The _Madrepora_ are better known than their congeners. They are sometimes, but erroneously, designated corals, since the coral forms no part of this group. The Madrepores are remarkable for the calcareous crust which always surrounds their tissue, and determines the formation of their polypidom. They are in other respects easily recognized by the star-like structure of their polypidom, in which may always be distinguished a visceral chamber, the circumference of which is furnished with perpendicular laminæ or partitions, which are always directed towards the axis of the body. When sufficiently developed they constitute, by their assemblage, a star-like body formed of a great number of rays. The polypidom is always calcareous. The consolidation of the envelope of each polyp produces at first a kind of sheath, to which Milne Edwards has given the name of the wall. The partitions which proceed from the interior towards the axis of the visceral chamber occupy the subtentacular cells; the terminal and open portion designated the calyx is in organic continuity with the polyp, which has retired thither more or less completely as into a cell. Milne Edwards remarks that the polypidom of the _Madrepora_ present in their structure five principal modifications, due in part to the fundamental number of which the chambered cells are the multiple, and in part to the mode of division in the visceral chamber, and finally to the manner in which its tissue is constituted. M. Edwards avails himself of this peculiarity of structure in order to divide the Madrepores into fixed sections; namely, _Madrépores apores_, _Madrépores perforés_, _Madrépores tabulés_, _Madrépores tuberleux_, and _Madrépores rugueux_. In the group of Aporous Madrepores, the polypidom is perhaps the most highly organized. We find there a well-developed and very perfect wall, and a well-developed visceral apparatus. The calyx is neatly starred; the number of rays in the earlier stages being six, which soon afterwards reach from twelve to twenty-four. The cells between the chambers are sometimes open in all their depth, sometimes more or less shut up by transverse plates; these, being independent of each other, are never reunited in the breadth of the visceral cavity, so that they constitute discoid plates such as we find in _tabular_ and _rugose_ Madrepores.