ANOMALOUS SERIES. 199 



an anomalous mode of forming the transitional 21 series in the 

 capitulum itself is clear from the form (29 + 47), fig. 54, in which 

 the contact parastichies of the involucre are seen to be (11 + 18), 

 and the rise of phyllotaxis so far follows the normal course. The 

 (29 + 47) capitulum is again of special interest in that it does not 

 represent the normal sequence of expansion from the (3 + 4), which 

 includes all the other anomalous heads. 



III. Low ratios of the anomalous series. 



Such constructions occur more commonly in plants which ex- 

 hibit marked xerophytic specialisations, and are associated with 

 normal spiral systems in closely allied species, but less generally 

 with the whorled condition in the assimilating shoots. There is 

 little reason for regarding them as markedly heriejicial to the plant, 

 although it is clear that the nearer the ratios approach equality 

 the less exposure there will be in the long run to intense light, if 

 the axis is condensed, although possibly no two leaves are mathe- 

 matically superposed ; the assumption that they represent variations 

 in the production of down-grade assimilating shoots appears more 

 probable. They should thus be especially characteristic of the 

 leafless Cactaceae and Euphorbiae, and such is in fact found to be 

 the case. {Of. special section.) 



Thus the very beautifully seven-spired Euphorbia biglandulosa closely re- 

 sembles in habit and glaucous foliage E. myrsinites, which possesses 

 normal (2 + 3) structure, and both form normal Cyathium inflorescence 

 shoots. E. myrsinites varies from (2 + 3) in weak axes to (3 + 4) in the 

 strongest : it is thus difiicult to avoid the conclusion that (3 + 4) repre- 

 sents a weakened form of (3 + 5) (fig. 77). 



Similar variations occur in succulent Saxifrages and Crassulaceae. 



Sedum acre with normal (3 + 5) foliage shoot passes into a whorled (5 + 5) 

 flower, symmetry being attained as usual beyond the calyx members. 



Sedum reflexum with a (3 + 4) or seven-spired shoot, produces terminal 8-merous 

 flowers, while the lateral scorpioid cymes contain 6-merous flowers, the 

 variation of the assimilating shoot being thus passed on to the reproduc- 

 tive shoot (figs 76a, b). 



Sedum elegans, as previously noted, varies from (5+8) to (6 + 10). 



Monanthes polyphylla forms rosettes oi (8 + 13) or (7 + 11), the flowers being 

 symmetrical and 6 - 8-merous : 7-merous flowers are common also 

 on (7 + 11) shoots. 



Such phenomena present a close parallel to the case of multijugate 



