lenticular, numerous, clustered on an exserted receptacle, which is a prolongation of the vein beyond the ordinary margin of the frond, so that the sori become extrorse marginal, or projected outwards as well as opening outwardly, while the fronds are pellucid-membranaceous; Schizæineæ, with the ring horizontal or transverse, situated quite at the apex of the oval sporangia, which is, in consequence, said to be radiate-striate at the apex; Ceratopteridineæ, one or two aquatic species, the sporangia sometimes furnished with a very rudimentary ring, reduced, as in Osmundineæ, to a few parallel striæ, sometimes furnished with a very broad and more lengthened ring; and Osmundineæ, with the spore-cases two-valved, bursting vertically at the apex, the ring very rudimentary, reduced to a few parallel vertical striæ on one side near the apex. In all but the last of these groups, the sporangia are not valvate, and consequently, when they open for the liberation of the spores, they burst partially or irregularly; but in the Osmundineæ they split at the top in two equal divisions.[72] A large portion of the Polypodineæ are either tropical or subtropical. The genus Polypodium itself is one of the most extensive and diversified genera of the group. It is chiefly distributed over the tropical regions of the western hemisphere, but four species are indigenous in Britain, and of these the Polypodium vulgare, or Common Polypody, is abundant about the trunks of moss-grown trees, on banks, rocks, and old thatched roofs. The young fronds appear in May, and rise from five or six to twelve or eighteen inches in height. They are lanceolate, deeply pinnatifid, with obtuse, linear, lanceolate, indistinctly serrated segments. The genus is distinguished by its naked globular sori, which in this species are regularly disposed in a line on each side of the mid vein, half way between it and the margin of the leaf. When young, they are of a yellow or bright orange colour, which changes to brown when they are ripe. The rhizome, which branches in all directions, is at first clothed with a skin densely covered with yellowish brown membranaceous lanceolate scales, which at length fall or become obliterated, leaving the surface nearly smooth. The Polypodium vulgare has many varieties, several of which are well marked, especially that called cambricum, which is twice pinnatifid. The plant is common in temperate climates. [Illustration: Fig. 57. Pinnule of Lastrea Filix-mas with sori.]