The fin-fold theory of Balfour, adopted by Dohrn, Weidersheim, Thacher, Mivart, Ryder, Dean, Boulenger, and others, and now generally accepted by most morphologists as plausible, is this: that "The paired limbs are persisting and exaggerated portions of a fin-fold once continuous, which stretched along each side of the body and to which they bear an exactly similar phylogenetic relation as do the separate dorsal and anal fins to the once continuous median fin-fold." "This view, in its modern form, was based by Balfour on his observation that in the embryos of certain Elasmobranchs the rudiments of the pectoral and pelvic fins are at a very early period connected together by a longitudinal ridge of thickened epiblast--of which indeed they are but exaggerations. In Balfour's own words referring to these observations: 'If the account just given of the development of the limb is an accurate record of what really takes place, it is not possible to deny that some light is thrown by it upon the first origin of the vertebrate limbs. The facts can only bear one interpretation, viz., that the limbs are the remnants of continuous lateral fins.' [Illustration: FIG. 58.--Shoulder-girdle of _Polypterus bichir_. Specimen from the White Nile.] "A similar view to that of Balfour was enunciated almost synchronously by Thacher and a little later by Mivart--in each case based on anatomical investigation of Selachians--mainly relating to the remarkable similarity of the skeletal arrangements in the paired and unpaired fins." A third theory is suggested by Mr. J. Graham Kerr (_Cambridge Philos. Trans._, 1899), who has recently given a summary of the theories on this subject. Mr. Kerr agrees with Gegenbaur as to the primitive nature of the archipterygium, but believes that it is derived, not from the gill-septum, but from an external gill. Such a gill is well developed in the young of all the living sharks, Dipnoans and Crossopterygians, and in the latter types of fishes it has a form analogous to that of the archipterygium, although without bony or cartilaginous axis. We may now take up the evidence in regard to each of the different theories, using in part the language of Kerr, the paragraphs in quotation-marks being taken from his paper. We may first consider Balfour's theory of the lateral fold.