The cause of this reduction is often, but not always, to be found in the fact that, whenever the dermal fin-rays take the form of stout spines, as in the anterior dorsal fin in many Acanthopterygian Teleostei, the segmentation of their radialia would obviously detract from their value as skeletal supports, and hence they rarely consist of more than their proximal segments, although the radialia which in the same Fish support soft rays may be bi-segmented or tri-segmented. The radialia are, however, unsegmented, even slightly branched, cartilaginous rods in the Cyclostomata; short simple rods in the Holocephali; and equally simple bony rods in the dorsal fin of _Polypterus_, where they support the strong spines of the numerous finlets; but they are bi-segmented in the soft-rayed anal fin. As previously mentioned, the proportional share taken by the radialia and the horny fibres or the dermal fin-rays in the support of the fins differs greatly in different Fishes. In the Cyclostomata radialia are the sole, and in Elasmobranchs the main supports, and they may extend nearly to the free margin of the fin. In the more specialised Fishes, as in most Teleostomi, the reverse is the case. The radialia sink into the muscles of the body-wall and leave the strongly developed fin-rays as the sole support of the visible portions of the fins. In not a few Fishes there is an obvious segmental correspondence between the radialia and the vertebral neural or haemal spines, to the extent that the former equal the latter in number and articulate with their distal extremities, as, for example, in the caudal region of _Pleuracanthus_ and in existing {236}Dipnoi. In others again, as in most Teleostomi, there is no such segmental relation, and the radialia are more numerous than the vertebrae whenever the two are co-extensive. The exoskeletal fin-supports exhibit similar relations to their radialia, but in inverse order. Much more numerous than the radialia in the Elasmobranchs, Holocephali, and the Dipnoi, the former become gradually reduced in the Teleostomi, until in the Holostei and Teleostei they correspond in number with the supporting radialia. Complete numerical correspondence between the neural and haemal spines and the radialia and fin-rays is very rare, and has only been observed in the caudal region of certain Crossopterygii (_e.g._ the Coelacanthidae).[211] [Illustration: FIG. 138.—The posterior dorsal fin of _Holoptychius leptopterus_ from the old Red Sandstone of Nairnshire. Traces of dermal fin-rays may be seen at the distal margin of the fin. (After Smith Woodward.)] [Illustration: FIG. 139.—A dermal fin-ray and its supporting radial or pterygiophore in the Trout (_Salmo fario_). _D.F.R_, Dermal fin-ray; PTG.1, PTG.2, _ptg.3_, the proximal, middle, and distal segments of which the tri-segmented radial consists; _ptg.3_ is cartilaginous; the other two are bony. (From Parker and Haswell.)]