the homologies of cell-segmentation. Two points 

 are specially striking in the expansion series of Dipsacus : first, the 

 extent of the stations of symmetry in the expanding system, which 

 subsequently give way to a renewal of the original ratio ; and 

 secondly, the beautiful approximation of the normal part of the 

 diagram to the segmenting blocks of protoplasm characteristic of 

 the tissues of many Algal forms (Melohesia, Ralfsia, Coleochaete). 



In such a working mechanism, again, as in ITelianthus, the 

 genetic spiral is completely lost sight of and forgotten, although 

 the two concurrent lines may be traced in numbering up the 

 members; even the oscillation-theory is weakened, and the con- 

 clusion that the system grows and segments along new paths of 

 distribution dependent on the pre-existing system, with the mathe- 

 matical accuracy of the " crystallisation " of the Micellar Theory, 

 is almost unavoidable. 



Dipsacus thus presents an example of a plant in which the 

 (2-f-3) system of the Fibonacci series is replaced by {2 + 4). This 

 phenomenon, rare in Helianthus, here becomes the rule, and the 

 whole construction of the main axis is bijugate. The reason for 

 this is still wanting, but it is clear that what in Helianthus re- 

 presents only an individual variation, is in Dipsacus a specific and 

 even family character {cf. Scabiosa, Gephalaria *). 



As will be described later, similar specific variations occur in 

 anomalous series, as for example, the (3-f-5) of Sedum acre, in con- 

 trast to the (3-f-4) of S. refiexum {cf. figs. 76a, V). 



That the true expansion type 16/26/42, given by the Bravais for 

 the great majority of the capitula of Dipsacus fullonum, does 

 actually obey the theoretical construction of fig. 65, is shown by a 

 similar section of a developing capitulum in fig. 66 ; the agreement 

 is perfect, and the addition of new curves is seen to follow the 



* Variation to a true (2 + 2) system was also found in Gephalaria tartarica; 

 while the variation in one plant of Dipsacus syh)estris to (3 + 6), giving " twisted- 

 whorls" of 3, is of special interest in connection with the readiness with which 

 (2 + 2) is in some plants replaced by (3 + 3). 



