Theopposition to the identification ofStigmariaas the “root‐system” ofSigillariahas gradually disappeared owing to the accumulation of evidence supporting Binney's discovery in 1845 of an organic connection betweenStigmariaandSigillaria.But the recognition of this fact and its subsequent extension to the case ofLepidodendrondid not settle definitely the morphological value of the Stigmarian axis. It might still be regarded either as a large bifurcating root bearing lateral roots or as an underground stem (rhizome), in which case its appendages might be adventitious roots (Scott) or leaves modified to serve absorptive purposes (Solms‐Laubach), or possibly both kinds of lateral organs might be present (Renault). Some recent observations have tended to reopen the discussion of the morphology of the appendages, particularly the recognition of peripheral “transfusion” tracheids in the Stigmarian appendages and the presence of a pariehnos‐strand in these organs. But though both have their counterpart in the leaves of the Lepidodendracese, I can only see analogy and not homology in these structures, and believe their presence is due to the physiological requirements of the organs in question.The older objection to the identification of the appendages as rootlets, namely their exogenous origin, is sufficiently answered by the fact that several recent Lycopodiales, such asPhylloglossumand the young sporophyte ofIsoëtes, have exogenous roots. The regular quincuncial arrangement of the rootlets similar to that of the leaves of the Lepidodendraceæ might be explained by the fact that we know of rootlets placed close to the base of the leaves of certain Sigillariæ (Sigillaria spinulosa).A suppression of the leaves on the underground axis might leave the rootlets with the same arrangement as the leaves in the aerial portion of the stem. These considerations and the very close agreement in structure of these problematical appendages with the monarch roots ofIsoëtes, seem to me strong reasons for regarding the Stigmarian appendages as true roots.As regards the axes on which they were borne, their structure, so different from that of the rootlets and so singularly unlike the roots of any living plant, seems to prevent our regarding them as main roots. Their cauline nature has been questioned on account of the difference in their structure from that of the aerial stems of the Lepidodendraceæ. But recent evidence in confirmation of Renault's observations of the existence ofStigmariœwith centripetal wood partially removes this objection. Still, in the case of the Lycopodiales we are not limited to the two alternatives root or stem, since Goebel and Bruchmann have shown that the rhizophores ofSelaginellaare indeterminate organs which can develop either as root‐bearers or as leafy shoots. Their position in the young sporophyte ofSelaginellais very suggestive of analogy with the Stigmarian axes, and attention has been drawn to this by Scott, Bower, and others. But the peculiarly root‐like structure of these rhizophores and the fact that they produce their roots endogenously, shows that they are inSelaginellavery highly specialised. The Stigmarian axes though undoubtedly analogous structures are more stem‐like in their character and probably more primitive. A more useful comparison might therefore be made betweenStigmariaand the very primitivePhylloglossum.Here we have not only exogenous and adventitious roots developed at the base of the leaves (cf.Sigillaria spinulosa), but in similar positions one or more outgrowths are produced which serve the purpose of vegetative reproduction. But though specialised for this function, they are, I believe, of the same indeterminate nature as the rhizophores ofSelaginella; and as they show more resemblance to true shoots and bear their roots exogenously, they are really more closely analogous to the Stigmarian axis. Organs of this nature would probably have bifurcated in the case of the extinct Lycopodiales, to keep pace with the physiological requirements of the branching main axis. They may possibly possess the power of forming under certain conditions upright leafy stems, which would explain some structures figured and described by Grand'Eury and others.The conformation of the underground axes ofStigmariopsisand the still more pronounced contraction of the base ofPleuromeiaand ofIsoëtes, would be explained by reduction of the requirements of the plants so far as roo