"This theory of the vertebrate paired limb seems to me, I confess, to be a more plausible one on the face of it than either of the two which at present hold the field. If untrue, it is so dangerously plausible as to surely deserve more consideration than it appears to have had. One of the main differences between it and the other two hypotheses is that, instead of deriving the swimming-fin from the walking and supporting limb, it goes the other way about. That this is the safer line to take seems to me to be shown by the consideration that a very small and rudimentary limb could _only_ be of use if provided with a fixed _point d'appui_. Also on this view, the pentadactyle limb and the swimming-fin would probably be evolved independently from a simple form of limb. This would evade the great difficulties which have beset those who have endeavored to establish the homologies of the elements of the pentadactyle limb with those of any type of fully formed fin." =Uncertain Conclusions.=--In conclusion we may say that the evidence of embryology in this matter is inadequate, though possibly favoring on the whole the fin-fold theory; that of morphology is inconclusive, and probably the final answer may be given by paleontology. If the records of the rocks were complete, they would be decisive. At present we have to decide which is the more primitive of two forms of pectoral fin actually known among fossils. That of _Cladoselache_ is a low, horizontal fold of skin, with feeble rays, called by Cope _ptychopterygium_. That of _Pleuracanthus_ is a jointed paddle-shaped appendage with a fringe of rays on either side. In the theory of Gegenbaur and Kerr _Pleuracanthus_ must be, so far as the limbs are concerned, the form nearest the primitive limb-bearing vertebrate. In Balfour's theory _Cladoselache_ is nearest the primitive type from which the other and with it the archipterygium of later forms may be derived. Boulenger and others question even this, believing that the archipterygium in _Pleuracanthus_ and other primitive sharks and that in _Neoceratodus_ and its Dipnoan and Crossopterygian allies and ancestors have been derived independently, not the latter from the former. In this view there is no real homology between the archipterygium in the sharks possessing it and that in the _Dipnoans_ and _Crossopterygians_. In the one theory the type of _Pleuracanthus_ would be ancestral to the other sharks on the one hand, and to Crossopterygians and all higher vertebrates on the other. With the theory of the origin of the pectoral from a lateral fold, _Pleuracanthus_ would be merely a curious specialized offshoot from the primitive sharks, without descendants and without special significance in phylogeny.