=Current Theories as to Origin of Paired Fins.=--There are three chief theories as to the morphology and origin of the paired fins. The earliest is that of Dr. Karl Gegenbaur, supported by various workers among his students and colleagues. In his view the pectoral and ventral fins are derived from modifications of primitive gill-arches. According to this theory, the skeletal arrangements of the vertebrate limb are derived from modifications of one primitive form, a structure made up of successive joints, with a series of fin-rays on one or both sides of it. To this structure Gegenbaur gives the name of archipterygium. It is found in the shark, _Pleuracanthus_, in _Cladodus_, and in all the Dipnoan and Crossopterygian fishes, its primitive form being still retained in the Australian genus of Dipnoans, _Neoceratodus_. This biserial archipterygium with its limb-girdle is derived from a series of gill-rays attached to a branchial arch. The backward position of the ventral fin is due to a succession of migrations in the individual and in the species. As to this theory, Mr. J. Graham Kerr observes: [Illustration: FIG. 54.--Skull and shoulder-girdle of _Neoceratodus forsteri_ (Günther), showing the archipterygium.] "The Gegenbaur theory of the morphology of vertebrate limbs thus consists of two very distinct portions. The first, that the archipterygium is the ground-form from which all other forms of presently existing fin skeletons are derived, concerns us only indirectly, as we are dealing here only with the _origin_ of the limbs, i.e., their origin from other structures that were not limbs. "It is the second part of the view that we have to do with, that deriving the archipterygium, the skeleton of the primitive paired fin, from a series of gill-rays and involving the idea that the limb itself is derived from the septum between two gill-clefts. "This view is based on the skeletal structures within the fin. It rests upon (1) the assumption that the archipterygium is the primitive type of fin, and (2) the fact that amongst the Selachians is found a tendency for one branchial ray to become larger than the others, and, when this has happened, for the base of attachment of neighboring rays to show a tendency to migrate from the branchial arch on to the base of the larger or, as we may call it, primary ray; a condition coming about which, were the process to continue rather farther than it is known to do in actual fact, would obviously result in a structure practically identical with the archipterygium. Gegenbaur suggests that the archipterygium actually has arisen in this way in phylogeny." [Illustration: FIG. 55.--_Acanthoessus wardi_ (Egerton). Carboniferous. Family _Acanthoessidæ_. (After Woodward.)] [Illustration: FIG. 56.--Shoulder-girdle of _Acanthoessus_. (After Dean.)] [Illustration: FIG. 57.--Pectoral fin of _Pleuracanthus_. (After Dean.)]