I would gladly have divided this genus, already including 45 species, into smaller genera; but so far from being enabled to do so, I have been compelled to form my Sections (immediately to be given) on characters not absolutely invariable, and far from obvious. I was particularly anxious to separate the elongated species with a boat-formed basis, which are attached to Gorgoniæ, and which form the genus Conopea of Say, but I was unable to effect their separation even as a sub-genus; for _B. navicula_ and _cymbiformis_ graduate in the most insensible manner through _B. galeatus_ (the type of Say's genus) and _B. calceolus_ into _B. stultus_, and this into _B. Ajax_; yet this latter species has even been described as a mere variety of the typical _B. tintinnabulum_! Indeed, so insensible is this graduation, that the first and second sections of the genus are hardly distinct. I fully admit, that if _B. stultus_ and _Ajax_ had never existed, _B. calceolus_ and its three allies might have formed as natural a little group, though difficult to be characterised, as does the sub-genus Acasta; or perhaps this group and Acasta might have been combined together. These same species, viz., _B. calceolus_ and its allies, are intimately allied to _B. terebratus_ and _inclusus_, which are contained in the last section (F) of the genus; and this shows that Dr. Gray's proposed genus Chirona, including the species with non-porose parietes in sections (E) and (F), could hardly have been instituted, even if the porosity of the parietes had not been variable in _B. unguiformis_, _balanoides_, and _glandula_. My fourth section (D), founded on the basis not being porose, is perhaps the weakest of the divisions, as may be seen in the list of exceptions appended to the sectional headings. The arrangement of the species is, I think, as natural as a linear one could be made: every one knows how irregularly and in how many directions the lines of affinity in every natural genus branch out. Some few species stand rather isolated, as _B. declivis_; and _B. allium_, _cepa_, and _quadrivittatus_ in a little group by themselves. I have already shown how the species in the first and second sections (A and B) blend into each other; and that the blending species are likewise allied to some in the last section (F); furthermore, I shall have occasion to show that these same species can hardly be separated naturally from the sub-genus Acasta. The first section, moreover, passes into the third (C) by _B. tulipiformis_; and the third into the fourth (D) by _B. improvisus_, _nubilus_, _corrugatus_, and _patellaris_: the fifth and sixth (E and F) sections are closely connected together by _B. cariosus_ and _flosculus_; and these two sections blend into the fourth (D) through _B. unguiformis_ and _balanoides_, and lastly, into the third (C) section by _B. dolosus_ and _improvisus_.