The discoverer of the _Ganoidei_ was succeeded by their explorer Johannes Müller (1801-1858). In his classical memoir _Über den Bau und die Grenzen der Ganoiden_ (Berl., 1846) he showed that the Ganoids differ from all the other osseous fishes, and agree with the Plagiostomes, in the structure of the heart. By this primary character, all heterogeneous elements, as Siluroids, _Osteoglossidae_, &c., were eliminated from the order as understood by Agassiz. On the other hand, he did not recognize the affinity of _Lepidosiren_ to the Ganoids, but established for it a distinct subclass, _Dipnoi_, which he placed at the opposite end of the system. By his researches into the anatomy of the lampreys and _Amphioxus_, their typical distinctness from other cartilaginous fishes was proved; they became the types of two other subclasses, _Cyclostomi_ and _Leptocardii_. Müller proposed several other modifications of the Cuvierian system; and, although all cannot be maintained as the most natural arrangements, yet his researches have given us a much more complete knowledge of the organization of the Teleostean fishes, and later inquiries have shown that, on the whole, the combinations proposed by him require only some further modification and another definition to render them perfectly natural. The discovery (in the year 1871) of a living representative of a genus hitherto believed to be long extinct, _Ceratodus_, threw a new light on the affinities of fishes. The writer of the present article, who had the good fortune to examine this fish, was enabled to show that, on the one hand, it was a form most closely allied to _Lepidosiren_, and, on the other, that it could not be separated from the Ganoid fishes, and therefore that _Lepidosiren_ also was a Ganoid,--a relation already indicated by Huxley in a previous paper on "Devonian Fishes." Having followed the development of the ichthyological system down to this period, we now enumerate the most important contributions to ichthyology which appeared contemporaneously with or subsequently to the publication of the great work of Cuvier and Valenciennes. For the sake of convenience we may arrange these works under two heads. I. VOYAGES, CONTAINING GENERAL ACCOUNTS OF ZOOLOGICAL COLLECTIONS A. _French._--1. _Voyage autour du monde sur les corvettes de S. M. l'Uranie et la Physicienne, sous le commandement de M. Freycinet_, "Zoologie--Poissons," par Quoy et Gaimard (Paris, 1824). 2. _Voyage de la Coquille_, "Zoologie," par Lesson (Paris, 1826-1830). 3. _Voyage de l'Astrolabe, sous le commandement de M. J. Dumont d'Urville_, "Poissons," par Quoy et Gaimard (Paris, 1834). 4. _Voyage au Pôle Sud par M. J. Dumont d'Urville_, "Poissons," par Hombron et Jacquinot (Paris, 1853-1854).