It is deserving of notice, that the analogies of the cranial cavities in this ancient Ganoid should point so directly on the cranial cavities of that special Ganoid of the present time which unites a true skull of cartilage to a dermal skull of osseous plates,—a circumstance strongly corroborative of the general evidence, negative and positive, on which I have concluded that the true skulls of the first Ganoids were also cartilaginous. It is further worthy of observation, that in all the sections of the cranium of _Dipterus_ which I have yet examined, the internal line is continuous, as in the Placoids, from nape to snout, and that the true skull presents no trace of those cerebral vertebræ of which skulls are regarded by Oken and his disciples as developments. Historically at least, the progress of the ichthyic head seems to have been a progress from simple cartilaginous boxes to cartilaginous boxes covered with osseous plates, that performed the functions whether active or passive, of internal bones; and then from external plates to the interior bones which the plates had previously represented, and whose proper work they had done. The principle which rendered it necessary that the divisions which exist in the dermal skulls of the first Ganoids should so closely correspond with the divisions which exist in the internal skulls of the osseous fishes of a greatly later period, does not seem to lie far from the surface. Of the solid parts of the ichthyic head, a certain set of pieces afford protection to the brain and cerebral nerves, and to some of the organs of the senses, such as those of seeing and hearing; while another certain set of pieces constitute the framework through which an important class of functions, manducatory and respiratory, are performed. The protective bones of merely passive function are fixed, whereas the bones of active function, such as the jaws, the osseous framework of the opercules, and the hyoid bones, are to the necessary extent free, _i. e._ capable of independent motion. Of course, the detached character necessary to the free cerebral bones would be equally necessary in cerebral plates united dermally to the pieces of the cartilaginous framework, which performed in the ancient fish the functions of these free bones. And hence jaw plates, opercular plates, and hyoid plates, whose homological relation with recent jaws and opercular and hyoid bones cannot be mistaken. They were operative in performing identical mechanical functions, and had to exist, in consequence, in identical mechanical conditions. And an equally simple, though somewhat different principle, seems to have regulated the divisions of the fixed cranial bucklers of the Old Red Ganoids, and to have determined their homologies with the fixed cerebral bones of the osseous fishes.