| 1 | Veins of larger fertile pinnules irregularly anastomosing, sometimes almost or even quite free (see also 3. L. orbiculata). |
| 1' | Veins of larger fertile pinnules regularly anastomosing, at least in the basal half of the pinnules. |
| 2 | Sori continuous; pinnules narrowed from base to apex, 5-15 mm long, 2-2% mm wide; veins adaxially impressed, abaxially prominulous; larger pinnules rarely entirely free-veined; sterile pinnules sinuate-dentate; petioles rarely pale, usually brown, abaxially obtusely to acutely bi-angular |
| 2' | Sori continuous or interrupted, the incisions of the pinnules not reaching 1 mm deep in fully fertile pinnules; pinnules very little narrowed close to the apex, 10-12 mm long, 3-4 mm wide, often 3½-4 times as long as wide; veins immersed; pinnules often quite free-veined; petiole pale, abaxially flat or convex, bi-angular, the angles evanescing downward; sterile pinnules broadly crenate-sinuate |
| 2'' | Sori interrupted; pinnules scarcely narrowed to the apex, 10-20 mm long, 4-6 mm wide, their incisions to 1 mm deep; veins immersed; pinnules often without any anastomoses; petiole pale, abaxially angular to the base, at least near the apex sulcate; sterile pinnules bicrenate. |
| 3 | Sori of larger, fully fertile pinnules continuous. |
| 3' | Sori of larger pinnules interrupted by incisions of the margin. |
| 4 | Upper pinnules little reduced, ± half as long as the larger ones; terminal segment comparatively large, lanceolate, free or nearly so (Fig. 32b). |
| 4' | Upper pinnules strongly reduced, some denticuliform ones connected with the narrow pinna-apex. |
| 5 | Pinnules twice as long as wide; petiole usually reddish brown |
| 5' | Pinnules 2%-3 times as long as wide; petiole stramineous |
| 6 | Pinnules not over twice as long as wide. |
| 6' | Pinnules 2.5 to over 3 times as long as wide. |
| 7 | Larger pinules 5-7 mm long, 3-4 mm wide; pinnae strongly ascending; outer veins, in small pinnules sometimes all or nearly all veins free; never 2 series of areoles. |
| 7' | Larger pinnules 9-15 mm long, 4-7 mm wide; pinnae laxly ascending; veins regularly anastomosing; not rarely two series of areoles between lower and upper margin. |
| 8 | Larger pinnules 16-20 mm long. |
| 8' | Larger pinnules to 12 mm long |
| 9 | Terminal pinnule free, cuneate or cuneate-flabellate (Fig. 34); rhizome not very short-creeping. |
| 9' | Terminal segment narrow, connected with some denticuliform upper pinnules, or, if ± free, triangular, acute. |
| 10 | Sori bi- to trinerval; pinnules translucent; terminal pinnule narrowly cuneate or with 2 narrowly cuneate divisions |
| 10' | Sori quadri- to plurinerval; pinnules opaque; terminal pinnule flabellate. |
| 11 | Pinnules 2-3½ cm long, 3-3½ times as long as wide; simply pinnate. |
| 11' | Pinnules under 2 cm long, not over 3 times as long as wide; lamina usually bipinnate. |
| 12 | Pinnules opaque, hardly narrowed to the obliquely truncate apex; outer margin distinct, with an incision; pinnae rather suddenly narrowed below the ± caudate, pinnatifid apex (Fig. 29); pinnule-bearing rachises abaxially brown, sulcate and pale-margined. |
| 12' | Pinnules with subacute to rounded apex, and/or distinctly narrowed to apex; or, if truncate, the outer margin not incised; pinnules often translucent; pinnae more gradually narrowed; pinnule- bearing rachises various. |
| 13 | Pinnules twice as long as broad, to 5 mm long |
| 13' | Pinnules more elongate, or, if not, at least 7 mm long. |
| 14 | Pinnae (if any) strongly ascending; pinnules 7-10 by 3.5-5 mm, 1.5-2.5 times as long as wide; indusium not reaching the margin by more than half its width. |
| 14' | Pinnae (if any) not strongly ascending; pinnules larger, or, if 10 mm or less long, over 2.5 times as long as wide, or the indusium closer to the margin. |
| 15 | At least the inner incisons reaching to 1/3 or 1/2 of the width of the pinnules; pinnules translucent; all lobes and receptacles distinctly convex; indusium reaching the margin or very nearly so |
| 15' | Pinnules more shallowly incised, or, if the inner incisions reach ⅓, the pinnules not translucent, or the inner or all lobes and receptacles straight. |
| 16 | Pinnules usually with the upper margin convex, the lower concave, i.e., slightly falcately decurved; a distinct outer margin present, joining the upper at an angle of less than 90°, its sorus mostly continuous with the outermost one of the upper margin; at least the inner incisions reaching considerably beyond the receptacle. |
| 16' | Pinnules usually as above; a distinct outer margin wanting, rounded into the upper; most or all incisions reaching considerably beyond the receptacle. |
| 16'' | Pinnules usually with both margins straight or faintly convex; no distinct outer margin developed, rounded into the upper; incisions reaching to the level of the receptacle or shallower |
