"But the researches of Prof. Johannes Müller on the anatomy and classification of the fishes culminated at length in his celebrated memoirs on those fishes for which he retained the ordinal name Ganoidei; those memoirs have left an impression on ichthyology perhaps more decided than made by any other contributions to science, and that published _in extenso_ will ever be classical; numerous as have been the modifications since introduced into the system, no forms except those recognized by Müller (unless it be Dipnoi) have been interjected since among the Ganoids. "It has been objected that the Ganoids do not constitute a natural group, and that the characters (i.e., chiasma of optic nerves and multivalvular bulbus arteriosus) alleged by Müller to be peculiar to the teleostomous forms combined therein are problematical, and only _inferentially_ supposed to be common to the extinct Ganoids so called, and, finally, such objections couched in too strong language have culminated in the assertion that the characters in question are actually _shared_ by other physostome fishes. "No _demonstration_, however, has been presented as yet that any physostome fishes do really have the optic chiasma and multivalvular _bulbus arteriosus_, and the statement to the contrary seems to have been the result of a venial misapprehension of Prof. Kner's statements, or the offspring of impressions left on the memory by his assertions, in forgetfulness of his exact words. "But Prof. Kner, in respect to the anatomical characters referred to, merely objects: (1) that they are _problematical_, are not confirmable for the extinct types, and were _probably_ not existent in certain forms that have been referred to the Ganoids; (2) the difference in number of the valves of the _bulbus arteriosus_ among recent Ganoids is so great as to show the unreliability of the character; (3) a spiral valve is developed in the intestine of several osseous fishes ('genera of the so-called intermediate clupeoid groups'), as well as in Ganoids; and (4) the chiasma of the optic nerves in no wise furnishes a positive character for the Ganoids. "It will be noticed that all these objections (save in the case of the intestinal spiral valve) are hypothetical and vague. The failure of the intestinal spiral valve, as a diagnostic character, has long been conceded, and in this case only have the forms that _prove_ the failure been referred to; in the other cases, where it would be especially desirable to have indicated the actual types falsifying the universality or exclusiveness of the characters, they have not been referred to, and the objections must be met as if they were not known to exist.