The pinnules, or leaflets, are from six to twelve lines long, and three or four broad, and are placed alternately on the rachises of the pinnæ. They are very numerous, seldom fewer than twelve on each side of one of the middle (or lower) rachises, and in large fronds sometimes as many as forty on each side. The outer rachises bear fewer and fewer pinnules, and the outermost of even a very large frond will not have more than eight or ten on each side. They are attached to the rachis by a very short and slender stalk. Their usual form is dimidiate-oblong; that is, they appear as if cut in two longitudinally, and the lower half removed, so that the lower edge is entire, and straight, or often slightly hollowed; the base, or edge nearest the rachis, is also straight and entire; it is parallel with the rachis, or even overlaps it a little; the upper edge is more or less lobed or incised, but in general nearly parallel with the lower, and the end is rounded and slightly lobed. The point of attachment is, of course, at the angle between the lower and basal edges. The terminal pinnule of each pinna, and the basal one, which, indeed, very often proceeds from one of the recurved branches _just below_ the origin of the pinna, are broadly cuneate or transversely oblong in shape, the two sides which meet at the point of attachment being equal; and the few pinnules near the basal one are shorter and more triangular than the middle ones. The texture is delicately membranaceous, but elastic; the color is a lively green, and both surfaces are very smooth. The upper surface appears to be destitute of stomata; and this may be the reason why water will not adhere to the pinnules, but either falls off, or stands in spheroids ready to fall. The veins are free: in the symmetrical basal and apical pinnules the veinlets fork repeatedly from the very base; but in the oblong middle pinnules there is a faint principal vein running close to the lower edge; and from this the veinlets diverge obliquely, and fork about three times before reaching the superior margin. The incisions of the superior margin are usually very narrow, and extend only to about one-third of the breadth of the pinnule; but in some specimens from California and Oregon they are wider and considerably deeper. The lobes are from four to six or seven in number: in sterile fronds they are minutely toothed at the end; but in the commoner fertile fronds they are reflexed and changed in character, so as to form somewhat crescent-shaped or transversely elongated involucres of a pale-brownish color. The tips of the veinlets extend into these involucres, and bear the sporangia on the under or inner surface. In this peculiarity is the essential generic character of _Adiantum_. The spores of this species are spheroid-tetrahedral, the three radiating angles marked with slender vittæ, or bands. They are mature in the latter part of summer; but the