The most striking characteristics of the appendages are as follows: the antennules are long, and turn backward instead of forward; none of the limbs projects beyond the margin of the dorsal test; the exopodites extend beyond the endopodites, reaching very nearly to the margin of the test; the endopodites are not stretched out at right angles to the axis, but the first three segments have a forward and outward direction as in _Triarthrus_, while the last four turn back abruptly so that they are parallel to the axis; the limbs at the anterior end of the thorax are much more powerful than the others; the dactylopodites of the endopodites show a fringe of setæ instead of three spines as in _Triarthrus_ and _Neolenus_. All these would, as Beecher has already suggested, seem to be adaptations to a burrowing habit of life, the antennules being turned backward and the other appendages kept within the shelter of the dorsal test in order to protect them, and the anterior endopodites enlarged and equipped with extra spines to make them more efficient digging and pushing organs. _Restoration of Cryptolithus._ (Text fig. 20.) It should be definitely understood that the present figure is a restoration and not a drawing of a specimen, and that there are many points in the morphology of _Cryptolithus_ about which no information is available, especially about the appendages under the central portion of the cephalon. The information afforded by all the figures published in this memoir is combined here. As gnathites are preserved on none of the specimens, those represented in the figure are purely conventional. A person who is acquainted only with _Cryptolithus_ preserved in shale, or with figures, usually has a very erroneous idea of the fringe It is not a flat border spread out around the front of the head, but stands at an angle about 45 in uncrushed specimens of most species. When viewed from the lower side, there is a single outer, concentric row of the cup-shaped depressions, bounded within by a prominent girder. This row is in an approximately horizontal plane, while the remainder of the doublure of the fringe rises steeply into the hollow of the cephalon. Since the front of the hypostoma is attached to this doublure, it stands high up within the vault and under the glabella. Two specimens, Nos. 231 and 233, show something of the hypostoma, and they are the only ones known of any American trinucleid. That of specimen 233, the better preserved, is very small, straight across the front, and oval behind. It seems that it is abnormally small in this specimen and I should not be surprised if in other specimens it should be found to be larger.