It was Carl Gegenbaur again who solved the difficult problem of tracing the skeleton of the limbs of the Vertebrates to a common type. Few parts of the vertebrate body have undergone such infinitely varied modifications in regard to size, shape, and adaptation of structure as the limbs or extremities; yet we are in a position to reduce them all to the same hereditary standard. We may generally distinguish three groups among the Vertebrates in relation to the formation of their limbs. The lowest and earliest Vertebrates, the Acrania and Cyclostomes, had, like their invertebrate ancestors, no pairs of limbs, as we see in the Amphioxus and the Cyclostomes to-day (Figures 2.210 and 2.247). The second group is formed of the two classes of the true fishes and the Dipneusts; here there are always two pairs of limbs at first, in the shape of many-toed fins--one pair of breast-fins or fore legs, and one pair of belly-fins or hind legs (Figures 2.248 to 2.259). The third group comprises the four higher classes of Vertebrates--the amphibia, reptiles, birds, and mammals; in these quadrupeds there are at first the same two pairs of limbs, but in the shape of five-toed feet. Frequently we find less than five toes, and sometimes the feet are wholly atrophied (as in the serpents). But the original stem-form of the group had five toes or fingers before and behind (Figures 2.263 to 2.265). The true primitive form of the pairs of limbs, such as they were found in the primitive fishes of the Silurian period, is preserved for us in the Australian dipneust, the remarkable Ceratodus (Figure 2.257). Both the breast-fin and the belly-fin are flat oval paddles, in which we find a biserial cartilaginous skeleton (Figure 2.336). This consists, firstly, of a much segmented fin-rod or "stem" (A, B), which runs through the fin from base to tip; and secondly of a double row of thin articulated fin-radii (r, r), which are attached to both sides of the fin-rod, like the feathers of a feathered leaf. This primitive fin, which Gegenbaur first recognised, is attached to the vertebral column by a simple zone in the shape of a cartilaginous arch. It has probably originated from the branchial arches.* (* While Gegenbaur derives the fins from two pairs of posterior separated branchial arches, Balfour holds that they have been developed from segments of a pair of originally continuous lateral fins or folds of the skin.)