"(4) Certain characters of the brain, e.g., the large size of the cerebellum; the presence of the so-called lobi inferiores on the infundibulum, and of tori semi-circulares in the mid-brain. "In spite of the undoubtedly important list of features to which we have just called attention, a list containing not less important characters, both embryological and adult, separating _Lepidosteus_ from the Teleostei, can be drawn up: "(1) The character of the truncus arteriosus. "(2) The fact of the genital ducts joining the ureters. "(3) The presence of vasa efferentia in the male carrying the semen from the testes to the kidney, and through the tubules of the latter into the kidney-duct. "(4) The presence of a well-developed opercular gill. "(5) The presence of a spiral valve; though this character may possibly break down with the extension of our knowledge. "(6) The typical Ganoid characters of the thalamencephalon and the cerebral hemispheres. "(7) The chiasma of the optic nerves. "(8) The absence of a pecten, and presence of a vascular membrane between the vitreous humor and the retina. "(9) The opisthocœlous form of the vertebræ. "(10) The articulation of the ventral parts of the hæmal arches of the tail with the processes of the vertebral column. "(11) The absence of a division of the muscles into dorso-lateral and ventro-lateral divisions. "(12) The complete segmentation of the ovum. "The list just given appears to us sufficient to demonstrate that Lepidosteus cannot be classed with the Teleostei; and we hold that Müller's view is correct, according to which _Lepidosteus_ is a true Ganoid. "The existence of the Ganoids as a distinct group has, however, recently been challenged by so distinguished an ichthyologist as Günther, and it may therefore be well to consider how far the group as defined by Müller is a natural one for living forms, and how far recent researches enable us to improve upon Müller's definitions. In his classical memoir the characters of the Ganoids are thus shortly stated: