The _Compartments_ are remarkably compact and solid; the parietal tubes are cylindrical and quite minute even close to the basis; they extend, however, nearly up to the top of the shell; the parietal septa at the basis are thick, and with blunt denticuli; the thickness of the walls in the upper part of the shell is excessive; in the lower part, it is also unusually great, owing to the thickness of the inner lamina, and hence the ribs, generally formed by the projection of the longitudinal septa on the inner lamina, are here visible only close to the basis. The _radii_ are rather wide; their summits are parallel to the basis; the septa on their sutural edges are thin, straight, and closely approximate, and most symmetrically furnished with little denticuli of equal sizes on both sides: the interspaces are nearly filled up solidly, but with some pores still left open. In the upper part of the shell, the radii, like the walls, are of extraordinary thickness: the septa are transverse and horizontal, as seen externally by slight variations in the colour of the radii; internally, as seen in a vertical section of the shell, the septa dip inwards at an angle of above 45°. The _alæ_ are thin, and have their summits oblique: their sutural edges are smooth. The pores in the basis are crossed by numerous transverse septa, and there is an underlying cancellated layer: the internal surface is very smooth. _Animal's body_ unknown. The strength of this Balanus is truly remarkable; and when, by repeated blows, a specimen which I was examining at last yielded, the radii broke sooner than separate at their sutures. In most of its characters, this species approaches _B. tintinnabulum_, and I believe has been included by Chenu as one of its varieties; but it comes almost equally near to _B. stultus_, to which it is much more closely allied in its habit of being attached to Milleporæ. By a close and unbroken chain of affinities, _B. Ajax_, through _B. stultus_, is connected with _B. calceolus_ and its allies in section (B), which live attached to Gorgoniæ. Some of the specimens of _B. Ajax_, are almost as much elongated in their rostro-carinal axis, as are the species in section (B); and there is an affinity in the same direction in the smallness of the pores in the radii of _B. Ajax_; indeed, had the basis in this species been generally more boat-or cup-formed, I should have placed it as the first species in section (B), instead of, as at present, the last species in section (A). The intermediateness of the characters of _B. Ajax_ has been one chief cause why I have rejected the genus Conopea, which was instituted by Say for the species living attached to Gorgoniæ. _Section_ B. _Parietes and basis sometimes permeated by pores, sometimes not: radii not permeated by pores: shell elongated in its rostro-carinal axis: basis boat-shaped: attached to Gorgoniæ and Milleporæ._