an undetermined question of theory. What is the origin of paired limbs? Are these formed, like the unpaired fins, from the breaking up of a continuous fold of skin, in accordance with the view of Balfour and others? Or is the primitive limb, as supposed by Gegenbaur, a modification of the bony gill-arch? Or again, as supposed by Kerr, is it a modification of the hard axis of an external gill?
If we adopt the views of Gegenbaur or Kerr, the earliest type of limb is the jointed archipterygium, a series of consecutive rounded cartilagenous elements with a fringe of rays along its length. Sharks possessing this form of limb (Ichthyotomi) appear in the earliest rocks, and from these the Dipnoi, on the one hand, may be descended and, on the other, the true sharks and the Chimæras.
On the other hand, if we regard the paired fins as parts of a lateral fold of skin, we find primitive sharks to bear out our conclusions. In Cladoselache of the Subcarboniferous, the pectoral and the ventral fins are long and low, and arranged just as they might be if Balfour's theory were true. Acanthöessus, with a spine in each paired fin and no other rays, might be a specialization of this type or fin, and Climatius with rows of spines in place of pectorals and ventrals might be held to bear out the same idea. But in all these, the tail is less primitive than in the Ichthyotomi. On the whole, however, there is much to be said on the primitive nature of the Ichthyotomi, and Pleuracanthus, with the tapering tail and jointed pectoral fin of a dipnoan, with other traits of a shark, is as likely as Cladoselache to point directly to the origin of the shark-like forms.
Hasse finds this origin in a hypothetical group of Polyospondyli which have many vertebra undifferentiated and without calcareous material. These fishes are represented only by fin spines (Onchus), which may have belonged to something else. These gave rise to Ichthyotomi, with jointed fins, and through these to Dipnoi and a long series leading to the bony fishes on the one hand and on the other to the Amphibia, Reptiles and Higher Vertebrates.
The branch of higher sharks would lead to the Diplospondyli of Hasse's system, of which Cladoselache should be a primitive example. These sharks have the weakly ossified vertebræ joined together in pairs and there are six or seven gill openings. This primitive type called Notidani has persisted to our day, the frilled shark (Chlamydoselachus) and the genera Hexanchus and Heptranchias, still showing its archaic characters.
Here the sharks diverge into two groups, the one with the vertebræ better developed and its calcareous matter arranged star fashion. This forms Hasse's group of Asterospondyli, the typical sharks. The earliest forms (Heterodontidæ, Hybodontidæ) approach the Notidani, and one such ancient type Heterodontus, still persists. The others diverge to
