MULTIJUGATE TYPES. 169 



affords no difficulty. The "decussate" axis requires further 

 investigation. 



Examination of the rosette of a seedling (fig 62a, Divsacus sylves- 

 tris) shows that the (2 + 4) system is well defined, and results in 

 the formation of alternating pairs of leaves in four spiral rows. 

 By taking lines drawn through the centre of the median vascular 

 bundles of each leaf on a drawing carefully made under the camera 

 lucida, the angle at which the planes of successive pairs of leaves 

 intersect may be measured with sufficient accuracy. That perfect 

 accuracy is not attainable is shown by the fact that such' lines do 

 not intersect over the centre of the growing point ; such disturb- 

 ances being the effect of unequal growth, further evidence of which 

 is seen in the drawing of Scdbiosa plumosa, in which the spirals are 

 not equally curved (fig 62b). 



The angle measured in such a diagram averages 75° (73°-77°) ; 

 by constructing a log. spiral theoretical system of (2 + 4) by means 

 of log. spiral curves (1 : 2), a similar system may be plotted out, and 

 lines drawn similarly through the " centre of construction " of the 

 " square " areas ; on such a figure the theoretical divergence angle 

 thus measured was found to approximate 73° (more correctly 72°). 



Observation of a Dipsacus plant which is commencing to send up 

 an erect axis shows that the terminal bud maintains the same 

 bijugate construction unchanged, and that the same system is 

 continued in aU the foliage leaves until the terminal inflorescence 

 is produced. The leaves are therefore not decussate at all, alternat- 

 ing pairs crossing at about 72°, and not at 90°. True symmetry is 

 thus never attained, the apparent decussation being due to a 

 bijugate (2-1-4) formation in which, owing to the fact that a 

 bijugate construction implies two concurrent ontogenetic spirals, 

 two members are produced at each node at points diametrically 

 opposed. 



The expansion of the system in the inflorescence is apparently 

 not so accurate as the system deduced for Hdianthus. Thus (2-1-4) 

 should normally expand to (6 + 10), (16 + 26), (42 + 68), but 

 Dipsacus fullonum gives terminal heads of the system (26 + 42) 

 as the type, and D. pilosm is even more constantly (10 + 16) 

 (fig. 60Z>). In noting this irregularity it may be pointed out that 



