In his account of _Lyginopteris_ stems published in 1873 Williamson[116] suggested that the vascular bundles met with outside the xylem-cylinder might be the leaf-traces of large fronds and expressed the opinion that the ‘stems or petioles’ previously described by him under the generic name _Edraxylon_ might belong to _Lyginopteris_. A year later he substituted the name _Rachiopteris aspera_ for the petioles previously referred to _Edraxylon_ and inclined to the view that this type of _Rachiopteris_ may be the petiole of the Carboniferous fronds known as _Sphenopteris Hoeninghausi_ Brongn., an inference based to a large extent on the occurrence of emergences on _Rachiopteris aspera_ (fig. 404, E) preserved as petrifactions like those on impressions of _Sphenopteris Hoeninghausi_ as figured by Brongniart (figs. 404, A; 405, D, D’). In 1890 Williamson was able to demonstrate the truth of the surmise that _Rachiopteris aspera_ and _Lyginopteris oldhamia_ are respectively the petiole and stem of the same plant, which he believed to be an arborescent fern[117]. The petioles of _Lyginopteris_ fronds, which may reach a diameter of 1 cm., are attached by a broad base to the stem, and as already suggested by the number of internodes traversed by each leaf-trace, the leaves are comparatively far apart. A transverse section of a petiole is shown diagrammatically in fig. 405 A. The hypodermal stereome is a prominent feature, but the narrow radial plates of the stem-cortex tend to be replaced in the rachis by broader and confluent masses of strengthening elements: the upper surface of the petiole is slightly grooved. Glandular and spinous emergences are often very abundant, as in the section reproduced in fig. 404, E. A glandular emergence is seen at _a_ in fig. 405, A. The spinous emergences may be compared with those of _Davallia_ (_Odontosoria_) _aculeata_[118], a West Indian fern of climbing habit and with the prickles on _Hemitelia_ and other recent Cyatheaceous fronds[119], while capitate glands, though simpler than those of _Lyginopteris_, occur on the leaf-stalks of some recent Polypodiaceous species[120]. The concentric meristele may consist in the lower part of the petiole of two separate and slightly curved strands like those seen in fig. 404, E, _m_: sooner or later the two strands unite to form a wide-open V or a W-shaped bundle with several slightly internal protoxylem groups close to the lower edge. The two sections represented in fig. 406, A and B show the gradual divergence of the two meristeles of a petiole as they approach the level where it divides into two equal branches, a characteristic feature of _Sphenopteris Hoeninghausi_ and allied fronds. At a lower level than that represented in fig. 406 the vascular strand of the petiole would have the form of a W as figured by Williamson in one of his earlier memoirs[121]. The phloem with scattered secretory sacs and the adjacent tissue of the leaf-stalk are