2. In most living Elasmobranchs the arches meet laterally round the centrum. The vertebrae are never ossified but endochondral calcification nearly always takes place, though it very rarely reaches the outer surface of the vertebrae. Elasmobranchs are sometimes subdivided into three groups according to the method in which this calcification takes place: 1. =Cyclospondyli= (_Scymnus_, _Acanthias_), in which the calcified matter is deposited as one ring in each vertebra. 2. =Tectospondyli= (_Squatina_, _Raia_, _Trygon_), in which there are several concentric rings of calcification. 3. =Asterospondyli= (Notidanidae, _Scyllium_, _Cestracion_), in which the calcified material instead of forming one simple ring, extends out in a more or less star-shaped manner. In _Heptanchus_ the length of the vertebral centra in the middle of the trunk is double that in the anterior and posterior portions, and as the length of the arches does not vary, the long centra carry more of them than do the short centra. In many Rays the skull articulates with the vertebral column by distinct occipital condyles. In BONY GANOIDS the skeletogenous layer becomes calcified ectochondrally in such a way that the notochord is pinched in at intervals, and distinct vertebrae are produced. Ossification of the calcified cartilage rapidly follows. In _Amia_ the vertebrae are biconcave, in _Lepidosteus_ they are opisthocoelous, cup and ball joints being developed between the vertebrae in a manner unique among fishes. The notochord entirely disappears in the adult _Lepidosteus_, but at one stage in larval life it is expanded vertebrally and constricted intervertebrally in the manner usual in the higher vertebrata, but unknown elsewhere among fishes. The tail of _Amia_ is remarkable from the fact that as a rule to each neuromere, as determined by the exit of the spinal nerves, there are two centra, a posterior one which bears nothing, and an anterior one which bears the neural and haemal arches, these being throughout the vertebral column connected with the centra by cartilaginous discs. In most TELEOSTEANS but not in the Plectognathi the neural arches are continuous with the centra, which are nearly always deeply biconcave. In some cases many of the anterior vertebrae are ankylosed together and to the skull. The vertebrae often articulate with one another by means of obliquely placed flattened surfaces, the zygapophyses. The centrum in early stages of development is partially cartilaginous, but the neural arches and spines in the trunk at any rate, pass directly from the membranous to the osseous condition. FINS. The most primitive fins are undoubtedly the unpaired ones, which probably originally arose as ridges or folds of skin along the mid-dorsal line of the body, and passed thence round the posterior end on to the ventral surface, partially corresponding in position and function to the keel of a ship.