According to the view more prevalent at the present time, the paired fins have been derived from two continuous folds of skin and their skeletal supports running forward from the anal region along the sides of the body, their character being similar to the fold that gave rise to the median fins. In support of this view it may be argued that the paired and unpaired fins are often identical in structure, and that some Elasmobranch embryos do show a ridge running between the pectoral and pelvic fins. Then from this continuous fold two pairs of smaller folds may have been specialised off, and in each a number of cartilaginous radiale may have been developed. The fin of _Cladoselache_ from the Carboniferous of Ohio apparently illustrates this condition. It consists of certain basal pieces which do not project beyond the body wall and bear a number of unsegmented cartilaginous radiale, which show crowding together and are sometimes bifurcated distally; they extend throughout the whole fin from the body wall to the margin. From this fin the archipterygium might be easily derived by the enlargement of one of the middle radiale and the segmentation and partial fusion of them all. Whether the archipterygium be a primitive or secondary type of fin, when it is once reached it is easy to derive all the other types from it. The fins of the other living Dipnoi,--_Protopterus_ and _Lepidosiren_--are simply archipterygia from which the radiale have almost or completely disappeared, leaving only the segmented axes. Archipterygia too are found in the pectoral fins of the Ichthyotomi, but the postaxial radiale are much reduced. The =ichthyopterygium=, or type of fin, characteristic of many modern Elasmobranchs such as _Scyllium_, may have been derived from the archipterygium by the gradual reduction of the rays on the postaxial side of the axis and their condensation on the pre-axial side. The Ichthyotomi such as _Xenacanthus_ show one stage in the reduction of the postaxial rays, and a further stage is seen in the Notidanidae and some other sharks like _Scymnus_ and _Acanthias_, in which a few postaxial rays still remain. The condensation of the pre-axial rays when further continued leads to one of the rays getting an attachment to the girdle. Thus the fin comes to articulate with the girdle by two basalia or basal pieces; a third attachment is formed in the same way and the three basalia are called respectively pro-, meso-, and meta-pterygia. By some authors the meta-pterygium and by others the meso-pterygium is regarded as homologous with the axis of the archipterygium.