The least varying, and therefore most important characters, must be taken from the internal structure of the parietes, radii, and basis: not that these characters are absolutely invariable; thus the porosity of the parietes is slightly variable in _B. glandula_, and highly variable in the fossil _B. unguiformis_; it is also highly variable in _B. balanoides_, but under a systematic point of view this is unimportant, as the section including this latter species is well defined by the membranous basis. The porosity of the basis is in some degree variable in _B. nubilus_, _improvisus_, and _patellaris_; and in _B. flosculus_ we see signs of a passage from a calcareous to a membranous basis. Characters derived from the general shape, and from the ridges and depressions on the under side of the scuta and terga, especially of the scuta, are highly serviceable. The terga, indeed, in many species, as in _B. amphitrite_, vary considerably, and are affected by the general shape of the shell. Unfortunately the differences are not very great between the scuta of the different species. The cause of the opercular valves offering more useful characters, as far as outline is concerned, than do the walls of the shell, is no doubt due to their being almost independent of any influence from the nature of the surface of attachment. Even the ridges and depressions on the under side of the scuta, which are in direct connection with the muscles and soft parts of the animal, vary to a certain extent: thus the length and prominence of the adductor ridge is decidedly variable in _B. concavus_ and _tintinnabulum_, and in a less degree in _B. lævis_; the size and form of the little cavity for the lateral depressor muscle varies in many species; so does the exact shape and degree of prominence of the articular ridge. There is one character in the terga, which at first would be thought very useful, namely, whether an open longitudinal furrow, or a closed fissure runs down the valve from the apex to the spur; but it is found that the furrow almost always gradually closes up during growth; and as a consequence of this, the width of the spur compared to that of the whole valve, as well as its distance from the basi-scutal angle, and the form of its basal extremity, all vary in some degree. The length of the spur sometimes varies considerably, as in _B. concavus_ and _amphitrite_. The parts of the mouth are only occasionally serviceable; for the teeth on the labrum, and the state of the lower teeth on the mandibles, and the presence of a step-formed projection at the lower angle of the maxillæ, are all often variable. The relative lengths of the two rami of the first pair of cirri, the degree of protuberance of the segments, and the number of pairs of spines on the segments of the posterior pairs of cirri, are sometimes useful; but the relative lengths of the cirri, and more especially the numbers of pairs of spines on the posterior cirri, are apt to vary. Finally, I must