As regards the origin of the limbs or paired fins of fishes there are two principal views. One view, that of Gegenbaur, considers that limbs and their girdles are derived from visceral arches which have migrated backwards. The other view, which probably now has the greater number of supporters, considers that the paired fins of fishes are of essentially the same nature as the median fins. According to Gegenbaur's view[47] the =archipterygium= of _Ceratodus_ (fig. 20) represents the lowest type of fin; it consists of a central cartilaginous axis bearing a large number of radiale. The dorsal or pre-axial radiale are more numerous than the ventral or postaxial, and at the margin of the fin[48] the cartilaginous endoskeletal radiale are replaced by horny exoskeletal fin-rays. [Illustration FIG. 20. LATERAL VIEW OF THE SKELETON OF _Ceratodus miolepis_ (after GÜNTHER). 1. ethmoid. 2. scleroparietal. 3. frontal. 4. cartilaginous posterior part of cranium. 5. pre-opercular (squamosal). 6. opercular. 7. suborbital. 8. orbit. 9. pectoral girdle. 10. proximal cartilage of pectoral fin. 11. pectoral fin. 12. pelvic girdle. 13. pelvic fin. 14. spinal column. 15. caudal fin (diphycercal).] It is impossible here to give a full discussion of the rival views, but some of the points which support Gegenbaur's view may be mentioned. The fact that migration of visceral arches has to be assumed is no difficulty, as it is obvious that migration in the opposite direction has taken place in many Teleosteans such as the Cod, whose pelvic fins are attached to the throat in front of the pectorals. If migration did take place, the pelvic fins being older than the pectoral should be the more modified, and this is the case. Again, if the pectoral girdle is a modified branchial arch, it must at some period have carried a gill, and in _Protopterus_ it does bear a vestigial gill.