172 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



special interest. Owing to the subsequent tendency of BipsacMS 

 to insert or lose curves on the main capitulum axis in order to 

 compensate local growth variations, each capitulum requires to be 

 taken on its own merits. The one selected suffices to indicate the 

 normal procedure as well as the possibility and extent of local and 

 individual variations. 



Dipsacus fullonum (Anomalous Expansion System). A ter- 

 minal head of a remarkably fine plant was taken at the end of 

 March, when the inflorescence was just becoming visible among the 

 leaves of the terminal bud. The plant had been growing fully 

 exposed during a mild winter, and should have flowered in the 

 preceding summer ; a series of hard frosts (22° F.) had also set in 

 just as the head commenced to develop. Very little protection is 

 afforded by the surrounding foliage leaves, and if external environ- 

 ment has any effect in producing anomalies, anomalous construction 

 should be expected, and as a matter of fact it was very marked. 



A section of such a capitulum (6 mm. in height), taken towards 

 the lower part, includes the whole of the involucre, and may readily 

 be drawn with considerable accuracy (fig. 64). Comparison of 

 the involucral members shows two large median members (1 and 

 1'), and on the sides of the drawing 3 and 3', and 5 and 5', fairly 

 clearly indicated, and diverging at something like the proper angle ; 

 but careful measurement shows that the angle between 1 and 3 is 

 only 60°, and that between 3 and 5, 70°. That a transition is in 

 progress is obvious from the regular segmentation by T-shaped 

 walls, which might be easily mistaken for a tissue-drawing. This, 

 again, is much clearer than in Helianfhus, owing to the fact that the 

 true primary members are here alone present and fill their rhombs, 

 while the florets they subtend are only just commencing and have 

 not as yet commenced to squeeze their bracts into the interstices 

 between them. 



The only modification of the theoretical orthogonal construction 

 is found in the dorsiventrality of the members, which includes a 

 slight normal slipping across the paths of the shorter curves. The 

 leaf-pairs 1, 3, and 5 having been determined, it is easy, by approxi- 

 mating the divergence angle, to locate 7, 9, and 11. The three 

 members 1, 11, 7 being in contact, it is clear that the phyllotaxls 



