Other mackerel-like fishes are the cutlass-fishes (Trichiuridæ), which approach the eels in form and in the reduction of the fins. In these the vertebræ are correspondingly numerous, the numbers ranging from 100 to 160. Aphanopus has 101 vertebræ; Lepidopus, 112; Trichurus, 159.

In apparent contradiction to this rule, however, the pelagic family of swordfishes (Xiphias), remotely allied to the mackerels, and with even greater powers of swimming, has the vertebræ in normal number, the common swordfish having but 24.

The Eels.—The eels constitute a peculiar group of soft-rayed ancestry, in which everything else has been subordinated to muscularity and flexibility of body. The fins, girdles, gill-arches, scales, and membrane bones are all imperfectly developed or wanting. The eel is perhaps as far from the primitive stock as the most highly "ichthyized" fishes, but its progress has been of another character. The eel would be regarded in the ordinary sense as a degenerate type, for its bony structure is greatly simplified as compared with its ancestral forms, but in its eel-like qualities it is, however, greatly specialized. All the eels have vertebræ in great numbers. As the great majority of the species are tropical, and as the vertebræ in very few of the deep-sea forms have been counted, no conclusions can be drawn as to the relation of their vertebræ to the temperature.

It is evident that the two families most decidedly tropical in their distribution, the morays (Murænidæ) and the snake-eels (Ophichthyidæ), have diverged farthest from the primitive stock. They are most "degenerate," as shown by the reduction of their skeleton. At the same time they are also most decidedly "eel-like," and in some respects, as in coloration, dentition, muscular development, most highly specialized. It is evident that the presence of numerous vertebral joints is essential to the suppleness of body which is the eel's chief source of power.

So far as known the numbers of vertebræ in eels range from 115 to 160, some of the deep-sea eels (Nemichthys, Nettastoma, Gordiichthys) having much higher numbers, in accord with their slender or whip-like forms.

Among the morays, Muræna helena has 140; Gymnothorax meleagris, 120; G. undulatus, 130; G. moringa, 145; G. concolor, 136; Echidna catenata, 116; E. nebulosa, 142; E. zebra, 135. In other families the true eel, Anguilla anguilla, has 115; the conger-eel, Leptocephalus conger, 156; and Murænesox cinereus, 154.

Variations in Fin-rays.—In some families the number of rays in the dorsal and anal fins is dependent on the number of vertebræ. It is therefore subject to the same fluctuations. This relation is not strictly proportionate, for often a variable number of rays with their interspinal processes will be interposed between a pair of vertebræ. The myotomes or muscular bands on the sides are usually coincident with the number of vertebræ. As, however, these and other characters are dependent on differences in vertebral segmentation, they bear the same relations to temperature or latitude that the vertebræ themselves sustain.

Thus in the Scorpænidæ, Sebastes, and Sebastolobus arctic genera have the dorsal rays xv, 13, the vertebræ 12+19. The tropical genus Scorpæna has the dorsal rays xii, 10, the vertebræ 10+14, while the genus Sebastodes of temperate waters has the intermediate numbers of dorsal rays xii, 12, and vertebræ 12+15.

Relation of Numbers to Conditions of Life.—Fresh-water fishes have in general more vertebræ than marine fishes of shallow waters. Pelagic fishes and deep-sea fishes have more than those which live along the shores, and more than localized or non-migratory forms. To each of these generalizations there are occasional partial exceptions, but not such as to invalidate the rule.