But it is impossible to define or limit the group by any single character or group of characters. It is connected with the _Malacopterygii_ through the _Haplomi_ on the one hand by transitional groups of genera which may lack any one of these characters. On the other hand, in the extreme forms, each of these distinctive characters may be lost through degeneration. Thus fin spines, ctenoid scales, and the homocercal tail are lost in the codfishes, the connection of ventrals with shoulder-girdle fails in the _Percesoces_, etc., and the development of the air-duct is subject to all sorts of variations. In one family even the adipose fin remains through all the changes and modifications the species have undergone. The various transitional forms between the _Haplomi_ and the perch-like fishes have been from time to time regarded as separate orders. Some of them are more related to the perch, others rather to ancestors of salmon or pike, while still others are degenerate offshoots, far enough from either. On the whole, all these forms, medium, extreme and transitional, may well be placed in one order, which would include the primitive flying-fishes and mullets, the degraded globefishes, and the specialized flounders. As for the most part these are spiny-rayed fishes, Cuvier's name _Acanthopterygii_, or _Acanthopteri_, will serve us as well as any. The _Physoclysti_ of Müller, the _Thoracices_ of older authors, and the _Ctenoidei_ of Agassiz include substantially the same series of forms. The order _Teleocephali_ of Gill (τελεός, perfect; κεφαλή, head) has been lately so restricted as to cover nearly the same ground. In Gill's most recent catalogue of families, the order _Teleocephali_ includes the _Haplomi_ and rejects the _Hemibranchii_, _Lophobranchii_, _Plectognathi_, and _Pediculati_, all of these being groups characterized by sharply defined but comparatively recent characters not of the highest importance. As originally arranged, the order _Teleocephali_ included the soft-rayed fishes as well. From it the _Ostariophysi_ were first detached, and still later the _Isospondyli_ were regarded by Dr. Gill as a separate order. We may first take up serially as suborders the principal groups which serve to effect the transition from soft-rayed to spiny-rayed fishes.