But in none of these cases is the correspondence perfectly exact, and in any system of classification we must choose characters for primary divisions so ancient and therefore so permanent as to leave no room for exceptions. The extraordinary difficulty of doing this, with the presence of most puzzling intergradations, has led Dr. Gill to suggest that the great body of bony fishes, soft-rayed and spiny-rayed, abdominal, thoracic, and jugular alike, be placed in a single great order which he calls _Teleocephali_ (τελεός, perfect; κεφαλή, head). The aberrant forms with defective skull and membrane-bones he would separate as minor offshoots from this great mass with the name of separate orders. But while the divisions of _Teleocephali_ are not strongly differentiated, their distinctive characters are real, ancient, and important, while those of the aberrant groups, called orders by Gill (as _Plectognathi_, _Pediculati_, _Hemibranchii_), are relatively modern and superficial, which is one reason why they are more easily defined. There seems to us no special advantage in the retention of a central order _Teleocephali_, from which the divergent branches are separated as distinct orders. While our knowledge of the osteology and embryology of most of the families of fishes is very incomplete, it is evident that the relationships of the groups cannot be shown in any linear series or by any conceivable arrangement of orders and suborders. The living teleost fishes have sprung from many lines of descent, their relationships are extremely diverse, and their differences are of every possible degree of value. The ordinary schemes have magnified the value of a few common characters, at the same time neglecting other differences of equal value. No system of arrangement which throws these fishes into large groups can ever be definite or permanent.