MULTIJUGATE TYPES. 179 



3' 2- 3" 2' 3 law in the case of both the longer and shorter paths ; 

 the two halves of the capitulum, on either side of any line drawn 

 through one pair of members, are images the one of the other; while 

 in this particular case, the whole diagram is taken as the reverse of 

 fig. 65, as the two systems are useful for reference. 



Identical constructions, tending to anomalous formations, occur in bijugate 

 species of Silphium among the Compositae ; thus 8. perfoliatum and 

 8. connatum are wholly bijugate in their foliage shoots, and present the 

 same pairs of "bucket" leaves as are characteristic of Dipsacus, while 

 S. laciniatum obeys the normal Fibonacci ratios. 



Silphium perfoliatum, L., normally produces terminal capitvda which are 

 bijugate of the same Dipsacus type (16 + 26) with variations. All sub- 

 sequent lateral capitula of the inflorescence system, which goes on rami- 

 fying to the third degree in the type of a symmetrical dichasium (the 

 ultimate ramifications being reduced as one prophyll alone remains 

 fertile), are of the (13+21) type, and attain this phyllotaxis by pro- 

 gressive expansion from beyond the insertion of the fertile prophylls. 

 The distinction between the bijugate and the normal capitula is obvious 

 on looking at the involucre from behind ; the normal capitulum pre- 

 senting a 3-5-8-star pattern, while the bijugate heads have four outer 

 members arranged in a cross (fig. 676). 



These terminal capitula commence the bijugate character normally in the 2, 

 4, 6, 10, etc., series, but the construction subsequently becomes irregular : 

 heads of 8. perfoliatum, taken after the flowering-period (fig. 67a), show 

 a remarkable similarity to the Dipsacus pattern of fig. 64 ; and a similar 

 uniformity of growth in the leaf-members results in the fact that the 

 transitional members become successively smaller in opposite pairs. The 

 central portion is not clear, but the fact that irregularity may commence 

 at an early stage is shown by the feeble development of 15, 15', while 

 17, 17' are still well-marked. Sections of such capitula, taken in the 

 bud-stage, do not show the construction so clearly as in the case of 

 Dipsacus ; irregularity in the curve system is very marked, an average 

 of 22-25 being observed among six capitula, and thus follows lines similar 

 to those already described (fig. 64) ; the same addition of anomalous 

 longer paths may be observed, and a similar loss of short curves ; the 

 capitula do not, however, present so typical an appearance, owing (1) to 

 the fact that dorsiventrality of the outer members is excessive, the four 

 external members meeting round the axis, so that new contacts are 

 established beyond those of the theoretical construction ; (2) the capitu- 

 lum is almost plane, and the number of members inserted on it limited, 

 hence the system commences to be destroyed almost as soon as the curve 

 paths reach their maximum. Many capitula are thus rendered incapable 

 of being counted. 



The essential point to note is that the system commences regular expansion 



