_lævis_, _flosculus_, _amphitrite_, and in several other species, the common white varieties are eminently deceptive. Besides the slight variation in the obliquity of the summits of the radii and alæ, dependent on the more or less cylindrical form of the shell, in some species, as in _B. tintinnabulum_, _amphitrite_, _improvisus_, _trigonus_, and _porcatus_, their obliquity also varies occasionally from unknown causes, and thus greatly affects the general appearance of the shell. In some few species, as in _B. perforatus_, the radii are often either not at all developed, or are of very variable width; in others, when the shell has become cylindrical, or when very old, the radii cease to grow, and from the disintegration of the whole upper part of the shell, with the continued growth of the lower part, the radii at last come to exist as mere fissures: I have seen instances of this in _B. psittacus_, _nigrescens_, and _porcatus_. Nevertheless, the obliquity of the upper margin, and the breadth of the radii are useful characters; and still more useful is the fact whether the upper margins are smooth and arched, or straight and jagged. The fact of the terga being more or less beaked is useful: as is, likewise, the presence of striæ, or furrows, or rows of pits, radiating from the apices of the scuta; but to ascertain the presence of these marks, it is almost invariably necessary to take out the scuta, clean, and examine them with a lens; these ridges and furrows, moreover, in some species, as is strikingly the case with _B. tintinnabulum_, and in less degree with _B. trigonus_, _lævis_, and _concavus_, appear and disappear, and vary without any apparent cause.