180 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



as in Di/psotcus, but in all the cases observed produced ' ultimately an 

 anomalous and perfectly indefinite construction, tbe only point in 

 common being the much closer approximation of the parastichy ratios 

 to equality, so far as they could be estimated. On the other hand, the 

 capitula in subsequent ramifications, right down to the smallest formed 

 buds, appeared to be constantly (13 + 21). There is so far, then, a distinct 

 tendency for the first-formed and best-nourished capitula, to not only 

 carry on the bijugate construction of the foliage-shoot, but to become 

 fiu-ther anomalous. It thus becomes of interest to compare allied species 

 in order to see how far these irregularities are of local and individual or 

 specific importance. 



8. connatwm, L., closely resembles S. perfoliatum, possesses the same " bucket- 

 type " of paired leaves, as also the same general habit and size, but flowers 

 about a month later. Of the terminal capitula, (B.G.O. 1901) some of the 

 first-produced showed the bijugate 2, 4, 6, 10 pattern in the involucre, 

 but the majority were of the normal (134-21) type, as in the rest of the 

 inflorescence. As the plants were growing side by side with 8. perfoliatum, 

 it is possible that a different period of flower-development may have had 

 a local influence. 



>3. laciniatum, L., with normal asymmetrical phyllotaxis, has a more reduced 

 inflorescence, while the size of the individual capitula is correspondingly 

 increased. The terminal head of a strong shoot gave 34 short curves, but 

 the longer were too irregular to count, although the approximation to 

 equality was evidently very close ; a lateral head gave (23-1-34), suggest- 

 ing a slight rise beyond a (21-1-34) system ; while the last formed heads 

 presented (21-1-34) exactly. ■ It is thus clear that in SilpMii/m, especially 

 in leading capitula, the capacity for the addition of excess curves is very 

 well marked, and the stations of the Fibonacci ratios are not observed 

 under conditions of special nutrition with the accuracy of the normal 

 plant for which Helicmthus was regarded as a type. In other words, 

 adopting the previous convention, the Fibonacci sense is less well-de- 

 veloped in 8ilphmm, and anomalous constructions due to the interpolation 

 of excess curves are readily produced ; but the tendency is again always 

 towards a nearer approximation to symmetry, as exhibited by an approach 

 to equality in the parastichy ratios. From these facts it is thus possible 

 to argue that the irregularities in the particular capitulum of Dipsacus 

 (fig. 64) were not due to the stimulus of external environment in the 

 form of low temperature variations, but are to be correlated with the 

 extra vigour in the main axis, due to the fact that the flowering period 

 had been delayed. Once more, also, it may be pointed out how hopeless 

 it is to express any of these irregular constructions in terms of " genetic- 

 spirals," while they are readily discussed from the standpoint of paras- 

 tichy ratios. 



Similar relations between terminal bijugate inflorescences, which under 

 excess nutrition tend to become anomalous, and lateral capitula of the 

 normal Fibonacci character, are general among other members of the 



