_Peduncle._--The membrane of the peduncle is thin; the whole surface is sparingly and quite irregularly studded with minute, much-branched filaments (Pl. IV, fig. 3, highly magnified); these are occasionally as much as l/5th of an inch in length; the degree of branching varies much, but is generally highly complex; the ordinary diameter of the branches is about 1/200th of an inch; their tips are rounded, and even a little enlarged, and frequently torn off, as if they had been attached to or buried in the flesh of the shark, in which the whole peduncle is imbedded. These filaments are formed of, and are continuous with the external transparent membrane of the peduncle, and they contain, up to the tips of every sub-branch, a hollow thread of corium, prolonged from the layer internally coating the whole peduncle. In all other Lepadidæ, the peduncle increases in length, chiefly at the summit where joined to the capitulum, and in diameter, throughout nearly its whole length, except close to the base; but, owing to the constant disintegration of the outer surface, the old outside coat does not split in defined lines, like the membrane of the capitulum. In Anelasma, however, owing to the imbedded position of the peduncle, the old outer coats are preserved, the lines in which they have split during continued growth being thus exhibited: those in the uppermost part almost symmetrically surround the peduncle, showing that here, as in other Lepadidæ, has been one regular line of growth; but in the lower part the lines are extremely irregular; and what is almost unique, it appears that the blunt basal end is constantly increasing in length and breadth, and, apparently, at a greater rate than any other part. I judge of this latter fact, from the whole bottom of the peduncle being covered with numerous curved, or nearly circular, lines of natural splitting, the nature of which can be best understood by examining the much-enlarged drawing (Pl. IV, fig. 3) of a small portion (taken by chance) of the membrane of the base, seen from the outside, and bearing some of the simplest branched filaments: other branches, as may be seen, have been cut off. This manner of growth explains the broad, blunt basal termination of the peduncle, so unlike that in other Lepadidæ. New membrane is formed, not continuously as in other cases, under the whole surface of the old membrane, but in irregular patches; thus the portion marked (_a_) runs under (_b_), but not under the little circles (_c_, _c_), for these are the last-formed portions and underlie the membrane (_a_) and (_b_). I do not understand how the splitting of the old membrane is effected; but no doubt it is by the same process by which the membrane of the capitulum in other genera, as in Scalpellum, splits symmetrically between the several valves. In the branched filaments it is particularly difficult to understand their growth, for it is not possible, after examining them, to doubt that they