_Basis._--In typical species the basis is calcareous, and consists of an upper and lower lamina, separated by radiating septa, forming pores. In the same manner as the septa of the parietes sometimes, though rarely, become irregularly divided near the outer lamina, forming outer pores, so it is, but in a much more marked degree, with the basis. The basis in such cases becomes extremely thick, and consists of an upper, thin lamina, with the regular radiating septa and pores, and of an underlying, thick, cancellated mass, which seems wholly to result from the dividing and sub-dividing of the septa. The basal radiating pores, like the parietal pores, are closed at intervals by calcareous transverse septa. The basal points of the parietal septa enter the orifices of the basal pores, and the threads of corium pass into the latter, between the denticuli of the parietal septa. In some species, as in _B. crenatus_ and _Hameri_, the basis is perfectly solid, the upper lamina being absent, just as in some species, the internal lamina of the parietes is absent. In _B. flosculus_ the basis is calcareous, but consists of so excessively thin a film as hardly to be distinguished: it presents, moreover, as also is the case with _B. imperator_, a beaded structure. Again, in some few species, as in _B. balanoides_, the basis is simply membranous. When the basis is thin, it is always flat, and is closely moulded to the irregular surface of attachment; and in this case, when specimens are crowded together, their elongation is effected exclusively by the growth of the walls; but, when the basis is thick, it sometimes becomes, in crowded groups, deeply, but irregularly, cup-formed, or cylindrical, as in _B. psittacus_ and _perforatus_. In _B. allium_, however, which inhabits massive corals, the basis is as regularly concave or cup-formed as in the genus Pyrgoma: in _B. calceolus_ and its allies, and in some varieties of the fossil _B. inclusus_, the basis is boat-formed, with its lower surface deeply grooved longitudinally from clasping the stem of the Gorgonia or other zoophyte, to which it was attached. In certain varieties of _B. lævis_ it is very remarkable that the deeply cup-formed basis becomes, owing apparently to the whole shell having grown too deep for the animal, half-filled up with irregular, calcareous, transverse plates (Pl. 4, fig. 2 _a_), resting one upon the other by irregular points or pillars. The cementing apparatus has been sufficiently described under the Family.