The most reasonable explanation has been suggested by Hay.[131] The mosaic polygonal components of the shell of _Sphargis_ are, so to speak, an earlier generation of osteodermal plates than the later generation of longer and broader bony plates which in the Thecophora come into contact, and fuse with, the neural arches and ribs. The osteoderms of _Sphargis_ belong to the same category as the dermal ossifications in the scutes of Crocodilia, whilst the plates of the carapace and plastron of the Thecophora belong to the category of the abdominal ribs. _Sphargis_ has the first kind in its peculiar shell, the second kind in the deeper lying plastron and in its nuchal plate. But it has lost, or perhaps had never developed, the horny shields. The only difficulty is, however, the presence of a plastron and of a typical neural plate in _Sphargis_. This difficulty is not very serious. The plastron is a very old institution. It occurs together with the more superficial osteoderms in _Caiman_, and the nuchal plate may be the oldest of all dorsals. We can scarcely imagine that the direct ancestors of _Sphargis_ had developed both kinds of shells, and that comparatively recently the inner shell of the carapace was lost, leaving only the nuchal plate. Fossils do not support such an assumption. Undoubted ancestral forms of _Sphargis_ are very rare. _Psephophorus_ of the Oligocene and Miocene of Europe had a continuous mosaic shell much resembling that of _Sphargis_; _Eosphargis_ is represented by a well-preserved skull from the London clay. Then follows a wide gap until we come to _Psephoderma_ of the Rhaetic, or Upper Trias of Bavaria; the large fragment of whose dorsal shell is composed of about 200 mosaic pieces. If this fragment really formed part of the shell {338}of a Chelonian, its age would speak greatly in favour of the Athecae being a very primitive and independent group. ORDER II. THECOPHORA. _Thoracic vertebrae and ribs united with a series of median or neural and a paired series of lateral or costal plates. Parietals prolonged downwards, meeting the pterygoids directly or by interposition of an epipterygoid._ SUB-ORDER 1. CRYPTODIRA.–_The carapace is covered with horny shields. The neck, if retractile, bends in an S-shaped curve in a vertical plane. The pelvis is not fused with the shell._ FAM. 1. CHELYDRIDAE.–The plastron is small and cross-shaped (Fig. 61, 2, p. 315); the bridge is very narrow, and the displaced abdominal shields are widely separated from the marginals by a few irregularly shaped inframarginals. The tail is long. The limbs, neck, and head are so stout that they cannot be completely withdrawn into the shell. Snout with a powerful hooked beak. American; only two genera, each with one species.