The systematic arrangement of the Ferns is chiefly founded on peculiarities of the sori and sporangia, characters which are quite intelligible by the aid of a good magnifying lens, these spore-cases being very pretty opaque objects under the microscope. Thus some of the primary divisions are founded on the presence or absence of the ring or annulus on the spore-case. Another series of divisions are founded mainly on the nature of the ring in those cases when it is present; and, for the rest, the form and position of the sori come in as discriminating characters. In this way the main groups are marked out, but, in the case of the genera, still further recourse is had to the sori and its covering, and by some modern authors supplementary characters derived from the venation are brought into use. The following is the arrangement adopted by Mr. Moore,[71] and which agrees in its general features with that of most modern observers. The two leading groups are the _Annulate_ and the _Exannulate_ Ferns, the first being much the larger division, and consisting of the order Polypodiaceæ, which comprises the True Ferns, while the second includes the two orders Marattiaceæ and Ophioglossaceæ, which are some times called Pseudo-Ferns. The POLYPODIACEÆ, distinguished by the ring or annulus, which more or less completely girts the sporangia, offer so much variety of structure that it becomes necessary to subdivide them; and for this purpose characters derived from the form, number, or position of the sporangia, or the structure or development of the ring, are chiefly relied on. This gives several groups, _e.g._ Polypodineæ, the most comprehensive of all, including some ten or twelve minor groups, in which the sporangia are almost equally convex, and have a vertical and nearly complete ring, and in which the dehiscence is transverse at a part called the stoma, where the striæ of the ring are elongated, and apparently weaker; Cyatheineæ, in which the spore-cases are sessile or nearly so, seated on an elevated receptacle, with the nearly complete ring more or less obliquely vertical, that is, vertical below, curving laterally towards the top, and the dehiscence transverse; Matonineæ, a single species only, in which the sporangia are sessile, bursting horizontally, not vertically, the ring being broad, suboblique, and nearly complete, and the dorsal sori oligocarpous, covered by umbonato-hemispherical indusia, affixed by a central stalk; Gleichenineæ, with the ring complete, transverse, either truly or obliquely horizontal, the sporangia globose-pyriform, forming oligocarpous sori, _i.e._ sori consisting of but few spore-cases (two or four to ten or twelve), situated at the back of the frond, sessile or nearly so, and bursting vertically, the fronds, moreover, being rigid and opaque, and usually dichotomously-branched; Trichomanineæ, with the ring resembling that of the Gleichenineæ, but the sporangia