"'These fishes are either provided with plate-like angular or rounded cement-covered scales, or they bear osseous plates, or are quite naked. The fins are often, but not always, beset with a double or single row of spinous plates or splints. The caudal fin embraces occasionally in its upper lobe the end of the vertebral column, which may be prolonged to the end of the upper lobe. Their double nasal openings resemble those of Teleostei. The gills are free, and lie in a branchial cavity under an operculum, like those of Teleostei. Many of them have an accessory organ of respiration, in the form of an opercular gill, which is distinct from the pseudobranch, and can be present together with the latter; many also have spiracles like Elasmobranchii. They have many valves in the stem of the aorta like the latter, also a muscular coat in the stem of the aorta. Their ova are transported from the abdominal cavity by oviducts. Their optic nerves do not cross each other. The intestine is often provided with a spiral valve, like Elasmobranchii. They have a swimming-bladder with a duct, like many Teleostei. Their pelvic fins are abdominal. "'If we include in a definition only those characters which are invariable, the Ganoids may be shortly defined as being those fish with numerous valves to the stem of the aorta, which is also provided with a muscular coat, with free gills, and an operculum, and with abdominal pelvic fins.' "To these distinctive characters he adds, in an appendix to his paper, the presence of the spiral valve, and the absence of a processus falciformis and a choroid gland. "To the distinctive set of characters given by Müller we may probably add the following: "(1) Oviducts and urinary ducts always unite, and open by a common urogenital aperture behind the anus. "(2) Skull hyostylic. "(3) Segmentation complete in the types so far investigated, though perhaps _Amia_ may be found to resemble the Teleostei in this particular. "(4) A pronephros of the Teleostean type present in the larva. "(5) Thalamencephalon very large and well developed. "(6) The ventricle in the posterior part of the cerebrum is not divided behind into lateral halves, the roof of the undivided part being extremely thin. "(7) Abdominal pores always present. "The great number of characters just given are amply sufficient to differentiate the Ganoids as a group; but, curiously enough, the only characters, amongst the whole series which have been given, which can be regarded as peculiar to the Ganoids are (1) the characters of the brain, and (2) the fact of the oviducts and kidney-ducts uniting together and opening by a common pore to the exterior. "This absence of characters peculiar to the Ganoids is an indication of how widely separated in organization are the different members of this great group.