"And it is true that there is a greater superficial resemblance between the Hyoganoids (_Lepisosteus_, _Amia_, etc.) and ordinary physostome Teleosts than between the former and the other orders of Ganoids, but it is equally true that they agree in other respects than in the brain and heart with the more generalized Ganoids. They all have, for example, (1) the paraglenal elements undivided (not disintegrated into hypercoracoid, hypocoracoid, and mesocoracoid); (2) a humerus (simple or divided, that is, differentiated into metapterygium and mesopterygium); and (3) those with ossified skeletons agree in the greater number of elements in the lower jaw. Therefore, until these coordinates fail, it seems advisable to recognize the Ganoids as constituents of a natural series; and especially on account of the superior taxonomic value of modifications of the brain and heart in other classes of vertebrates, for the same reason, and to keep prominently before the mind the characters in question, it appears also advisable to designate the series, until further discovery, as a subclass. "But it is quite possible that among some of the generalized Teleosts at least _traces_ of some of the characters now considered to be peculiar to the Ganoids may be discovered. In anticipation of such a possibility, the author had at first discarded the subclass, recognizing the group only as one of the 'superorders' of the Teleostomes, but reconsideration convinces him of the propriety of classification representing known facts and legitimate inferences rather than too much anticipation. "It is remembered that all characters are liable to fail with increasing knowledge, and the distinctness of groups are but little more than the expressions of our want of knowledge of the intermediate forms; it may in truth be said that ability to segregate a class into well-defined groups is in ratio to our ignorance of all the terms." CHAPTER II THE GANOIDS—Continued =CLASSIFICATION of Ganoids.=—The subdivision of the series of Ganoidei into orders offers great difficulty from the fact of the varying relationships of the members of the group and the fact that the great majority of the species are known only from broken skeletons preserved in the rocks. It is apparently easy to separate those with cartilaginous skeletons from those with these bones more or less ossified. It is also easy to separate those with bony scales or plates from those having the scales cycloid. But the one type of skeleton grades into the other, and there is a bony basis even to the thinnest of scales found in this group. Among the multitude of names and divisions proposed we may recognize six orders, for which the names _Lysopteri_, _Chondrostei_, _Selachostomi_, _Pycnodonti_, _Lepidostei_, and _Halecomorphi_ are not inappropriate. Each of these seems to represent a distinct offshoot from the first primitive group.