| Fronds 6–20 in., ovate-lanoeolate, brownish-green; stipes and rhachis bristly. Sori terminal; indusium orbicular | 9. H. scabrum. |
| Fronds 3–9 in., pale glistening-green; lower pinnæ often flabellate. Stipes woolly at the base. Sori terminal, small; indusium broadly ovate or orbicular | 10. H. flabellatum. |
| Fronds ½–1½ in., deltoid, very delicate. Stipes, rhachis, and costæ with silky flexuous hairs. Sori terminal, small, partly immersed; indusium ovate-orbicular | 11. H. rufescens. |
| ** Fronds with the margins and both surfaces densely clothed with stellate hairs. | |
| Fronds 2–6 in., oblong; rhachis broadly winged throughout, the wing decurrent along the upper part of the stipes. Sori terminal, immersed | 12. H. ciliatum. |
| Fronds 2–10 in., oblong-lanceolate; rhachis winged only towards the top; stipes naked. Sori terminal, immersed | 13. H. subtilissimum. |
| Fronds 2–8 in., linear-oblong, rigid and coriaceous, everywhere hidden by dense tomentum; rhachis not winged. Sori terminal, free | 14. H. Malingii. |
| B. Leptocionium. Margins of the frond spinulose-dentate. | |
| Fronds minute, ¼–1 in., simple or forked or digitately divided. Indusium with entire valves | 15. H. Cheesemanii. |
| Fronds minute, ¼–1 in., pinnatifid. Sori solitary, free, terminating the main rhachis; indusium with the valves spinulose on the back and margins | 18. H. minimum. |
| Fronds 1–4 in., pinnate; pinnæ divided. Sori lateral, near the base of the pinnee, free; indusium with the valves smooth on the back, spinulose-dentate on the margins | 17. H. Tunbridgense. |
| Fronds 1–4 in., pinnate; pinnse divided. Sori lateral, near the base of the pinnæ, free; indusium with the valves smooth on the back; margins entire | 18. H. unilaterale. |
| Fronds 4–8 in., 3–4-pinnatifid. Sori lateral, near the base of the pinnas, free; indusium large, often decurved, obovoid; valves with entire margins | 19. H. multifidum. |
| Fronds 6–12 in., 3–4-pinnatifid. Sori terminal, immersed in the tips of the segments; indusium ovate-orbicular, valves with entire margins | 20. H. bivalve. |
1. H. rarum, R. Br. Prodr. 159.—A very delicate pale glistening-green pellucid species, forming matted patches on the trunks of trees or on rocks. Rhizomes creeping, much branched, very slender, wiry, black. Fronds very variable in size and shape, usually from 1 to 4 in. long, but sometimes dwarfed to ½ in., and occasionally lengthened out to 6 or 8 in., broadly oblong to linear-oblong, 2-pinnatifid, in large specimens pinnate at the base, pendulous, membranous, flaccid, quite glabrous. Stipes extremely slender, capillary, often half the length of the whole frond; main rhachis usually winged throughout. Pinnæ close, often overlapping, once or twice forked or pinnatifid, rarely simple. Segments erecto-patent, ¼–½ in. long, 110 in. broad, flat, obtuse, quite entire. Sori mostly near the summit of the frond, sunk in the tips of the segments. Indusium large, almost as broad as the segments,
